Find the area of the future. Round to the nearest tenth if necessary.

use the formulas

for a circle
\(a = \pi r ^{2} \)
for a semi circle
\(a = \frac{1}{2} \pi r ^{2} \)
for a triangle
\(a = \frac{1} {2} bh\)
for a trapezoid
\(a = \frac{1}{2} (b _{1} + b_ {2})h\)
for a parallelogram
\(a = bh\)
​

Belle bought 24 apples, and Amy bought 34 apples and Amy paid approximately $2.35 per apple.

Let x be the number of apples Belle bought.

Then, Amy bought 10 more apples than Belle, so Amy bought x + 10 apples.

Since each of them spent $40, we can write:

40 = cost of x apples for Belle

40 = cost of (x + 10) apples for Amy

We know that Amy used a coupon that gave her a 20% discount. This means that she paid 80% of the original price for her apples. We can write:

0.8 * (cost of (x + 10) apples for Amy) = cost of x apples for Belle

Now we can solve for x:

0.8 * (40 + 40) = 32 + 0.8 * 10 + 32

0.8 * 80 = 8 + 32 + x

64 = x + 40

x = 24

So Belle bought 24 apples, and Amy bought 34 apples (10 more than Belle)

To find the cost per apple for Amy, we can divide her total cost by the number of apples:

cost per apple for Amy = (40 + 40) / (x + 10) = 80/34

Therefore, Amy paid approximately $2.35 per apple.

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To simplify the expression 3x^3 + 2y^3 + 6x^3 + 5y, we can combine like terms to get 9x^3 + 2y^3 + 5y.

The given expression has two terms with x cubed and two terms with y cubed. We can combine the coefficients of the x cubed terms and the coefficients of the y cubed terms to get:

3x^3 + 6x^3 = 9x^3

2y^3 = 2y^3

Therefore, the simplified expression so far is 9x^3 + 2y^3.

The last term in the given expression is 5y, which is not like the first two terms. Therefore, the expression cannot be simplified any further by combining like terms. The final simplified expression is 9x^3 + 2y^3 + 5y.

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Answer:

85.2

Step-by-step explanation:

add all scores (98+78+84+75+91)

then with that answer (426)

divide by how many scores there are (5)

Answer:

85.2

Step-by-step explanation:

Since the terms oscillate but do not approach one single value, the sequence appears to diverge

To find the first n terms of the sequence with the given terms a1 = 1, a2 = 2, and the rule for n ≥ 2, \(an = 1/2((an-1)(an-2))\), let's use n = 30.

1. Start with the given terms: a1 = 1 and a2 = 2.
2. Use the formula to find the next terms, up to n = 30.

It's important to calculate some of the terms in the sequence to determine if it converges or diverges. However, due to the character limit, I can't list all 30 terms here. Nevertheless, let's calculate the first few terms:

⇒ \(a_{3}= \frac{1}{2} ((a_{3})(a_{3})\)

= \(= \frac{1}{2} ((2)(1))\)

= 1
⇒\(= a_{4}= \frac{1}{2} ((a_{3})(a_{2}))\)

= \(\frac{1}{2} ((1)(2))\)

= 1
⇒\(a_{5}= \frac{1}{2} ((a_{4}) (a_{3}))\)

\(=\frac{1}{2} ((1)(1))\)

= 0.5

By examining the terms of the sequence, we can see that they oscillate but do not approach one single value. Therefore, the sequence appears to diverge.

Since the terms oscillate but do not approach one single value, the sequence appears to diverge.

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If p is a prime number and a and n are positive integers, then p raised to the power of n divides a raised to the power of p.

Let's assume that p is a prime number, and a and n are positive integers. We want to prove that p raised to the power of n divides a raised to the power of p, denoted as \(p^n|a^p\).

By the fundamental theorem of arithmetic, we know that any positive integer can be uniquely represented as a product of prime numbers. Therefore, we can express a as a product of primes: a = \(p1^k1 * p2^k2 * ... * pm^km\), where p1, p2, ..., pm are distinct prime factors of a, and k1, k2, ..., km are positive integers.

Now, let's consider \(a^p\). When we raise a to the power of p, each prime factor in the prime factorization of a is raised to the power of p. Thus,\(a^p = (p1^k1 * p2^k2 * ... * pm^km)^p = p1^(k1p) * p2^(k2p) * ... * pm^(km*p).\)

Since p is a prime number, p divides \(p1^(k1p), p2^(k2p), ..., pm^(km*p).\)Therefore,\(p^n\) divides \(a^p\), which can be written as \(p^n|a^p\).

Thus, we have proven that if p is a prime number and a and n are positive integers, then \(p^n\)divides \(a^p\).

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To find the equation of a plane in scalar form, we can use the equation ax + by + cz = d, where a, b, and c are the coefficients of the normal vector and d is the constant term. The normal vector is given as =10, so a=10, b=0, and c=0.

