I need help finding each measure.

Answer:

To determine which ratio is proportional to 80:60, we need to simplify the ratio by dividing both terms by their greatest common factor. In this case, the greatest common factor of 80 and 60 is 20, so:

80/20 = 4

60/20 = 3

Therefore, the simplified ratio is 4:3.

Now we can compare this ratio to the given options to see which one is proportional to 4:3:

16:15 is not proportional

16:12 is proportional (since 16/4 = 4 and 12/3 = 4)

18:15 is not proportional

18:12 is proportional (since 18/3 = 6 and 12/2 = 6)

Therefore, the ratio that is proportional to 80:60 is 16:12.

Therefore, the simplified expression is (c).-5.05u - 6.

To simplify an expression, you typically want to combine like terms and perform any necessary operations in the correct order. Here are the steps you can follow:

Identify any like terms in the expression. Like terms are terms that have the same variables raised to the same powers.

Combine the coefficients of like terms. If there are no like terms, leave the expression as is.

Simplify any operations in the expression, such as multiplication, division, addition, or subtraction, according to the order of operations.

Check if the expression can be simplified further. If it can, repeat steps 1-3 until the expression cannot be simplified further.

Here's an example of how to simplify the expression. [tex]3x + 2x^2 - 5x - x^2[/tex]:

Identify like terms: 3x and -5x are like terms, as are [tex]2x^2[/tex] and [tex]-x^2[/tex].

Combine the coefficients of like terms: [tex]3x - 5x = -2x[/tex], and [tex]2x^2 - x^2[/tex]= x^2. So, the expression becomes:

[tex]-2x + x^2[/tex]

The expression is already simplified in terms of like terms, so there are no further operations to perform.

The expression cannot be simplified further, so the final answer is [tex]-2x + x^2.[/tex]

(3.65u − 11) − (−5 + 8.7u) can be simplified as follows:

First, distribute the negative sign in the second parenthesis:

[tex](3.65u -11) + (5 -8.7u)[/tex]

Next, combine like terms:

[tex]3.65u - 8.7u - 11 + 5[/tex]

Simplify:

[tex]-5.05u - 6[/tex]

Therefore, the simplified expression is -5.05u - 6.

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the complete question: Simplify the expression.

(3.65u − 11) − (−5 + 8.7u)

(a).12.35u + (−6)

(b). −5.05u + (−16)

(c). −5.05u + (−6)

(d).12.35u + (−16)

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)=4\implies 2^{\log_2(16x)}=2^4\implies 16x=2^4\implies x=\cfrac{2^4}{16}\implies x=1[/tex]

Answer:

11 1/2

Step-by-step explanation:

The slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

The slope of the linear regression prediction equation can be calculated by using the formula:

slope = (y2 - y1) / (x2 - x1)

where y2 is the second data point (in this case, 28,600),

y1 is the first data point (in this case, 27,000),

x2 is the second value of the independent variable (in this case, 13 years of schooling), and

x1 is the first value of the independent variable (in this case, 12 years of schooling).

Plugging in the values, we get:

slope = (28,600 - 27,000) / (13 - 12)

slope = 1,600 / 1

slope = 1,600

Therefore, the slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

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the probability that an American man is 69.8 inches or taller is 0.5 (or 50%).

To solve this problem, we can use the properties of the normal distribution and the standard normal distribution.

First, we need to standardize the variable (the height of men) to a standard normal variable (with a mean of 0 and a standard deviation of 1). We can do this using the formula:

[tex]z = (x - mu) / sigma[/tex]

where z is the standard normal variable, x is the original variable, mu is the mean of the original variable, and sigma is the standard deviation of the original variable.

In this case, we want to find the probability that an American man is 69.8 inches or taller. So we need to calculate the z-score for x = 69.8:

[tex]z = (69.8 - 69.8) / 3.5 = 0[/tex]

The z-score is 0 because 69.8 is equal to the mean of the distribution.

Next, we can use a standard normal distribution table (or a calculator with a normal distribution function) to find the probability that a standard normal variable is less than or equal to 0. We can also use the fact that the area under the standard normal curve is 1.

Using a standard normal distribution table, we find that the probability that a standard normal variable is less than or equal to 0 is 0.5.

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The expression that represents the total price of buying g pounds of grapes, b pounds of bananas, and p pounds of pears is Total cost = $2.19g + $0.59b + $1.49p

In this case, we need to use the given prices per pound of each fruit to calculate the total cost of purchasing a certain amount of each fruit. We can do this by multiplying the price per pound by the number of pounds of each fruit we want to buy, and then adding up these values.

