The cross-section of the prism below is a compound shape formed of two
rectangles.
Work out the volume of the prism.
Give your answer in cm³.
6 cm
4 cm
2 cm
8 cm
15 cm

One example of a polynomial function is given as follows:

p(x) = x^3+4x^2-3x+2

There are two conditions for a polynomial function, and they are listed as follows:

For the example, we have that the exponents are 3, 2, 1 and 0, while it contains only a numerator.

The problem is incomplete, hence the general procedure to identify a polynomial function was given.

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This graph is the rotation of 90° counterclockwise about the origin.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

We have the three points of the figure in graph as P(-2, 3), T(-3, 5) and J(-4, 4).

A point (x, y) after the rotation of 90° counterclockwise would be the point (-y, x).

P(-2, 3) after the rotation of 90° will be (-3, -2), which is the point P'.

T(-3, 5) after the rotation of 90° will be (-5, -3) which is the point T'.

J(-4, 4) after the rotation of 90° will be (-4, -4) which is the point J'.

Hence the image of the figure is the transformation of rotation of 90° counterclockwise.

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Your question is incomplete. The graph of possible figure is given below.

The count of letter f (any case) in ' if fred is from a part of france, then of course fred's french is good', is 8.

A word, phrase, or sentence in which no letter of the alphabet appears more than once is known as a heterogram (from the prefix hetero-, meaning "different," and the suffix -gram, meaning "written"). The same idea has also been denoted by the phrases isogram and nonpattern word.

Language on Vacation: An Olio of Orthographical Oddities, written by Dmitri Borgmann in 1965, mentions the idea, however he refers to it as an isogram. Borgmann asserts that he "introduced" the term "isogram" in a 1985 essay. Although he uses the term "isogram" in the paper itself, he also offers the name "asogram" to prevent confusion with lines of constant value like contour lines.

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Answer: The amount Julie spent on gasoline can be calculated as g * $2.75 = 8.4 * $2.75 = $23.10.

The amount Julie spent on oil can be calculated as c * $3.35 = 7 * $3.35 = $23.45.

So, the total amount Julie spent on gasoline and oil can be calculated as $23.10 + $23.45 = $46.55.

The expression to determine the total amount Julie spent on gasoline and oil can be written as g * $2.75 + c * $3.35.

Step-by-step explanation:

The base of the given parallelogram is 11. 8 cm and the height is 6. 5 cm.

The area of the parallelogram is 76. 7 cm ²

The base is the dimension of the parallelogram that is shown either at the top or bottom of the shape. In this case, it is 11. 8 cm. The height is the distance from the top to the bottom which is 6. 5 cm in this case.

The area of a parallelogram is:

= Base x Height

= 11. 8 x 6 . 5

= 76. 7 cm ²

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y² - 1 should be multiplied on both sides to solve the equation.

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

(y² - 5) / (y² - 1) = (y² + y + 2) / (y + 1)

This can be written as,

y² - 1 = (y + 1) (y - 1)

So,

Multiplying y² - 1 on both sides.

(y² - 1) x (y² - 5) / (y² - 1) = (y² - 1) x (y² + y + 2) / (y + 1)

(y² - 5) = (y² + y + 2) (y - 1)

y² - 5 = y³ + y² + 2y - y² - y - 2

y² - 5 = y³ + y - 2

y³ - y² + y - 2 + 5

y³ - y² + y + 3

Thus,

Multiplying y² - 1 on both sides will solve the equation.

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Answer:

1b

Step-by-step explanation:

The number of years that it takes to double your money will be 12 years.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

They say that if you invest with them at 6% interest compounded annually they will double your money. If you invest $500 in the account. Then the equation is given as,

$1,000 = $500 x (1 + 0.06)ⁿ

2 = (1.06)ⁿ

ln 2 = n ln 1.06

n = ln 2 / ln 1.06

n = 11.90

n ≈ 12 years

The number of years that it takes to double your money will be 12 years.

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There are 7 train stations. One way ticket indicates a departing station and an arriving station. Total 42 tickets are needed.

There are 7 train stations.