Next, we can plug in the coordinates of the given point (6,4,7) into the equation to solve for d:
10(6) + 0(4) + 0(7) = d
60 = d
So, the equation of the plane in scalar form is:
10x + 0y + 0z = 60
Or simplified:
10x = 60
This is the equation of the plane with normal vector =10 passing through the point (6,4,7) in scalar form.

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To the right of the top equation it states x = -1

This means if x = -1 use that equation.

No replace x in the equation with -1 and solve:

(X + 2) ^2 = (-1 +2)^2 = 1^2 = 1

The answer is 1

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.

The given information about the vertex of the function does not appear to be relevant to the question about mulch for a flower bed. However, we can still solve the problem using the given radius of the flower bed.

The formula to find the recommended amount of mulch for a circular flower bed is:

Mulch = π * r^2 * d

Where r is the radius of the flower bed and d is the desired depth of the mulch.

Assuming a desired depth of 0.5 feet, we can plug in the given radius of 20 feet to the formula:

Mulch = π * (20 feet)^2 * 0.5 feet

Mulch = π * 400 square feet * 0.5 feet

Mulch = 200π cubic feet

To find the approximate value in decimal form, we can use the approximation π ≈ 3.14:

Mulch ≈ 200 * 3.14

Mulch ≈ 628 cubic feet

Rounding to the nearest tenth, we get:

Mulch ≈ 628.3 cubic feet

Therefore, the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.

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To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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So the rate of change of the area of the rectangle is 88 in^2/sec.

The area of the rectangle is given by the formula A = lw, where l is the length and w is the width of the rectangle. If the length and width of the rectangle are changing at rates of 7 in/sec and 4 in/sec, respectively, then the rate of change of the area is given by the formula:

dA/dt = l * dw/dt + w * dl/dt

Plugging in the values given in the problem, we get:

dA/dt = 1 * 4 + 12 * 7 = 4 + 84 = 88 in^2/sec

So the rate of change of the area of the rectangle is 88 in^2/sec.

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Answer:

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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Answer:

12 is the median

Step-by-step explanation:

as u have to cancel each number out at each side together till you reach the middle

The median of the given data in the box-and-whisker plot is 9.5. Therefore, option C is the correct answer.

A box and whisker plot is a special type of graph that is used to show groups of number data and how they are spread. It shows the median, which is the middle value of the numbers in your data, the lowest number, the highest number and the quartiles, which divides the data into four equal groups.

From the given box-and-whisker plot

Minimum is 3

Maximum is 15

Q₁ is 7

Q₃ is 13

Median is 9.5

The median of the given data in the box-and-whisker plot is 9.5. Therefore, option C is the correct answer.

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Answer:

21 quarters and 21 dimes

Step-by-step explanation:

21 quarters = 5 dollars and 25 cents

21 dimes = 2 dollars and 10 cents

add together and you get the total

21 quarters and 21 dimes

The dimensions of the largest rectangle that can be inscribed in the semicircle are length = 7.07 cm and breadth = 7.07 cm and diagonal length of 9.09 cm.

To find the dimensions of the largest rectangle that can be inscribed in a semicircle of diameter 20 cm, we can first draw a diagram of the semicircle and the inscribed rectangle. Since the diameter of the semicircle is 20 cm, its radius is 10 cm.

Next, we can label the sides of the rectangle as length and width, and use the Pythagorean theorem to relate them to the radius of the semicircle. Specifically, if the length and width of the rectangle are x and y, respectively, then we have:

x^2 + y^2 = 10^2

We want to find the dimensions of the largest possible rectangle, which means we want to maximize the area of the rectangle. The area of a rectangle is given by:

A = xy

To find the maximum area, we can use the equation x^2 + y^2 = 10^2 to solve for one variable in terms of the other, and substitute into the equation for the area. For example, we can solve for y in terms of x:

y = √(10^2 - x^2)

Substituting into the equation for the area, we get:

A = x √(10^2 - x^2)

To find the maximum value of A, we can take the derivative with respect to x, set it equal to zero, and solve for x:

dA/dx = √(10^2 - x^2) - x^2/√(10^2 - x^2) = 0

Solving for x, we get:

x = 10/√(2)

Substituting this value of x back into the equation for y, we get:

y = 10/√(2)

length = x = 10/√(2) ≈ 7.07 cm

width = y = 10/√(2) ≈ 7.07 cm

This rectangle has a diagonal length of:

√((10/√(2))^2 + (10/√(2))^2) ≈ 9.90 cm

which is the same as the diameter of the semicircle. Therefore, this rectangle is the largest possible rectangle that can be inscribed in the semicircle.

