Ryan is building a ramp so he can easily move things in and out of an overhead storage area in his garage. The storage area is 8 feet off the ground, and Ryan has 15 feet of space along the ground to build the ramp.


A triangle with side lengths 15 feet, 8 feet, and an unlabeled hypotenuse.


What is the length of the ramp Ryan will build?

7 feet

10 feet

17 feet

23 feet

we apply alternate angles approach to solve questions like this

Answer:

y ≈1*(1+0.59)^t. The rate of change is = 59%

Step-by-step explanation:

We have t mulitplied by 8 in the expression of y. We can write that power with a power of powers, using the property

[tex]a^{bc} = (a^b)^c = (a^c)^b[/tex]

Therefore,

[tex]a^{8t} = (a^8)^t[/tex]  

If we replace a with 1.06, we obtain

[tex] y = 1.06^{8t} = (1.06^8)^t \approx 1.59^t = 1*(1+0.59)^t[/tex]

Thus, y ≈1*(1+0.59)^t. The rate of change is ln(1.59) * 1.59^t. After 1 unit of time t, the rate of change is 0.59*100 = 59%

The given function represents exponential growth with a rate of change of 6%. The function already fits the form y = a(1 + r)^t with a = 1 and r = 0.06.

To rewrite the function y = (1.06)^8t in the form y = a(1 + r)^t, we can identify a as the initial amount and r as the rate of change. In this case, the initial amount a is implied to be 1 (since it is not explicitly multiplied by the base), and the base 1.06 represents the growth factor. Seeing as the base is greater than 1, this function represents exponential growth.

The percent rate of change can be found by subtracting 1 from the base and then converting it to a percentage. Therefore, the rate r is 1.06 - 1, which equals 0.06 or 6% when expressed as a percentage. Thus, the function in the requested form is y = (1 + 0.06)^8t, or simplifying the exponent, y = (1.06)^8t.

To the nearest percent, the rate of change is 6%.

Answer:

The height of the stone at the time it is thrown is 15.

Step-by-step explanation:

You have a quadratic function of the form h (x) = ax² + bx + c. In this case it is h (x) = -5x²+10x+15, where a =-5, b =10, c =15, x is the time and h (x) is the height of the stone after being thrown.

The moment the stone is thrown is instant zero. So if x = 0, h (0) is calculated:

h(0)= -5*0² +10*0 +15

h(0)= 0 + 0 + 15

h(0)= 15

The height of the stone at the time it is thrown is 15.

Answer:

Compounded Semiannually: $17,574.89

Compounded Quarterly: $17,588.68

Compounded Monthly: $17,597.98

Compounded Continuously: $17,602.66

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 4% into a decimal:

4% -> [tex]\frac{4}{100}[/tex] -> 0.04

Now, plug in the values to the equation:

Compounded Semiannually:

[tex]A=15,000(1+\frac{0.04}{2})^{2(4)}[/tex]

[tex]A=17,574.89[/tex]

Compounded Quarterly:

[tex]A=15,000(1+\frac{0.04}{4})^{4(4)}[/tex]

[tex]A=17,588.68[/tex]

Compounded Monthly:

[tex]A=15,000(1+\frac{0.04}{12})^{12(4)}[/tex]

[tex]A=17,597.98[/tex]

To find the value if compounded continuously, use the following formula:

[tex]A = Pe^{rt}[/tex]

[tex]A=15,000e^{0.04(4)}[/tex]

[tex]A=17,602.66[/tex]

The accumulated value of an investment is calculated differently depending on the compounding period - semiannually, quarterly, monthly or continuously. This involves the compound interest formula and understanding of how interest rates work.

The subject of this question is about calculating the accumulated value of an investment at a given interest rate with various compounding periods i.e., semiannually, quarterly, monthly, and continuously. We first need to understand that compound interest is calculated on the principal plus the accumulated interest.

To calculate the future value of the investment, we use the compound interest formula: P*(1+r/n)^(nt), where P is the principal (or initial investment), r is the annual interest rate (in decimal form), n is the number of compounding periods per year, and t is the time in years.

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Answer:

8:12 or blue to white

I hope this helps! If it does, please mark brainliest UwU

Answer: The difference between the mean cost to treat dogs at A New Leash on Life

Animal Clinic and the mean cost to treat cats at A New Leash on Life Animal

Clinic is about 10 times the MAD This is a large difference.

Step-by-step explanation:

I GOT THIS RIGHT! THIS IS THE ANSWER

The differences in mean costs to treat dogs and cats compared to the MAD at A New Leash on Life Animal Clinic suggest different levels of variability in the data. A 19 times difference labeled as 'moderate' implies high variability, while if labeled as 'large', the implication is that the variability is lower.

The question relates to the comparison of the mean costs to treat dogs and cats at A New Leash on Life Animal Clinic, using the Mean Absolute Deviation (MAD) as a measure of variability. When we say that the difference between the mean cost to treat dogs and cats is about 19 times the MAD, and that this is a moderate difference, it suggests that the variability within each of the distributions is quite high, making a 19-fold difference in means seem less extreme. Conversely, the same difference being described as a large difference implies that the variability (MAD) is comparatively lower, hence a difference of the same scale appears more substantial relative to the spread of the data. This provides insight into the differences in treatment costs and the consistency of those costs within each group of animals.

