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Answer:

x = 2

Step-by-step explanation:

a) The test statistic is: t = 1.85.

b) The p-value is: 0.0648.

c) The null hypothesis is not rejected.

d) There is not sufficient evidence to conclude that the population mean is different of 4.

The standard deviation is known only for the sample, hence the t-distribution is obtain the test statistic.

The test statistic of the t-distribution is given by the equation presented as follows:

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

In which the variables of the equation are given as follows:

For this problem, the values of these parameters are as follows:

[tex]\overline{x} = 4.32, \mu = 4, s = 4.24, n = 600[/tex]

Hence the test statistic is obtained as follows:

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

[tex]t = \frac{4.32 - 4}{\frac{4.24}{\sqrt{600}}}[/tex]

t = 1.85.

The p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, with 600 - 1 = 599 df and t = 1.85, hence it is of 0.0648.

Since the p-value is greater than the significance level of 0.01, it is found that the conclusion regarding the null hypothesis is that it is not rejected, meaning that the sample does not give sufficient evidence to conclude that the population mean is different of 4.

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[tex]{ \pink{ \boxed{ \purple{ \sf{f(3) = 98}}}}}[/tex]

Step-by-step explanation:

[tex]{ \blue{ \tt{f(x) = 2 {x}^{4} - 8 {x}^{2} + 5x - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2( {3})^{4} - 8( {3})^{2} + 5(3) - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 2(81) - 8(9) + 15 - 7}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 72 + 8}}}[/tex]

[tex]{ \blue{ \tt{f(3) = 162 - 64}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{f(3) = 98}}}}}[/tex]

Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

The quadratic equation in standard form that contains the roots 5 + 4√10 and 5 - 4√10 is y = x² - 10 · x - 135.

In this question we must derive a quadratic equation in standard form, that is, a polynomial of the form:

y = a · x² + b · x + c

Where b / a = - r₁ - r₂ and c / a = r₁ · r₂ and r₁ and r₂ are the roots of the polynomial. If we know that a = 1, r₁ = 5 + 4√10 and r₂ = 5 - 4√10, then the quadratic equation is:

y = a · [x² + (b / a) · x + (c / a)]

y = x² + (- 5 - 4√10 - 5 + 4√10) · x + (5 + 4√10) · (5 - 4√10)

y = x² - 10 · x + 25 - 160

y = x² - 10 · x - 135

y = x² - 10 · x - 135 is the quadratic equation in standard form.

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The value of the the two numbers are 5/8and 1/6

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.

They are called simultaneous equations because the equations are solved at the same time.

if the first number is x and second number is y then

x+y= 19/24 equation 1

x-y= 11/24 equation 2

using elimination method, subtract equation 1 from 2

x-x+y-(-y)=19/24-11/24

2y= 8/24

2y=1/3

divide both side by 2

y= 1/3×1/2= 1/6

substitute 1/6 for y in equation 2

x+1/6=19/24

x= 19/24-1/6

x= 15/24

x= 5/8

Therefore the value of the two numbers is 5/8 and 1/6

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The expression will be; part (a) (f o g)(-2) = 2 and part (b) (g o f)(-2) = -95

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the functions as;

f(x)=4x-2

g(x)=5-x^2

We need to find (f o g)(-2)

So, first, we will find the function (f o g)(x) as follows:

[tex]\begin{gathered} \mleft(f\circ g\mright)(x)=f\lbrack g(x)\rbrack=4(5-x^2)-2 \\ (f\circ g)(x)=20-4x^2-2 \\ (f\circ g)(x)=18-4x^2 \end{gathered}[/tex]

Now, substitute with x = -2 then we get;

[tex](f\circ g)(-2)=18-4\cdot(-2)^2=18-4\cdot4=18-16=2[/tex]

Thus, the answer to the part is (a) (f o g)(-2) = 2

b) (g o f)(-2)

We need to find (g o f)(x) as follows:

[tex](g\circ f)(x)=g\lbrack f(x)\rbrack=5-(4x-2)^2[/tex]

Now Substitute with x = -2, then we get;

[tex]\begin{gathered} (g\circ f)(-2)=5-(4\cdot-2-2)^2 \\ =5-(-8-2)^2 \\ =5-(-10)^2 \\ =5-100 \\ =-95 \end{gathered}[/tex]

Thus, the answer to the part (b) is (g o f)(-2) = -95

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Answer:

--------------------------

The length and breadth expressions where one dimension is the GCF are; 7y and (2y²-5).

