Answers
Answer:
30.25π mm^2
Step-by-step explanation:
The area of a circle is π · r^2. simply plug in the radius of 5.5 into "r" and then you square it. Squaring it would result in 30.25. Finally, you multiply it with π. Since you are multiplying two unlike terms, you put the coefficient first and then the variable. The measurements are in millimeters squared so you would have to add them after 30.25π otherwise it would be wrong.
Related Questions
There are 32 crates. Each crate holds 27 cans of soup. Which expressions that are NOT good ways to use compatible numbers to estimate the number of cans in the crates.a. 30 X 20b. 30 X 30c. 32 X 27d. 25 X 32e. 25 X 30
Answers
a)30*20 b)30*30 d)25*32 e)25*30 are NOT good ways to use compatible numbers to estimate the number of cans in the crates.
And the best expressions that is the good ways to use compatible numbers to estimate the number of cans in the crates is 32*27
As given in the question,
There are 32 crates. Each crate holds 27 cans of soup.
i.e. Number of total crates = 32
Number of can of soups in each crate = 27
The total number of cans of soup in every crates = 32*27
The total number of cans of soup in every crates = 864
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A p-value of 0.04 obtained from a two-tailed t-test means that there is a ____ % chance that the obtained results are due to _______. Given the conventional significance level, you would accept that the _________ hypothesis is correct.
Answers
A p-value of 0.04 obtained from a two-tailed t-test means that there is a 4% chance that the obtained results are due to chance. Given the conventional significance level, you would accept that the alternative hypothesis is correct.
The P=0.04 defines that if the null hypothesis is true and if you perform the study a large number of times and in exactly the same manner.
Drawing random samples from the population on each occasion, then, on 4% of occasions, you would get the same or greater difference between groups.
In statistical hypothesis testing, we need to express the null hypothesis, which is the no statistical difference within the groups, and the alternative hypothesis, which is the statistical difference.
Then, we determine the test statistic, which is a standardized quantitative measure of the group difference.
The null hypothesis predicts that the test statistic value will be small, but there is a slight possibility that it will be big by chance. We utilize the test statistic to compute the p-value once we determine the test statistic.
The p-value is described as the calculated probability of determining the observed result from the value of the test statistic, or larger, under the null hypothesis.
Therefore, we can conclude that the value of the definition of the p-value is the probability that we would see a test statistic this extreme or more if the null hypothesis were true.
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math homework help me
Answers
Answer:
D
Step-by-step explanation:
Option A has a dot on -25 and the arrows point from there to the left of the number line, going down from there. Representing x<-25.
Option B has a dot on -25 and the arrow goes to the right from there meaning it goes up. Representing x>-25
Option C has a dot on 25 and an arrow pointing to the left going down. Representing x<25
Finally, option D has a dot on 25 and an arrow pointing to the right meaning the number is going upward as intended by the question.
find the standard deviation for the distribution of the number of people you talk to before finding your first piece of gum.
Answers
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed.
What is standard deviation?The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range. The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.How dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed value from the mean. Any distribution will have roughly 95% of values within 2 standard deviations of the mean.To learn more about standard deviation refer to:
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For the same particle as in question 1, write and evaluate an integral expression, in terms of sine and cosine, that gives the distance the particle travels from t = 1.5 to t = 2.75.
Answers
An integral expression, in terms of sine and cosine, that gives the distance the particle travels from t = 1.5 to t = 2.75 is 1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt.
We have been given two functions representing the displacement of the particle,
x(t)=2cos(πt)
y(t)=4sin(πt)
To find the velocity vector with the help of these functions, we have to differentiate them with respect to time
i.e,
dx(t)/dt=d{2cos(πt)}/dt=-2sin(πt)
dy(t)/dt=d{4sin(πt)}/dt=4cos(πt)
and finally, the velocity vector would be written as,
v(t)=-2sin(πt) i +4cos(πt) j
Now to get the distance for the given limits we have to integrate the magnitude of the given velocity
i.e, integrate 1.5→2.75 √{(-2sin(πt))²+(4cos(πt))²} dt
which would approximately result in a value of 3.69 units in length.
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g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y
Answers
The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.
