What is the total volume of Diet
Coke in this six pack? Each can
is 5 inches tall and has a diameter
of 3 inches.
a. 47.1 in 3
b. 141.3 ins
c. 35.3 in
d. 211.95 in3

You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.

To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).

According to the given information, the total interest earned from both investments is $130. So we can set up the equation:

0.03x + 0.04($4000 - x) = $130

Simplifying the equation:

0.03x + 0.04($4000 - x) = $130

0.03x + $160 - 0.04x = $130

-0.01x = $130 - $160

-0.01x = -$30

x = -$30 / -0.01

x = $3000

Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

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9514 1404 393

Answer:

  sin: 0, (√(2-√3))/2, 1/2, (√2)/2, (√3)/2, (√(2+√3))/2, 1

  cos are the same values in reverse order

Step-by-step explanation:

Given the side ratios of the "special" right triangles, we know that ...

  sin(30°) = cos(60°) = 1/2

  sin(45°) = cos(45°) = 1/√2 = (√2)/2

  sin(60°) = cos(30°) = (√3)/2

Using the half-angle formulas in the second attachment, we can find exact values for the 15° and 75° angles.

  sin(15°) = sin(30°/2) = √((1 -cos(30°)/2) = √((1 -(√3)/2)/2) = (√(2 -√3))/2

  cos(15°) = √((1 +cos(30°)/2) = √((1 +(√3)/2)/2) = (√(2 +√3))/2

Then the exact table values are ...

_____

Additional comments

The numerical sine and cosine values in the attachment are computed by the spreadsheet functions SIN( ) and COS( ). Those functions require an argument in radians. The RADIANS( ) function converts from degrees to radians.

The "special" right triangles are the isosceles right triangle with side ratios 1:1:√2, and the 30°-60°-90° triangle with side ratios 1:√3:2.

We have the next equation

We apply the subtraction property of equality with 1.6

Then we apply the division property of equality with 6

ANSWER

x=9.4

Answer:

216.1.4 is 4325÷20 so yup that's what I think

The result of converting 4325 to base 20 is 5

Therefore,

Converting 4325 to base 20.

4 × 20³ = 32,000

3 × 20² = 1,200

2 × \(20^{1}\) = 40

5 × \($20^{0}\) = 5

Adding all to get Ans = \($4325_{20}\)

Hence, The result of converting 4325 to base 20 is 5

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D or A not sure

The Twenty-fourth Amendment (Amendment XXIV) of the United States Constitution prohibits both Congress and the states from conditioning the right to vote in federal elections on payment of a poll tax or other types of tax.

Answer:

(D) they do not pay their taxes ​

Step-by-step explanation:

I got it correct on an exam I did.

Answer:

4*9

Step-by-step explanation:

It's obvious.

Answer:

between 4 and 10

Step-by-step explanation:

its 8.36 which is closest to between 4 and 10

Answer:

Part A: 512 ft²

Part B: 3 cans

Step-by-step explanation:

Part A:

We can divide the shape into 2 areas or rectangles.

The top rectangle's area: 20 x 12 =240

The bottom: 34 x 8 = 272

add these 2 up, 240 +272, and you get 512, the area of this figure.

Part B:

We have to divide the number of feet covered by the area:

512/200 = 2.56

However, we half to round up, cause we cant buy part of a can, we have to buy a whole one.

So, we get 3 cans.

Answer:

3 liquid gallons

Step-by-step explanation:

3 + 4 + 5 = 12

12 ÷ 4 = 3 liquid gallons

The perimeter does indeed equal 254 meters, which confirms that our answer is correct.

Any two-dimensional closed shape's perimeter is defined as the entire distance encircling it. The perimeter of a rectangle, such as the following: Square perimeter equals the sum of its four edges. Rectangle perimeter equals the sum of its four edges.

Let's call the rectangle's unidentified size x.

P = 2l + 2w, where l is the length and w is the breadth, gives the perimeter of a rectangle.

