There are 38 men and 20 women running a race. What is the ratio of the number of female runners to the number of male runners?There are 38 men and 20 women running a race. What is the ratio of the number of female runners to the number of male runners?There are 38 men and 20 women running a race. What is the ratio of the number of female runners to the number of male runners?

The break-even point of the Astronomical Telescope model is 61.6 units.

The given parameters;

The break-even point in units is determined from the point at which the total revenue is equal to expenditure.

Revenue = expenditure

\(305 u = 5420 + 217u\\\\305u - 217u = 5420\\\\88u = 5420\\\\u = \frac{5420}{88} \\\\u = 61.6 \ units\)

Thus, the break-even point of the Astronomical Telescope model is 61.6 units.

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Answer:

She will have $375,769.33 in her retirement plan at the time of retirement.

Explanation:

According to the question,

Periodic Payments(P) = $200

Rate of Return(r) = 12%(annual)

                           \(=\frac{12}{12}%\)  

                           = 1% monthly

                           = 0.01

Number of payments(n) = 65 - 40

                                        = 25(annual)

                                        = 25 × 12 monthly

                                        = 300 monthly

Future value =?

The formula for calculating future value is:

Future Value = \(P[\frac{(1+i)^{n}-1 }{i}]\)

                      = \(200[\frac{(1+0.01)^{300}-1 }{0.01}]\)

                      = \(200[\frac{19.7884663-1}{0.01}]\)

                      = 200[1878.84663]

                      = 375,769.326

                      = 375,769.33

Final Answer:

Therefore, the future value of her retirement when she retires is

$ 375,769.33 .

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Answer:

The median is 37

Step-by-step explanation:

The median is the middle number in the set when organizaed from low to high:

15, 22, 37, 49, 82

From this arrangement, we can see that 37 is the middle number making it the median.

The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer: 678

Step-by-step explanation: ii

Answer:

-2^5

Step-by-step explanation:

Answer:

24^3-52x^2+34x+18

Answer:

instincts

Step-by-step explanation:

i luv u!

Answer:

shape?Draw a tree diagram to display all the possible outcomes that can occur when you flip a coin and then toss a six-sided die.(b) How many outcomes contain a head and a number greater than 2?(c) Assuming the outcomes displayed in the tree diagram are all equally likely, what is the probability that you will get a head and a number greater than 2 when Sure, I can help you with that! Here's a tree diagram showing all the possible outcomes of flipping a coin and rolling a six-sided die: ``` H T / \ / \ 1 2 3 4 / \ / \ / \ / \ 1 2 3 4 5 6 1 2 ``` Each branch represents a possible outcome, with the first letter indicating the outcome of the coin flip (H for heads, T for tails), and the second number indicating the outcome of the die roll. (b) To find the number of outcomes that contain a head and a number greater than 2, we can look at the branches that start with H and have a 3, 4, 5, or 6 on the second level. There are four of

Answer: There are 3 outcomes that contain greater than 2

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The average power radiated by each square meter of the sun's surface is approximately 386 W/m². This value is calculated by dividing the total power radiated by the sun (approx. 386 billion Megawatts) by its surface area (approx. 6.08 x 10¹⁸ square meters). The formula for the surface area of a sphere is 4πr².

The average power radiated by each square meter of the sun's surface can be calculated as follows:

       The total power radiated by the sun is approximately 386 billion

       Megawatts (3.86 x 10³³ erg/s).

        The surface area of the sun can be calculated using the formula for

        the surface area of a sphere:

        A = 4πr², where r is the radius of the sun (approx. 6.96 x 10⁸

        meters).

        Plugging in the values, we get:

        A = 4π (6.96 x 10⁸)² = 6.08 x 10¹⁸ square meters.

        Finally, divide the total power by the surface area to get the

        average power radiated by each square meter of the sun's surface:

        P = 3.86 x 10³³ erg/s / 6.08 x 10¹⁸ m² = 386 W/m².

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The 9/32 of whole pizza Troy had for breakfast. The whole bag of coffee weighs 10/7 pounds

A fraction is defined as a part of a whole quantity.

1. Leftover pizza = 3/8

Pizza used as breakfast = 3/4 of left-over pizza

= 3/4 of 3/8

The of is calculated by the use of multiplication

The fractions are multiplied as follows:

Pizza used as breakfast = 3/4 * 3/8

= 3 * 3 / 4 * 8

= 9/32

2. 3/5 of bag of coffee weighs = 6/7 pounds

1 bag of coffee weighs = 6/7 ÷ 3/5

The fractions are divided as follows:

Thus, = 6/7 * 5/3

= 6 * 5 / 7 * 3

= 30/21

= 10/7 pounds

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Answer:

Step-by-step explanation:

The right angle means that you are working with a right angle triangle. Therefore one of the 3 basic trig functions must be used to define x.

Sin(x) = opposite / hypotenuse.

opposite = 15

hypotenuse = 17

Sin(x) = 15/17

Sin(x) = 0.8824

But that's not what you are asked for. You are asked for an angle. That means you must use the inverse of the sine function.

x = sin-1(0.8824)

x = 61.93  

That's about as brief as I can make it.

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

a

Step-by-step explanation:

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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The coordinates of point H' will be: H'(3, 9)

We know that a translation is basically a transformation that occurs when an object is moved from one place to another place.

The original object's dimensions, orientation, or shape are unaffected by translation.

Translating a point P(x, y) 1 unit up means we need to add to use P'(x, y+1), that is adding 1 unit to the y-coordinate of the point P'(x, y).

Now we have to translate the triangle 1 unit up. So, use the formula

P(x, y) → P'(x, y + 1)

Thus, the coordinates of point H' will be:

H( 3, 8) → H'( 3, 8+1) → H'(3, 9)

Therefore, the coordinates of point H' will be: A'(3, 9).

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Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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Answer:

x=-11

Step-by-step explanation:

not entirely sure what it means by DBJ, but lets see..

i believe the answer is x=-11.

please resend the problem fixed

Hello !

Answer:

\(\Large \boxed{\sf length=13cm}\)

Step-by-step explanation:

The volume of a pyramid is given by \(\sf V_{pyramid}=\frac{1}{3} \times B\times h\) where B is the area of the base and h is the height.

This is a rectangular pyramid. We have where \(\sf B=l\times w\) l is the length and w is the width (breadth).

So \(\sf V_{pyramid}=\frac{1}{3} \times l\times w\times h\)

Given :

Let's replace h, w, l, \(\sf V_{pyramid}\) with their values in the previous formula :

\(\sf 728=\frac{1}{3} \times x\times 8 \times 21\\728=56x\)

Let's solve for x !

Divide both sides by 56 :

\(\sf \frac{56x}{56} =\frac{728}{56}\\ \boxed{\sf x=13cm}\)

Have a nice day ;)

Answer:

15

Step-by-step explanation:

First you would replace the x and y's with 1/2 and 3.

So it would look like: (1/2) (3) + 3 1/2 + 20 (1/2)

Next, you go by PEMDAS (parenthesis, exponents, multiplications, division, addition, subtraction)

So you would first multiply and the parenthesis that I added mean multiplication.

1.5 + 3.5 + 10

So then all that is left to do is add because I multiplied everything out.

So it is 5 + 10 which is 15

From the ratio gotten, the total cost of the pepper will be $129.90.

Since the students planted 8 tomato plants and 16 pepper plants in a school garden. The ratio will be:

= 8/16 = 1:2

This year, the students planted 15 tomato plants, the number of pepper will be:

= 15 × 2 = 30

Since pepper plants cost $4.33 each, the total cost will be:

= 30 × $4.33

= $129.90

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The large counts condition is met for both samples.

What is random condition ?

The random condition is one of the assumptions necessary for making statistical inferences about a population based on a sample. It requires that the sample be selected randomly from the population, meaning that every individual in the population has an equal chance of being selected for the sample.

The conditions for constructing a confidence interval for the difference in proportions are:

Random condition: The samples must be randomly selected from their respective populations. In this case, Mr. Roby selects random samples of 20 out of 75 male students and 17 out of 100 female students, so this condition is met.

10% condition: The sample sizes should not exceed 10% of their respective populations. Since 20 is less than 10% of 75, and 17 is less than 10% of 100, this condition is met.

Large counts condition: Both sample sizes should be large enough that the expected number of successes and failures in each sample is at least 10. This condition can be checked using the following formulas:

np1 >= 10

np2 >= 10

n(1-p1) >= 10

n(1-p2) >= 10

where np1 and np2 are the expected number of successes in the two samples, n is the total sample size, and p1 and p2 are the proportions of successes in the two populations.

For the male sample, np1 = 20*(5÷20) = 5 and n(1-p1) = 20*(1-5÷20) = 15, both of which are greater than 10. For the female sample, np2 = 17*(8÷17) = 8 and n(1-p2) = 17*(1-8÷17) = 9, both of which are also greater than 10. Therefore, the large counts condition is met for both samples.

So, all the conditions for inference are met in this case, and we can proceed to construct a confidence interval for the difference in proportions.

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Random condition:

Met

10% condition:

Not met

Large Counts condition:

Not met

Are all the conditions for inference met?

No

Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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Answer/Step-by-step explanation:

Equation to represent the daily rental cost for each type of truck can be written as follows:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Where, m = Emily's mileage

To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.

\( 42 + 0.72m = 70 + 0.12m \)

Collect like terms

\( 0.72m - 0.12m = 70 - 42 \)

\( 0.6m = 28 \)

Divide both sides by 0.6

\( \frac{0.6m}{0.6} = \frac{28}{0.6} \)

\( m = 46.7 \)

At approximately 47 miles, both trucks would cost the same amount.

Check:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Plug in the value of x = 47

= 42 + 0.72(47) = $75.84 ≈ $76

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Plug in the value of x = 47

= 70 + 0.12(47) = $75.64 ≈ $76

Answer:

Lisa played 4.35 hours over the weekend :)

Step-by-step explanation: