Express the volume of the part of the ball p < 5 that lies between the cones т/4 and
т/3.

The annual compound rate of return on this 20-year zero coupon bond is 6%. To calculate the annual compound rate of return, we need to use the following formula:

Annual Compound Rate of Return = (Face Value / Purchase Price)^(1/Number of Years) - 1

Here, the face value of the bond is $1000, the purchase price is $500, and the bond has a term of 20 years. Substituting these values in the above formula, we get:

Annual Compound Rate of Return = (1000/500)^(1/20) - 1

Simplifying this expression, we get:

Annual Compound Rate of Return = 1.06 - 1

Annual Compound Rate of Return = 0.06 or 6%

Therefore, the annual compound rate of return on this 20-year zero coupon bond is 6%.

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Answer:

Step-by-step explanation:

25x3x15

Using the t-distribution table with a sample size of 36 and a significance level of 0.05, we find the critical t-value to be ±2.03 (with 34 degrees of freedom, which is n-1).

To explain, we use the t-distribution to find the critical values because the population standard deviation is known. Since the alternative hypothesis is two-tailed (H_A: μ ≠ 40), we need to find two critical values.

With a sample size of 36, the degrees of freedom are 34 (n-1), so we use a t-distribution table with 34 degrees of freedom and a significance level of 0.05. From the table, we find the critical t-value to be ±2.03.

Therefore, if the calculated t-value falls outside of this range, we can reject the null hypothesis H0: μ = 40 in favor of the alternative hypothesis H_A: μ ≠ 40.

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Angle WXY is vertical to angle WXZ, they are equal, therefore, angle WXY is also 141 degrees.

To find the angle WXY, we need to use the properties of angles formed by intersecting chords in a circle. The angles formed by intersecting chords are related to the arcs intercepted by those chords.

Given that the arc WVX is equal to (13x + 9) and the angle WXZ is equal to (5x + 36), we can set up an equation:

Angle WXZ = [tex]\frac{1}{2}[/tex] * Arc WVX

(5x + 36) = [tex]\frac{1}{2}[/tex] * (13x + 9)

To solve for x, we'll multiply both sides of the equation by 2 to eliminate the fraction:

2(5x + 36) = 13x + 9

10x + 72 = 13x + 9

Subtracting 10x and 9 from both sides, we get:

72 - 9 = 13x - 10x

63 = 3x

Dividing both sides by 3, we find:

x = 21

Now that we have the value of x, we can substitute it back into the equation for the angle WXZ to find its value:

Angle WXZ = 5x + 36 = 5(21) + 36 = 105 + 36 = 141 degrees

Since angle WXY is vertical to angle WXZ, they are equal. Therefore, the angle WXY is also 141 degrees.

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To find out Sally's total earnings for the week, we need to consider her base salary and the commission on her sales. Her base salary is $450, and she earns a 6.5% commission on $650 worth of merchandise.

First, let's calculate her commission:
6.5% of $650 = 0.065 * $650 = $42.25

Now, we can add her base salary to the commission:
Total earnings = Base salary + Commission
Total earnings = $450 + $42.25
Total earnings = $492.25

So, Sally would make $492.25 in a work week if she sold $650 worth of merchandise.

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Answer: C

Step-by-step explanation: after rotating, if you split it in half horizontally, you have two cones

The three-dimensional figure formed when the triangle is rotated around the dashed line through B and C is a cone.

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

When we rotate a two-dimensional shape around an axis, we create a three-dimensional solid. This process is known as "revolution" or "rotational symmetry".

In this particular case, we have a triangle that can be rotated around the line segment that connects points B and C. If we were to rotate the triangle around this axis, we would create a three-dimensional solid. To figure out what kind of solid this is, we can think about the cross-sections that would be created if we were to slice through the solid perpendicular to the axis of rotation.

If we were to slice through the solid perpendicular to the axis of rotation, we would get a circle. This means that the solid created by rotating the triangle is a cylinder.

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Answer:

Let's solve this in steps:

1. Convert mixed numbers to fractions:

```

3 1/2 = 7/2

9 3/4 = 39/4

```

2. Perform the subtraction:

```

7/2 - 39/4 = -11/4

```

3. Divide by -2.5:

```

-11/4 / -2.5 = 4.4

```

Therefore, the value of the expression is **4.4**.

2a) The equation used to answer the question is (1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak).

2b) It would take 40 minutes to fill the pool with water when there is a small hole causing a leak.

To solve this, we can use the concept of rates of work.

