the volume of a right circular cylinder with a radius of 4 in. and a height in 12 in is ___ pi^3

Answer:

It gives you -7

Step-by-step explanation:

Think of the problem as 8 - 15, because 8 is a smaller number and 15 is bigger, you'll get a negative number.

The next step is use the rule**a-b = -(b-a)**which is - (15 - 8)

Then when you simplify it, it will be - (15 - 8)= - 7**(which is the answer)

Hope this helps:)

Answer:

y = 7 is the desired equation

Step-by-step explanation:

If the line is horizontal, then its slope is zero (0).  If this horizontal line passes through (4, 7), then y = 7 is the desired equation.

The fractions that shows equivalent expressions are all the listed fractions. That is option A,B, and C.

An equivalent expression is defined as the type of expression that work the same as another expression even though they look different.

This shows that either way that this expression is written, they both mean the same thing.

From the given expressions above;

8⁹/² = (√8)⁹

4⁵/² = (√4)⁵

(³√125)⁷ = 125⁷/³

But the expression that is not an equivalent;

12⅐ = (√12)⁷ but (⁷√12)

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The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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B

Step-by-step explanation:

Answer:

  2√34 ≈ 11.66 units

Step-by-step explanation:

The distance between two points is given by the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

__

For your points, the distance is ...

  d = √((3 -(-7))² +(0 -6)²) = √(10² +(-6)²) = √(100 +36) = 2√34

The distance between the points is ...

  2√34 ≈ 11.66 . . . . units

_____

Additional comment

The distance formula is based on the Pythagorean theorem. It models the distance as the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates of the points.

By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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The rate of the first athlete is greater than the rate of the second athlete.

To determine if the rate of the first athlete is greater than, less than, or equal to the rate of the second athlete, we need to compare their average speeds.

The average speed of an athlete is calculated by dividing the distance traveled by the time taken.

For the first athlete who runs 3 miles in 24 minutes, the average speed can be calculated as:

Speed1 = Distance1 / Time1 = 3 miles / 24 minutes = 1/8 miles per minute.

For the second athlete who runs 4 miles in 33 minutes, the average speed can be calculated as:

Speed2 = Distance2 / Time2 = 4 miles / 33 minutes.

To make a comparison, we need to convert both rates to a common unit. Let's convert both rates to miles per minute:

Speed2 =\((4 miles / 33 minutes) * (24 minutes / 24 minutes)\) = (96 miles / 792 minutes) ≈ 0.1212 miles per minute.

Comparing the two rates, we see that Speed1 (1/8 miles per minute) is greater than Speed2 (0.1212 miles per minute). The rate of the first athlete is greater than the rate of the second athlete.

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Option A

The length of AB which is the missing length side of the similar triangles would be = 28 cm.

To calculate the missing length of the triangle = AB , the scale factor should be determined.

The scale factor that exists between two similar object shows the number of times the original object can be found in the new formed one.

The scale factor = dimensions of new object/ dimensions of original object.

A side of original = EF =22cm

A side of the new triangle = BC = 44

Scale factor = 44/22 = 2

Therefore the missing length of the new triangle = 14×2 = 28cm

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Answer:

a = 38⁰

b = 54⁰

c = 54⁰

Step-by-step explanation:

a + 142⁰ = 180⁰ because a straight line = 180⁰

b + 38⁰ + 88⁰ = 180⁰ because the angles of a triangle equal 180⁰, and the missing measurement = 38⁰ because it is a vertical angle to angle a

c + 88⁰ = 142⁰ because the angles are corresponding angles

Answer:

130 degrees

Step-by-step explanation:

Answer:

130 degrees

Step-by-step explanation:

This is a supplementary angle (or whatever the term was for two or more angles that add together to get 180 degrees). There is a total of 7x and 5 degrees. So you would set up the equation 180= 7x+5. Use the properties of equality and subtract 5 from both sides getting 175= 7x. Use the division property of equality to isolate the variable. Divide by 7 to get 25=x. Now just substitute for x in 5x+5 getting 125+5= 130. Sorry if I did a bad job at explaining

