Find the value of x.
15
X
36

Answer:

Cathy is 18 Katie is 6

Step-by-step explanation:

mhm

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The data is considered discrete (D). Discrete data refers to information or values that can only take on specific, separate, and distinct values.

The data described, which is the numbers of wheels on different vehicles, is discrete because the data can only take on specific values. Vehicles can have either 2, 4, 6, or more wheels, but cannot have a fractional or continuous number of wheels. Discrete data refers to information or values that can only take on specific, separate, and distinct values. These values are typically integers or whole numbers, although they can also be categorical or nominal. Discrete data is characterized by gaps or jumps between values, as there are no intermediate values or fractions. Examples of discrete data include:

The number of students in a class (can only be whole numbers).

The number of cars in a parking lot (cannot have fractions or partial cars).

The number of goals scored in a soccer match (cannot have half or fraction of a goal).

The results of a survey question with options like "Yes" or "No" (categorical).

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The amount earned is $88,709.68

It is a payroll tax that is paid on wages earned by employees.

We have,

We will assume the current Social Security tax rate for employees as 6.2%.

Now,

The amount earned.

= 5,500 / 6.2%

= 5500 / 0.062

= $88,709.68

Thus,

The amount earned is $88,709.68

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Equation in slope-intercept form for the required line which passes through (-2, 2) and perpendicular to  y= -5x-8 is equal to y = 5x+12.

As given in the question,

Line passes through the point ( -2, 2)

Required line is perpendicular to the given line y = -5x -8.

Let the point by ( x₁ , y₁) = ( -2, 2)

Standard equation of line is

y =mx +c

Slope = m

Slope of given line is -5

Lines are perpendicular

Slope of required line is 5

Required equation in slope-intercept form is:

y -2 =5(x-(-2))

⇒ y -2 = 5x +10

⇒ y= 5x +12

Therefore, equation in slope-intercept form for the required line which passes through (-2, 2) and perpendicular to  y= -5x-8 is equal to

y = 5x+12.

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Answer:

The answer to your problem is, A. Larger

Step-by-step explanation:

First in order to know to the answer lets learn about different types of fractions:

For example, 1/4, 3/4, 3/8, are all proper fractions.

4/3, 5/2, are all improper fractions.

When we have to multiply a whole number with fractions less than 1, then the resulting number will be less the number originally

Example; 3 x \(\frac{3}{4}\)

If we then multiplying numerators together and the denominators together.

3 x \(\frac{3}{4}\) = \(\frac{3}{1}\) x \(\frac{3}{4}\) = \(\frac{9}{4}\) = 2\(\frac{1}{4}\) < 3

Example /\

Thus the answer to your problem is, A. Larger OR Multiply.

The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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A triangle whose sides are all equal is called an equilateral triangle and its area is given by A=\(\frac{\sqrt{3} }{4}\) \(x^{2}\), where x is the side of the triangle.

The area of a rectangle is found by using the formula

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

The given figure can be split into two shapes: a rectangle and an equilateral triangle as shown in the diagram. Let l be the length of the rectangle.

Add all of the sides of the window and equate their result to 16. Then solve for l.

x + x + l + x + l = 16

3x + 2l = 16

2l = 16 - 3x

l = \(\frac{16-3x}{2}\)

The total area of the window will be the sum of the area of the equilateral triangle ABE and the area of rectangle BCDE.

A = \(\frac{\sqrt{3} }{4}\)\(x^{2}\) + lx

Subsitute  \(\frac{16-3x}{2}\) for l into the obtained equation and simplify.

A =\(\frac{\sqrt{3} }{4}\)\(x^{2}\) + ( \(\frac{16-3x}{2}\))x

A = \(\frac{\sqrt{3} }{4} x^{2}\) + 8x - \(\frac{3}{2} x^{2}\)

Differentiate the obtained equation with respect to x and equate the first derivative to 0 to calculate the critical point x .

\(\frac{dA}{dx}\) = \(\frac{\sqrt{3} }{4}\) (2x) + 8 - \(\frac{3}{2}\) (2x)

0 = \(\frac{\sqrt{3} }{2}\) x - 3x + 8

x (3 - \(\frac{\sqrt{3} }{2}\)) = 8

x = \(\frac{16}{6-\sqrt{3} }\)≈3.74887

Again, differentiate the equation

\(\frac{dA}{dx}\) = \(\frac{\sqrt{3} }{2}\)x - 3x + 8  with respect to x.