In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property. To determine this property, we can look at the two-dimensional transformation above, where y = ax + b. In order for the PDFs of x and y to be the same, the linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1. The linear transformation a must be an involution, meaning it must be its own inverse, such that a^2 = 1.In order for the probability density functions (PDFs) of x and y to be equal, the linear transformation a must satisfy a certain property.
The complete question is : g as a generalization of the two-dimensional transformation above, what property must the linear transformation a satisfy if the pdfs for x and y, where y = ax + b, are to be the same?
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In a class there are 42 students. the numbers of girls is 2times the numbers of boys. how many boys and girls are there in the class
Answers
x = No. of girls
y = no. of boys
2y + y = 42
3y = 42
y = 14
no. of girls = 2 × 14 = 28
no of boys = 14
A school group is going on a trip to a museum. Admission is $10 per student. Eight students have guaranteed they will go, but additional students may be going. The total admission the group will have to pay can be represented by the expression 10(8 + x). The group leader simplifies this expression to 80 + x to calculate how much money they will need. Is this correct? If 6 additional students go, will they have enough money to cover the admission cost?
Answers
The value of the equation is y = 10 ( 8 + x ) = 80 + 10x , where y is the total cost of admission
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The cost of admission per student is c = $ 10
Let the total cost of admission be represented as y
Now , the number of students = 8 students
The number of additional students = x
So , the total cost of admission y = 10 ( x + 8 )
On simplifying the equation , we get
The total cost of admission y = 10x + 80
Now , if 6 more students go , the equation will be
The total cost of admission y₁ = 10 ( x + 6 + 8 )
On simplifying the equation , we get
The total cost of admission y₁ = 10x + 140
Hence , the equation is y = 10x + 80
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David draws a quadrilateral. Opposite sides are parallel. The shape has no right angles. All four sides are not the same length. What quadrilateral did David draw?
Answers
Since David drew a quadrilateral with opposite sides parallel, no right angles and all four sides are not the same length, the quadrilateral would be referred to as a scalene trapezoid.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapezoidWhat are properties of a scalene trapezoid?Generally speaking, some of the properties of a scalene trapezoid include the following:
The opposite sides of a scalene trapezoid are parallel. A scalene trapezoid has no right angles. All four sides of a scalene trapezoid are not the same length.In conclusion, we can reasonably infer and logically deduce that David drew a scalene trapezoid.
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convert the following numbers from the given base to the other three bases listed in the table: decimal binary octal hexadecimal 369.3125 ? ? ? ? 10111101.101 ? ? ? ? 326.5 ? ? ? ? f3c7.a
Answers
Decimal: 369.3125 Binary: 101111001.0101 Octal: 571.5 Hexadecimal: 171.A8. The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows: Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8.
Decimal: 10111101.101 Binary: 10111101.101 Octal: 277.125 Hexadecimal: BD.1A
Decimal: 326.5 Binary: 10100010.1 Octal: 502.1 Hexadecimal: 142.8
Decimal: F3C7.A82 Binary: 1111001111100111.10101000010 Octal: 36367.5212 Hexadecimal: F3C7.A82
To convert a number from one base to another, we can use the following steps:
1. Identify the number and its base.
2. Convert the number to its equivalent in decimal form.
3. Convert the decimal form of the number to the desired base.
For example, to convert the number 369.3125 from decimal to binary, octal, and hexadecimal, we can follow these steps:
1. Identify the number and its base: 369.3125 is a decimal number.
2. Convert the number to its equivalent in decimal form: 369.3125 is already in decimal form, so we don't need to convert it.
3. Convert the decimal form of the number to the desired base:
Binary: 101111001.0101
Octal: 571.5
Hexadecimal: 171.A8
The number 369.3125 can be converted from decimal to binary, octal, and hexadecimal as follows: Binary: 101111001.0101, Octal: 571.5, Hexadecimal: 171.A8. Similarly, the number 10111101.101 can be converted to binary, octal, and hexadecimal as follows: Binary: 10111101.101, Octal: 277.125, Hexadecimal: BD.1A. Finally, the number 326.5 can be converted to binary, octal, and hexadecimal as follows: Binary: 10100010.1, Octal: 502.1, Hexadecimal: 142.8, and the number F3C7.A82 can be converted to binary, octal, and hexadecimal as follows: Binary: 1111001111100111.10101000010, Octal: 36367.5212, Hexadecimal: F3C7.A82.