(a.) 0.09

equation:

f(x) = log(x)

rate of change:

\(\sf \rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}\)

\(\sf \rightarrow \sf \dfrac{log(4) -log(6)}{4-6}\)

\(\sf \rightarrow 0.088\)

\(\sf \rightarrow 0.09\)

Answer:

\(A.\: 0.09\)

Step-by-step explanation:

Rate of Change is: \(\frac{y{_1-y{_2} } }{x_2-x_1}\)

\(\frac{log(4)-log (6)}{4-6}\)

\(0.088\)

\(0.09\)

Answer:

c

Step-by-step explanation:

it's a property of powers, when the base is the same (-5) , you need to

sum the powers when both terms are multiplyng

subtract the powers when both terms are dividing (numerator power minus denominator power, in that order)

Answer:

a) [-9,8)

b) [-5,5]

c) (-4,0), (1,6)

d) [-9,-4), (6,8)

e) [0,1]

f) just the y-value: 5;  as a point: (-8,5)

g) just the y-value: -5;  as a point: (-4,-5)

Step-by-step explanation:

a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).

b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.

For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.

c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?

d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?

e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?

f) Look for the highest non-infinity point on the graph

g) Look for the lowest non-infinity point on the graph

Answer:

B. p=(50-25)÷5

Step-by-step explanation:

Answer:

with what

Step-by-step explanation:

ask your teacher

There are 13 $20 bills and 16 $5 bills 6 in the collection.

A system of linear equations is a set of two or more linear equations involving the same variables. The solution to a system of linear equations is the values of the variables that satisfy all the equations in the system.

To solve the following problem use variables and form linear equations according to the given conditions in the problem. Solve the equation for the values of variables.

Here we have

Part of the proceeds from a garage sale was ​$340 worth of ​$5 and ​$20 bills. There were 3 more ​$5 bills than ​$20 ​bills

Let's use variables to represent the number of $5 and $20 bills.

Let x be the number of $20 bills, then the number of $5 bills is x + 3.

The total value of the $20 bills is 20x,

The total value of the $5 bills is 5(x + 3) = 5x + 15.

According to the problem,

The total value of the bills is $340, so we can set up the equation:

20x + 5x + 15 = 340

Simplifying and solving for x, we get:

25x = 325

x = 13

Therefore,

There are 13 $20 bills and 16 $5 bills 6 in the collection.

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In order to prove that ∠E = ∠I, we can use the following statements and reasons:

1. Statement: ∠E = ∠FGL

Reason: Opposite angles in a parallelogram are congruent

2. Statement: ∠FGL = ∠KLG

Reason: Alternate interior angles

3. Statement: ∠KLG = ∠I

Reason: Opposite angles in a parallelogram are congruent

4. Statement: ∠E = ∠I

Reason: Transitive property of the equality (∠E = ∠FGL, ∠FGL = ∠KLG and ∠KLG = ∠I, so ∠E = ∠I)

The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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Answer:

B. Share them with the office to celebrate a job well-done.

Step-by-step explanation:

This is a question about ethics.

There are 3 dozen doughnuts, which is equal to 36 doughnuts, probably enough to go round the office of the newsroom.

The feature profile from yesterday was a team work, you were not the only one involved, since the doughnut was brought to the newsroom, it is ethical that you share them with the office to celebrate a job well-done. This shows that you appreciate the team work put together by the whole office.

As noble and benevolent as taking the doughnut to the homeless center, it wont be ethical in this situation.

Answer:

the mode is 12

Step-by-step explanation:

Arrange the numbers in order : 1 , 3, 6, 6, 9, 9, 12, 12, 12, 12, 12, 15, 15, 15, 15

Then count how many numbers that appears the most, so the number that appears the most is 12, therefore, the mode in the data set is 12 .

Answer: 14%

Step-by-step explanation: To find the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade, we divide the number of members who meet both criteria (14) by the total number of members (100) and multiply by 100 to get a percentage. Therefore, the probability is approximately 14%.