Answer:

B

Step-by-step explanation:

The equation of line is y=-1/2 x+3 as it takes the form of y=mx+c

From this, the graph having gradient of -1/2 then the line will run from left to right. This eliminates options A and D

The pictures are not clear but we must ensure where the line crosses y intercept, the value of y should be 3 hence the only graph having these properties is option B.

Step-by-step explanation:

1/2s+38=1642

0.5s=1642-38

s=1604/0.5

s=3208

Answer:

There are 2/3 of the content as servings in 4 bags

Step-by-step explanation:

In this question, we are asked to calculate the amount of servings in 4 bags

From the question, we can see that the amount of servings in a single bag is 1/6 of the bag.

Now the number of servings in 4 bags will be mathematically equal to ; 1/6 + 1/6 + 1/6 + 1/6 = 4 * 1/6 = 4/6 = 2/3

This means that in 4 bags, 2/3 of the total content is the servings

Answer: 9647

Step-by-step explanation:

Answer:

9647000

Step-by-step explanation:

Probability of rolling a number different from 9 is 1.

Given,

Cube with numbered 1 to 6.

Now,

Numbers on cube: 1, 2 , 3 , 4 , 5 ,6 .

Then, the sample space is

S= {1, 2, 3, 4, 5, 6}

The probability of rolling a number different from 9,

Since we don't have 9 in the sample space, then the probability of rolling a number different from 9 will be the have 1,2,3,4,5 and 6 as the outcome

Then,

P(rolling number different from 9) = 6 / 6 = 1

P(rolling number different from 9) = 1.

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Answer:

the second one

Step-by-step explanation:

Option (b) represents the graph of r = 4 sin θ.

"A polar curve is a shape constructed using the polar coordinate system."

We have been given a function r = 4 sin θ .

We need to determine the graph for given function.

We know, r = a sin θ is a circle where “a” is the diameter of the circle that has its bottom-most edge at the pole (origin).

This means, r = 4 sin θ is a circle that has bottom-most edge at the origin (0, 0).

In the graph (b), a circle has bottom-most edge at the pole.

Therefore, the correct graph is option (b)

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Answer:

7

Step-by-step explanation:

Convert 87.5% to a decimal.

87.5%/100%=.875

Multiply it with 8 to get 7

.875*8=7

Answer:

7

Step-by-step explanation:

When a right cone is sliced parallel to its base, the resulting cross section is always a circle.

If a cone is sliced parallel to its base, the shape that results is a circle. This is an aspect of conic sections, which are the curved shapes created when a plane intersects a cone. Other than circles, other possible shapes that we can obtain from slicing a cone include ellipses, parabolas, and hyperbolas, depending on the angles and location of the slice made. However, when the cut is parallel to the base, a circle is always formed. This is due to the consistent radius from the cone's axis to its slant height along the same parallel plane.

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Answer:

r=2.5%

Step-by-step explanation:

An exponential growth distribution is generally expressed as:

[tex]P_t=P_oe^{rt}[/tex]

where:

#Substitute the given values to solve for r:

[tex]P_{2010}=P_{1999}e^{(2010-1999)r}\\\\56780=43129e^{11r}\\\\1.31652=e^{11r}\\\\\\r=\frac{In \ 1.31652}{11}\\\\=0.024999\approx 2.5\%[/tex]

Hence, the rate of growth is approximately 2.5%

The population of Cirque City was growing exponentially at a rate of approximately 2.5% per year from 1999 to 2010.

To determine the exponential growth rate of the population in Cirque City, we will use the formula for exponential growth:

P(t) = P0 × [tex]e^{rt}[/tex]

Here, P(t) is the population at time t, P0 is the initial population, r is the growth rate, and t is the time period. Given data: P0 = 43,129 (population in 1999), P(t) = 56,780 (population in 2010), and t = 11 years. Our goal is to find r.

Start with the formula and substitute the known values:

P(t) = 43,129 × [tex]e^{11r}[/tex] = 56,780

Isolate the exponential term:

[tex]e^{11r}[/tex] = 56,780 / 43,129

[tex]e^{11r}[/tex] ≈ 1.315

Take the natural logarithm (ln) of both sides to solve for r:

ln( [tex]e^{11r}[/tex]) = ln(1.315)

11r = ln(1.315)

r ≈ ln(1.315) / 11

Calculate the value:

r ≈ 0.025

Convert to a percentage:

r ≈ 2.5%

Therefore, the population of Cirque City was growing at an exponential rate of approximately 2.5% per year.

Answer:

V≈381.7in³

Step-by-step explanation:

V=4/3πr³

=4/3•π•4.5³

≈381.70351in³

The volume of a sphere with a radius of 4.5 inches, calculated using the volume formula V = 4/3 * π * r^3, comes out to approximately 381.51 cubic inches.

The volume of a sphere can be calculated using the formula for volume, V = 4/3 * π * r^3, where V denotes the volume, π is approximately 3.14, and r is the radius of the sphere. In this case, the radius (r) of the sphere is 4.5 inches. Plugging these values into our formula gives:

V = 4/3 * 3.14 * (4.5)^3

When you perform the calculations, you'll find the volume of the sphere to be approximately 381.51 cubic inches.

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Answer:

9 yd

Step-by-step explanation:

15 yd - 6 yd = 9 yd

Please mark my answer as brainiest

Answer:

9 yd

Step-by-step explanation:

The top has a length of 15 yd

The bottom has a length of 6 +x

15 = 6+x

Subtract 6 from each side

15-6 = 6-6+x

9 = x

9 yds in the missing length

Answer: its a ^

Step-by-step explanation:

y = 0.433x2 is the quadratic equation that best models the data in the graph. Therefore, the correct option is option A.

A second-order equation with the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real-number coefficients and a 0. Applications in the real world involve quadratic equations. For instance, if school administration decides to build a prayer hall with a floor size of 400 square metres.

A length that is two metres longer than its width, we will need the aid of a quadratic formula to determine the length and breadth. y = 0.433x2 is the quadratic equation that best models the data in the graph.

Therefore, the correct option is option A.

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Your question is incomplete but most probably your full question was,  

Which quadratic equation best models the data in the graph? y = 0.433x2 y = 2.31x2 y = (0.433x)2 y = (2.31x)2

Answer:

6

Step-by-step explanation:

P(6) = ⅙

Expected no. of trials for first 6:

1 ÷ (1/6) = 6

Measures of the center, such as mode, median, and mean, provide a summary of typical values in a data set.

The measures of the center, "such as the mode, median, and mean", provide a summary of the typical values in a data set. The mode is the most frequent value, the median is the middle value, and the mean is the arithmetic average. These measures help describe the central tendency of the data, giving insight into what is considered a typical response or value.

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Answer:

17.6 ounces to make the pecan pies. I dont know how much honey she used to make the apple pie so if you could pls say I could edit the answer :)

Step-by-step explanation:

Betty used a total amount of honey equal to 4 times the ounces of honey needed for one apple pie plus 17.6 ounces of honey for the pecan pies. The exact total amount of honey used cannot be determined without knowing the amount of honey (x) used in an apple pie.

The question is asking how much honey Betty used to bake apple and pecan pies. First we need to determine the amount of honey required per pie and then add the total amounts for each type of pie. Let's say it takes x ounces of honey to make one apple pie. Since Betty baked 4 apple pies, she would use 4x ounces of honey for the apple pies. For the pecan pies, each requires 4.4 ounces of honey, so for 4 pecan pies she would use 4 × 4.4 ounces which equals 17.6 ounces of honey.

To find the total honey used, add the honey used for apple pies and pecan pies: 4x + 17.6 ounces. Without the specific amount of honey for the apple pies (x), we cannot calculate the exact total amount of honey used.

This is sorta late, but here's the answer for the people who are going to be searching it up in the future:

The first one is sum

The second one is equal to

The third one is 35

Good luck, guys!!

Answer:

sum

equal to

35

Step-by-step explanation:

The theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.

The missing length is  35 feet.

Answer:

that is the solution to the question

Answer: Angles A and B are complementary angles

If Sin A ≈ 0.766 then Cos B ≈ 0.766.

If Cos B ≈ 0.766 then Sin A ≈ 0.766

Step-by-step explanation: In any given right angled triangle, one angle measures 90 degrees while the addition of the other two angles equals to 90 degrees. Hence if angle C is given as 90 degrees, then angles A and B added together equals 90 degrees (complementary angles equal 90 degrees).

Also, Sin A cannot be the same value as Sin B, since angle A and angle B are not equal in measurement. However, being complementary, the Sin of angle A equals the Cos of angle B.

If Sin A ≈ 0.766, then angle A ≈ 50 degrees

That makes angle B equal to 40 degrees. The Cos of B ≈ 0.766

Therefore if Sin A ≈ 0.766, then Cos B ≈ 0.766

If Cos B ≈ 0.766 then Sin A ≈ 0.766 are both correct

Answer:

[tex]\sigma=547.1125[/tex]

Step-by-step explanation:

-The margin of error is calculated using the formula:

[tex]ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\[/tex]

-We substitute the values, n=900 and ME=30 in the formula to solve for standard deviation:

[tex]ME=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}\\\\\\30=1.645\times\frac{\sigma}{\sqrt{900}}\\\\\sigma=\frac{30^2}{1.645}\\\\=547.1125[/tex]

Hence, the population standard deviation is 547.1125

Answer: The length of the rectangle would be 97 yards.

Step-by-step explanation:

87 multiplied by 2 would be 174.

Subtract 174 from 368 to get 194.

194 divided by two equals 97.

To check,

97 plus 97 equals 194.

87 plus 87 equals 174.

174 plus 194 equals 368, the perimeter.