A swimming pool shaped like a rectangular prism measures 12 feet deep, 26 feet long, and 14 feet wide. determine the volume, v = lwh, of the pool in cubic meters. round the answer to the nearest cubic meter. (1 foot = 0.305 meter) 4,368 cubic meters 1,332 cubic meters 406 cubic meters 124 cubic meters

The formula for nth term in the given arithmetic sequence is 10 - 3n

For an nth term in an arithmetic sequence

U(n) = a + (n - 1)d

Where n is the number of terms

a is the first term

d is the common difference

From the sequence above

a = 7

d = 4 - 7 = - 3

The formula for an nth term is

U(n) = 7 + (n - 1)-3

= 7 - 3n + 3

Hence, the formula for nth term is 10-3n

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Answer:

Using formula to calculate the circumference of wheel: c=d/n

where

D is the distance bike travel

n is the number of times rotation

C is the circumference of the wheel

As per the statement:

Lin’s bike travels 100 meters when her wheels rotate 55 times.

here, n = 55 rotation and D = 100 meter.

then by definition:

meter c=100/55=20/11

Therefore, the circumference of her wheel is 1 9/11

The expression that can be used to find the temperature after it changes is 85°F + C

Temperature refers to the degree of hotness or coldness of a body at a particular time. It is measured in degree Celsius, degree Fahrenheit an Kelvin.

The instrument used to measure temperature is a thermometer.

let

The change in temperature = 85°F + C

= 85°F + (-11°F)

= 85 - 11

= 74°F

Therefore, the new temperature after a decrease in 11°F is 74°F

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Answer:

27

Step-by-step explanation:

The cat weighs 7 kg.

The rabbit weighs 3 kg.

The dog weighs 17 kg.

You can check these answers by adding them together.

A cat plus the rabbit is 10 kg.

The rabbit and the dog is 20 kg.

The dog and cat is 24 kg.

The first four terms of the sequence would be -

9, 12, 15, 18

Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -

3, 6, 9, 12, 15

x, x + 2, x + 4, x + 6

We have the following sequence -

f(n) = 3n + 6

We can write the first four terms as -

f(1) = 3 x 1 + 6 = 9

f(2) = 3 x 2 + 6 = 12

f(3) = 3 x 3 + 6 = 15

f(4) = 3 x 4 + 6 = 18

Therefore, the first four terms of the sequence would be -

9, 12, 15, 18

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Answer:

Option D: 160 square feet

Step-by-step explanation:

Area of the lawn

= (7 feet × 8 feet) + (13 feet × 8 feet)

= 56 square feet + 104 square feet

= 160 square feet

Answer:

9/34

Step-by-step explanation:

I find when multiplying fractions, its easier to separate them into the numerator and denominator.

So we have 12 x 3, and 17 x 8

12 x 3 = 36

17 x 8 = 136

So we have 36/136

Simplified, that is 9/34

There are zero or null real fourth roots of -1.

This means that the square root of the square root of a number is equal to the number's fourth root. Symbolically, the fourth root is also represented by multiplying the radical by 4, creating the number 4. The fourth root of 16, for instance, is 2, which means that 2 2 2 2 = 16. n, also known as the degree of the root, is a positive integer in this situation. The terms "square root" and "cube root" are used to describe roots of degree 2 and 3, respectively. The ordinal numbers fourth root, twentieth root, etc. are used to refer to roots of higher degree. It is a root extraction to calculate the nth root. A integer y such that y2 = x is referred to as the square root of an x in mathematics.

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Answer:22.5

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

mean is when you add all the numbers divide it by the amount of terms

So to find the sum of the terms we just multiply 5 by 4

20 is the sum and since the mean is 8 with 6 terms we multiply those also

8x6

48 and to find the number we subtract 48 by 20

48-20

28

Hopes this helps please mark brainliest

Answer:

x=-4

Step-by-step explanation:

-3x-18=-6

-3x=12

x=-4

Answer:  x=-4

Step-by-step explanation:

Start off with the equation: -3x-18=-6

Add 18 to both sides: -3x=12

Divide by -3: x=-4

Hope this helped!

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

66.6% = 0.6666... = [tex]\frac{2}{3}[/tex]

Answer:

Fraction = 2/3

Step-by-step explanation:

Given information,

→ Percentage = 66.6%

→ Decimal = 0.6

→ Fraction = ??

Then the required fraction is,

→ Percentage ÷ 100

→ 66.6/100

→ 2/3

Hence, the fraction is 2/3.

The surface area of the triangular prism is  936 cm².

In geometry, a triangular prism is a three-sided prism.

Therefore, the surface area of the triangular prism can be calculated as follows:

surface area of triangular prism = bh + L(x + y + z)

where

Therefore,

surface area of triangular prism = 24 × 18 + 7(18 + 30 + 24)

surface area of triangular prism = 432 + 7(72)

surface area of triangular prism = 432 + 504

surface area of triangular prism = 936 cm²

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Answer is :

The chosen at random is 25 - 44 years old is  = 26 %.  

Probability determines how likely it is that a stated event would

occur. This event would occur. This probability lies between 0 and 1.

The probability that a person chosen at random is at least

15 years = sum of percentages of people at least 15 years old :

14 + 13 + 13 + 15 + 12 + 13 = 80%

the probability that a person chosen at random is 25 - 44 years old :

13% + 13% = 26%

Therefore The probability is 26%.

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To select the community, there are 20 ways available.

What is Combination?

A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant.

Solution:

Since 2 particular students are to be included,

we have to arrange 3 students from 6 students.

nCr = n! / (n-r)!*r!