\(\frac{d^{2}A }{dx^{2} }\) = \(\frac{\sqrt{3} }{2}\) - 3

The value of the second derivative is \(\frac{\sqrt{3} }{2}\)−3, which is negative. This implies that the area will be maximum at the critical point.

Subsitute x = 3.74887 into the equation

l = \(\frac{16-3x}{2}\) and simplify

l = \(\frac{16-(3)(.74887)}{2}\) ≈ 2.3767

The maximum light will enter through the window when the triangular portion will have the side length of 3.74887 feet and the dimensions of the rectangular portion will be 3.74887-ft-by-2.3767-ft.

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

16,17,18,19

Step-by-step explanation:

one guy guessed. probably using a calculator

another guy took the 4th root of 100,000 and rounded down a number

(a third way started like this

n*(n+1)*(n+2)(n+3)=100000

I hope this helps you

(3+19)+(4i-5i)

22-i

Answer:

y = x +1

Step-by-step explanation:

y= mx + b

where m is the slope and b is the y-intercept

m = (y2-y1)/ (x2-x1) = 2+4 / 3+3 = 6/6 = 1

from the point -slope equation we have

y-y1 = m* (x-x1)

y-3 = 1* ( x-2)

y= x -2+3

y= x +1

so the slope m=1 and the y-intercept b=1

(a) The range of values for the sample mean would be expected 95% of the time is 490.8 to 569.2.

(b) The range of values would be expected 95% of the time if the sample size were n = 100 is 514.32 to 545.68.

The standard error (SE) of a statistic is the approximate standard deviation of the statistical sample population.

Standard error is a statistical term used to measure how well a sampling distribution uses the standard deviation to represent a population. In statistics, the difference between the mean of a sample and the true mean of a population; this deviation is the standard error of the mean.

According to the Questions:

a. With n = 16 the standard error is am = 20 points. Using z = ± 1.96, the 95% range extends from 490.8 to 569.2.

b. With n = 100 the standard error is only 8 points and the range extends from 514.32 to 545.68.

Complete Question:

The SAT scores for the entering freshman class at a local college form a normal distribution with a mean of p = 530 and a standard deviation of a = 80.

a. For a random sample of n = 16 students, what range of values for the sample mean would be expected 95% of the time?

b. What range of values would be expected 95% of the time if the sample size were n = 100?

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The triangle ABC is equal to triangle ADE by Angle-Angle-Side theorem.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In triangle ABC and ADE -

It can be seen that ∠B = ∠E.

Also the line segment AB is equal to line segment AE.

AB = AE

The angles ∠BAC and ∠DAE are vertically opposite to each other.

So, they are also equal.

∠BAC = ∠DAE

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Therefore, Δ ABC ≅ Δ ADE according to AAS theorem.

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All the numbers between 0 and 9 (including 0 and 9) belong to the domain of the function that describes the fare per kilometer.

The function that describes the fare per kilometer in a jeepney ride is:

$$f(x)=\begin{cases}9, & x \in [0,4) \\\ 1.40(x-4)+9, & x \in [4,9]\end{cases}$$

Here, x is the number of kilometers of the jeepney ride.

The first 4 kilometers cost Php 9 per kilometer. Thus, the fare for the first 4 kilometers is fixed at Php 9 per kilometer. For the distance from 4 to 9 kilometers, the cost is Php 1.40 per kilometer. So, the fare per kilometer in this interval is $1.40(x-4)$.

However, we have to add Php 9 since the first 4 kilometers already cost Php 9. Therefore, the fare function for this interval is $1.40(x-4)+9$.

To determine the domain of this function, we have to consider only the values of x that fall between 0 and 9 kilometers since the jeepney's route is at most 9 kilometers. Thus, the domain of the function is:

$$D=\{x \in \mathbb{R} : 0 \leq x \leq 9\}$$

Therefore, all the numbers between 0 and 9 (including 0 and 9) belong to the domain of the function that describes the fare per kilometer.

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Answer:

A.)

Rise = 2

Run = 5

m = 2/5

B.)

Rise = 2

Run = - 4

m = - 1/2

C.)