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Solution

Given that the Perimeter is: 340 yards. Lenght is 91 yards

Since P = 2(L + W)

where L is the Length

W is the width

=> 340 = 2(91 + W)

=> 340 = 182 + 2W

=> 158 = 2W

Dividing both sides by 2

=> W = 79

Hence, the width is 79 yards

Answer: it would be 79yards

Step-by-step explanation: 91•2=182

340-182=158

158/2=79yards

Answer:

7n-12

Step-by-step explanation:

Answer:

Step-by-step explanation:

12 n - 12

Therefore, the angle between the biker's line of sight and the trail is changing at a rate of approximately 0.039 radians per second when she is 25 feet away from the tree.

To solve this problem, we need to use trigonometry and calculus. Let's call the angle between the biker's line of sight and the trail θ, and let's call the distance from the traffic cone to the aspen tree x. Then we can use the tangent function to relate θ and x:

tan(θ) = x/15

We can also use the Pythagorean theorem to relate x and the distance d between the biker and the tree:

d^2 = x^2 + 25^2

Taking the derivative of both sides with respect to time t, we get:

2d (dd/dt) = 2x (dx/dt)

Now we can substitute the equation for x in terms of θ and solve for (dθ/dt):

tan(θ) = x/15

sec^2(θ) (dθ/dt) = (1/15) (dx/dt)

(dθ/dt) = (1/15) (dx/dt) sec^2(θ)

We can use the equation for d to solve for x:

x^2 = d^2 - 25^2

2x (dx/dt) = 2d (dd/dt)

(dx/dt) = (d/dd) (sqrt(d^2 - 25^2)) (dd/dt)

(dx/dt) = (d/ sqrt(d^2 - 25^2)) (dd/dt)

Now we can substitute this expression for (dx/dt) into the previous equation and evaluate it when d = 25 and θ = arctan(15/25):

(dθ/dt) = (1/15) [(d/ sqrt(d^2 - 25^2)) (dd/dt)] sec^2(arctan(15/25))

(dθ/dt) = (1/15) [(25/ sqrt(25^2 - 25^2)) (13)] sec^2(arctan(15/25))

(dθ/dt) = (13/375) sec^2(arctan(15/25))

(dθ/dt) ≈ 0.039 radians per second

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2/12 or 1/6

you count how many numbers there were 12, and there were 2;3s so that gives you 2/12 and a simplified answer 1/6 you divide the numerator and denominator by 2

(a) Probability that a randomly selected is 9.68%; (b) 29.12% will receive the tax break; (c) Minimum and the maximum starting salaries are 35,679.71 and 4,320.29. (d) 6.3% of the total number of students.

a) P(X>30,400) = P(Z>(30,400-20,000)/8,000)

                          = 1-P(Z<1.3)

                          = 0.0968

                         = 9.68%

b) P(X<15600) = P(Z<(15600-20000)/8000)

                        = 29.12%

c) Maximum of the starting salaries of the middle 95% is

                     (x - 20,000)/8,000 = 1,96

                                                  x  = 35,679.71

Minimum of the starting salaries of the middle 95% is

                      (x - 20,000)/8,000 = -1,96

                                                   x = 4,320.29

d) P(X>32,240) = 1-P(Z<(32,240-20,000)/8,000)

                         = 0.063

Therefore, the 189 represents 6.3% of the total number of students, means that the total number is 3,000.

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Answer:

625

Step-by-step explanation:

5 times 5 is 25. 25 times 5 is 125. 125 times 5 is 625. Notice how I multiplied 5 repeatedly 4 times.

Answer:

625

Step-by-step explanation:

5 x 5 (=25) x 5 (=125) x 5 = 625

Hope this helps :)

Answer:

y = 5

Step-by-step explanation:

2(40 - 5y) : 80 - 10y

10y + 5(1 + y) : 5y + 5

80 - 10y = 5y +5

-10y = 5y -75

-10y - 5y = 5y - 75 - 5y

-15y/-15 = -75/-15

-15y/-15 : y

-75/-15 : 5

Hence, The answer should be 5

If a function is not continuous, it may or may not be differentiable.

The differentiability of a function is not determined solely by its continuity.

A continuous function is a function that can be drawn without picking up a pen. In mathematical terms, a function f(x) is continuous if, as x approaches a point a, f(x) approaches f(a).

For a function to be differentiable, it must be continuous. If a function is not continuous, it is not differentiable. However, the opposite is not always true; a function may be continuous but not differentiable.

In summary, a function that is not continuous may or may not be differentiable, while a function that is differentiable must be continuous.

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Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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Given data:

The list of the observations.

The range tell us the lower limit to upper liit of the observation which is the minimum to maximum value of the data.

Here the minimum value is 12.336799

and maximum value is 17.35

Thus, the rangle is 12.336799 to 17.35.

7 and and -12 is the answer correct me if im wrong

HOPE IT HEPLS:)

Answer:

1 - A and B 2 - $111 3 - 8.2 and 49.2 4 - 8 and 224 5 - 0.26 and 1.56

Step-by-step explanation: