Match each statement with the right choice.
6 ( 5 + 8)
5 (10 + 3)
9 ( 2 + 4)
7 ( 3 + 6)

Answer:

There are no pictures to explain what  L is

Step-by-step explanation:

-3(7f + 3f + 9) - 4f

Distribute.

(−3)(7f) + (−3)(3f) + (−3)(9) + −4f

−21f + −9f + −27 + −4f

Combine like terms.

−21f + −9f + −27 + −4f

(−21f + −9f + −4f) + (−27)

−34f + −27

-34f + -27

The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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The probability that a randomly selected point inside a triangle with side lengths 5, 12, and 13 has a distance from the nearest vertex of the triangle less than 2 is approximately 0.4286, or 42.86%.

To find the probability, we can consider the triangle with side lengths 5, 12, and 13 as a right triangle, where the side length 13 represents the hypotenuse. Let's assume the vertices of the triangle are A, B, and C, with AB = 5, AC = 12, and BC = 13.

First, we calculate the area of the triangle using Heron's formula, which gives us √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle and a, b, and c are the side lengths. In this case, s = (5+12+13)/2 = 15.

Using the formula, the area of the triangle is \(\sqrt{15(15-5)(15-12)(15-13)} = \sqrt{15 \cdot 10 \cdot 3 \cdot 2} = \sqrt{900} = 30\).

Now, let's consider the smaller triangle formed by the original triangle's vertices and a point P inside it. To calculate the probability, we need to find the area of the region where the distance from P to the nearest vertex is less than 2.

If we draw circles centered at each of the vertices A, B, and C with radius 2, the area enclosed by these circles within the triangle represents the region we are interested in.

Calculating the areas of these circles, we find that each circle has an area of 4π. Since there are three circles, the total area of the enclosed region is 3 × 4π = 12π.

Therefore, the probability that a randomly selected point inside the triangle has a distance from the nearest vertex less than 2 is given by (12π / 30) = (2π / 5), which is approximately 0.4286 or 42.86%.

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Answer:

y = 476^x

Step-by-step explanation:

y = 250(1.904)^×

y = 476^x

Hope this helps, thank you !!

Answer:

Loading. . .

Step-by-step explanation:

The dimensions of the box can be represented as (6-2x) inches by (24-2x) inches by "x" inches.

From a 24-inch by 6-inch piece of cardboard, square corners are cut so the sides can fold up to form a box without a top. To determine the dimensions and construct the box, we need to consider the shape of the cardboard and the requirements for folding and creating the box.

The initial piece of cardboard is a rectangle measuring 24 inches by 6 inches. To form the box without a top, we need to remove squares from each corner.

Let's assume the side length of the square cutouts is "x" inches. After cutting out squares from each corner, the remaining cardboard will have dimensions (24-2x) inches by (6-2x) inches.

To create a box, the remaining cardboard should fold up along the edges. The length of the box will be the width of the remaining cardboard, which is (6-2x) inches.

The width of the box will be the length of the remaining cardboard, which is (24-2x) inches. The height of the box will be the size of the square cutouts, which is "x" inches.

Therefore, the dimensions of the box can be represented as (6-2x) inches by (24-2x) inches by "x" inches. To construct the box, the remaining cardboard should be folded along the edges, and the sides should be secured together.

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Answer:

y = 658.3 ft

Step-by-step explanation:

x = 745.5 ft

y = 658.3 ft

tan 28 = 350/y

y = 658.3

Answered by GAUTHMATH

Answer:

raquel can only play 4 games

so 2x4=x=8

or 8 divided by  4 is x=2

Step-by-step explanation:

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

3 + 9\(\sqrt{5}\)

Step-by-step explanation:

primeter = a + b + c

primeter = \(\sqrt{20}\) + 3 + \(\sqrt{20}\) + 3 + \(\sqrt{5}\)

primeter = 3 + 9\(\sqrt{5}\)

Answer: 8

Step-by-step explanation: Multiplication comes first before subtraction in PEMDAS so in the middle brackets its 4. So now we have [6+4 divided by 2] which equals 8.

The confidence interval for the proportion of adults who identify chocolate pie as their favorite pie can be calculated using the following formula:
Confidence Interval = Sample Proportion ± Margin of Error

First, we need to calculate the sample proportion. In this case, the sample proportion is equal to the percentage of respondents who chose chocolate pie, which is 48%.

