Problem 2: The perimeter of the UNC Chapel Hill basketball court is 100 meters and the
length is 16 meters more than the width. What are the dimensions?

Answer:

<a = 90°   (180-90 supplementary angle)

<b = 90°   (180-90 supplementary angle)

<d = 48°   (180-132 supplementary angle)

<e = 132°  (opposite angle)

<c = 42°     (interior angles of a triangle equal 180.  180-48-90=42)

Step-by-step explanation:

<a = 90°   (180-90 supplementary angle)

<b = 90°   (180-90 supplementary angle)

<d = 48°   (180-132 supplementary angle)

<e = 132°  (opposite angle)

<c = 42°     (interior angles of a triangle equal 180.  180-48-90=42)

Answer:

>

Step-by-step explanation:

\(3^{-1} = \frac{1}{3}\)

\(\frac{1}{3} > \frac{1}{4}\)

There are 96 ways for four people to sit in six chairs so that the leftmost chair is occupied and the rightmost is empty.

There are 4 guests and the leftmost seat is to be occupied, so there are 4  such ways to choose the occupant of that seat.

Then, for each of those 4 ways, there are 4 ways to decide the occupant for the second seat -- the remaining three people plus the possibility of that seat being empty, that makes a total of 16 ways to decide the configuration of the first two seats.

Then, for each of those 16 ways, there are 3 ways to choose the occupant for the third seat (either 3 remaining guests if the second seat was left empty, or the two remaining guests plus the possibility of leaving the 3rd seat empty). Hence, 16 times 3 is 48. For each of those ways, there are two choices for the next seat, i.e. 48 times 2 = 96, and finally one choice for the fifth seat. So in all, there are 96 ways.

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Answer:

1:50 P.M

Step-by-step explanation:

12:15+35 = 12:50

1 hour = 60 minutes

60 + 12:50 = 1:50

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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Answer: 78°

Similar triangles are different from congruent triangles. Congruent triangles have equal angles and sides, while similar triangles have equal angles and proportional side lengths. In this case, because the triangles are similar, the angles should be equal. The sum of the angles of triangles are always 180°. Because triangle ABC has angle measures of 28° and 74°, the equation should appear as 28+74+x=180. Add the like terms to get 102. Subtract 102 on both sides to get x=78. Although we only solved for Triangle ABC, again, similar triangles have the same corresponding angle measures, so it applies to Triangle DEF, as well.

A = P(1+r/n)(nt), where P is the original principal, r is the annual interest rate, n is the number of times the interest is compounded annually, and t is the number of years the money has been held, is the formula for compound interest.

To calculate the final amount of money in the account:

 First, divide the 8% annual interest rate by 100 to get a decimal value: 0.08.

Find the number of times the interest is compounded annually. Since it is done quarterly, the answer is n = 4.

Put these values into the formula now, along with the $1200 principle sum and the number of years, 5, to complete it:

A = $1200(1+(0.08/4))^(4*5) = $2490.07

  to determine how long it will take for the initial sum to double to $2400.

 Divide the final sum by the starting sum: 2400/1200 = 2

 Take the natural logarithm of 2: ln(2) = 0.693

Decimalize the result and divide it by the interest rate: 0.693 / 0.08 = 8.66 years

 Therefore, the time it will take for the initial sum of money to double to $2400 is 8.66 years.

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The PERCENTILE function returns the x value that corresponds to the 90th percentile.

To find the x value associated with the highest 10%, you can use the PERCENTILE function in Excel.

Assuming the x values are in a range of cells, the following expression can be used to find the x value associated with the highest 10%: =PERCENTILE(range, 1-0.1*(AVERAGE(range)))

The range in this expression is the range of cells containing the x values, and AVERAGE(range) computes the mean of the x values. The 90th percentile is calculated by the expression 1-0.1*(AVERAGE(range)), which is the value associated with the highest 10%..

Finally, the PERCENTILE function returns the x value that corresponds to the 90th percentile.

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer: ≈ 18.91 cm

Step-by-step explanation:

r²= 114 ÷ pi/3.14 = 5700/157

r = √r²

≈ 6.025

Circumference = r × pi/3.14

≈ 18,91 cm

Answer:

  (a)  x^2 +4x +3

Step-by-step explanation:

The attachment shows the synthetic division. The quotient is ...

  x^2 +4x +3

_____

Additional comment

Please make sure your math posts include all necessary math symbols and formatting. Some Brainly input methods seem to drop + signs and/or make spacing adjustments that render questions indecipherable. It is helpful if you separate answer choices with punctuation, letter designators, and/or spacing (one per line, for example).

Answer:a

Step-by-step explanation:

Answer:

Cost for 35 songs:  1(35)+11=46

Cost for s songs:  1s+11

Step-by-step explanation:

there is a formula A = 2π r h + 2π r².

=> h = (A - 2π r²) / 2π r

=> h = ( 616 - 2π(7)^2) / 2π(7)

=> h = 7.0

Hope you could understand.

If you have any query, feel free to ask.

As per the given sample size, the shape of the population distribution when conducting t test is approximately normal.

Sampling.

in statistics, sampling refers the statistical procedure that is concerned with the selection of the individual observation; it helps us to make statistical inferences about the population.

Given,

Here we have the sample size is 81.

Now, we need to find the shape of the population distribution when conducting the t test.

Let us consider you are the manager of a restaurant for a fast-food franchise. And in last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes.

Now, you are selecting a random sample of 81 orders.

As per the sample size, the sample mean waiting time is 3.72 minutes, with a sample standard deviation of 0.8 minute.

Now, we complete parts (a) and (b) below.

a. here at the 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.9 minutes.

And state the null and alternative hypotheses.

H0: μ▼ H1: μ ▼

So, H0 is sufficient insufficient evidence to conclude that the population mean waiting time is different from 3.9 minutes .

b. According to the sample size is 81,

The shpe of the population distribution when conducting t test is approximately normal. As in the t test is appropriate for a large sample size.

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The proportion used to find the value of a is a/18 = 16/a

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given are three similar triangles, (refer to attached figure to separately see the similar triangles)

We know that, similar triangle have corresponding sides in equal ratio,

Therefore,

a/18 = 16/a

Hence, the proportion used to find the value of a is a/18 = 16/a

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Answer:

2 days

Step-by-step explanation:

12 - 4 = 8

8/3 = 2.7

Answer:

B.   10.75 cu. in.

Step-by-step explanation:

Vol. of cylinder = π\(r^{2}\)h = 32.25

If the cone has the same radius and height,

then the vol. of the cone = π\(r^{2}\)h/3 = 32.25/3 = 10.75 cu. in.

Answer:

5/6x+4 1/6=y

Step-by-step explanation:

The equation to find a slope-intercept is mx+b=y

m=slope

x=x coordinates

y=y coordinates

b= y intercept

m=5/6

x=-1

y=-5

b=4 1/6

Y intercept:

5/6(-1)+b=-5

-5/6+b=-5

b=4 1/6

However, it asks for an equation of the line, not (-1,-5), so we only need to write m and b, but not x and y.

So: 5/6x+4 1/6=y

Hope this helps!

To find the average value of the function f(x, y) = 8x + 5y over the given triangle, we need to calculate the double integral of f(x, y) over the region and then divide it by the area of the triangle.

The vertices of the triangle are (0, 0), (2, 0), and (0, 7). We can set up the integral as follows:

∬R f(x, y) dA = ∫₀² ∫₀ᵧ (8x + 5y) dy dx

Integrating with respect to y first, the inner integral becomes:

∫₀ᵧ (8x + 5y) dy = 8xy + (5y²/2) |₀ᵧ = 8xᵧ + (5ᵧ²/2)

Now integrating with respect to x, the outer integral becomes:

∫₀² (8xᵧ + (5ᵧ²/2)) dx = (4x²ᵧ + (5ᵧ²x)/2) |₀² = (8ᵧ + 10ᵧ² + 20ᵧ)

To find the area of the triangle, we can use the formula for the area of a triangle: A = (1/2) * base * height.

The base of the triangle is 2 and the height is 7.

A = (1/2) * 2 * 7 = 7

Finally, to find the average value, we divide the double integral by the area of the triangle:

Average value = (8ᵧ + 10ᵧ² + 20ᵧ) / 7

Simplifying this expression gives:

Average value = (8 + 10ᵧ + 20ᵧ) / 7 = (8 + 10(7) + 20(7)) / 7 = 142/7 = 20 2/7

Therefore, the correct answer is not listed among the options provided.

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Answer:

Restudy and try to take it again.

Step-by-step explanation:

Try watching math videos and do extra studying on the areas you missed on your last attempt.

Answer:

Talk with your teacher

Step-by-step explanation:

 I recommend talking with your teacher and asking if you can retest or do extra credit to get your grade back up.

 Make sure you study and get really good grades on the rest of your assignments / next test to keep a passing grade.

A firm experiences increasing returns to scale if inputs are doubled and output more than doubles.

When the firm's output grows at a faster rate than the growth in inputs, increasing returns to scale result. In this case, the company experiences economies of scale, which makes it more effective as it grows its production.

The firm is able to boost productivity and efficiency as it expands its scale of operations if inputs are doubled and output more than doubles.

