a street light is at the top of a pole that has a height of 15 ft . a woman 5 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. how fast is the tip of her shadow moving away from the pole when she is 36 ft from the base of the pole? (leave your answer as an exact number.)

The experimental (empirical) probability that the next child is a boy given that a family has five children: 3 boys and 2 girls is 0.6.

Given that the family has five children, 3 of whom are boys and 2 are girls. If we want to know the experimental probability that the next child is a boy, we need to find the ratio of the number of boys to the total number of children. Since the family has three boys and two girls, the total number of children is:
Total number of children = 3 + 2 = 5
Therefore, the probability of the next child being a boy is given by the ratio of the number of boys to the total number of children.
P(B) = Number of boys/Total number of children
P(B) = 3/5P(B) = 0.6
Therefore, the experimental (empirical) probability that the next child is a boy is 0.6.

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To achieve the maximum output from his electrical system, Steve should set the input to 6, the x-coordinate of the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex].

To find the input that will result in the maximum output of the electrical system, we need to find the vertex of the parabola described by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola is the point where the curve reaches its highest or lowest point, depending on whether the parabola opens upward or downward. In this case, the coefficient of [tex]x^2[/tex] is negative, which means the parabola opens downward, and the vertex represents the maximum point.

We need to find the vertex of the parabola given by the equation [tex]y = -x^2 + 12x - 20[/tex]. The vertex of a parabola with equation [tex]y = ax^2 + bx + c[/tex] is given by the formula x = -b/2a.

In this case, a = -1, b = 12, and c = -20, so the x-coordinate of the vertex is:

x = -b/2a = -12/(2*(-1)) = 6

Therefore, the input at which Steve will reach his maximum output is x = 6.

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Andy has 15 coins made up of quarters and half dollars, and their total value is $5.00.

He has 10 quarters and 5 half dollars.

To find this answer, we can set up the following equation: 0.25Q + 0.50H = 5.00, where Q represents the number of quarters and H represents the number of half dollars. Solving for Q, we get Q = 10. Therefore, Andy has 10 quarters and 5 half dollars.

To solve this equation, we can use algebra to isolate the variable Q. We can start by subtracting 0.50H from both sides, giving us 0.25Q = 5.00 - 0.50H.

Next, we can divide both sides by 0.25, giving us Q = (5.00 - 0.50H) / 0.25. Therefore, we can substitute the values for 5.00 and 0.50H and solve for Q, giving us Q = 10.

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Answer:9/2

Step-by-step explanation:

Answer:

To convert mixed number 4 1/2 to improper fraction, you follow these steps: Multiply the whole number by the denominator 4 × 2 = 8 Add the product from Step 1 to the numerator

Step-by-step explanation:

First, note that 4 1/2 is a mixed number, also know as mixed fraction. It has a whole number and a proper fraction. The numbers in the mixed fraction are defined as follow:

4 = whole number

1 = numerator

2 = denominator

To convert mixed number 4 1/2 to improper fraction, you follow these steps:

Multiply the whole number by the denominator

4 × 2 = 8

Add the product from Step 1 to the numerator

8 + 1 = 9

Write answer from Step 2 over the denominator

9/2

The mixed number 4 1/2 converted to improper fraction is therefore :

9/2

The value of both numbers in fractions will be 207/2 and 207/2.

Given that:

Equation: x + y = 207

The two numbers' product is:

P = xy

P = x(207 - x)

P = 207x - x²

Differentiating P with regard to x. Then we have

dP/dx = 0

207 - 2x = 0

x = 207/2

Then the other number is calculated as,

x + y = 207

207/2 + y = 207

y = 207/2

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The approximate circumference of this Spaceship is equal to 157 meters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

By substituting the given points into the volume of a sphere formula, we have the following;

65,417 = 4/3 × 3.14 × r³

r³ = 65,417/4.1867

Radius, r = ∛15,624.96

Radius, r = 25 meters.

Mathematically, the circumference of a sphere can be calculated by using this mathematical expression:

Circumference of a sphere, C = 2πr

Circumference of a sphere, C = 2 × 3.14 × 25

Circumference of a sphere, C = 157 meters.

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The value 2,649 represents the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 and the estimated population was 618.4.

The formula for population growth can be represented as:

P = P0ert

Here, P is the population of elephants, P0 is the initial population, e is the base of the natural logarithm, r is the rate of growth or decay, and t is the time in years.