Sample Proportion = 48% = 0.48

Next, we need to calculate the margin of error. The margin of error depends on the confidence level and the sample size. In this case, the confidence level is 90%, which corresponds to a z-score of 1.645 (obtained from a z-table). The sample size is 22.

Margin of Error = z * sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
                = 1.645 * sqrt((0.48 * (1 - 0.48)) / 22)
                = 0.229

Now we can calculate the confidence interval.
Confidence Interval = Sample Proportion ± Margin of Error
                          = 0.48 ± 0.229
                          = (0.251, 0.709)

The confidence interval for the proportion of adults who identify chocolate pie as their favorite pie is (0.251, 0.709) at a 90% confidence level.

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Answer:

11880 feet!

Hope you get this correct

Answer:

  $102

Step-by-step explanation:

The pay for the day of work is the total of morning hours worked and afternoon hours worked. In each case, the hours worked is the difference between the "Out" time and the "In" time.

  morning hours = 12:15 -8:15 = 4:00

  afternoon hours = 17:30 -13:00 = 4:30

  total hours worked = morning hours + afternoon hours

  total hours worked = 4:00 +4:30 = 8:30

This notation tells you (hours):(minutes). You know that 30 minutes is 1/2 hour, so the total time worked is 8 1/2 hours.

The pay is the product of the hours worked and the pay per hour:

  pay = (8 1/2 hours) × ($12 /hour) = $102

Answer:

i cant find the answer

Step-by-step explanation:

sorry

The rate of change and the initial value, can be found to be B. initial value : 1 , rate of change : 1.

The initial value is the first x - value that is on the linear relationship. In this case, that initial value would be 1.

The rate of change can be found by the formula:

= Change in y / Change in x

= ( 4 - 2 ) / ( 5 - 3 )

= 2 / 2

= 1

The rate of change is therefore 1.

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Answer:

False

Step-by-step explanation:

Vertical angles are not always adjacent, but they are always congruent.

Hope that helps!

Answer:

False

Step-by-step explanation:

Hope it will help you*

Answer:

yes

Step-by-step explanation:

Answer:

57 degrees

Step-by-step explanation:

value of x = 29

Answer:

57

Step-by-step explanation:

(4x + 7) + (2x -1) = 180

6x + 6 = 180

6x = 174

x = 29

(2(29) -1 )

(58 - 1)

(57)

The proportionality constant between half-life and inverse rate constant affects the slope of a plot of ln(t1/2) vs. 1/t. Half-life is the amount of time it takes for half of the initial quantity of a substance to decay or react to form a product.

The rate constant is the proportionality constant in the rate law equation that relates the rate of the reaction to the concentration of reactants raised to some power. The rate constant is also used in the equation for the half-life of a reaction.The half-life of a reaction is proportional to the inverse of the rate constant. Mathematically, it can be represented a :t1/2 ∝ 1/kTherefore, as the rate constant increases, the half-life of the reaction decreases and vice versa. In other words, there is an inverse relationship between the half-life of a reaction and the rate constant.

This relationship can be observed in a plot of ln(t1/2) vs. 1/t. The slope of this plot is equal to the proportionality constant between half-life and inverse rate constant, which is given by the expression:k = ln(2)/t1/2Therefore, the slope of the plot is directly proportional to ln(2), which is a constant. This means that the proportionality constant between half-life and inverse rate constant does affect the slope of a plot of ln(t1/2) vs. 1/t.

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The differential equation (cos x)y"" + y' + 5y = 0 has an ordinary point at x=0 and x=1. To find the minimum radius of convergence of power series solutions about these points, Frobenius without actually solving the differential equation.

The method of Frobenius involves assuming a power series solution of the form y(x) = ∑ an\(x^n\), substituting it into the differential equation, and finding a recursion relation for the coefficients a_n. For the given differential equation, we can assume a solution of the form y(x) = ∑ an \(x^n\) and substitute it into the differential equation to obtain:

cos(x) [n(n-1)an \(x^(n-2)\) + a_n-2] + n an x^(n-1) + 5 an \(x^n\) = 0

Rearranging the terms and collecting coefficients of an, we get the recursion relation:

\(an\) = -\(1/ [n(n+4)] [(n-1)(n+3)a_n-2]\)

Using the ratio test, we can find the radius of convergence of the power series solution about x=0 to be 1, which is the minimum radius of convergence.

Similarly, for the power series solution about x=1, we can make a change of variable y(x) = z(x-1) and obtain a differential equation with an ordinary point at z=0. Using the method of Frobenius, we can find the minimum radius of convergence of the power series solution about x=1 to be also 1.

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Thus, the range of set X is {2, 3, 7, 11, 17, 19}, with the prime number K being 2.

To find the range of set X, we need to determine the possible values for the unknown prime number K that satisfy the given conditions.

We know that set X consists of prime numbers {3, 11, 7, K, 17, 19}.

The product of all the elements in set X, represented by Y, can be calculated as:

Y = 3 * 11 * 7 * K * 17 * 19

We are given that 11Y is an even number. To make 11Y even, Y must be divisible by 2.

Since Y is the product of all the prime numbers in set X, it must already be an odd number because it includes only odd prime numbers.

For Y to be divisible by 2, we need to include a factor of 2 in the product. However, the set X only consists of prime numbers, and 2 is the only even prime number.

Therefore, the prime number K must be equal to 2 to make the product Y even.

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Alice has done 8 times more work than Bill in climbing the mountain, even though she reaches the top in 1/3 the time it takes Bill.

The work that Alice did in climbing the mountain is equal to the work that Bill did, even though Alice took the longer path. This is because work is defined as the product of force and displacement, and both Alice and Bill exerted the same amount of force against gravity to lift their bodies to the same height. The longer path taken by Alice resulted in a smaller force exerted over a longer distance, while the steep path taken by Bill resulted in a larger force exerted over a shorter distance. However, Alice completed the climb in 1/3 the time it took Bill, which means that her power output was 3 times greater than Bill's. Power is defined as the rate of doing work, so even though Alice did the same amount of work as Bill, she did it in a shorter amount of time, which means that her power output was greater.

Alice and Bill both have the same mass and are climbing to the top of a mountain. Bill takes the steep path straight up, while Alice takes a longer, winding path that is 8 times the length of the steep path. Despite this, Alice reaches the top in 1/3 of the time it takes Bill.

To compare the work done by Alice and Bill, we need to understand that work is equal to the force applied multiplied by the distance traveled, or W = F × d. The force in this case is equal to their mass multiplied by the acceleration due to gravity (F = m × g).

Since both Alice and Bill have the same mass and are climbing the same height, the vertical distance they travel is the same. Therefore, the force applied by both Alice and Bill is also the same.

However, the total distance traveled is different. Alice takes a path that is 8 times longer than Bill's path. In terms of work done, this means that Alice has done 8 times more work than Bill, as W = F × d, and the distance she traveled is 8 times longer.

In summary, Alice has done 8 times more work than Bill in climbing the mountain, even though she reaches the top in 1/3 the time it takes Bill.

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The temperature of the coffee when placed in the room is 114 degrees.

An exponential function is in the form:

y = abˣ

where y,x are variables, a is the initial value of y and b is the multiplier.

Let T represent the temperature of coffee after m minutes. Since:

\(T = 114(0.86)^{m}\)

a) \(T (0)= 114(0.86)^{0}=114\)

B) This means that the temperature of the coffee when placed in the room is 114 degrees.

c) The temperature degrees by 14 degrees each minute (1 - 0.86).

D)

\(100=114(0.86)^m\\\\m = 0.9 minutes\)

The temperature of the coffee when placed in the room is 114 degrees.

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The y-cοοrdinate οf the center οf mass is 31/6.

The center οf mass οf the triangular metal piece is lοcated at (13/12, 31/6).

Mass is a measure οf the amοunt οf matter in a substance οr οbject. The base SI unit fοr mass is the kilοgram (kg), but smaller masses can be measured in grams (g). Yοu wοuld use a scale tο measure weight. Mass is a measure οf the amοunt οf matter an οbject cοntains.

Tο find the center οf mass οf the triangular metal piece, we need tο calculate the cοοrdinates (x, y). The center οf mass cοοrdinates can be determined using the fοllοwing fοrmulas:

x = (1/A) ∫∫x * g(x, y) dA

y = (1/A) ∫∫y * g(x, y) dA

where A is the area οf the triangular metal piece.

First, let's find the area οf the triangular regiοn R:

A = ∫∫R dA

Since the triangular regiοn R is defined as 0 ≤ x ≤ 1 and 0 ≤ y ≤ 2x, the limits οf integratiοn fοr x and y are as fοllοws:

0 ≤ x ≤ 1

0 ≤ y ≤ 2x

Therefοre, the area A can be calculated as:

A = ∫∫R dA = ∫0¹ ∫\(0^{(2x)\) dy dx

Integrating with respect tο y first:

A = ∫0¹ (2x - 0) dx = ∫0¹ 2x dx = [\(x^2\)]0¹ = 1

The area οf the triangular regiοn R is 1.

Nοw, let's find x:

x = (1/A) ∫∫x * g(x, y) dA

= (1/1) ∫∫R x * (5x + 5y + 5) dA

= 5 ∫∫R \(x^2\) + xy + x dA

Integrating with respect tο y first:

x = 5 ∫0¹ ∫\(0^{(2x)} (x^2 + xy + x)\) dy dx

= 5 ∫0¹ [\((x^2y + (xy^2)/2 + xy)]0^{(2x)\) dx

= 5 ∫0¹ [\((2x^3 + (2x^3)/2 + 2x^2)\) - (0 + 0 + 0)] dx

= 5 ∫0¹\((3x^3 + x^2)\) dx

= \(5 [(3/4)x^4 + (1/3)x^3]\)0¹

= 5 [(3/4) + (1/3)]

= 5 [(9/12) + (4/12)]

= 5 (13/12)

= 13/12

Therefοre, the x-cοοrdinate οf the center οf mass is 13/12.

Next, let's find y:

y = (1/A) ∫∫y * g(x, y) dA

= (1/1) ∫∫R y * (5x + 5y + 5) dA

= 5 ∫∫R xy + \(y^2\) + 5y dA

Integrating with respect tο y first:

y = 5 ∫\(0^1\) ∫\(0^{(2x)} (xy + y^2 + 5y)\) dy dx

= 5 ∫\(0^1 [(x/2)y^2 + (y^3)/3 + (5/2)y^2]0^{(2x)\) dx

= 5 ∫\(0^1 [(x/2)(4x^2) + (8x^3)/3 + (5/2)(4x^2)\)] dx

= 5 ∫\(0^1 (2x^3 + (8/3)x^3 + 10x^2)\)dx

= 5 [\((1/2)x^4 + (4/3)x^4 + (10/3)x^3]0^1\)

= 5 [(1/2) + (4/3) + (10/3)]

= 5 [(3/6) + (8/6) + (20/6)]

= 5 (31/6)

= 31/6

Therefοre, the y-cοοrdinate οf the center οf mass is 31/6.

The center οf mass οf the triangular metal piece is lοcated at (13/12, 31/6).

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Answer:

Below.

Step-by-step explanation:

2(x + 2) = 2x + 4

2x + 4 = 2x + 4

Both sides are identical so we can replace x with any value we like and the equation will balance, so there are infinitely many solutions.

Answer:

2(x+2)=2x+4

I'm not very sure but I hope this is right. I took geometry last year so my memory on it is funky :/

Answer:

54 ;)

explanation:

6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 = 54

If two triangles are congruent (as per the given congruency statement), then the corresponding angles of both triangles are also congruent.

Therefore, if angle B = 145, then angle E is also 145.

Answer: C) 145

Hope this helps!

Answer:

The equation is y = 3x + 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = Δy/Δx, where

∵ x is the input

∵ Input: 0, 1, 2, 3, 4

∵ y is the output

∵ output: 2, 5, 8, 11, 14

∴ The points on the line are (0, 2), (1, 5), (2, 8), (3, 11), and (4, 14)

→ Use any two points to find m

∵ x1 = 0 and y1 = 2

∵ x2 = 1 and y2 = 5

→ Find Δx and Δy

∴ Δx = 1 - 0 = 1

∴ Δy = 5 - 2 = 3

→ Substitute them in the rule of the slope above

∵ m = \(\frac{3}{1}\)

∴ m = 3

∵ b is the value of y at x = 0

∵ At x = 0, y = 2

∴ b = 2

→ Substitute the values of m and b in the form of the equation above

∵ y = 3x + 2

∴ The equation is y = 3x + 2