Use the figure showing two parallel lines cut by a transversal. Find the measure of angle 2 if the measure of angleUse the figure showing two parallel lines cut by a transversal. Find the measure of angle 2 if the measure of angle 1 is 65 degrees.
1 is 65 degrees.

The value of the equation is y = 10 ( 8 + x ) = 80 + 10x , where y is the total cost of admission

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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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.

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 -

Answer:M<R corresponds to M<T, meaning M<R is 4x+1.

Step-by-step explanation:

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.

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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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

The unit rate of change in this situation is 0.25 mile per hour.

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The area of the walkway around the garden is 17x+14.

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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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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They have both travelled a total of 160 miles, they will now combine. They will get together at 5:46:40.

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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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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There can be a maximum of 5 teams.Three persons will be excluded.

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.

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed.

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Step-by-step explanation:

soln on

n(s)=6

n(p)=3

therefore

probability =6/3

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

The hypotheses are

We fail to reject the null hypothesis in (b) and (c)

Here, we have

The mean of the 10 strawberry plants differs from 205

So, the hypotheses are

We 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.

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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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.

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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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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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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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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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

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

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

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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The 3 corresponding points that must be on the graph are (1,0),(4,1),(16,2).  for proper calculation please scroll down.

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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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.

In Geometry, there are different types of quadrilateral and these include the following:

Generally speaking, some of the properties of a scalene trapezoid include the following:

In conclusion, we can reasonably infer and logically deduce that David drew a scalene trapezoid.

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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).

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

(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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