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1. Consider the graph of the function y = sin x + cos x. Describe its overall shape.
Is it periodic?
How do you know?
2. Using a graphing calculator or other graphing device, estimate the x- and y-values of the maximum point for the graph (the first such point where x > 0). It may be helpful to express the x-value as a multiple of π.
3. Now consider other graphs of the form y = A sin x + B cos x for various values of A and B.
Sketch the graph when A = 2 and B = 1, and, find the x - and y-values for the maximum point. (Remember to express the x-value as a multiple of π, if possible.)
Has it moved?
4. Repeat and sketch the graph for A = 1, B = 2.
Is there any relationship to what you found in part (2)?
5. Explain what you have discovered from completing this activity using details and examples.
Answers
It is revealed through completing the task that the graph of y = sin x + cos x is periodic, having a maximum point at x 0.94 and y 2.24. We've also noted that changing the values of A and B causes the graph to move to the left, with the highest point at x 0.44 and y 2.84. This demonstrates that the ratio of A and B determines the greatest point of the graph.
What does this activity shows?This activity has demonstrated the effect of changing the coefficients of sine and cosine functions when combined. For example, when A and B are both 1, the graph of y = sin x + cos x creates a wave-like shape with a maximum point at (π/2, 2). When A is increased to 2 and B is kept at 1, the maximum point moves to the right and increases in y-value to (2π/3, 3). When B is increased to 2 and A is kept at 1, the maximum point moves to the left and increases in y-value to (π/3, 3). This shows that when the coefficient of the sine term is increased, the maximum point moves to the right, and when the coefficient of the cosine term is increased, the maximum point moves to the left. This also shows that the maximum point of the graph y = A sin x + B cos x increases in y-value as A and B increase.
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H
The 3 points plotted below are on the graph of y=b².
Based only on these 3 points, plot the 3 corresponding points that must be on the graph of
y = log, z by clicking on the graph.
y
161
14+
12-
10+
8
6
4-
Click to add points
2+
●
6
8
10
12
14
16
Answers
The 3 corresponding points that must be on the graph are (1,0),(4,1),(16,2). for proper calculation please scroll down.
What is Function?A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
Points on the graph are A(0,1), B(1,4),C(2,16).
Now, these are the points on the graph for the function
y=b^x
Since, we know that the funtion
y=[tex]log_{b}X[/tex]
is the inverse of
y=b^x
Therefore, the points are the reflection of the given point.
So, change the x coordinate with y and y with x to get the points for the function
y= [tex]log_{b}X[/tex]
The points will become,
(0, 1) ~ (1, 0)
(1, 4) ~ (4, 1)
(2, 16) ~ (16, 2)
Therefore, the 3 corresponding points that must be on the graph are (1, 0), (4, 1), (16, 2).
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Find the x-intercept of the line -5x-2y=15
Answers
Answer:
The x intercept is -3
Step-by-step explanation:
To find the x intercept, let y = 0 and solve for x.
-5x-2y=15
-5x-2*0=15
-5x=15
Divide each side by -5
-5x/-5 = 15/-5
x = -3
The x intercept is -3
3. Consider a large slice of air over a city to be a box 125 km x 125 km (L x W) that reaches up to an altitude of 1.5 km. Clean air is blowing into the box along one of its sides with a speed of 4 m/s. Suppose an air pollutant with a reaction rate of k = 0.23/hr is emitted into the box at a total mass loading rate of 10 kg/s. a. Find the steady state concentration if the air in the box is assumed to be perfectly mixed. b. If the wind speed suddenly drops to 1 m/s, estimate the concentration of this pollutant 3-hr later.
Answers
a. Steady state concentration = 10/0.23 = 43.48 kg/m^3
b. Concentration 3 hrs later = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3
a. The steady state concentration of the air pollutant can be found by the equation C = M/k, where C is the concentration, M is the mass loading rate, and k is the reaction rate. In this case, C = 10 kg/s/0.23/hr = 43.48 kg/m^3. b. To calculate the concentration of the pollutant 3 hours later, we can use the equation C = M/k * e^(-kt), where t is the time in hours. In this case, C = 10/0.23 * e^(-3*0.23/1) = 34.99 kg/m^3. This equation takes into account the decrease in wind speed and the decrease in reaction rate due to the decrease in concentration.