So, to create the expression, we can start by using the given prices to calculate the cost of each fruit:

Grapes: $2.19/pound

Bananas: $0.59/pound

Pears: $1.49/pound

Next, we can use the variables g, b, and p to represent the number of pounds of each fruit we want to buy. We then multiply each price by its respective variable to get the cost of each type of fruit:

Cost of grapes: $2.19/g x g = $2.19g

Cost of bananas: $0.59/b x b = $0.59b

Cost of pears: $1.49/p x p = $1.49p

Finally, we can add up the costs of all three types of fruit to get the total cost:

Total cost = $2.19g + $0.59b + $1.49p

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Therefore, the value of x that makes the equation true is x = 2/3.

What is equation?

An equation is a mathematical statement that states that two expressions are equal. It typically consists of variables, constants, and mathematical operators (such as addition, subtraction, multiplication, and division) that are used to describe a relationship between two or more quantities. Equations are often used in various fields of mathematics, science, engineering, and economics to model real-world phenomena and solve problems.

The equation is:

[tex]x + 4 = 4x + 2[/tex]

We need to find the value of x that makes this equation true.

First, we can simplify the equation by subtracting x from both sides:

[tex]4 = 3x + 2[/tex]

Next, we can simplify further by subtracting 2 from both sides:

[tex]2 = 3x[/tex]

Finally, we can solve for x by dividing both sides by 3:

[tex]x = 2/3[/tex]

Therefore, the value of x that makes the equation true is x = 2/3.

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Answer:

-3

Step-by-step explanation:

To find the slope (m) of the line that passes through Point A(3, -9) and the origin (0, 0), we can use the formula:m = rise/run = (change in y)/(change in x)We can calculate the change in y and change in x as follows:

Change in y = y2 - y1 = 0 - (-9) = 9

Change in x = x2 - x1 = 0 - 3 = -3

Substituting these values into the formula, we get:

m = rise/run = 9/-3 = -3

Therefore, the slope of the line that passes through Point A(3, -9) and the origin is -3.

The value of C of is 49/4

Completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k. In other words, completing the square places a perfect square trinomial inside of a quadratic expression.

10k²+7k+C , to find the value of c that will make the expression a perfect square we divide b by 2 and Square it.

Since b = 7

therefore c =( b/2)²

c = (7/2)² = 49/4

therefore the value of C is 49/4.

The expression can now be written as;

10k²+7k +49/4

and it can be simplified as;

40k²+28k +49

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Here are the given expressions and their respective variables and coefficients:

12s + 4t | Variables: s, t | Coefficients: 12, 4

46rs + 10x | Variables: r, s, x | Coefficients: 46, 10

12q + 14x | Variables: q, x | Coefficients: 12, 14

10x + 10y | Variables: x, y | Coefficients: 10, 10

17rs + 32x | Variables: r, s, x | Coefficients: 17, 32

5x + 7y - 12z | Variables: x, y, z | Coefficients: 5, 7, -12

36ab + 70m | Variables: a, b, m | Coefficients: 36, 70

3r + 19a + 10m | Variables: r, a, m | Coefficients: 3, 19, 10

7k + 16m | Variables: k, m | Coefficients: 7, 16

8r + 5s | Variables: r, s | Coefficients: 8, 5

9h + 120m | Variables: h, m | Coefficients: 9, 120

12k + m | Variables: k, m | Coefficients: 12, 1

7g + 15h + w | Variables: g, h, w | Coefficients: 7, 15, 1

4c - 8d + 12f | Variables: c, d, f | Coefficients: 4, -8, 12

6t + 17r - 35j | Variables: t, r, j | Coefficients: 6, 17, -35

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The distance of the base of the tower and the airplane is 348.5 ft,  and the right option is 4. 348.5 ft.

Distance is the length between two points.

To calculate the distance of the base of the tower and the airplane, we use the formula below.

Formula:

Where:

From the diagram,

Given:

SUbstitute these values into equation 1 and solve for A

Hence, the right option is 4. 348.5 ft.

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Yes, 2 is a zero of the polynomial  [tex]Xe3-8xe2+18x-12[/tex]

To determine if 2 is a zero of the polynomial [tex]Xe3-8xe2+18x-12[/tex], we can plug in 2 for x and see if the result is 0.

So, if we substitute x=2, we get:

[tex](2)^3 - 8(2)^2 + 18(2) - 12 = 0[/tex]

Simplifying this equation, we get:

8 - 32 + 36 - 12 = 0

This equation is true, which means that 2 is indeed a zero of the polynomial [tex]Xe3-8xe2+18x-12.[/tex]

Therefore, we can conclude that the polynomial can be factored as:

[tex](X-2)(X^2-6X+6)[/tex]

This means that the other two zeros of the polynomial are the solutions of the quadratic equation [tex]X^2-6X+6=0[/tex] which can be found using the quadratic formula.