Now, as per the given data, P = 2,649P0 = initial population r = 1.045 (as per the given expression)b = t - 1995 (as per the given formula)Now, putting these values in the population growth formula,

P = P0ert2,649 = P0e1.045(b-1995)Dividing by P0 on both sides, we get:e1.045(b-1995) = 2649/P0

Taking the natural logarithm on both sides,

ln e1.045(b-1995) = ln (2649/P0)

Applying the property of logarithm,1.045(b-1995) ln e = ln (2649/P0)1.045(b-1995) = ln (2649/P0)

vAs we need to find the value of P0, substitute the value of b = 0,1.045(0-1995) = ln (2649/P0)-1.045*1995 = ln (2649/P0)ln (2649/P0) = -2069.95

Taking anti-logarithm or exponentiation on both sides,2649/P0 = eln (2649/P0) = e^(-2069.95)2649/P0 = 4.29P0 = 2649/4.29P0 = 618.4

Therefore, the estimated population of elephants in Northwestern Namibia and Etosha National Park in 1995 was 618.4.


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Answer:

53°

Step-by-step explanation:

it’s vertical, verticals are always identical, I think  

Answer:

1. reduction

2.  scale factor of 1/2

Step-by-step explanation:

1. the second image is smaller than the original

2. 18*1/2= 9 and 6*1/2=3

a. Total purchase price: 15.The total selling price plus the sales tax.

b. Unit pricing: 18. Locating the best value for your money

c. Comparison shopping: 14. A technique that allows shoppers to compare prices

d. Coupons: 16. Discount

e. Rebates: 16. discount

f. Markdown: 17. regular selling price minus the markdown.

g. Markdown rate: 16. Discount

h. Sale price: 18. Locating the best value for your money

Selling price is the amount of money a customer pays for a product or service. It is the amount that a customer pays for the product or service after any discounts, taxes, or fees have been applied.

a. Total purchase price: The total selling price plus the sales tax. This amount is the total cost the customer pays for the good or service, including any taxes and fees.

b. Unit pricing: The cost per unit of a good or service. This allows shoppers to compare the cost of similar items and make an informed decision about which item offers the best value.

c. Comparison shopping: A technique that allows shoppers to compare prices, quality, and other factors when making a purchase.

d. Coupons: A form of discount that can be used when making a purchase. Coupons are often found in newspapers, magazines, or online and can be used to reduce the total purchase price.

e. Rebates: A form of discount where customers receive money back after making a purchase. Rebates are often found in the form of a check or a prepaid debit card.

f. Markdown: The regular selling price minus the markdown. The markdown is the amount that is discounted from the regular selling price.

g. Markdown rate: The percentage of the regular selling price that is discounted. This rate is used to calculate the amount of the markdown.

h. Sale price: The discounted price of a good or service. This is the amount the customer pays after any discounts or coupons have been applied.

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The area of the trapezoid is 70 square centimeters.

locating a right trapezoid's area. A = (a + b) x h/2 is the formula to calculate the area of a right trapezoid.

We must apply the following calculation to determine the area of the trapezoid:

A = (b1 + b2) * h/2

where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides (or the distance between the parallel sides).

We can observe that in this instance, b1 = 12 cm, b2 = 8 cm, and h = 7 cm. When we plug these numbers into the formula, we get:

A is equal to (12 + 8) x 7 cm / 2.

A = 20 cm * 7 cm / 2

A = 70 cm²

Hence, the trapezoid has a surface area of 70 square centimetres.

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Answer:

16%

Step-by-step explanation:

translation

x% times 2800 = 448

x% = 448 divided by 2800

x% = 0.16 = move decimal 2 spaces to the right = 16%

To find the commission rate we just have to divide the total commission by the total amount of merchandise sold. The commission was $448 and the amount of merchandise sold was $2800.

[tex]\dfrac{448}{2800}=0.16[/tex]

Then, to rewrite a decimal as a percentage, we just need to multiply the number by 100.

[tex]0.16=\dfrac{0.16\times100}{100} =\dfrac{16}{100} =16\%[/tex]

The commission rate is 16%.