This can be ascribed to a number of things, including specialisation, labour division, the use of capital-intensive technology, discounts for bulk purchases, and spreading fixed costs over a higher output. Lower average costs per unit of output result in higher profitability and competitiveness for the company.

The firm gains a number of benefits from growing returns to scale. First off, it lets the company to benefit from cost savings brought about by economies of scale, allowing it to manufacture goods or services for less money per unit. This may enable more competitive pricing on the market or result in larger profit margins.

Second, raising returns to scale can result in better operational effectiveness and resource utilisation. As the company grows in size, it will be able to use resources more wisely and profit from production volume-related synergies.market prices that are competitive.

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Answer:

$64.75

Step-by-step explanation:

$35+85%=$64.75

is there a option for all of them?

Answer and Step-by-step explanation:

The answer would be High Intensity Interval Training (HIIT), because it will cause the most amount of weight loss when doing for 12 weeks.

#teamtrees #PAW (Plant And Water)

Answer:

DIY

Step-by-step explanation:

Although I would like to help you, you would have to do this yourself.

All you need to do is:

1. Use a ruler and measure the distance from the first location to the second location.  *make sure to use the inch side.

2. Distance times 170. *Your product will be in mi( unit).

The solution to the surface integral ∬S x^2z^2 ds is π * [(3^7 - 1)/7].

To solve the surface integral ∬S x^2z^2 ds over the surface S, which is the part of the cone z^2 = x^2 + y^2 that lies between the planes z = 1 and z = 3, we can proceed with the integration.

In cylindrical coordinates, the surface element ds is given by ds = r * dr * dz * dθ.

We need to determine the limits of integration for r and θ.

Since the cone is defined by z^2 = x^2 + y^2, in cylindrical coordinates, this becomes r^2 = z^2.

Therefore, the limits of r are from r = 0 to r = z.

The limits of θ can be taken as θ = 0 to θ = 2π since we want to integrate over the entire surface.

Now, we can set up the integral:

∬S x^2z^2 ds = ∫θ=0 to 2π ∫z=1 to 3 ∫r=0 to z (r^2 * z^2 * r) dr dz dθ

Let's evaluate this integral step by step:

∫r=0 to z (r^2 * z^2 * r) dr = ∫r=0 to z r^3 * z^2 dr

Integrating with respect to r gives: (1/4) * z^4 * z^2 = (1/4) * z^6

∫z=1 to 3 (1/4) * z^6 dz = (1/4) * [(1/7) * z^7] evaluated from z=1 to z=3

= (1/4) * [(1/7) * 3^7 - (1/7) * 1^7]

= (1/4) * [(3^7 - 1)/7]

Finally, we multiply the result by 2π to account for the integration over the angle θ:

2π * (1/4) * [(3^7 - 1)/7] = π * [(3^7 - 1)/7]

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Answer:

5/6 (option 3)

Step-by-step explanation:

\(P(A^C)\) is asking what the complement of A is. This means we are asking what the probability of NOT getting A is. This would be 1 - P(A).

P(A) = The probability of getting a 3 = 1/6

We can solve for the probability of the complement of the A and get:\(P(A^C) = 1 - P(A) = 1 - \frac{1}{6} = \frac{5}{6}\)

Thus, the answer is 5/6 (which I believe is the 3rd option you are given)

We use the Taylor series expansion of e⁽⁻ˣ²⁾and evaluate the infinite series up to a point where the next term is smaller than 0.001.

To approximate the definite integral i = 0.5 x^2e⁽⁻ˣ²⁾ dx within the indicated accuracy of |error| < 0.001, we need to use a series approximation.

To do this, we can use the Taylor series expansion of e⁽⁻ˣ²⁾, which is given by:

e⁻ˣ² = 1 - x₂ + (x⁴)/2 - (x⁶)/6 + …

Substituting this into the integral expression, we get:

i = 0.5 ∫ x²(1 - x² + (x⁴)/2 - (x⁶)/6 + …) dx

We can then integrate each term separately:

∫ x² dx - ∫ x⁴ dx/2 + ∫ x⁶ dx/6 - …

= (x³)/3 - (x⁵)/10 + (x⁷)/42 - …

Evaluating this from 0 to infinity, we get:

i = lim(x→∞) [(x³)/3 - (x⁵)/10 + (x⁷)/42 - …] - [(0³)/3 - (0⁵)/10 + (0⁷)/42 - …]

The series converges rapidly, so we can stop after a few terms. To ensure that the error is less than 0.001, we can compute the next term and check that it is smaller than 0.001. If it is, then we can stop and use the computed sum as our approximation.

Therefore, to approximate the definite integral i to within the indicated accuracy, we use the Taylor series expansion of e⁽⁻ˣ²⁾ and evaluate the infinite series up to a point where the next term is smaller than 0.001.

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