6C2 = 6!/ (6-3)! 3!

6C2 = 6*5*4*3!/ 3! * 3*2

6C2 = 5*4 = 20

Thereofre, there exists 20 ways of doing the above mentioned.

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The length of the shorter piece is 33 inches.

According to the question,

We have the following information:

A 132 ​-inch is cut into two pieces. One piece is three times the length of the other.

Now, let's take the length of the shorter piece to be x inches and the length of another piece will be 3x inches.

Now, we have the following expression:

x+3x = 132

4x = 132

4 is in multiplication on the left hand side. So, it will be in the division on the right hand side.

x = 132/4

x = 33 inches

Hence, the length of the shorter piece is 33 inches.

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Answer:

12 tables per classroom.

Step-by-step explanation:

We will assume that the teacher uses all of the 4/5 oz of paint.  We can find how many samples of 1/30 oz are contained in the 4/5 oz by dividing:

(4/5)÷(1/30) = (4/5)*(30/1)

(4/5)*(30/1)  = (120/5)

(120/5) = 24 samples of 1/30 oz paint in (4/5) oz total paint.

Each of the 2 Pre-K classrooms have the same number of tables, so we can divide 24 samples by 2 to find the number of tables in each classroom,

*24 samples/2 classrooms) = 12 tables/classroom

Answer:75

Step-by-step explanation:

since there are 15 students and they each need 5 plates you just do 15x5 and get 75

Jade and Jordan both have a total of 35 trading cards altogether.

Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.

As, Jade has 28 trading cards

Let Jordan has 'x' trading cards.

Now, as Jade has 4 times as many trading cards as Jordan.

So, 28 = 4x

4x = 28

x = 7

So, Jordan has 7 trading cards.

Now, they both have a total of 35 trading cards altogether.

Hence, Jade and Jordan both have a total of 35 trading cards altogether.

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The image point of (-8, 1) after the transformation D₂ о R180° is equal to (16, -1).

A rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the coordinates (-x, -y).

For a dilation with a scale factor of 2, we have:

Point A (-8, 1)   →   (-8 × 2, 1 × 2)  = Point A' = (-16, 2)

By applying a rotation of 180° to the given point, the coordinates of its image is given by:

(x, y)                           →               (-x, -y)

Points A' = (-16, 2)   →  Points A' = (-(-16), -(1)) = (16, -1).

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Complete Question:

What is the image point of (-8, 1) after the transformation D₂ о R180°?

x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

What is, axis of symmetry, vertex and x - intercept?

A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.

A line's x-intercept is the location at which the x-axis is crossed.

Consider, the given equation,

[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]

Let,

[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex]             ..(1)

To find x - intercept, plug y = 0 in above equation,

[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]

Therefore, x = 1 and x = -7 are the x - intercepts.

Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.

So,

[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]

Plug x = -3 in equation (1)

[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]

Therefore, the vertex is, (-3, -4).

The x - coordinate of the vertex is the axis of symmetry.

Therefore, axis of symmetry is x = -3.

Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

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Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.

Given,

12 fair dice rolled,

Probability that the product of the numbers on the top faces is prime:

⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁

6 × (1/6)⁵ × 3/6

1/2(1/6)⁴

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

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The level of a independent variable known to as the "Control group" is designed to portray a neutral state.

The cause is the independent variable. Its value is unaffected by the other study variables.

You plan a study out whether variations in the room's temperature have an impact on students' math test results.

Consequently, "control group" refers to a level of such an independent variable that is meant to stand in for "no treatment" or a neutral circumstance.

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By using the property of similar triangles, it can be obtained that

Value of x is 7.2

What are similar triangles?

Two triangles are said to be similar if the corrosponding angles are equal and the corrosponding sides are similar.

The different axioms of similarity are-

SAS axiom, AA axiom, SSS axiom

By the property of similar triangles,

[tex]\frac{9}{9 + 6} = \frac{x}{12}\\x = \frac{9}{15} \times 12\\x = 7.2[/tex]

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The three consecutive even integers are -2, 0 and 2.

Let the three consecutive even integers be x, x+2 and x+4.

Since the product of the first two is taken, the result is four less than the square of the third one. This will be:

x(x + 2) = (x + 4)² - 4

x² + 2x = x² + 8x + 16 - 4

x² + 2x = x² + 8x + 12

Collect like terms

x² - x² + 2x - 8x - 12

-6x - 12 = 0

-6x = 12.

Divide

x = -12/6

x = -2

x + 2 = -2 + 2 = 0

x + 4 = -2 + 4 = 2

They're -2, 0, and 2.

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A 90% confidence interval for the average speed of all drivers on interstate 94 is (73.69, 76.31)

Given that,

Imagine asking a sample of 16 people how quickly they travel on Interstate 94. You determine the average speed to be 75 mph and the variance to be 9 mph after gathering your sample.

Solution is as given below :

90% Confidence Interval for μ is

μ = X ± tₐ/2 (n-1) 5/[tex]\sqrt{n}[/tex]

μ = 75  ± (1.75) * 3/[tex]\sqrt{16}[/tex]

μ = (73.69, 76.31)

Consequently, a 90% confidence interval for the interstate 94 average speed of all drivers is μ = (73.69, 76.31)

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Graph will shift in both horizontal and vertical direction by 4 units.

What is straight line?

An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.

What is general equation of a Straight Line?

The general equation of a straight line can be given as ax + by + c = 0, where

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.

We have function,

fn(x) = x + 5

when the graph is translated by 4 units, we can write it as;

g(x) = fn(x) + 4

the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.

Therefore, graph will shift in both horizontal and vertical direction by 4 units.

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