So that we can create an equation:

254 = 2l + 2(6)

Simplifying the right side:

254 = 2l + 12

Subtracting 12 from both sides:

242 = 2l

Dividing both sides by 2:

121 = l

Consequently, the rectangle's undetermined measurement (length) is 121 metres.

We can compute the perimeter using both variables to confirm our conclusion:

P = 2(121) + 2(6) = 242 + 12 = 254

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Answer:

if the length of segment A'B' is 12 units, what is the scale factor of the dilation?

Step-by-step explanation:

The solution of the inequality 2(n + 1) ≤ 3(n − 2) will be greater than or equal to 8. Then the correct option is D.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

2(n + 1) ≤ 3(n − 2)

Simplify the inequality, then the value of the variable 'n' will be given as,

2(n + 1) ≤ 3(n − 2)

2n + 2 ≤ 3n − 6

3n − 2n ≥ 6 + 2

n ≥ 8

The arrangement of the disparity 2(n + 1) ≤ 3(n − 2) will be more noteworthy than or equivalent to 8. Then the right choice is D.

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ANSWER: "There is not enough information to determine the answer". Option D is correct.

Step-by-step explanation:

For a case that was ruled by a court to be reversed by a higher court, they must be conditions in the ruling of the lower court that has been reconsidered by the higher court. This is regardless of the jurisdiction of the court or judge that ruled the case.

A case from all the courts in the options can be reversed by a higher court if the courts judgement lacks merit by the higher court, at any given times, irrespective of the court.

9514 1404 393

Answer:

  $1512.27

Step-by-step explanation:

The future value formula for monthly compounded interest is ...

  FV = P(1 +r/12)^(12t) . . . . interest rate r for t years

Filling in the given values gives ...

  2000 = P(1 +0.04/12)^(12·7) = P(1.003333...)^84 = 1.322513864P

Then the required principal is ...

  P = 2000/1.322513864 ≈ 1512.27

The principal needed is about $1512.27.

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

Answer:

Step-by-step explanation:

To find the annual rate of interest as a percent on the musician's loan for the trumpet, we can use the simple interest formula:

$$\sf\:I = P \cdot r \cdot t \\$$

Where:

We can rearrange the formula to solve for r :

$$\sf\:r = \frac{I}{P \cdot t} \\$$

Substituting the given values:

$$\sf\:r = \frac{792}{2200 \cdot 3} \\$$

Now, we can calculate the value of r :

$$\sf\:r = \frac{792}{6600} \\$$

Simplifying the fraction:

$$\sf\:r = 0.12 \\$$

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

$$\sf\:r = 0.12 \times 100 \\$$

Therefore, the annual rate of interest on the musician's loan for the trumpet is 12%.\(\)

The given function y = 4(3/8)^x represents exponential decay.

As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

The given function is y = 4(3/8)^x. To determine if the function represents growth, decay, or neither, we need to examine the base of the exponent, which is (3/8).

When the base of an exponential function is between 0 and 1, such as (3/8) in this case, it represents exponential decay. This is because as the exponent (x) increases, the value of the function decreases.

In the given function, the coefficient 4 multiplied by the decaying exponential term (3/8)^x indicates that the function starts with an initial value of 4 and then exponentially decreases. The term (3/8)^x represents the decay factor, where x determines the extent of decay.

Therefore, we can conclude that the given function, y = 4(3/8)^x, represents exponential decay. As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

In summary, the given function y = 4(3/8)^x represents exponential decay.

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Answer:

21 miles

Step-by-step explanation:

Let's assume the distance from the school to the duck pond is "d" miles.

The time it took for the team to reach the duck pond at a speed of 3 mph is given by:

Time = Distance / Speed

Time = d / 3

The time it took for the team to run back to the school at a speed of 7 mph is given by:

Time = Distance / Speed

Time = d / 7

According to the given information, the total trip took 10 hours. Therefore, we can set up the equation:

Time to duck pond + Time back to school = 10

(d / 3) + (d / 7) = 10

To solve this equation, we can find a common denominator and simplify:

(7d + 3d) / 21 = 10

10d / 21 = 10

Now, we can cross-multiply and solve for "d":

10d = 10 * 21

10d = 210

d = 210 / 10

d = 21

Therefore, the distance from the school to the duck pond is 21 miles.