One way ticket indicates a departing station and an arriving station.

We have to determine how many tickets are needed.

A permutation is a specific arrangement of objects. Set members or elements are arranged in a sequence or linear order here.

In permutation, the elements must be arranged in a specific order, whereas in combination, the order of the elements is irrelevant.

Generally A permutation is the configuration of objects in a specific manner or order. When dealing with permutation, one should consider both selection and arrangement.

From the question;

n = 7

r = 2

[tex]^{n}P_{r}=\frac{n!}{(n-r)!}[/tex]

[tex]^{7}P_{2}=\frac{7!}{(7-2)!}[/tex]

[tex]^{7}P_{2}[/tex] = 7!/5!

[tex]^{7}P_{2}[/tex] = (7 × 6 × 5!)/5!

[tex]^{7}P_{2}[/tex] = 7 × 6

[tex]^{7}P_{2}[/tex] = 42

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The sum of the squares of the solutions of the mentioned equation is 161.38.

The solution of the given quadratic equations can be calculated through factorization. So, rewriting the equation to factorize it.

x² - 13x + 4 = 0

Based on Dharacharya formula, stated as -

x = - b ± ✓b² - 4ac/ 2a, we get the roots -

x = 12.7 and 0.3

Now, the next formula to solve will be -

x = 12.7² + 0.3²

Taking the square of each number

x = 161.29 + 0.09

Performing addition on Right Hand Side of the equation

x = 161.38

Thus, the required answer is161.38.

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Answer:

1. D

2. C

3.D

4.D

5.C

6. A

7.B

The area and the perimeter of the room having rectangular shaped base are respectively,   121 feet² & 44 feet

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Given that,

2 of the walls are 11 and 11,

The room is into rectangle shape,

Base area of room = length x width

                               =  11 x 11

                               =   121 feet²

Perimeter of base of the room = Sum of lengths and widths

                                                   = 11 + 11 + 11 + 11

                                                   =   44 feet

Hence, the area and perimeter are respectively 121 feet² & 44 feet

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Answer:

Below

Step-by-step explanation:

There is only ONE step

g/16 = 16      multiply both sides of the equation by 16

g = 256    Done.

Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.

What is area of a circle ?

Area of circle can be defined as product of pi and square of radius .

To find the area of the semicircle, we need to use the formula for the area of a circle, but divide it by 2 since we only have half of a circle. The formula for the area of a circle is:

A = πr²

where A is the area of the circle, and r is the radius.

In this case, we have a semicircle, so we need to use half of the formula:

A = (πr²)/2

We are given that R = 314, so we can substitute that into the formula:

A = (π(314)²)/2

Using a calculator and rounding to the nearest hundredth, we get:

A ≈ 49106.15

Therefore, Mr. Brunson will need to cover approximately 49,106.15 square units of the patio with concrete sealer.

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Answer:

120 student

Step-by-step explanation:

We know

45% of the students take the bus to school

100% - 45% = 55%

So, 55% travel by car or walk to school

400 x 0.55 = 220 students

So, 220 student travel by car or walk to school

We know

20 more students walk than travel by car

220 - 20 = 200 students

200/2 = 100 students

100 + 20 = 120 students

So, 120 students walk to school

Before solving this expressions, you must understand the PEMDAS rule.

This rule must be used to solve this problem.

Question: 64 ÷[4 ×(27 - 5²)]

According to PEMDAS rule, we start with parentheses.

The equation is now 64 ÷[4×(2)]

    2. Step 2: [4×2] = 4×2 = 8.

The equation is now 64 ÷ 8.

    3. Step 3: 64 ÷ 8 = 8.

The answer to 64 ÷[4 ×(27 - 5²)] = 8.

This concludes solving 64 ÷[4 ×(27 - 5²)]. If this helps you, please leave a heart and stars to rate this answer. Leave a comment if you have questions or concerns.

The exponential equation for the decay of the Kangaroo is written as [tex]y = 73000(\dfrac{1}{3})^x[/tex].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the most recent estimate, conducted this year, concluded that there are about 73,000 giant kangaroo rats in the desert. The population is expected to decrease by a factor of 1/3 each decade.

The exponential expression can be written as:-

[tex]y = 73000(\dfrac{1}{3})^x[/tex]

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Answer: Observational

Step-by-step explanation:

If it is a experiment then you can conclude that a variable caused a response

In statistics, correlation refers to the degree to which two variables are related or associated with each other. When the correlation between two variables is close to 1.0, it indicates a strong positive relationship between them. However, it is important to note that this strong correlation does not necessarily imply a cause-and-effect relationship between the two variables, especially in a study where certain conditions may not be met.

A study is a systematic investigation aimed at acquiring knowledge and understanding of a particular phenomenon or subject matter. In order to establish a causal relationship between two variables, certain conditions need to be met, such as the establishment of a temporal sequence, a clear association between the variables, and the elimination of any confounding variables that may influence the outcome. These conditions are essential for any study seeking to establish a cause-and-effect relationship between variables.

In the absence of these conditions, even if the correlation between two variables is close to 1.0, it cannot be concluded that the explanatory variable causes changes in the response variable. This is because correlation does not imply causation. Correlation simply indicates the strength of the association between two variables, but it does not provide information about the direction or the underlying mechanisms of the relationship.

For instance, consider a study examining the relationship between smoking and lung cancer. The study finds a strong positive correlation between smoking and lung cancer, indicating that smokers are more likely to develop lung cancer than non-smokers. However, this correlation alone does not necessarily prove that smoking causes lung cancer. There may be other factors such as air pollution, family history, or genetics that could influence the development of lung cancer.

In summary, the correlation between two variables is a measure of the strength of the association between them. A high correlation does not necessarily imply a cause-and-effect relationship between the variables, especially in a study where certain conditions may not be met. It is important to consider these conditions and rule out other factors that could influence the outcome before drawing any conclusions about the causal relationship between two variables.

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Step-by-step explanation:

you add all the numbers then you can get the answer

The required numerical expression for the amount of water in ounces that he drinks in a week is 7× (8+6+16+16+32) ounces and the value is 546 ounces.

Lamar drinks water with,

Breakfast = 8 ounces

Vitamins = 6 ounces

Lunch = 16 ounces

Dinner = 16 ounces

Bottle = 32 ounces

To find A numerical expression for the amount of water in ounces that he drinks in a week.

One day consumption of water by Lamar is

We know that,

1 week = 7 days

One day consumption of water = 78 ounces

1 week (7 days) consumption of water = 7× One day consumption of water

 = 7× (8+6+16+16+32) ounces                                                                

 = 7×78 ounces

 = 546 ounces

Therefore, the required numerical expression for the amount of water in ounces that he drinks in a week is 7× (8+6+16+16+32) ounces and the value is 546 ounces.  

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The interval of continuity of the function is continuous given y = 2 (x + 4 ) 2 + 8 is (-∞, ∞).

A function is continuous at a point if the function value exists and is finite at that point, and the limit of the function as the input approaches that point from the left and right side is equal to the function value at that point. In other words, the function has no sudden jumps or discontinuities at that point.

In the case of the function y = 2(x + 4)² + 8, the function is defined and continuous for all real numbers x. There are no values of x for which the function is undefined or has a discontinuity, so the function is continuous for all values of x, meaning that the interval of continuity is (-∞, ∞).

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The coordinate of the image of the point (-3/2, -1/2) under reflection in the x-axis is (-3/2, 1/2).

When we want to reflect a point with respect to x-axis, the value of ordinate is negated. Reflection with respect to x-axis does not alter the value of abscissa but the ordinate value changes.

(i) The image coordinates of the point (2, -5) under reflection in the x-axis are (2, 5). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).

(ii) The image of the point (-3/2, -1/2) under reflection in the x-axis has the coordinates (-3/2, 1/2). This signifies that the point's x-coordinate remains constant while its y-coordinate changes sign (from negative to positive).

(iii) The image coordinates of the point (-7, 0) under reflection in the x-axis are (-7, 0). This signifies that the point's x-coordinate remains constant while its y-coordinate remains constant (zero).

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The complete question is: 1. Find the co-ordinates of the images of the following points under reflection in the x- axis:

(i) (2, -5)

(ii) (-3/2, -1/2)

(iii) (-7, 0)

The circumference of the dome will be 149.15 feet or 47.5π feet

A scale is defined as the ratio of the dimensions of an object that is represented as a draft to the real or true dimensions of the object being drafted.

The figure on the left of the ratio sign can represent the size and dimensions of the model with respect to the actual size or dimensions of the object.

On the other way, the figure on the right-hand side represents the actual dimensions and size of the real object.

So, if an object is being drawn with the ratio, of 1cm: 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always represent 1cm in the drawing.

If the object is being drawn by a scale of 5cm: 1cm then the actual size of the object will be increased. After that for every 1cm in the actual dimensions of the object, it can be a 5cm representation in the drawing.

Now, draws a scale of 0.25 inches: 1 foot. If the diameter of the dome is 23.75 inches, then the actual diameter of the dome is:

0.25 inches ------- 1 foot

23.75 inches -------? feet

= 23.75/0.25 × 1

d= 95 feet

so, the real diameter of the dome is 95 feet.

The dome is a hemisphere that is half of a sphere. So, the formula for finding the circumference of a sphere is πd, then the hemisphere will be πd/2. As we know the diameter is 95 feet, and the circumference of the hemisphere =

(π × 95)/2

=47.5π feet

Or

if the value of π = 3.14, then the circumference is calculated as (3.14 × 95)/2 = 149.15 feet

Therefore, the circumference of the dome is 149.15 feet or 47.5π feet.

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The approximate surface area of this wheel of cheese is 437.6 square inches.

As per the given data, a wheel of cheese has a radius of 7 inches.

Radius r = 7 inches.

Also, a wheel of cheese has a height of 3 inches.

Height h = 3 inches

Also, given to consider the value of pi as 3.14.

π = 3.14

Here we have to determine the total surface area (TSA)of the wheel of cheese.

Since the cheese is a cylinder shaped thing.

The formula for the total surface area (TSA) of the wheel:

TSA = 2πr (r + h)

Substituting the values of the variables into the formula, we have

= 2 (3.14)(7)(7 + 3)

= 2 (21.88)(10)

= 2 (218.8)

= 437.6 square inches.

Therefore the total surface area is 437.6 square inches.

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Answer:

a = - 2

Step-by-step explanation:

Since the point (x, y) = (1, a) lies on the line, substituting this value of x = 1 should give the corresponding value of y which is a

y = 3x - 5

At  (1, a)
a = 3(1) - 5

a = 3 - 5

a = - 2

Answer

The solution to the system of equations in this problem is given as follows:

The system of equations for this problem is defined as follows:

From the first equation, we have that:

ab^6 = 42

a = 42/(b^6)

a = 42b^(-6).

Replacing on the second equation, we have that the value of b is obtained as follows:

15 = 42b^(-6) x b^9

15 = 42b³

b = (15/42)^(1/3)

b = 0.71.

Then the value of a is obtained as follows:

a = 42 x (0.71)^(-6)

a = 327.9.

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AnswerStep-by-step explanation:

.99 is right, you already know.

So first,

8 Down arrow 2

means sqrt8

The 8 goes inside the sqrt and the 2 goes outside (its called an index) but we like never write that 2. Its just a normal square root. If you are using a calculator (I think practically, you must use a calculator) you can find sqrt8. Then

take

sqrt8 UpArrow 6

means (sqrt8)^6

this is 8^3 or on the calculator 512.

Next,

512 SideArrow 500

means 500/512

this is .9765625

Lastly,

.9765625 DownArrow 4

means

4throot(.9765625)

Your calculator might have a 4throot button, but you can use 1/4 power instead because all roots can be written like fraction powers.

When .9765625 is in your calculator screen you can just use the ^ button or x^y button to raise it to the 1/4 power. (Use .25 for 1/4 or use parenthesis on the (1/4) )

(.9765625)^.25

~= 0.99

see image.