2a) The equation we would use to answer the question is:

(1/Time to fill the pool) = (1/Time taken by hose) - (1/Time taken by leak)

2b) Let's plug in the values given in the question:

(1/Time to fill the pool) = (1/30 minutes) - (1/120 minutes)

To find the time to fill the pool, we first need to find a common denominator for the fractions. The common denominator is 120, so we can rewrite the fractions as:

(1/Time to fill the pool) = (4/120) - (1/120)

Now, add the fractions on the right side:

(1/Time to fill the pool) = (3/120)

Next, take the reciprocal of both sides to solve for the time to fill the pool:

Time to fill the pool = 120/3

Time to fill the pool = 40 minutes

So, it would take 40 minutes to fill the pool.

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The fractions between 1/16 and 5/8 are 3/16 and 5/16

The fraction expressions are given as

1/16 and 5/8

The above fractions are proper fractions because numerator < denominator

Express the fraction 5/8 as a denominator of 16

So, we have the following equivalent fractions

1/16 and 10/16

This means that the fractions between 1/16 and 5/8 can be represented as

a/16

Where

1 < a < 10

So, we have

Possible fraction = 3/16 and 5/16

Hence, the fractions between 1/16 and 5/8 are 3/16 and 5/16

Note that there are other possible fractions too

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The length of the component in the drawing is 2.125 centimeters.

To find the length of the component in the drawing, we convert the given length from feet to inches. Since 1 foot is equal to 12 inches, the actual length of 12.75 feet is equivalent to 12.75 x 12 = 153 inches.

Next, we apply the scale of the drawing, which is 1 cm: 60 in. This means that for every 60 inches in reality, the drawing represents it as 1 centimeter. To find the length in centimeters, we set up a proportion:

1 cm / 60 in = x cm / 153 in

Cross-multiplying and solving for x, we get:

x = (1 cm * 153 in) / 60 in = 2.55 cm

Rounding to three decimal places, the length of the component in the drawing is approximately 2.125 centimeters.

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The transformation of the triangle is reflection over the x-axis

Given data ,

Let the transformation be represented as A

Now , the triangle is given as XYZ

where the coordinates are X ( 6 , 1 ) , Y ( 2 , 4 ) and Z ( -2 , 0 )

Now , the coordinates of the transformed triangle is

X' ( 6 , -1 ) , Y' ( 3 , -4 ) and Z' ( -2 , 0 )

The reflection of point (x, y) across the x-axis is (x, -y)

Hence , the transformation is reflection over x-axis

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases.

we have here a total of 6 + 8 + 6 = 20 marbles.

to not pull a blue or yellow marble is in this context the same event as pulling a red marble.

so, the desired cases are 6 (red).

which we can get directly from the 6 red marbles, or by counting off the undesired cases : 20 - 8 - 6 = 6.

and the probabilty for not pulling a blue or yellow marble (or simply pulling a red marble) is

6/20 = 3/10 = 0.3

_____________________________

_____________________________

Earl works a total of 3 days in a week. From Monday through Friday, he works in the bookstore on 1 day and in the athletic center on 2 days. On Saturday and Sunday, he cooks food on 50% of the days, which would be a total of 1 day. Therefore, he works a total of 3 days in a week.

To calculate the percentage of Monday through Friday that Earl works, we need to first calculate the total number of days in a week, which is 7. Then, we need to subtract  the weekend days, which are Saturday and Sunday, leaving us with 5 days.

Finally, we can calculate the percentage by dividing the number of days Earl works from Monday through Friday (which is 1) by the total number of weekdays (which is 5), and multiplying by 100. So, Earl works 20% of Monday through Friday.

In summary, Earl works 3 days in a week, 1 day in the bookstore and 2 days in the athletic center. He also cooks food on 1 day during the weekend. Earl works 20% of Monday through Friday.

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The absolute maximum of f(x) = 4x / (x² + 1) on the interval [-4,0] occurs at x = 2 and the absolute minimum occurs at x = -4.

To find the absolute extrema, we first find the critical points by setting the derivative of f(x) equal to zero:

f'(x) = (4(x² + 1) - 8x²) / (x² + 1)² = 0

Simplifying, we get:

4 - 4x² = 0

x² = 1

x = ±1

Since x = -4 and x = 0 are also endpoints of the interval, we evaluate f(x) at these five points:

f(-4) = -8/17

f(-1) = -4/5

f(0) = 0

f(1) = 4/5

f(2) = 8/5

Thus, the absolute maximum occurs at x = 2, where f(x) = 8/5, and the absolute minimum occurs at x = -4, where f(x) = -8/17.

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The expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.

The area of the shaded region is the area of the semicircle subtracted from the area of the rectangle

radius of the semicircle is also the width of the rectangle, so;

area of the rectangle = 8 yd × 4 yd = 32 yd²

area of the semicircle = (π × 4 yd × 4 yd)/2

area of the semicircle = 8π yd²

area of the shaded region = 32 yd² - 8π yd²

area of the shaded region = 8(4 - π) yd²

Therefore, the expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.

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find the position at time t = 9. a(t) = −cos ti − sin tj v(0) = j + k, r(0) = i v(t) = r(t) = r(9) = This gives you the position vector r(9) as a function of sin(9) and cos(9).

To find the velocity vector v(t) and position vector r(t), we need to integrate the given acceleration function a(t) and apply the initial conditions. Here's a step-by-step explanation:

1. Given acceleration function: a(t) = -cos(t)i - sin(t)j
2. Integrate a(t) with respect to t to find v(t):
  v(t) = ∫(-cos(t)i - sin(t)j) dt = (sin(t)i + cos(t)j) + C, where C is a constant vector.
3. Apply initial condition v(0) = j + k:
  v(0) = sin(0)i + cos(0)j + C = j + k
  C = -i + j + k
4. The velocity function is: v(t) = sin(t)i + cos(t)j - i + j + k

Now let's find the position vector r(t):

5. Integrate v(t) with respect to t to find r(t):
  r(t) = ∫(sin(t)i + cos(t)j - i + j + k) dt = (-cos(t)i + sin(t)j + t(k) + D, where D is another constant vector.
6. Apply initial condition r(0) = i:
  r(0) = -cos(0)i + sin(0)j + 0(k) + D = i
  D = i
7. The position function is: r(t) = -cos(t)i + sin(t)j + tk + i

Finally, let's find the position at time t = 9:

8. r(9) = -cos(9)i + sin(9)j + 9k + i

This gives you the position vector r(9) as a function of sin(9) and cos(9).

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Tomas earns a commission of $122.50 on the sale of the new car.

Tomas earns a 0.5% commission on the sale price of a new car. On Wednesday, he sells a new car for $24,500. To determine the commission Tomas earns, we need to multiply the sale price by the commission rate. The commission rate is given as 0.5%, which can be expressed as a decimal by dividing by 100. So, 0.5% is equal to 0.005 as a decimal.

Now, we can calculate Tomas's commission by multiplying the sale price by the commission rate. In this case, we multiply $24,500 by 0.005:

$24,500 x 0.005 = $122.50

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Answer:

100

Step-by-step explanation:

i think this is right

To compute the integral JSS, udv, where U is the part of the ball of radius 3, centered at 0,0,0), that lies in the 1st octant, we can use spherical coordinates. Since the region is defined as having all three coordinates nonnegative, we can set our limits of integration as follows: 0 ≤ ρ ≤ 3, 0 ≤ θ ≤ π/2, and 0 ≤ φ ≤ π/2.

Using the Jacobian transformation, we have:

JSS, udv = ∫∫∫U ρ²sinφ dρdθdφ

Substituting in our limits of integration, we get:

JSS, udv = ∫0^π/2 ∫0^π/2 ∫0³ ρ²sinφ dρdθdφ

Evaluating the integral, we get:

JSS, udv = (3³/3) [(sin(π/2) - sin(0))] [(1/2) (π/2 - 0)]

JSS, udv = 9/2 π

Therefore, the value of the integral JSS, udv, over the part of the ball of radius 3 that lies in the 1st octant is 9/2π.
To compute the integral JSS, udv, over the region U, which is the part of the ball of radius 3 centered at (0,0,0) and lies in the first octant, we will use spherical coordinates for this computation as it's more preferable.

In spherical coordinates, the volume element is given by dv = ρ² * sin(φ) * dρ * dφ * dθ, where ρ is the radial distance, φ is the polar angle (between 0 and π/2 for the first octant), and θ is the azimuthal angle (between 0 and π/2 for the first octant).

Now, we need to set up the integral for the volume of the region U:
JSS, udv = ∫∫∫ (ρ² * sin(φ) * dρ * dφ * dθ), with limits of integration as follows:
ρ: 0 to 3 (radius of the ball),
φ: 0 to π/2 (for the first octant),
θ: 0 to π/2 (for the first octant).

So, the integral becomes:
JSS, udv = ∫(0 to π/2) ∫(0 to π/2) ∫(0 to 3) (ρ² * sin(φ) * dρ * dφ * dθ)

By evaluating this integral, we will obtain the volume of the region U in the first octant.

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The interest earned on Option A is $2400 and Option B is $666.18.  Option A is the better option as Option A has a higher total value of $5400 compared to Option B's total value of $3666.18.