1 cube = 6 Faces

2 cubes = 10 Faces

7 cubes = 36 Faces

2÷7 = 3 × 10 = 30 + 6 = 36

The Answer is 36

Answer:

2 cubes = 10 faces

3 cubes = 14 faces

4 cubes = 18 faces

5 cubes = 22 faces

6 cubes = 26 faces

7 cubes = 30 faces

10 faces = 2 cubes

14 faces = 3 cubes

18 faces = 4 cubes

Step-by-step explanation:

We know that 1 cube shows 6 faces, and 2 cubes shows 10 faces. With 3 cubes, it shows 14 faces.

With this pattern, we can conclude that

f(x) = 2 + 4x

f(x) is a function for where f is the value of faces and x is the amount of cubes connected.

To find the amount of faces for the cubes used

f(2) = 2 + 4(2) = 2 + 8 = 10

f(3) = 2 + 4(3) = 2 + 12 = 14

f(4) = 2 + 4(4) = 2 + 16 = 18

f(5) = 2 + 4(5) = 2 + 20 = 22

f(6) = 2 + 4(6) = 2 + 24 = 26

f(7) = 2 + 4(7) = 2 + 28 = 30

For the amount of cubes used given the amount of faces

10 = 2 + 4x

-2   -2

8/4 = 4x/4

2 = x

x= 2

14 = 2 + 4x

-2    -2

12/4 = 4x/4

3 = x

x = 3

18 = 2 + 4x

-2   -2

16/4 = 4x/4

4 = x

x = 4

Your welcome! If you have any questions, please post them in the comments section of this answer! If you could mark this answer as the brainliest, I would greatly appreciate it! :D

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

NO.

Step-by-step explanation:

The Professor's hypothesis:

An introductory course in Logic will affect college students with their other studies (will affect their Great Point Average - GPA).

25 students are used as the experimental group while the rest of the class are the control group.

The mean GPA in a sample size (SS) of 6 is = 2.58

The mean GPA in the full sample size of 25 would be = 10.75 by crossmultiplying.

This makes me believe the question was written wrongly. I assume SD (standard deviation) of 0.6 instead of SS (sample size) of 6.

Going by this, if standard deviation is 0.6 then the interval within which the GPA of the experimental group (the 25 students) falls is:

[2.58 - 0.6] to [2.58 + 0.6]

= 1.98 to 3.18

The rest of the graduating class (the control group) had a mean GPA of 2.33

Can the professor conclude that the GPA for the sample is significantly different from that of the control group?

The answer is NO because the GPA of the control group falls within the GPA interval of the experimental group!

Answer:

here

Step-by-step explanation:

Answer:

made this one myself

Step-by-step explanation:

Answer:

More than likely no full answer key however there might be answers for each individual question.

The perimeter and the area of a circular sector are 56π / 5 centimeters and 392π / 5 square centimeters.

In this question we must determine the perimeter of the minor sector, that is, of the sector related to an circle arc, and the area of the same sector. The arc length formula is introduced below:

s = θ · r

Where:

First, determine the arc length:

s = (2 / 5) · 2π · (14 cm)

s = (4π / 5) · (14 cm)

s = 56π / 5 cm

And the area of the circular sector is introduced below:

A = (θ / 2) · r²

A = (2π / 5) · (14 cm)²

A = 392π / 5 cm²

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The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Answer:

The height of the squirrel is 31 feet.

Step-by-step explanation:

You need to know your Right Triangle Trigonometry to do this problem.

Rt Triangle trig is all about ratios. Angles and ratios.

In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.

tan Angle = opposite/adjacent

tan 48° = x/28

multiply both sides by 28

28•tan48° = x



You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"



Enter 28 × tan48° =

It will return 31.0971504152

Your question asks you to round to the nearest whole.

x = 31

The squirrel's height in the tree is 31ft.