- Lizzy ˚ʚ♡ɞ˚

We have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.

Matrices are a type of mathematical structure used to store and analyze data. They are represented as a series of rows and columns, with each cell in the matrix containing a number or other value. Matrices are used to solve systems of equations, perform matrix multiplication and determine the inverse of a matrix. They are also used in linear programming, cryptography, and other areas of mathematics.

Row equivalence is defined as a pair of matrices A and B being row equivalent if there is a sequence of row operations that can transform A into B, or vice versa. This means that if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations.

A reduced row echelon form is defined as a matrix in which all non-zero rows are above any rows of all zeroes and the leading coefficient of each non-zero row is 1. In other words, all of the non-zero rows have a leading coefficient of 1, and any rows of all zeroes are below the non-zero rows.

Therefore, if A and B are row equivalent, then A and B can be transformed into one another by a series of row operations. This means that we can use the same series of row operations to transform A and B into the same reduced row echelon form. This proves that if A and B are row equivalent, then A and B have the same reduced row echelon form.

On the other hand, if A and B have the same reduced row echelon form, then they must have been transformed into the same form by a series of row operations. This means that the same series of row operations must have been used to transform A and B into the same reduced row echelon form, which means that A and B are row equivalent. This proves that if A and B have the same reduced row echelon form, then A and B are row equivalent.
To prove that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form, we can use the definition of row equivalence and the definition of a reduced row echelon form.


Therefore, we have proven that if A and B are m x n matrices, then A and B are row equivalent if and only if A and B have the same reduced row echelon form.

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Answer:

  25 = c

Step-by-step explanation:

You had a good start on filling in the values in the Pythagorean Theorem. The work needed to be finished.

  \(a^2 +b^2 = c^2\\\\20^2 +15^2=c^2\\\\400+225=c^2\\\\625=c^2\\\\\sqrt{625}=\sqrt{c^2}\\\\\boxed{25=c}\)

The composite mapping (f o g)(x) ≥ 3 for the functions f(x) = 2x + 1 and g(x) = x² + 1. And (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

A mapping is composite when the co- domain of the first mapping is the domain of the second mapping.

For the functions f(x) = 2x + 1 and g(x) = x² + 1

If x > 0, say x = 1 then;

g(x) = 1² + 1

g(x) = 2

(f o g)(x) = 2(2) + 1

(f o g)(x) = 4 + 1

(f o g)(x) = 5

If x = 0, then;

g(x) = 0² + 1

g(x) = 1

(f o g)(x) = 2(1) + 1

(f o g)(x) = 2 + 1

(f o g)(x) = 3

For the functions f(x) = x² and g(x) = x

If x < 0, say x = -0.5, then;

g(x) = -0.5

(f o g)(x) = (-0.5)²

(f o g)(x) = 0.25

In conclusion, the composite mapping (f o g)(x) ≥ 3 for functions f(x) = 2x + 1 and g(x) = x² + 1 and (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

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The fraction for the value of tan Z is 39/80

Trigonometric Identities are simply described as equalities that involves several trigonometry functions and also one that holds true for all the values of variables given in the equation.

The types of trigonometric functions as;

From the information given, we have that;

Hypotenuse = 89

Opposite side = 39

Adjacent = 80

tan Z = opposite/adjacent

substitute the values

tan Z = 39/80

Hence, the equation is 39/80

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Answer:

Wind

Hydroelectric Power

Solar

Geothermal

Answer:

The first equation; x-2y=8

Step-by-step explanation:

Hi there!

We're told that Ty wants to isolate x in one of the equations. To do so in either, he will need to use inverse operations to cancel out values and leave just x remaining on one side of the equation.

In the second equation, he would need to subtract both sides by 6y and then divide both sides by 4 to isolate x. It's a two-step process.

However, in the first equation, he only needs to add 2y to both sides to isolate x.

I hope this helps!

Answer:

using the first equation

cause Being that the first equation has the simplest coefficients (1, -2, for x, and y respectively), it seems logical to use it to develop a definition of one variable in terms of the other