Math XL for School Practice X
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8-9; MathXL for School: Practice & Problem Solving
Due 05/11/21
X8.9.PS-14
Question Help
2 cm
A glass bead has the shape of a rectangular prism with a smaller rectangular
prism removed. What is the volume of the glass that forms the bead?
2am
6cm
7 cm
6 cm
(The figure is not to scale)
The volume of the glass that forms the bead is cm3,

Start with any random elements of sets and compute LHS and RHS individually.

a) The proof of f(S ∪ T) = f(S) ∪ f(T) is explained below.

b) The proof of f(S ∩ T) ⊆ f(S) ∩ f(T) is expliane dbelow.

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Let, The set A = {1, 2, 3, 4, 5} and B = {2, 4, 5}.

Therefore, S = {1, 2, 3} and T = {1, 4, 5}.

Now, f(S ∪ T) = {1, 2, 3, 4, 5} and f(S) ∪ f(T) = {1, 2, 3} ∪ {1, 4, 5}.

Hence,  f(S ∪ T)=f(S) ∪ f(T).

Now, f(S ∩ T) = {1} and  f(S) ∩ f(T) =  {1, 2, 3} ∩ {1, 4, 5} = {1}.

Therefore,  f(S ∩ T) ⊆ f(S) ∩ f(T). (⊆ implies improper subset)

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Answer: solve the same variables

Step-by-step explanation:

1. 3y + 4.1

2. 4x +

3. 5x + 22½

4. 4y²

5. + 25

6. 0

Answer:

To determine the inverse of function f, change f(x) to y, switch x and y, and solve for y.

[tex]\frac{1}{8} (x-4)^3[/tex]

Step-by-step explanation:

f(x) = [tex]\sqrt[3]{8x} +4[/tex]

Change f(x) to y: y = [tex]\sqrt[3]{8x} +4[/tex]

Switch x and y: x = [tex]\sqrt[3]{8y} +4[/tex]

Solving for y: x - 4 = [tex]\sqrt[3]{8y}[/tex]

(x-4)^3 = 8y

y = [tex]\frac{1}{8}[/tex][tex](x-4)^3[/tex]

Therefore: inverse of function f = [tex]\frac{1}{8} (x-4)^3[/tex]

The inverse function of f(x) will be f⁻¹(x) = 1/8(x - 4)³.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given below.

f(x) = ∛(8x) + 4

Then the inverse function of f(x) will be

Put x = f⁻¹(x) and f(x) = x. Then we have

            x = ∛{8f⁻¹(x)} + 4

∛{8f⁻¹(x)} = x - 4

Cube on both sides, then we have

8f⁻¹(x) = (x - 4)³

 f⁻¹(x) = 1/8(x - 4)³

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Answer:

B. 434.89

Step-by-step explanation:

A basketball is a sphere and the volume formula is:

V = 4/3πr³

Given:

d = 9.4

r = 9.4/2

r = 4.7

Work:

V = 4/3πr³

V = 4/3π(4.7)³

V = 4/3π(103.823)

V = 434.89

Answer:

Calculate the number of whole years it takes for the population to decrease from 2180 to less than 1000Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

164 seats

Step-by-step explanation:

you make the equation 4+ 8X to deteremine the seats and x equals the rows and you get your answer.

An arithmetic sequence is a sequence where each consecutive term has a common constant difference. The total number of seats that the theatre has is 156 seats.

An arithmetic sequence is a sequence where each consecutive term has a common constant difference.

An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.

Let the starting term be 'a' and the common difference be 'd', then we get the arithmetic sequence as:

a, a+d, a+2d, .....

The sum of those 'n' terms is:

[tex]\rm a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n}{2}[2a + (n-1)d ][/tex]

The condition is a case of an arithmetic progression. Therefore, the common difference in the progression is of 8 and the first term of the sequence is 4. Therefore, the sum of the series for the first 20 terms will be,

aₙ = 4 + (20-1)8

   = 4 + (19)8

   = 4 + 152

   = 156

Hence, the total number of seats that the theatre has is 156 seats.

