If the similar figure is smaller than the original then the scale factor is a fraction. If the similar figure is larger than the original then the scale factor is a whole number.
How do scale factors work ?The scale factor is a ratio that compares the corresponding side lengths of two similar figures. If the similar figure is smaller than the original, the scale factor is a fraction less than 1, for example, 2/3 or 3/4. This means that the corresponding side lengths of the similar figure are 2/3 or 3/4 of the corresponding side lengths of the original figure.
On the other hand, if the similar figure is larger than the original, the scale factor is a whole number greater than 1, for example, 2 or 3.
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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
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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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?
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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You buy a milkshake from a shoppe that only has chocolate, vanilla, and strawberry flavors. Find the probability that your milkshake consists of more than 3
flavors.
Step-by-step explanation:
soln on
n(s)=6
n(p)=3
therefore
probability =6/3
Write the number in standard form.
-2+√-8
2
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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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.
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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please help! Thank you
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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HELP!! i want the answer
The tangent line to the given circle passing through the point B is given by the image presented at the end of the answer.
What is a tangent line?A tangent line to a circle is a line that only touches the circumference of the circle, not crossing.
If the line crosses the circle, then the line is called a secant line, which crosses the circumference of the circle twice.
Then the tangent line, only touching the circumference of the circle, is given by the image presented at the end of the answer.
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In our class, there are 11 female and 14 male students. Among 11 female students, 5 get grade A. Among 14 male students, 4 get grade A.
Let A= `pick a student randomly, the grade of this student is A', and M=` pick a student randomly, this student is a male’.
Then, the conditional probability P(A|M) is:
The conditional probability that the selected student is male and got grade A is 2/7.
Define the term conditional probability?The possibility of an outcome or an event happening contingent on the incidence of a prior event or outcome is known as conditional probability. The likelihood of an event happening given the another has already happened.P(A|M) stands for the probability of such a considering that M has happened.
Then, formula for the conditional probability is-
P(A|M) = P(A∩M) / P(M)
P(A∩M) = Probability that the student is male M and got grade A = 4/25.
P(M) = Probability that the student is male M = 14/25.
Then,
P(A|M) = 4/25 / 14/25
P(A|M) = 4/14 = 2/7
Thus, the conditional probability that the selected student is male and got grade A is 2/7.
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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
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
Consider the linear system
x+y-y z=2
x+2y+ z=3
x+y+(k^2-5)z= k
where k is an arbitrary constant. For which value(s) of k does this system have a unique solution? For which value(s) of k does the system have infinitely many solutions? For which value(s) of k is the system inconsistent?
The system is inconsistent for k=0.
The system has a unique solution when k=1 and k=-3. To see this, we plug in these values of k into the system and solve the resulting three equations in three unknowns. For k=1, we have x=2, y=1, and z=0. For k=-3, we have x=3, y=2, and z=0.
The system has infinitely many solutions when k=5. In this case, we have x+y-5z=2, x+2y+z=3, and x+y+25z=5, which yields the solution x=2, y=1, and z=0/5. Since any non-zero value of z will also satisfy the system, the system has infinitely many solutions.
The system is inconsistent when k=0. In this case, we have x+y=2, x+2y+z=3, and x+y-z=0, which has no solution. Therefore, the system is inconsistent for k=0.
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The attached file, data_red_banjo_pints_sold.xlsx, lists the daily sales of IPA beer, in pints, for the first three years of operations of Red Banjo Brewing Company. Construct a histogram with lower bin limit of O and bin width 50 for the variable IPA beer (pints). Which of the following best describes the sales data? symmetric negatively skewed positively skewed flat A C 1 Day 2 3 4 3 4 8 9 8 6 7 8 9 10 11 12 13 14 15 B IPA (pints) 1 158 2 169 162 4 154 5 154 6 275 7 277 8 154 9 161 10 166 11 159 12 168 13 262 14 283 15 154 16 164 17 165 18 156 19 164 20 258 21 260 22 155 23 155 24 159 25 164 26 165 27 255 28 268 29 152 30 162 CO 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Red Banjo Pints Produced А B C D 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 163 154 267 272 158 162 162 166 138 260 267 160 148 152 164 168 267 267 152 164 150 160 170 248 275 160 162 153 157 79 80 81 82 83 84 85 86 87 85 86 88 87 89 90 91 88 89 90 157 273 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 273 270 162 164 164 150 168 258 263 158 166 165 154 169 250 270 160 164 157 157 168 265 285 150 150 162 155 160 262 260 160
The data can be analyzed to determine the distribution of the data.