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which pattern should replace the question mark in column 4?this question is required. * circle pattern up one
Answers
The answer to column 4 is a circle pattern that is shifted one unit up. This pattern consists of a series of overlapping circles that expand outward in a vertical direction.
To replace the question mark in column 4, you need to identify the pattern that is shifted one unit up. To do this, start by looking at the pattern in column 3 and imagining it shifted upwards one unit. This will give you the pattern for column 4. The pattern is a series of overlapping circles which expand outward in a vertical direction. To create the pattern, start by drawing a circle in the center of the column. Then, draw circles around the center circle that are slightly larger than the previous one. Repeat this process until the circles reach the edge of the column. This will create the circle pattern that is shifted one unit up. Finally, connect the circles with straight lines to create the full pattern. This pattern will replace the question mark in column 4.
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The complete question: which pattern should replace the question mark in column 4? this question is required. * circle pattern up one circle pattern down one
1.4.3 Quiz: Draw a Diagram
Question 2 of 6
Read the problem below and find the solution. Draw a diagram on your own
paper to help solve it.
A group of 23 friends gets together to play a sport. First, people must be
divided into teams. Each team has to have exactly 4 players, and no one can
be on more than one team. How many teams can they make? (It is possible
that not everyone can be on a team.)
(Do not include units in your answer.)
Answer here
+
SUBMIT
Answers
There can be a maximum of 5 teams.Three persons will be excluded.
What is an expression?Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to denote the logical syntax's operation order and other properties.
Considering that 23 pals gather to play a sport together.The participants must first be divided into teams. There must be exactly 4 participants on each team, and no one may play for more than one team.
The number of teams will be determined using the formulas below:
Total teams = 23 / 4 = 20 / 4 = 5.
Three persons will be left.
Therefore, there can be a maximum of 5 teams.Three persons will be excluded.
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To find the number of teams that can be made with 23 friends, where each team has exactly 4 players, we can divide the total number of friends by the number of players per team.
Number of friends = 23
Number of players per team = 4
To find the number of teams, we divide the number of friends by the number of players per team:
23 / 4 = 5 remainder 3
Since we cannot have a team with 3 players, we can only form complete teams of 4 players. Therefore, the maximum number of teams that can be formed is 5.
Therefore, the answer is 5 teams.
a group of students were asked if they carry a credit card. the responses are listed in the table. if a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. round your answer to three decimal places.
Answers
The probability that the student owns a credit card given that they are a freshman is 0.350 (3 d.p.)
[tex]Probability\: of\: an\: event\: occurring = \frac{Number\: of \:ways\:it\:can\:occur}{Total\:no.\:of\:possible\:outcomes}[/tex]
Let P(A) = probability that the student is a freshman
Let P(B) = probability that the student owns a credit card
Use the given table to calculate the probability that the student is a freshman:
[tex]= > P(A)=\frac{60}{100} =0.6[/tex]
And the probability that the student is a freshman and owns a credit card:
[tex]= > P(A \cap B)=\frac{21}{100}=0.21[/tex]
To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of B given A is:
[tex]P(B |A)=\frac{P(A\cap B)}{P(A)}[/tex]
Substitute the found values into the formula:
[tex]P(B|A)=\frac{0.21}{0.6} =0.35[/tex]
Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35.
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The complete question is:
A group of students was asked if they carry a credit card. the responses are listed in the table. if a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. round your answer to three decimal places.
the cost of chesse increased by 25%. how much is the new price of the cheese that originally cost $4.20. PLEASE HELP WILL GIVE BRAINLIST FOR SOLULTIONS
Answers
Answer:
$5.25
Step-by-step explanation:
Original cost of cheese = $4.20
An increase in price of 25% means the cost increase = 25% of $4.20
25% in decimal = 25/100 = 0.25 (or 1/4)
25% of $4.20 = 0.25 x $4.20 = $1.05
or, if you are more comfortable working with fractions
25% of $4.20 = 1/4 x $4.20 = $1.05
This is only the cost increase.
Add this increase to the original cost to get the new price:
New price = $4.20 + $1.05 =$5.25
3. Solve these systems of equations without graphing. Show your work using formal algebra.
a. 2x + 3y = 7
2y = 12x 2
b. 2x 9y = 12
3x + 18y = 18
Answers
a. 2x + 3y = 7
2y = 12x - 2
To solve this system of equations, we can begin by isolating one of the variables. Let's first isolate y in the second equation:
2y = 12x - 2
y = 6x - 1
Now we can substitute this expression for y into the first equation:
2x + 3(6x - 1) = 7
2x + 18x - 3 = 7
20x = 10
x = 1/2
Now that we know the value of x, we can substitute it back into the equation y = 6x - 1 to find the value of y:
y = 6(1/2) - 1
y = 3/2 - 1
y = -1/2
So the solution to this system of equations is (x, y) = (1/2, -1/2).
b. 2x - 9y = 12
3x + 18y = 18
To solve this system of equations, we can begin by using the first equation to solve for one of the variables. Let's solve for x:
2x - 9y = 12
2x = 9y + 12
x = (9y + 12)/2
Now we can substitute this expression for x into the second equation:
3((9y + 12)/2) + 18y = 18
(27y + 36) + 18y = 18
45y = -18
y = -4/5
Now we can substitute this value of y back into the equation x = (9y + 12)/2 to find the value of x:
x = (9(-4/5) + 12)/2
x = (3 + 12)/2
x = 15/2
So the solution to this system of equations is (x, y) = (15/2, -4/5).
Note that triangle ABD from part A is a 30 - 60 - 90 triangle.
Drag the tiles to the correct box to show how the Pythagorean theorem can be used to find
Answers
We will examine the 30-60-90 triangle concept in this session and learn everything there is to know about it, including its formula, definition, sides, area, and the rules that apply to this triangle.
What is the triangle of 30-60-90?A 30-60-90 triangle is a special sort of right triangle that always has angles that are 30, 60, and 90 degrees.
The angles of the triangles ABC and PQK in this instance are 30°, 60°, and 90°, respectively.
The side opposing the 30° angle, AB = y, will always be smaller because 30° is the triangle's smallest angle.
The side opposing the 60° angle, BC = y 3 = y 3, will be of medium length because 60° is the triangle's mid-sized degree angle.
The hypotenuse AC = 2y will be the greatest side on the side across from the 90° angle because 90° is the largest angle.
Considering that the Pythagorean Theorem is given by:
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Complete question -
2. If 9 men can do a piece of work in 6 days, how long will it take 12 men to do the same work?
Answers
Answer: 4.5 Days
Step-by-step explanation:
The work requires 9 men x 6 days or 54 man-days.
So 12 men will do the same work in 54 man-days/12 men
= 4.5 days.
I hope this is right sorry if its not
Yields of 10 strawberry plants in a uniformity trial are given by two researchers as
3
239, 176, 235, 217, 234, 216, 318, 190, 181, and 225. Using these data:
a. Write the null and alternate hypotheses given you want to determine if the mean of
the 10 strawberry plants differs from 205 g.
b. Conduct a t-test at the 95% level of confidence to test the null hypothesis in part a.
c. Test the same hypothesis in part a at the 95% level of confidence using a Confidence
Interval
Answers
The hypotheses are
Null hypothesis: The mean of the 10 strawberry plants is equal to 205g (μ=205).Alternate hypothesis: The mean of the 10 strawberry plants is not equal to 205g (μ≠205).We fail to reject the null hypothesis in (b) and (c)
The null and alternate hypothesesHere, we have
The mean of the 10 strawberry plants differs from 205
So, the hypotheses are
Null hypothesis: μ=205Alternate hypothesis: μ≠205)A t-test at the 95% level of confidenceWe start by calculating the mean and the sample standard deviation
Using an online calculator, we have
Mean = 223.1
Standard deviation = 40.4
Calculate the t-statistic
t-statistic = (223.1 - 205) / (40.4 / √10) = 1.42
The degrees of freedom for this test are 9 (n - 1).
Using a t-distribution table, the critical value for a one-tailed t-test with 9 degrees of freedom and a 95% level of confidence is 1.833.
Since the calculated t-statistic of 1.42 is less than the critical value of 1.833, we fail to reject the null hypothesis.
Test the same hypothesis at the 95% level of confidence:Calculate the standard error:
Standard Error = 40.4 / √10 = 12.78
Calculate the z-statistic:
z-statistic = (223.1 - 205) / 12.78 = 1.41
In this case, the z-statistic (1.41) is less than the critical value (1.960) from the standard normal distribution table, so we accept the null hypothesis.
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please help! Thank you
Answers
The unit rate of change in this situation is 0.25 mile per hour.
What is the unit rate of change in this situation?The unit rate of change in this situation is 0.25 mile per hour.This means that for every 1 hour the painting crew works, they will paint 0.25 mile of the road.This rate of change can be calculated by dividing the total distance painted (9.5 miles) by the total amount of time (hours) it took to paint it (38 hours). Therefore, 9.5 miles/38 hours = 0.25 mile/hour.This unit rate of change indicates that the painting crew is consistently painting 0.25 mile of the road per hour.This is important because it helps the crew accurately plan how long it will take to complete the 24-mile stretch of road, as well as how much paint they need to purchase and how much manpower is needed.To learn more about the unit rate of change refer to:
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let f be the function defined above, for what value of b is f continuous at x=2?
Answers
For f to be continuous at x=2, b must be equal to 6. That is, when b=6, there is no break in the function at x=2, and the function is continuous.
To determine the value of b for which f is continuous at x=2, we need to first find the limit of f(x) as x approaches 2 from the left and from the right. From the left, the limit is 4b-4. From the right, it is 2b+2. To make the function continuous at x=2, we need to make sure that the left- and right-hand limits are equal. Setting the two limits equal to each other, 4b-4 = 2b+2, and solving for b yields b=6. Therefore, for f to be continuous at x=2, b must be equal to 6.
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The numbers 840 and 8316, written as the products. of their prime factors, are 840= 2¹ × 3 × 5 × 7 and 8316= 22 x 3³ x 7 x 11. Hence, find
(i) the greatest whole number that will divide both 840 and 8316 exactly,
(ii) the smallest non-zero whole number that is divisible by both 840 and 8316.
Pls help asap
Answers
Answer:
1) 84
2) 83160
Step-by-step explanation:
Greatest common divisor and Least common multiple
840 = 2³ * 3 * 5 * 7
8316 = 2² * 3³ * 7 * 11
i) The greatest whole number that will divide both 840 and 8316 is the
Greatest common divisor. Find only the common factors.
Greatest common divisor = 2² * 3 * 7
= 84
84 is the greatest whole number that divides both 840 and 8316.
Answer: 84
ii) The smallest non-zero whole number that is divisible by 840 and 8316 is Least common multiple of 840 & 8316.
Least common multiple = 2³ * 3³ * 5 * 7 * 11
= 8 * 27 * 5 * 7 * 11
=83160
Find the values of x and y in each parallelogram
Answers
The value of x and y of the first parallelogram is x = 7 and y = 9
The value of x and y of the second parallelogram is x = 3 and y = 6
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
a)
Let the first parallelogram be ABCD
Now , the opposite sides are parallel and opposite sides are congruent
So , The measure of AB = measure of CD
And , the measure of AD = measure of BC
Substituting the values in the equation , we get
3x - 5 = 2x + 2 be equation (1)
On simplifying the equation , we get
Subtracting 2x on both sides of the equation , we get
x - 5 = 2
Adding 5 on both sides of the equation , we get
x = 7
Now , 2y - 6 = y + 3 be equation (2)
On simplifying the equation , we get
Subtracting y on both sides of the equation , we get
y - 6 = 3
Adding 6 on both sides of the equation , we get
y = 9
Therefore , the value of x and y of the parallelogram is 7 and 9 respectively
b)
Let the second parallelogram be ABCD
Now , the the diagonals of a parallelogram bisect each other
Let O be the point of intersection of diagonals
So , The measure of AO = measure of CO
And , the measure of DO = measure of BO
Substituting the values in the equation , we get
2x + 5 = 11 be equation (1)
On simplifying the equation , we get
Subtracting 5 on both sides of the equation , we get
2x = 6
Divide by 2 on both sides of the equation , we get
x = 3
Now , y + 4 = 2x + 4 be equation (2)
On simplifying the equation , we get
Substitute the value of x = 3 in the equation , we get
y + 4 = 2 ( 3 ) + 4
y + 4 = 10
Subtracting 4 on both sides of the equation , we get
y = 6
Therefore , the value of x and y of the parallelogram is 3 and 6 respectively
Hence , the measures of parallelogram is solved
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A rectangular garden has a walkway around it. The area of the garden is 2(5.5x +3.5). The combined area of the garden and the walkway is 3.5(8x + 6). Find the area of the walkway around the garden as the sum of two terms.
Answers
The area of the walkway around the garden is 17x+14.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, the area of the garden is 2(5.5x +3.5). The combined area of the garden and the walkway is 3.5(8x + 6).
Area of a walkway = The combined area of the garden and the walkway - The area of the garden
= 3.5(8x+6)-2(5.5x +3.5)
= 28x+21-11x-7
= 17x+14
Therefore, the area of the walkway around the garden is 17x+14.
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A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 75 mph. Another train leaves Boston for New York on an adjacent set of tracks at 4:00 P.M. and averages 65 mph. At
what time will the trains meet? (Round to the nearest minute.)
Answers
They have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.
What time will the trains meet?50t = 40(t+1)
10t = 40
They are not travelling in the same way. They would cross paths in 4 hours if they were travelling in the same direction.
Before the NY train departs for Boston, a Boston train goes 40 miles.
After they have both travelled a total of 160 miles, they will now combine.
40x+50x=160
90x=160
x=16/9
1:46:40
After they have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.
They will get together at 5:46:40.
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Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)(a) P(0≤Z≤2.54)(b) P(0≤Z≤2)(c) P(−2.40≤Z≤0)(d) P(−2.40≤Z≤2.40)(e) P(Z≤1.36)(f) P(−1.25≤Z)(g) P(−1.40≤Z≤2.00)(h) P(1.36≤Z≤2.50)(i) P(1.40≤Z)(j) P(|Z|≤2.50)
Answers
(a) P(0≤Z≤2.54) represents the area under the standard normal curve between 0 and 2.54 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2.54, which is approximately 0.4966.
(b) P(0≤Z≤2) represents the area under the standard normal curve between 0 and 2 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 0 and 2, which is approximately 0.4772.
(c) P(−2.40≤Z≤0) represents the area under the standard normal curve between −2.40 and 0 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 0, which is approximately 0.3821.
(d) P(−2.40≤Z≤2.40) represents the area under the standard normal curve between −2.40 and 2.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.40 and 2.40, which is approximately 0.7621.
(e) P(Z≤1.36) represents the area under the standard normal curve to the left of 1.36 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the left of 1.36, which is approximately 0.9155.
(f) P(−1.25≤Z) represents the area under the standard normal curve to the right of −1.25 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of −1.25, which is approximately 0.1151.
(g) P(−1.40≤Z≤2.00) represents the area under the standard normal curve between −1.40 and 2.00 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −1.40 and 2.00, which is approximately 0.7170.
(h) P(1.36≤Z≤2.50) represents the area under the standard normal curve between 1.36 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between 1.36 and 2.50, which is approximately 0.0951.
(i) P(1.40≤Z) represents the area under the standard normal curve to the right of 1.40 on the x-axis. This can be found by using a standard normal table or calculator to find the area to the right of 1.40, which is approximately 0.0821.
(j) P(|Z|≤2.50) represents the area under the standard normal curve between −2.50 and 2.50 on the x-axis. This can be found by using a standard normal table or calculator to find the area between −2.50 and 2.50, which is approximately 0.5199.
In all cases, a standard normal table or calculator is used to find the area under the standard normal curve. The area represents the probability of the given event.
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Write the number in standard form.
-2+√-8
2
Answers
The standard form of the given number -2+√-8 is -2+2i
What is the imaginary number?
An imaginary number is a number that can be written in the form of a real number multiplied by the imaginary unit, denoted by the symbol "i". The imaginary unit, "i", is defined as the square root of -1, which is a number that when multiplied by itself results in -1.
The given number cannot be written in standard form, because √-8 is an imaginary number and cannot have a real value. The square root of a negative number is an imaginary number, and these numbers are denoted by the imaginary unit, i.
The imaginary unit is defined as the square root of -1.
The number -2+√-8 is equal to -2+i*2.
The standard form of a complex number is a+bi, where a and b are real numbers and i is the imaginary unit.
So, The standard form of the given number -2+√-8 is -2+2i
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