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Answer:

13/7

Step-by-step explanation:

multiply the 7 x 1 then add 6. 13 would be the numerator.

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9514 1404 393

Answer:

  3025

Step-by-step explanation:

We observe that increasing x by 1 from 0.5 to 1.5 causes the function value to be multiplied by 55 (from 1 to 55).

So, increasing the x-value by 1 again, from 1.5 to 2.5, will again multiply the function value by 55.

  f(2.5) = 55·f(1.5) = 55^2

  f(2.5) = 3025

Answer:=Answer1 has the regression analysis with all 4 independent variables. Using the stepwise method, we toss the one with the largest non-significant p-value which is Senior Present. Then do another regression analysis with only 3 independent variables. Answer2 has this. From this analysis we can toss education (has the largest non-significant p-value) and do another analysis which is in Answer3. In this analysis we see that Income is not quite significant (p=.0586) at the 0.05 level so we can toss it and do an analysis with Family Size as the only independent variable. This result is given in Answer4. The final regression equation has Family Size as the only independent variable and it can stay in the regression equation because it is statistically significant (p=.0003). The prediction equation is given at the bottom of Answer4. This should answer your question. If not let me know.

Step-by-step explanation:

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Answer:

[tex]perimeter = 14 \frac{3}{4} + 4 \frac{1}{2} + 8 \frac{1}{2} + 10 \frac{2}{5} + 10 \frac{2}{5} + 12 \frac{4}{5} \\ = \frac{59}{4} + \frac{9}{2} + \frac{17}{2} + \frac{52}{5} + \frac{52}{5} + \frac{64}{5} \\ = 61 \frac{7}{20} \: units[/tex]

Answer:

3x²

Step-by-step explanation:

3x²

They would all reduce to 1, 2x^4, and -4x

Answer:

No

Step-by-step explanation:

The ratio used should have been 6 parts yellow paint to 2 parts blue paint

hope this helps

Answer:

B) y=1/2x

Step-by-step explanation:

y=1/2x

Answer:

Pretty Sure its D!

Step-by-step explanation:

Step-by-step explanation:

hope this is right hehe.....

9514 1404 393

Answer:

  d)  x = 3

Step-by-step explanation:

The given equation resolves to a quartic equation in (3^x). It has a solution near ...

  x = 0.541770946714

__

Perhaps you want the solution to ...

  3^(x+9) = 81^(x)

Rewriting in powers of 3, this is ...

  3^(x+9) = (3^4)^x = 3^(4x)

Taking logarithms base 3 gives ...

  x +9 = 4x

  9 = 3x . . . . . . subtract x

  3 = x . . . . . . . divide by 3 . . . . matches choice D

_____

Additional comment

The Order of Operations requires that exponential terms be evaluated before addition and subtraction. That means (3^x) must be evaluated before the sum (3^x) + 9. If you want the sum of x and 9 to be evaluated first, it must be in parentheses: 3^(x+9).

In typeset equations, the superscript font serves to group parts of the exponent. In plain text, a grouping symbol (parentheses) must be used.

The expression 6² - 2(5 + 1 + 3) after evaluation gives 18.

BODMAS rule is rule for operation of numbers in a specific order when more than one type of operations is involved.

BODMAS is the abbreviated form for Brackets, Order including powers and exponents, Division, Multiplication, Addition and Subtraction.

Given expression is, 6² - 2(5 + 1 + 3).

First we should do the operation in brackets.

6² - 2(5 + 1 + 3) = 6² - 2 (9)

Now we should do the power operations.

6² - 2 (9) = 36 - 2 × 9

Now we do multiplication.

36 - 2 × 9 = 36 - 18

Now we do subtraction.

36 - 18 = 18

Hence the answer of the expression given is 18.

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The correct answer is 571 quotient and 1 is remainder.We can solve easily by partial quotients.