In order to construct a histogram for the daily sales of IPA beer, in pints, for the first three years of operations of Red Banjo Brewing Company, the lower bin limit is set to 0 and the bin width is set to 50. The data can be analyzed to determine the distribution of the data. To calculate the distribution, the data points are counted and the number of occurrences of each data point is divided by the total number of data points.
Using this formula, the data can be analyzed to determine if the data is symmetric, negatively skewed, positively skewed, or flat. The formula used is:
(Number of Occurrences / Total Number of Data Points) * 100
In the case of the Red Banjo Brewing Company data, the data is found to be positively skewed. This means that there are more data points in the higher range than in the lower range. This suggests that the brewery has seen a steady increase in the sale of IPA beer over the past three years.
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Y=2x + 9; 6x -3y = 0 / 4x -2y = 3; 2x -4y -3 cual de la siguientes parejas de rectas no son paralelas?
Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.
How to solve the problem?Two lines are parallel if they have the same slope. The slope of a line is represented by the letter "m" in the equation y = mx + b.
In this case, Y=2x + 9 has a slope of 2 and 4x -2y = 3 has a slope of -1/2, these slopes are different, which means that these two lines are not parallel.
On the other hand, 6x -3y = 0 and 2x -4y -3 are parallel because they have the same slope, -3/2. The slope of a line is the amount of change in the y coordinate for each unit of change in the x coordinate.
Yes, 6x -3y = 0 and 2x -4y -3 are parallel. This is because they both have the same slope, -3/2. The slope of a line can be calculated from its equation, by dividing the coefficient of the x term by the coefficient of the y term.
In the case of 6x -3y = 0, the slope is -3/6 = -1/2. In the case of 2x -4y -3, the slope is -4/2 = -2. Since both lines have the same slope, they are parallel. This means that they never intersect and have the same direction.
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NEED HELP ASAP!!! DUE TOMORROW
Answer:M<R corresponds to M<T, meaning M<R is 4x+1.
Step-by-step explanation:
The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (5,100) and (7,140) to find the number of soda bottles the machine can make each minute.
Based on the graph which shows the relationship between time and the number of soda bottles a machine can make, this machine can make 20 soda bottles each minute.
How to calculate the number of soda bottles?In Geometry, the rate of change of any straight line simply refers to the slope and it can be calculated by using this mathematical equation (expression);
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the graph above, we can logically deduce the following data points located on the line:
Points on the x-coordinate = (5, 7).Points on the y-coordinate = (100, 140).Substituting the given data points into the rate of change formula, we have the following;
Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope), m = (140 - 100)/(7 - 5)
Rate of change (slope), m = 40/2
Rate of change (slope), m = 20.
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let f be the function defined above, for what value of b is f continuous at x=2?
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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In a bag of keys, there are 15 silver keys, 6 black keys, 8 copper keys, and 4 painted keys of various cálors. One key is drawn out
at random. What is the probability that the key that is drawn is silver or copper?
A. 7/11
B. 8/33
C. 5/11
D. 23/33
Answer:
C
Step-by-step explanation:
Answer:
23/33
Step-by-step explanation:
The copper keys and the silver keys in total is 23 and the amount of keys in total is 33.
Factor the trinomial by grouping. -
8x²2² +14x+3.
a. Find two numbers whose product is 8.3=24 and whose sum is 14.
b. Write 14x using the factors from part (a).
c. Factor by grouping.
a. The two numbers whose product is 24 and whose sum is 14 are 6 and 4
b. 14x = 6x + 8x
c. 8x²2² + 6x + 8x + 3
=8x²2² + (6x + 8x) + 3
=8x²2² + 14x + 3
The trinomial 8x²2² + 14x + 3 can be factored by grouping as (8x²2² + 14x) + 3
Prove that (sinθ-cosθ)^2(sinθ+cosθ)^2 = 2
Step-by-step explanation:
(sinθ + cosθ)^2 + (sinθ − cosθ)^2
= (sin^2 θ + cos^2 θ + 2sinθ cosθ)+(sin^2 θ+cos^2 θ − 2sinθ cosθ)
= (1 + 2sinθ cosθ) + (1 − 2sinθ cosθ)
= 1 + 2sinθ cosθ + 1 − 2sinθ cosθ
= 1 + 1 = 2
Therefore, (sinθ+cosθ)^2 + (sinθ−cosθ)^2 = 2
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.
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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In a bowling class, the students are organized into teams. The number of students in the class is used to calculate how many teams will be formed.
s = the number of students in the class
t = the number of teams to be formed
Which of the variables is independent and which is dependent?
In a group of 30 pupils, 13 play the flute only. 1 plays the piano only. 4 play both instruments. A student is chosen at random. What is the probability the student plays neither instrument?
A student who is chosen at random has a 2/5 chance of playing neither instrument.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, a group of 30 pupils, 13 play the flute only. 1 plays the piano only. 4 play both instruments
From the general formula of probability:
Probability = desired outcome / total outcomes
Total outcomes = 30
In our case desired outcome = is chosen student plays neither instrument
desired outcome = 30 - 13 -1 -4
desired outcome = 12
thus,
Probability = 12/30
probability = 2/5
Therefore, the probability of a randomly selected student playing neither instrument is 2/5.
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Alewuya invests $1,000 at 13% simple interest for 6 years. How much is in the account at the end of the 6 year period?
Answer: $
The amount of money with the simple interest is A = $ 1,780
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Now , the amount with simple interest A = P + I
Now , the principal P = $ 1,000
The interest rate R = 13 %
The number of years T = 6 years
And , Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
Simple Interest I = ( 1000 x 13 x 6 ) / 100
On simplifying the equation , we get
Simple Interest I = $ 780
Now , the amount after 6 years = $ 1,000 + $ 780
The amount after 6 years = $ 1,780
Hence , the simple interest is $ 780
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What does 4 x -1 equal
Answer -4
Step-by-step explanation:
The area of a triangle can be calculated using various formulas. For example, Heron’s formula is used to calculate the triangle’s area, when we know the length of all three sides. Trigonometric functions are also used to find the area of a triangle when we know two sides and the angle formed between them. However, the basic formula that is used to find the area of a triangle is:
The basic formula that is used to find out the area of a triangle is:
Area = (1/2) * base * height.
where "base" is one of the sides of the triangle, and "height" is the perpendicular distance from the vertex opposite the base to the line formed by the base. This formula is based on the fact that the area of a triangle is equal to half of the product of its base and its height. The height is also known as the altitude, and it is the distance from the vertex opposite the base to the line formed by the base. It is important to note that the height must be perpendicular to the base. This formula is valid for any type of triangle, whether it is right-angled or not, and it works well when the base and the height are known. This formula can be used in any triangle, and can be applied to any side as base, not only the bottom side. Another important formula is Heron's formula which is used to find the area of a triangle when the lengths of all three sides are known. Heron's formula is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is said as semi-perimeter of the triangle, and a, b and c are the lengths of the three sides of a given triangle.
Finally, trigonometric functions like sine, cosine, and tangent can also be used to find the area of a triangle when we know two sides and the angle formed between them. The formula used is:
Area = (1/2) * a * b * sin(C)
where let us assume a and b are the lengths of two sides of the given triangle and C is the angle which is between them.
In conclusion, there are different formulas for calculating the area of a triangle, the most common one is the base times height formula, but depending on the information you have, you can also use Heron's formula or trigonometric functions.
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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
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.
There are three children, three pets, and three favorite colors. the children are: angela, lisa, and susan. the pets are: a cat, a dog, and a fish. the colors are: blue, green, and red.
6 is the number of ways described when There are 3 children, 3 pets, and 3 favorite colors. We can represent the children, pets, and colors in a list and explained below .
Children:
1. Angela
2. Lisa
3. Susan
Pets:
1.Cat
2. Dog
3. Fish
Colors:
1.Blue
2.Green
3. Red
We can use the combination rule to find the number of ways to assign a child, a pet, and a color to each other. The combination rule states that if we have n items and want to choose k items at a time, the number of ways to do this is given by the formula:
n! / (k! (n-k)!)
Where n! denotes the factorial of n, meaning the product of all positive integers less than or equal to n.
In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:
3! / (1! (3-1)!) = 3! / (1! 2!) = 3 * 2 * 1 / (1 * 2) = 3
So there are 3 ways to assign a child, a pet, and a color to each other.
We can also use the permutation rule to find the number of ways to assign a child, a pet, and a color to each other. The permutation rule states that if we have n items and want to choose k items at a time and order matters, the number of ways to do this is given by the formula:
n! / (n-k)!
In this case, we have 3 children, 3 pets, and 3 colors, and we want to assign one of each to each other. So we can use the formula to find the number of ways to do this:
3! / (3-3)! = 3! / 0! = 3 * 2 * 1 / 1 = 6
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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
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).
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
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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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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)
(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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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
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