Answer:

20/52 or simplified to 5/13

Step-by-step explanation:

The Venn Diagram is provided

Let
n(A) =  number of customers who had syrup
n(B) =  number of customers who had sprinkles

n(A and B) = number of customers who had both syrup and sprinkles = 16
This would be the number in the overlapping region

n(A or B) = number of customers who had either syrup or sprinkles or both
= n(A) + n(B) - n(A and B)
= 48 + 28 - 16
= 60

Therefore number of customers who had neither topping = 80 - 60 = 20

This number is indicated outside both circles but within the rectangle

The number of customers who had only syrup is given by set difference

= No. of customers who had syrup - No. of customers who had both
= n(A) - n(A and B)
= 48 - 16
= 32

This is the figure inside the left circle

Let's consider the statement: Customers who didn't have sprinkles

This would be customers who had only syrup(32) + customers who had neither topping(20)
= 32 + 20 = 52

Number of customers who did not have either topping = 20
P(selected customer doesn't have either topping, given that they don't have sprinkles)
= 20/52
= 5/13

To solve this problem, we can use the method of mixtures. Let x be the number of pounds of chocolate to be mixed with the trail mix. We can set up the following equation based on the given information:

(21.10x + 3.10(14)) / (x + 14) = 12.41

Simplifying and solving for x, we get:

21.10x + 43.40 = 12.41x + 173.54

8.69x = 130.14

x = 15

Therefore, the store owner should mix 15 pounds of chocolate costing $21.10 per pound with 14 pounds of trail mix costing $3.10 per pound to create a mixture worth $12.41 per pound.

To check this answer, we can verify that the total cost of the mixture equals the total cost of the chocolate and trail mix:

15(21.10) + 14(3.10) = 315 + 43.40 = 358.40

And the total weight of the mixture is:

15 + 14 = 29

So the cost per pound of the mixture is:

358.40 / 29 = 12.41

which matches the desired cost per pound.

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Triangle DAC and triangle CAB are congruent triangles using the SAS criteria.

Both triangles are said to be congruent if the three sides and three angles of one triangle match those of the other triangle's corresponding angles and sides. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They have a similar size and form. In triangles, there are several congruence criteria. The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its form by its three angles.

Given that, AD = AB and AC bisects angle DAB.

As AC bisects DAB, it divides the angle in two half angles that is:

angle DAC = angle CAB

In triangle DAC and triangle CAB.

AD = AB (Given)

angle DAC = angle CAB (AC bisects DAB)

AC = AC

Thus, triangle DAC and triangle CAB are congruent triangles using the SAS criteria.

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Answer:

If x = 3 and y = 2.3^3, then we can evaluate y using exponents:

y = 2.3^3 = 2.3 × 2.3 × 2.3 = 12.167

So, y = 12.167 when x = 3.

Next, if we want to solve the equation y = 2[?] using order of operations, we need to evaluate what is inside the brackets first. We know that y = 12.167, so we can substitute that value into the equation:

y = 2[?]

12.167 = 2[?]

To solve for the missing value inside the brackets, we need to divide both sides by 2:

12.167 ÷ 2 = ?

6.0835 = ?

Therefore, the solution is y = 2(6.0835), or y = 12.167, which we already found earlier.

Step-by-step explanation:

5x-2(x+1)=10

5x-2x+2=10

3x+2=10

3x=10-2

3x=8

8/3

2.7 if you do round it

2.666666667 before you do

x=2.7

(I think it's right Because I've already been taught this if not just tell me.)

Answer:

m(slope) = -1.8 or -1 and 4/5s

Step-by-step explanation:

To find the slope between any two points, a good equation to always remember would be the slope equation.

y2-y1

--------

x2-x1

Or in simple words, the difference of y divided by the difference of x.

-10-8= -18, so the difference in y= -18.

3- (-7)= 3+7= 10, so the difference in the x values= 10.

Finally, divide -18/10= -1.8 or -1 and 4/5s

The function f(x) = 3x - 5 has the defined set of range and domain of the function.

The range {−11,−5,1,7,13} and the domain {−2,0,2,4,6} of the function

Taking the first function;

f(x) = 3x - 5

When x = -2, f(x) = 3(-2) - 5 = -11

When x = 0, f(x) = 3(0) - 5 = -5

When x = 2, f(x) = 3(2) - 5 = 1

When x = 4, f(x) = 3(4) - 5 = 7

When x = 6, f(x) = 3(6) - 5 = 13

Therefore, the function f(x) = 3x - 5 produces the given range when the domain is {−2,0,2,4,6}.

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complete question :

Which function produces a range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6}

f(x) = 3x − 5

f(x) = −3x + 4

f(x) = x + 2

f(x) = −5x + 3

the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.

The formula for radioactive decay is given by:

a = [tex]e^(-kt)\\[/tex] * A

where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.

We can use the given information to solve for k as follows:

When t = 0, a = A. So, we have:

A = [tex]e^(0 * k)[/tex] * A

Simplifying this gives:

1 = e^0

Therefore, we can see that k = 0 at the start of the decay process.

Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:

550 = [tex]e^(-8k)[/tex] * 700

Dividing both sides by 700 and taking the natural logarithm of both sides, we get:

ln(550/700) = -8k

Simplifying this gives:

k = ln(700/550)/8

Using a calculator, we can evaluate this expression to get:

k ≈ 0.0445

Therefore, the decay constant for this material is approximately 0.0445.

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Answer:

Step-by-step explanation:

they're perpendicular

Answer: 63056$

Step-by-step explanation: i learned that in school 2 hours ago

To find:-

Answer:-

We are here given that 1 gallon of paint can be used to paint 400 sq ft. of an area .

There are 4 walls in a room and the area of opposite walls are equal.

So let's find out the area of wall ABCD , its area would be equal to the area of the wall EFGH . So ,

Area of wall ABCD and EFGH :-

Area = lb

Area = 18ft * 8ft

Area = 144ft.²

Therefore area of wall EFGH will also be 144ft.² .

===============================================

Again,

Area of wall DAHE and CBGF :-

Here both the areas of the wall would again be equal, as they have same dimensions of 14ft × 8ft .

Area = lb

Area = 14ft * 8ft

Area = 112ft.²

Therefore area of walls DAHE and CBGF is 112ft.²

==============================================

Calculating total area of the four walls :-

Total area = 2( 112ft.² + 144ft.² )= 512ft.²

Hence total area of four walls is 512ft.²

Now since there will be two coats of paints , total area to be painted would become double that is 1024ft.²

Now we may use Unitary Method :-

To paint 400ft.² 1 gallon of paint is needed.

To paint 1ft.² 1/400 gallon of paint is needed.

To paint 1024ft.² , 1/400*1024 = 2.56 gallons of paint would be needed.

Hence the total paint required is 2.56 gallons.

and we are done!

Answer:

3 one-gallon containers of paint.

Step-by-step explanation:

First, find the total surface area that needs to be painted.

To find the surface area of the walls of a rectangular room, calculate the area of each of the four walls and then add them together.

The area of a rectangle is the product of its width and length.

For the walls of the given room, the "length" is the height of 8 ft, since we want to paint from the floor to the ceiling.

The room has four walls:

Therefore, the total surface area is:

[tex]\begin{aligned}\textsf{Total surface area}&=2(14 \times 8)+2(18 \times 8)\\&=2(112)+2(144)\\&=224+288\\&=512\;\sf ft^2\end{aligned}[/tex]

Since we want to apply two coats of paint, we need to double the surface area:

[tex]\implies 2 \times 512=1024 \; \sf ft^2[/tex]

Now, we can find how many gallons of paint are needed by dividing the total surface area by the coverage per gallon:

[tex]\implies \dfrac{1024}{400}=2.56\; \sf gallons[/tex]

Therefore, we need 2.56 gallons of paint to paint two coats of each wall of the rectangular room.

Since we cannot buy a fraction of a gallon, we need to round up to the nearest gallon. Therefore, we need to buy 3 one-gallon containers of paint.

Answer:

400

Step-by-step explanation:

480-80=400

Answer

x=6

Step-by-step explanation:

80*x=480

80*6=480

To get an output of 5 from a function, the second point must be at a distance of 5 units above the x-axis.

The function represents the relationship between the inputs and the outputs. The function's domain is the set of all possible input values, while the range is the set of all possible output values. The function's graph is the set of all ordered pairs (x, y), where x is the input and y is the output.To get an output of 5 from the function, the second point must be at a distance of 5 units above the x-axis. This implies that the y-value of the second point is 5. The x-value of the second point is arbitrary, and it can be any value. The point (0,5) is an example of a point that is 5 units above the x-axis.

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Answer:

x = 3, y = 4

Step-by-step explanation:

Substitute 4x - 8 in for y and then solve for x:

4x + 2(4x - 8) = 20

Then, 4x + 8x - 16 = 20 --> 12x = 36 --> x = 3.

Once you have x, you can solve for y.

y = 4x - 8 = 4(3) - 8 = 12 - 8 = 4

So, x = 3, y = 4

Answer:

I believe the answer would be 30 people.

Step-by-step explanation:

To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.