Rise = 3

Run = 1

m = 3

Step-by-step explanation:

Rise = y2 - y1

Run = x2 - x1

Slope, m = Rise / Run

A.) (0,0) ; (5 2)

x1 = 0 ; y1 = 0

x2 = 5 ; y2 = 2

Rise = 2 - 0 = 2

Run = 5 - 0 = 5

m = 2/5

B.) (1, 2) ; (-3, 4)

x1 = 1 ; y1 = 2

x2 = - 3 ; y2 = 4

Rise = 4 - 2 = 2

Run = - 3 - 1 = - 4

m = 2/-4 = - 1/2

C.) (5,2) ; (6,5)

x1 = 5 ; y1 = 2

x2 = 6 ; y2 = 5

Rise = 5 - 2 = 3

Run = 6 - 5 = 1

m = 3/1 = 3

The solution is, 83.6 kilograms does Miguel weigh.

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

here, we have,

given that,

Miguel weighs himself and discovers he weighs 83,600 grams.

now.,, we have to find that how many kilograms does Miguel weigh.

we know that,

1000 grams = 1 kg

so, we have,

he weighs 83,600 grams

so,

as, 1000 grams = 1 kg

so, 1 gram = 1/1000 kg

we get,

83,600 grams =  1/1000 * 83,600 kg

i.e. 83,600 grams = 83.6 kg

Hence, 83.6 kilograms does Miguel weigh.

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Answer:

Step-by-step explanation:

A correlation coefficient of 0.55 implies a weak positive correlation, because it's close to 0.50. Remember that strong correlations are 1 or -1, positive or negative, and the middle of the interval represents no correlation.

Having said that, 0.55 indicates some correlation, but weak. Therefore, the right answer is C.

Her prediction will be somewhat likely to be close to the actual value.

We have given that,

Madelina wants to make a prediction using a linear model with a correlation coefficient of 0.55.

We have to determine the correct statement.

The correlation coefficient is a statistical measure of the strength of the relationship between the relative movements of two variables.

A correlation coefficient of 0.55 implies a weak positive correlation because it's close to 0.50. Remember that strong correlations are 1 or -1, positive or negative, and the middle of the interval represents no correlation.

Having said that, 0.55 indicates some correlation, but weak.

Therefore, the right answer is C.

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A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components 〈14, 23〉. The characteristics of the vector representing the path of the ship are "components: 〈7, 11.5〉, magnitude: 13.46".

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is x units.

Then, the distance between B and the fueling station is 2x units.AB = 2x units. The fueling station is located at 〈14, 23〉. And A is located at (0, 0)Now we can calculate the distance between A and the fueling station using the distance formula.= √[(14 - 0)² + (23 - 0)²]= √(196 + 529)= √725= 26.92 approx.

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is 26.92 units. Then, the distance between B and the fueling station is 2 × 26.92 = 53.85 units.

Now we can calculate the vector AB using the below formula: AB = OB - OAwhere, OA = (0, 0)OB = (7, 11.5)

So, AB = OB - OA= (7, 11.5) - (0, 0)= (7, 11.5)

Magnitude of vector AB = √(7² + 11.5²)= √(49 + 132.25)= √181.25= 13.46 approx.

So, the correct answer is "components: 〈7, 11.5〉, magnitude: 13.46".

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Answer:

45

Step-by-step explanation:

Hope this helped

Answer:

I do believe the answer is A

a. A central angle is: angle GFH; b. A major arc is: arc GJH; c. A minor arc is: arc GH.

d. measure of arc GJH = 265°; e. measure of angle GH = 95°

A major arc is an arc of a circle that measures greater than or equal to 180 degrees. It is sometimes called a large arc or a wide arc. If a circle has a central angle that measures more than 180 degrees, then the corresponding arc is a major arc.

On the other hand, a minor arc is an arc of a circle that measures less than 180 degrees. It is also called a small arc or a narrow arc. If a circle has a central angle that measures less than 180 degrees, then the corresponding arc is a minor arc.

Using the information given, we have:

a. A central angle in the figure given is: angle GFH.

b. A major arc in the figure given is: arc GJH.

c. A minor arc in the figure given is: arc GH.

d. measure of arc GJH = 360 - measure of arc GH

Measure of arc GH = measure of angle GFH = 95°

Therefore:

measure of arc GJH = 360 - 95 = 265°.

e. measure of angle GH = 95°

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(A) The regression equation in the form \(`y=2.5(1.358)^x`\). (B) The number of Internet hosts in 2031 is approximately 13195.

Given the table that shows the number of internet hosts from 1994 to 2012: Year Hosts1994 2.51997 16.42000 69.12003 181.32006 362.42009 611.22012 864.2

(A) Write the regression equation in the form\(y=ab^x\)

Regression equation of the form\(`y = ab^x`\)can be obtained using the following steps:

Calculate the values of a and b using the following formulas: \(`b=(y2/y1)^(1/(x2-x1))`\) and \(`a=y1/b^x1`\)

Substitute the values of a and b in the equation \(`y = ab^x\)` to get the exponential regression equation.

Here, x = number of years since 1994, y = number of internet hosts.

Using the formula `b=(y2/y1)^(1/(x2-x1))`:let (x1,y1) = (0,2.5) and (x2,y2) = (18,10586.57)

We have, b = (10586.57/2.5)^(1/18)≈1.358

Using the formula \(`a=y1/b^x1`\): we get, a = 2.5/1.358^0 ≈ 2.5

Now, substituting the value of a and b in the equation `y = ab^x`, we get the regression equation of the form\(`y=2.5(1.358)^x`.\)

(B) Use the model to estimate the number of hosts in 2031.To find the number of hosts in 2031, we need to find the number of years since 1994 (the year the table starts) which is x = 2031 - 1994 = 37.

Substituting x = 37 in the equation \(`y=2.5(1.358)^x`,\)we get:\(y ≈ 2.5(1.358)^37≈ 2.5(5278.25)\)≈ 13195

Internet hosts in 2031 will be approximately 13195.

Answer: (A) The regression equation in the form \(`y=2.5(1.358)^x`\). (B) The number of Internet hosts in 2031 is approximately 13195.

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Answer:

when two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°.

Step-by-step Explanation:

The relationship between an intercepted arc and an inscribed angle is given as:

the measure of the intercepted arc = twice the inscribed angle that intercepts it.

Also, by virtue of this, when two inscribed angles intercepts the same arc, both inscribed angles are said to be congruent. And the measure of both angles equal the measure of the arc they both intercept.

Therefore, if the measure of an arc, that is intercepted by 2 inscribed angles, is given as 75°, both inscribed angles equal 75° as well. Thus, each of the inscribed angles is half the measure of the intercepted arc.

Therefore, the statement that is true about inscribed angles is: "when two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°."

(a) First month's payment: $4,030 interest, -$3,519.10 principal.

(b) Total paid over 20 years: $122,616.

(a) In the first month's payment, we can calculate the interest and principal amounts. Let's use the following variables:
P = Loan amount = $62,000
r = Monthly interest rate = 7.8% / 12 = 0.065
M = Monthly payment = $510.90

To find the interest amount, we multiply the loan amount by the monthly interest rate:
Interest amount = P * r = $62,000 * 0.065 = $4,030

To find the principal amount, we subtract the interest amount from the monthly payment:

Principal amount = Monthly number payment - Interest amount = $510.90 - $4,030 = -$3,519.10

It's important to note that in this case, the principal amount is negative.

This occurs because the interest payment exceeds the monthly payment, resulting in a decrease in the outstanding loan balance.

(b) Over the 20 years, the total amount paid will be the sum of all the monthly payments. Since the monthly payment remains constant, we can multiply it by the total number of payments:

Total amount paid = Monthly number payment * Number of payments = $510.90 * (20 years * 12 months/year) = $122,616

Therefore, the total amount paid over the 20 years will be $122,616. This includes both the principal amount and the interest payments.

The monthly payments are designed to gradually pay off the loan balance while covering the accrued interest.

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Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

Step-by-step explanation:

so we can make a system of equations

y=hotdogs

x=hamburgers

you need a combination that sums to 23, so add the two and get 23:

y+x=23

and then you need to account for how much money you have and the cost.

1.50x+1.10y=32.10

still working on it, will edit in rest so that you can see what I did

Answer:

The sum of their ages in 6 years time is (2x+20) years.

Step-by-step explanation:

Given that,

Ethen is ‘x’ years old.

Raj is 8 years older than Ethen.

Raj's age = (x+8) years

We need to find the sum of their in 6 years.

After 6 years,

Ethen's age = (x+6) years

Raj's age = (x+8)+6

= (x+14) years

Sum of ages = (x+6) + (x+14)

= 2x+20

Hence, the required answer is (2x+20) years.

Answer:

F. a1 = –5, an = 5an-1

Step-by-step explanation:

a1 = -5                    <---- Answer

r = -25/-5 = 5

an =  r(an - 1)

an =  5(an - 1) <---- Answer

Hope this helps!

g

Step-by-step explanation:

Answer:

3 Remainder

Step-by-step explanation:

Answer:

23 remainder 3

Step-by-step explanation: