The ratio of boys to girls is 4:5 what fraction of the club is boys?

As per the side splitter theorem, the segment length would complete the proportion is GJ

In math, the side splitter theorem states that "if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally".

Here we have to find the segment length that would complete the proportion by using the side splitter theorem.

According to this theorem and by using the following diagram, we can elaborate the following proportion

=> GH/HE = GJ/JF

Here we have identifies that the segment that completes the proportion is GJ, because it must be used according to the theorem.

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Answer:

Aerobic

Step-by-step explanation:

Oxygen = aerobic

no oxygen = anaerobic

Answer:

-4

Step-by-step explanation:

-4b + 2 = 18

subtract 2 from 2

subtract 2 from 18

-4b = 16

divide -4 by -4

divide 16 by -4

b = -4

The 95% confidence interval for average amount its credit card customers spent is $39.424, $61.576.

How to calculate the confidence interval?

Confidence interval is the mean or average of the estimate value minus or plus the variation in the same estimate value.

n = 15

μ = $50.50

σ = \(\sqrt{400}\) = 20

α = 1 - 95% = 0.05

df = n - 1 = 15 - 1 = 14

Since, there are only 15 samples in the question. we will use t-distribution,

Confidence interval = CI = μ ± \(t_{df,\alpha }\)\(\frac{\sigma}{\sqrt{n}}\)

= 50.50 ± \(t_{14,0.05}\)\(\frac{20}{\sqrt{15}}\)

= 50.50 ± (2.145)(5.164)

= 50.50 ± 11.076

= (39.424, 61.576)

Thus, the 95% confidence interval for average amount its credit card customers spent is $39.424, $61.576.

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Their sum plus their product has a maximum potential value of 420.

Given that the product of the two positive numbers and their sum is 39.

The highest feasible value of the total of their products must be determined.

Let's tackle this issue step-by-step:

Assume x and y are the two positive integers.

The product's sum is xy, while the two integers' sum is x + y.

The answer to the issue is 39, which is the product of the two integer sums and their sum.

\(\mathrm{xy + (x + y) = 39}\)

We need to maximize the value of to discover the biggest feasible value of the product of their sum and their product \(\mathrm {(x + y) \times xy}\).

Now, we can proceed to solve the equation:

\(\mathrm {xy + x + y = 39}\)

To make it easier to solve, we can use a technique called "completing the square":

Add 1 to both sides of the equation (1 is added to "complete the square" on the left side):

\(\mathrm {xy + x + y + 1 = 39 + 1}\)

Rearrange the terms on the left side to form a perfect square trinomial:

\(\mathrm{(x + 1)(y + 1) = 40}}\)

\(\mathrm{(x + 1)(y + 1) = 2 \times 2 \times 2 \times 5 }}\)

Now, we want to maximize the value of \(\mathrm {(x + y) \times xy}\), which is equal to \(\mathrm{(x + 1)(y + 1) + 1}\)

Finding the two positive numbers (x and y) whose sum is as close as feasible to the square root of 40, or around 6.3246, is necessary to maximize this value.

The two positive integers whose sum is closest to 6.3246 are 5 and 7, as 5 + 7 = 12, and their product is 5 × 7 = 35.

Finally, \(\mathrm {(x + y) \times xy}\)

= \((5 + 7) \times 5 \times 7\)

= 12 × 35

= 420

So, the largest possible value is 420.

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Based on the information provided, the true sentences are that route B has a more consistent number of rides (B), and the typical number of riders is greater on route A (D).

To begin, these whisker plots compare the number of riders in two routes. In this context, the graph shows the median for route A is 40 and for the route, B is 35, which means the "typical number of riders is greater on route" (option D). Besides this, it can be observed that the number of riders varies more for route A than for route B, which makes B to be true.

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Answer:

288

Step-by-step explanation:

amount of money made divided by the price of each cookie

72/0.25=288

The measure of the angle ∠XWZ will be half of the measure of the angle ∠XWY.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The measure of the angle ∠XWY is twice the measure of the angle ∠XWZ.

∠XWY = 2 ∠XWZ

Simplify the equation, then we have

∠XWZ = ∠XWY / 2

Then the measure of the angle ∠XWZ will be half of the measure of the angle ∠XWY.

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Answer:

Manny.

Step-by-step explanation:

Because they split cleaning on Thursday and Manny finished first, then on Friday Manny will clean more stalls because they are faster.

The next step after drawing an arc with the compass from the first point of the construction will be, to pick a point on the arc that will be the second endpoint of the new segment. (a)

To copy a line we have to follow a few steps of the procedure.

The steps are;

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Answer:

R:  (16, 2)

Step-by-step explanation:

Let (x, y) be the point R

(x - 10)/2 = 3       and (y + 12)/2 = 7

x - 10 = 6                     y + 12 = 14

x = 16                           y = 2

R:  (16, 2)

The annual decay rate of the radioactive substance is approximately 0.0470%.

To calculate the annual decay rate of a radioactive substance with a half-life of 1475 years, we can use the formula:

decay rate = (ln(2)) / half-life

First, let's calculate ln(2):

ln(2) ≈ 0.693147

Now, we can substitute the values into the formula:

decay rate = (0.693147) / 1475

Calculating this expression, we find:

decay rate ≈ 0.00046997

To express this decay rate as a percentage, we multiply by 100:

decay rate ≈ 0.046997%

Rounding to four significant digits, the annual decay rate of the radioactive substance is approximately 0.0470%.

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Answer:

0.57 feet per minute.

Step-by-step explanation:

If the caterpillar moves 4 feet every 7 minutes, it can be written as a ratio: 4/7. When you divide 4 by 7, you'll find the feet per minute rate.

The presence of a negative externality causes the MSC to be higher than the MSB, which leads to the market over-producing the good. This is because producers are only taking their private costs and benefits into account, not the costs and benefits to society as a whole. The difference between the private and social optima is known as the deadweight loss. In this case, the deadweight loss is equal to the shaded triangle in the attached image.

1. This is a negative externality. We can see this by the MSC being higher than the MSB. This means that the cost to society of producing the good is higher than the benefit to society, resulting in the market over-producing the good.2. See the attached image. 3. At private decision making, we set the MSB equal to the MPC: 12-0.5Q = 2+0.5Q. Solving for Q gives Q = 8. 4. To find the socially optimal quantity, we need to set MSB equal to MSC: 12-0.5Q = 2+1.5Q. Solving for Q gives Q = 4. 5. The private and social optima are different because of the negative externality.

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Answer: you need to add a picture

Step-by-step explanation:

so people know what kinda of problem there trying to figure out

The value of y varies directly as the square of x When x = 7, the value of y is 24.5.

The direct variation formula is y = kx2, where k is the constant of variation.

When x = 2, we know that y = 2. Therefore, we can substitute this information into the direct variation formula and solve for k:

2 = k(2)

2 = 4k

k = 0.5

Now that we know k = 0.5, we can substitute it into the direct variation formula and solve for y when x = 7:

y = 0.5(7)2

y = 24.5

When x = 7, the value of y is 24.5.

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The amount of refund Johnny is entitled to would depend on various factors,

Terms and conditions of rental list purchase, any guarantees or representations made by you regarding the accuracy of the list,

And the applicable consumer protection laws in your jurisdiction.

If you provided a guarantee or representation that the rental list would only include pet-friendly rentals, and it was found to be inaccurate.

Johnny may have grounds to request a refund.

In such a case, he would generally be entitled to a refund of the amount he paid for the rental list.

It's important to review terms and conditions of purchase agreement or any written guarantees provided to determine the specific refund policy.

Additionally, consulting with a legal professional or seeking advice from a consumer protection agency.

In your jurisdiction would be advisable for a more accurate assessment of the situation based on the specific circumstances.

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Answer:

See below ~

Step-by-step explanation:

We need to prove they are equal.

Equate the values to each other.

Now input the x-value in the 1st equation.

Now input the same in the 2nd equation.

Since the same x-value, on inputting in both equations, give the same y-value, it is proved they touch each other.

Point of Contact

Answer:

x = -32

Step-by-step explanation:

You must get the variable (x) on one side in order to solve this problem. Do this by multiplying 4 on both sides in order to get rid of the fraction. -8 times 4 is -32, so the equation should now read to be x=-32

To move triangle KLM so that point K lies on the Y-axis, you need to apply a translation that shifts the entire triangle horizontally. By translating triangle KLM using the vector (-4, 0), point K now lies on the Y-axis.

To move the triangle so that point K lies on the Y axis, we need to perform a translation. First, we need to determine how far point K is from the Y axis. We can do this by finding the x-coordinate of point K, which is 4. This means that point K is 4 units away from the Y axis.

Next, we need to determine the direction of the translation. Since we want to move point K onto the Y axis, we need to move the triangle in the negative x direction. Therefore, the translation that will move the triangle so that point K lies on the Y axis is a horizontal translation of -4 units. We can express this translation as follows:

T(-4, 0)

This means that we need to move each point of the triangle 4 units to the left (negative x direction) to achieve the desired position of point K on the Y axis.

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Answer:

128

Step-by-step explanation:

Answer:

x=21.3

Step-by-step explanation:

hope this helps

Answer:

symmetry with respect to the y-axis

Step-by-step explanation:

f(x) = |x| has symmetry with respect to the y-axis. It looks like a V with the vertex at the origin.

The symmetry of the function \(f(x)=|x|\) is represented by the y-axis.

The given function is \(f(x)=|x|\).

The function can be defined as,

\(f(x)=x;\;\;x\geq0\\f(x)=-x;\;\;x<0\)

The function will always give the positive value of y or f(x) for all values of x.

The graph of the function is in the shape of V which is symmetric about the y-axis.

See the attached image.

Therefore, the symmetry of the function \(f(x)=|x|\) is represented by the y-axis.

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25 is the answer/ third option

The addition of the numbers is 9.9748 * 10^-7 which is expressed in scientific notation

In the question given, we have to add or sum up the two numbers given which are already written in scientific notation.

Here are the rules. When adding or subtracting numbers in scientific notation, the exponents must be the same. The exponents are the same, so add the coefficients. When adding or subtracting numbers in scientific notation, the exponents must be the same.

To add or subtract quantities in scientific notation, numbers are manipulated so that they contain similar bases and exponents. This is done in order to ensure uniformity of the exponents

In this case, we can proceed with the addition operation as

\(9.9*10^-^7 + 7.48 * 10^-^9 = 9.9748*10^-^7\)

The result of the operation is 9.9748 * 10^-7

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We can easily see this by noting that if we multiply this matrix with \underset{x}{\rightarrow}= (x1,x2,x3), we get

|x1 + 2x2 + 3x3|

|4x1 + 5x2 + 6x3|

|7x1 + 8x2 + 9x3|

which to the equation 3x1 + 2x2 + x3 = 0.

A 3x3 matrix for which the kernel is the set of all vectors \underset{x}{\rightarrow}∈ R3 satisfying 3x1 + 2x2 + x3 = 0 is

|1  2  3|

|4  5  6|

|7  8  9|

This matrix has a kernel consisting of all vectors \underset{x}{\rightarrow}= (x1,x2,x3) that satisfy the equation 3x1 + 2x2 + x3 = 0.

We can easily see this by noting that if we multiply this matrix with \underset{x}{\rightarrow}= (x1,x2,x3), we get

|x1 + 2x2 + 3x3|

|4x1 + 5x2 + 6x3|

|7x1 + 8x2 + 9x3|

which to the equation 3x1 + 2x2 + x3 = 0.

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Answer:

94.0 km/hr * 1.03 min = 96.82 km/m

Answer:

Step-by-step explanation:

speed of sound in air = 94 km/hr.

with a time of 1.03 min.

find distance traveled in meters

solution:

distance = velocity x time

              = 94 km  x      1 hr.     x  1.03 min  x   1 000 m

                      hr.          60 min.                              1 km

              =  1,613.7 m