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The expression that gives the area as a function of the width is 4w²+3w.( option B)

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of a rectangle is expressed as ;

A = l×w, where l is the length and w is the width.

Since the length is 3 inches more than four times the width, then;

l = 3+4w

Representing 3+w for l in the area formula, then we have;

A = (3+4w)(w)

A = 4w²+3w

therefore the expression that represents the area is 4w²+3w

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The correct statement regarding the null hypothesis is: the null hypothesis claims the opposite of what the researcher believes.

The null hypothesis is the claim that no relationship exists between two sets of data or variables being analyzed. The

null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative

relationship does not exist, hence the term "null".

In research, the null hypothesis is a statement of no effect or no relationship between variables, while the alternative

hypothesis represents the effect or relationship the researcher is interested in demonstrating.

The purpose of statistical testing is to determine whether there is enough evidence to reject the null hypothesis in

favor of the alternative hypothesis.

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Answer: D

Step-by-step explanation:

Zach won because 3 16/24 is less than 3 15/24. Then, 3.666666 is less than 3.625

(a) The probability that the sum of the numbers is 8 is 0.1.

(b) The probability that the sum of the number is 6 or less is 0.5.

(c) The probability that the first number is 2 or the sum is 5 is 0.35.

A probability is the number of desired outcomes divided by the number of total outcomes.

The possible outcomes are:

(1,2), (1,3), (1,4), (1,5).

(2,1), (2,3), (2,4), (2,5).

(3,1), (3,2), (3,4), (3,5).

(4,1), (4,2), (4,3), (4,5).

(5,1), (5,2), (5,3), (5,4).

Total outcomes = 20

(a) The sum of the numbers is 8.

There are only two ways to get a sum of 8: (3, 5), (5,3). So the probability of getting a sum of 8 is:

P(sum of 8) = 2/20

= 0.1

Therefore, the required probability is 0.1.

(b) The sum of the number is 6 or less.

To get a sum of 6 or less, we can have the following combinations:(1, 2), (1, 3), (1, 4), (1, 5), (2,1), (2, 3), (2,4), (3,1), (3,2), (4,1), (4,2), (5,1).So the probability of getting a sum of 6 or less is:

Total outcomes = 20

P(sum of 6 or less) = 10/20

=0.5

Therefore, the required probability is 0.5.

(c) The first number is 2 or the sum is 5

There are three ways to satisfy this condition:(2,1), (2, 3), (2,4), (2, 5), (1,4), (3, 2), (4,1). So the probability of getting a number that satisfies this condition is:

Total outcomes = 20

P(first number is 2 or sum is 5) = 7/20

= 0.35.

Therefore, the required probability is 0.35.

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1) The name of the shape is rectangle

2) The name of the shape is trapezoid

3) The name of the shape is rhombus

4) The name of the shape is rectangle

From the question, we are to state the most specific name for each of the given figures

1.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

2.

We have a quadrilateral

Only a pair of opposite sides are parallel

The name of the shape is trapezoid

3.

We have a quadrilateral

Opposite sides are parallel and equal

All sides are equal

None of the angle is a right angle

The name of the shape is rhombus

4.

We have a quadrilateral

Opposite sides are parallel and equal

Each interior angle is a right angle

The name of the shape is rectangle

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Answer: 3 additional men are needed to reduce the work by 1 hour.

Step-by-step explanation: There is a relationship between working men and the hours needed to complete the work, both are inversely proportional to each other.

Let, x represent the number of men required to complete the work in :

5-1 = 4 hours

then,

4x = 5 * 12 = 60

Hence,

x = 60/4 = 15

There are 12 men, who are working currently on the job and 15 men are required to complete the work in 1 hour less time.

Then,

15 - 12 = 3

3 additional men are required to reduce work by 1 hour.

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The total area of the figure with of the semicircle and triangle is 12.27 sq. ft.

Half of a circle is known as a semicircle, and the diameter of the circle is equal to the length of the semicircle's straight edge. A sector of a circle is a section of a circle that is bounded by an arc, two radii, and both. A semicircle is always half of a circle and has a constant central angle of 180 degrees, but a sector can be any part of a circle and has a central angle that can vary from 0 to 360 degrees. This is the major distinction between the two.

Given, the diameter of the semicircle is 3 ft, so its radius is 1.5 ft.

Now, area of the semicircle is given as:

A = 1/2 * pi * (1.5)² = 1.77 sq ft

The area of the triangle is:

A = 1/2 * 3 ft * 7 ft = 10.5 sq ft

Adding the areas we have the total area of the figure:

1.77 sq ft + 10.5 sq ft = 12.27 sq ft

Hence, the total area of the figure is 12.27 sq. ft.

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Answer:

6x² + 19x + 15

Step-by-step explanation:

(2x+3)(3x + 5)

= 6x² + 10x + 9x + 15

= 6x² + 19x + 15

So, the answer is 6x² + 19x + 15

Answer:

x> - 15

Step-by-step explanation:

I guess this will help

Hong rode the scooter for approximately 86 minutes.

Let's start by using algebra to solve for the number of minutes Hong rode the scooter.

Let's say the number of minutes Hong rode the scooter is "m". Then, we can set up the following equation:

Total cost = $5 fee + 9 cents per minute x m minutes

$12.74 = $5 + $0.09m

Next, we'll solve for "m" by isolating it on one side of the equation:

$12.74 - $5 = $0.09m

$7.74 = $0.09m

m = $7.74 ÷ $0.09

m ≈ 86

Therefore, Hong rode the scooter for approximately 86 minutes.

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Answer:

Step-by-step explanation:

Here you go:

64 = 512x - 4

64 + 4 = 512x - 4 + 4

68 = 512x

Hope this helps

If 75 kids of the 90 kids were girls. The ratio of boys to girls is 1:5.

If there were 75 girls out of 90 kids in total, then the number of boys can be found by subtracting 75 from 90:

The Number of boys = 90 - 75 = 15

Therefore, the ratio of boys to girls is:

The Number of boys : The Number of girls

15 : 75

To simplify this ratio, we can divide both sides by 15 (which is the greatest common factor of 15 and 75):

15 ÷ 15 : 75 ÷ 15

1 : 5

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Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.

Given statement is True.

The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.

By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.

This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.

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The equation (x + 6)^2 + (y + 4)^2 = 36 is in the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle, and r is the radius of the circle. Comparing this with the given equation, we see that the center of the circle is (-6, -4), and the radius of the circle is 6.

Therefore, the signal is located at the point (-6, -4), which is the center of the circle. This is the point from which the radio signal is transmitted.

The range of the signal is the distance from the center of the circle to any point on the circumference of the circle, which is equal to the radius of the circle.

In this case, the radius is 6, which means that the range of the signal is 6 units in all directions from the center. This means that any receiver within 6 units of the center can pick up the radio signal transmitted from this source.

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A. The number of 7-card stud poker hands is 133,784,560 and the number of 7-card stud poker hands is 674,274,182,400.

B. The number of hands of 7-draw poker that contain the ace of hearts is 18,009,460.

C. The probability that a 7-card draw hand contains the ace of hearts is 0.135.

a) The number of 7-card draw poker hands can be calculated using the combination formula, which is:

[tex]^{n} C_{r}[/tex] = n! / (r! * (n - r)!)

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card draw poker hands is:

[tex]^{52} C_{7}[/tex] = 52! / (7! * (52 - 7)!)

= 133,784,560.

The number of 7-card stud poker hands can be calculated using the permutation formula, which is:

[tex]^{n} P_{r}[/tex] = n! / (n - r)!

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card stud poker hands is:

[tex]^{52} P_{7}[/tex] = 52! / (52 - 7)!

= 674,274,182,400.

b) To count the number of hands of 7-draw poker that contain the ace of hearts, we can treat the ace of hearts as a special card that must be included in each hand. Then, we need to choose the remaining 6 cards from the 51 cards that are not the ace of hearts.

So, the number of hands of 7-draw poker that contain the ace of hearts is:

[tex]^{51} C_{6}[/tex] = 51! / (6! * (51 - 6)!)

= 18,009,460.

c) To calculate the probability that a 7-card draw hand contains the ace of hearts, we can use the formula:

P(event) = number of favourable outcomes / total number of possible outcomes

The total number of possible 7-card draw hands is 133,784,560, which we calculated in part (a).

The number of favourable outcomes is the number of hands of 7-draw poker that contain the ace of hearts, which we calculated in part (b).

So, the probability that a 7-card draw hand contains the ace of hearts is:

P(ace of hearts) = 18,009,460 / 133,784,560 ≈ 0.135

The required probability is 0.135.

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Answer:

[tex]36x^{3}a+45xa^{2}=9xa(4x^{2} +5a)[/tex]

Step-by-step explanation:

You can factor out both 9, x, and a, as all the terms can be divided by 9xa.

Hope this helped!

For events A and B to be independent, the condition that must be true is:
P(A ∩ B) = x * y

The correct condition that must be true if events A and B are independent is:

P(A ∩ B) = P(A) x P(B).

where P(A) is the probability of event A, P(B) is the probability of event B, and P(A ∩ B) is the probability of both events A and B occurring together.

In other words, if events A and B are independent, then the probability of both events occurring together is equal to the product of their individual probabilities.

When two events A and B are independent, the following condition must be true:
P(A ∩ B) = P(A) * P(B)
In your case, the probability of event A is x, and the probability of event B is y.

Therefore, the correct answer is:

P(A ∩ B) = x*y

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