To calculate the interest earned and total value for each option, we can use the following formulas:

For Option A:

- Interest earned = principal x rate x time = 3000 x 0.04 x 20 = $2400

- Total value = principal + interest earned = 3000 + 2400 = $5400

For Option B:

- Interest earned = principal x (1 + rate/n)^(n x time) - principal = 3000 x (1 + 0.02/1)^(1 x 10) - 3000 = $666.18

- Total value = principal + interest earned = 3000 + 666.18 = $3666.18

Therefore, the interest earned and total value for each option are as follows:

Option A:

- Interest earned = $2400

- Total value = $5400

Option B:

- Interest earned = $666.18

- Total value = $3666.18

To compare the two options, we need to consider the total value of each option. Option A has a higher total value of $5400 compared to Option B's total value of $3666.18. Therefore, Option A is the better option.

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The value of M is a^4.

Given the information, we can express the given logarithms as follows:

1) log_a(MN) = 6
2) log_a(N/M) = 2
3) log_a(N^m) = 16

From equation (1), we can write:
MN = a^6

From equation (2), we can write:
N/M = a^2 → N = a^2 * M

Now, substitute N from equation (2) into equation (3):
log_a((a^2 * M)^m) = 16

Using the power rule of logarithms, we get:
m * log_a(a^2 * M) = 16

Since log_a(a^2 * M) = 2log_a(a) + log_a(M) = 2 + log_a(M), we have:
m * (2 + log_a(M)) = 16

We don't have enough information to determine the value of 'm', but we don't need it to find the value of 'M'.

Now, substitute N back into the equation MN = a^6:
M * a^2 * M = a^6

Divide both sides by M * a^2:
M = a^(6-2) = a^4

So, the value of M is a^4.

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The mean of a sample is computed by summing all the data values and dividing the sum by the number of items in the sample. Thus, the correct answer is d.

Option a is incorrect because the mean of a sample is not always equal to the mean of the population, unless the sample is a complete representation of the population (which is often not the case).

Option b is incorrect because the mean of a sample can be greater than, equal to, or smaller than the mean of the population, depending on the sampling method and the characteristics of the population.

Option c is incorrect because the sample mean is computed by summing the data values and dividing the sum by the number of items in the sample minus one only if the sample is taken from a normally distributed population and the standard deviation of the population is unknown. Otherwise, the sample mean is computed by dividing the sum of the data values by the number of items in the sample.

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Answer: To determine if the series –128 + 96 – 72 + 54 – ... is a geometric series, we need to check if the ratio between consecutive terms is constant.

Let's calculate the ratio between the second and first terms:

96 / (-128) = -3/4

Now let's calculate the ratio between the third and second terms:

-72 / 96 = -3/4

The ratio between the fourth and third terms is:

54 / (-72) = -3/4

We can see that the ratio between consecutive terms is always the same: -3/4. Therefore, the series –128 + 96 – 72 + 54 – ... is a geometric series with a common ratio of -3/4.

So the answer is r equals negative three fourths.

Step-by-step explanation:

The series provided is a geometric series because each term after the first is found by multiplying the previous term by -3/4. Therefore, the common ratio 'r' equals -3/4.

In a geometric series, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In the series given –128 + 96 – 72 + 54 – …, the second term (96) divided by the first term (-128) equals -3/4, the third term (-72) divided by the second term (96) also equals -3/4, and so on. This constant ratio between successive terms demonstrates that this is indeed a geometric series. Therefore, the statement that proves this is a geometric series is 'r equals negative three fourths' where r represents the common ratio.

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Answer:

x = 4, y = 7

Step-by-step explanation:

3y + 9 = 2y + 16

y = 7

10x - 24 = 5x - 4

5x = 20

x = 4

values of x is 4 and y is 7

Answer:

option d

Step-by-step explanation:

24

pls mrk me brainliest (⁠*⁠￣⁠(⁠ｴ⁠)⁠￣⁠*⁠)

Answer:

504 cm^2.

Step-by-step explanation:

By Pythagoras:

(2x + 5)^2 = (2x + 3)^2 + (x - 14)^2

4x^2 + 20x + 25 = 4x^2 + 12x + 9 + x^2 - 28x + 196

20x - 12x + 28x + 25 - 9 - 196 = x^2

x^2 - 36x + 180 = 0

(x - 6)(x - 30) = 0

x = 6, 30.

As one of the sides is x - 14, x mst be 30 as its length has to be positive.

So the area of the triangle

= 1/2 * (x - 14) 8 (2x + 3)

= 1/2 * (30-14)(60 + 3)

= 1/2 * 16 * 63

= 504 cm^2.

Answer:

The answer to your problem is, 201.06 or 201.1

Step-by-step explanation:

To find the area you use the formula:

A = π [tex]r^2[/tex]

R = Radius

A = Area

We know the radius of the circle is 8

So replace A = π [tex]r^2[/tex]

= π × 8 ≈ 201.06193

Or 201.06 or 201.1

Thus the answer to your problem is, 201.06 or 201.1