Partial quotients division is a deviation from the standard method. The divisor is multiplied with a number and the multiple obtained is deducted from the dividend. This multiple of the divisor is as close as possible to the dividend, that is less than or equal to the dividend.

Partial quotient division provides natural differentiation because we can have students solve at a level they are comfortable with and then we can challenge them to find a more efficient way. And this means using fewer steps and solve easily.

Now we solve

first 9 multiply with 500 so we get 4500. 5140-4500=640

then 9 multiply with 70 so we get 630. 640-630=10

then 9 multiply with 1 so we get 9.   10-9=1

Hence       500+70+1=571

And our remainder is 1.

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Answer:

The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.

Step-by-step explanation:

Slope of a line:

Suppose we have two points in a line. The slope is the change in y divided by the change in x. It states how much y changes when x changes by 1.

In this question:

x: Time in hours to move a lawn.

y: Area of land.

Two of his points are (3, 1.5) and (5, 2.5).

Change in y: 2.5 - 1.5 = 1

Change in x: 5 - 3 = 2

Slope: 1/2 = 0.5

The slope of the line through these two points is 0.5, which means that for each hour moving a lawn, 0.5 more lands of area are mowed.

Answer:

x + (x + 55) = 180

2x =125

The angle is 62.5 degrees

Double-Check

62.5 + (62.5 + 55) = 180

125 + 55 = 180

62.5 is the smaller angle

Step-by-step explanation:

Answer:

62.5

Step-by-step explanation:

Answer:

(-2,-6)

Step-by-step explanation:

we can solve this system of equations with the substitution method because y is already by itself.

since they are both equal to y, we can set both equations equal to each other.

4x+2=x-4

subtract 2 from both sides

4x=x-6

subtract x from both sides

3x=-6

divide both sides by 3

x = -2

now that we know x, we can plug this value into one of the original equations and solve for y.

y=-2-4

y=-6

so on a graph, these two equations will intersect at the point (-2,-6)

Since matching angles are formed and the equal corners are congruent when a line joins two parallel lines, one of the choices isc=d.

Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.

Here,

Given :  vertical angles, A = d also represents a solution.

B+d=180 as a result of b+c=180 therefore

B+d=180 as a result of b+c=180 therefore Since a=d, c=d, and b+d=180, the answer is B,C,E.

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Answer:

An 18-month loan with a 4.75% annual simple interest rate

Step-by-step explanation:

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may i please have a branlliest

It's 8, it gave Y so pretty easy from there on

y = 4

y = 1/4 x + 2

______________

4 = 1/4 x + 2

4 - 2 = 1/4 x + 2 - 2

2 = 1/4 x

2 × 4 = 4 × ( 1/4 ) × x

x = 8

Thus the correctly answer is option D.

Answer:

The p-value for her test is 0.0075.

Step-by-step explanation:

She will then perform a hypothesis test to determine if the sample mean daily revenue provides significant evidence to conclude that the population mean daily revenue is less than $900 when the advertising dollars are reduced.

At the null hypothesis, we test that the mean is less than 900, that is:

[tex]H_0: \mu = 900[/tex]

At the alternate hypothesis, we test that the mean is less than 900, that is:

[tex]H_a: \mu < 900[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

900 is tested at the null hypothesis:

This means that [tex]\mu = 900[/tex]

Sample of 64 days. The first co-owner observes a sample mean daily revenue of $892.50 with a sample standard deviation of $24 when the advertising dollars have been reduced.

This means that [tex]n = 64, X= 892.50, s = 24[/tex]

Value of the test:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{892.50 - 900}{\frac{24}{\sqrt{64}}}[/tex]

[tex]t = -2.5[/tex]

What is the p-value for her test?

The pvalue of the test is the probability of a sample mean below 892.5, which is a left-tailed test for t = -2.5 with 64 - 1 = 63 degrees of freedom.

Using a calculator, the p-value for her test is 0.0075.

Answer:

the answer is 0.7 by the way!

Step-by-step explanation:

This is talking about the distance from zero sooo...