Area of a Rectangle

Given that a rectangle is a two-dimensional shape with one of the dimensions being the GCF, as specified in the question;

Consequently, the length and breadth expressions are 7y and (2y²-5) respectively.

Additionally, the rectangle's area when y=2 is; 14(2³) - 35(2) = 52.

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The quantity that is needed for you to be able to use arcsine to calculate the percentage grade is D. The change in elevation along a section of road

A geographic location's elevation is its height above or below a set reference point, most typically a reference geoid, which is a mathematical model of the Earth's sea level as an equipotential gravitational surface.

Elevation is described as the height above the ground or other surface, as well as a location or position of elevation. A plane flying 36,000 feet above the ground is an illustration of elevation. A pope being elevated to the position of saint is an example of elevation.

When driving on mountain roads, road signs frequently reflect the route's steepness as a percentage grade, which represents the angle of elevation as the road increases. In this case, the correct option is D.

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The balance in Lee's account at the end of 6 years is $384,830.53.

The first step is to determine the future value of the initial amount deposited in the savings account.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Balance at the end of 3 years: $17,000 x (1.045)^(3 x2) = $22,138.42

The total value of the account after $42,000 is deposited is:

$42,000 + $22,138.42 = $64,138.42

The future value of $64,138.42 at the end of 6 years is:

Balance at the end of 6 years: $64,138.42 x (1.045)^(3 x2) = $384,830.53

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The equation that models the cost of the van rental is V = $183 + (m - 120)0.39. (first option)

The number of miles that Tim and Jessica can travel roundtrip on vacation is Ashville MC (second option)

The equation that represents the total cost of renting the camper van is a linear equation. A linear equation is an equation that has single variable that is raised to the power of one.

The general form of a linear equation is: y = mx + b

Where:

The form of the linear equation is:

total cost = cost of renting the van + [(total miles driven - 120) x cost per mile)

V = $183 + (m - 120) x 0.39

V = $183 + (m - 120)0.39

Total miles that can be driven if they have to spend $598.74

$598.74 = $183 + (m - 120)0.39

$598.74 = $183 + 0.39m - 46.80

$598.74 = $136.20 + 0.39m

$598.74 - $136.20 = 0.39m

$462.54 = 0.39m

m = $462.54 /0.39

m = 1186

Distance Tim and Jessica can travel from the rental company to the destination = 1186 / 2 = 593 miles

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Answer:

D.

Step-by-step explanation:

just click the rotate button until it matches one of the answers

The additional weeks, w, will it take for their total distance run to be equal is 7 weeks.

From the information, Laura has already

run 36 miles and begins running 21 miles per week. This will be 36 + 21w.

Kirk has run 64 miles and runs 17 miles per week. This will be 64 + 17w

where w = number of weeks

This will be equated as:

36 + 21w = 64 + 17w

Collect like terms

21w - 17w = 64 - 36

4w = 28

Divide

w = 28/4

w = 7

It'll take 7 weeks.

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Answer:

[tex]\dfrac{1}{2}[/tex]

Step-by-step explanation:

   Number of cards = 52

 Number of black cards = 13 (club) + 13 (spade)

                                        = 26

[tex]\sf P(\text{getting a black card})=\dfrac{26}{52}[/tex]

                                     [tex]\sf =\dfrac{1}{2}[/tex]

The total cans collected by both Elizabeth and Herman is 650 and the total amount of money realized is 1300 cents.

A rate is a ratio in which the two terms being compared have different unit's.For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.

The aluminum cans collected by Elizabeth from Monday to Fridays is 50× 5days = 250 cans

Herman collected double from Monday to Thursday and collected non on Friday, therefore the total cans collected by Herman = 50×2× 4 days= 400cans

the total cans collected = 250+ 400 cans = 650cans

therefore the total money realized since 1 can is with 2 cent is 650× 2= 1300cents

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The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

Given,

When using re-grouping to solve 25 x 45, we have to find the problems that would be calculated to find the final answer;

Here,

25 × 45 = 1125

Now,

This is simply multiplicity;

1. 20 x 40: 20 x 5: 40 x 5

800 ; 100 ; 200

1100

This is not the problem.

2. 20 x 40; 5 x 40; 20 x 5 ; 5 x 5

800 ; 200 ; 100 ; 25

1125

This is the problem

3. 20 x 40 ; 5 x 20 ; 20 x 5 ; 5 x 5

800 ; 100 ; 100 ; 25

1025

This is not the problem

4. 20 x 20 ; 40 x 40 ; 20 x 5 ; 5 x 5

400 ; 1600 ; 100 ; 25

2125

This is not the problem

Therefore,

The problem that would be calculated to find the final answer is 2)  20 x 40; 5 x 40; 20 x 5 ; 5 x 5 = 1125

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Answer: 17%

Step-by-step explanation:

If you add up 34%, 23%, 5%, & 25% that would equal 83%, if you subtract the 83% from 100%, you would get 17%.The 17% is equivalent to 510. So Rachel Teeter will have $510 in her savings account.

Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

WE have been given an expression as 43πr³ represents the volume of a sphere, with radius r.

Terms can be added or subtracted to make a polynomial. They are composed of variables and constants all in multiplication.

So we know that if there is one term, then the polynomial will be called monomial.

Therefore, this expression is a monomial which have inly one term as 43πr³ .

Degree of a polynomial is the highest power that its terms contain which is 3 in the given monomial.

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The quotient of 5 divided by 3/10 is equal to 50/3

When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.

So, if we want to divide A by the fraction (b/c), then we can write:

A÷(b/c)

That will be equal to A*(c/b), so:

A÷(b/c) =  A*(c/b)

Here we want to divide 5 by 3/10, then we need to solve:

5÷(3/10)

Using the above rule we will get:

5÷(3/10) = 5*(10/3) = 50/3

That is the quotient.

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Answer:7,800

Step-by-step explanation:

Answer:

Option B (3,510ft) would be correct.

Step-by-step explanation:

The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape), the unit that is used to express the volume of the rectangular prism is cm3, m3 and so on. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid.

The value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

Given function is f(x) = 2x⁴ + 2x³− x²+ 2x + 3

The value of the function is calculated as,

f(x) = 2x⁴ + 2x³− x²+ 2x + 3

(fg)(x) = (2x⁴ + 2x³− x²+ 2x + 3)(x+1)

(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)

The value of (fg)(x) is calculated as,

(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)

(fg)(-4) = (2(-4)⁵ + 2(-4)⁴ + (-4)³ + (-4)² +5x-4 +3)

(fg)(-4) = -2048 +1024-64+16-20+3

(fg)(-4) = -1089

Therefore, the value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.

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Answer:

21%

Step-by-step explanation:

126 out of 600=126/600

=0.21 *100 for

21%

Answer:

C. -16

Step-by-step explanation:

Hope this helps you! :))

16

Step-by-step explanation:

the answer is c

just took a test and I got it right

The rate of change of the equation, y = 2/3x - 18, is: 2/3.

The rate of change of a linear equation that is expressed in slope-intercept form as y = mx + b is represented by the value of m in the equation. It is also referred to as the slope of the equation.

For example, if we are given the equation, y = 4x + 5, the value of m is 4. This implies that the rate of change, which is the slope, is equal to 4.

In the same vein, we are given the equation, y = 2/3x - 18.

The value of m, which is the slope or rate of change in the equation y = 2/3x - 18 is equal to 2/3.

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The next three terms in the sequence are  -1/16, 1/32, -1/64

The correct option is option C)

What is a sequence?

A sequence is an set of values separated by commas Referring to a generalized rule. They have a relation among them. One of the common sequences are arithmetic progression

We are given a sequence of -1, 1/2, -1/4, 1/8,

We have to describe the next three terms of the sequence

If we notice closely the given sequence is an geometric sequence

Hence they have a common factor known as common ratio

in it we divide a term by its previous term

Hence

Ratio= (1/2)/-1

Ratio = -1/2

Now to find the next terms we multiply this with the last term we get

1/8*-1/2= -1/16

Now Hence the next three terms are -1/16, 1/32, -1/64

The correct option is option c)

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By using the concept of growth, it can be calculated that

Value of coin in 8 years is $3.52

[tex]3(\frac{51}{50})^x[/tex] is the required exponential function

Domain of the function is all positive real number

Range is [tex](0, \infty)[/tex]

y- intercept is 3

This means initial value of the coin is $3

What is growth?

Growth is the exponential increase in the value of the product at a certain rate over a certain period of time

Here, concept of growth has been used

Present value of the coin = $3

Rate = 2%

Time = 8 years

Future value =

[tex]3(1 + \frac{2}{100})^8\\\\3(1 + \frac{1}{50})^8 \\\\3(\frac{51}{50})^8[/tex]

= $3.52

If the time is x years, the given exponential function is

y =

[tex]3(1 + \frac{1}{50})^x\\\\3(\frac{51}{50})^x[/tex]

This is the required exponential function.

Since x represents time here, then x has to be positive

Domain of the function is all positive real number

Now

As  [tex]x\rightarrow \infty[/tex], [tex]f(x) \rightarrow \infty[/tex]

As  [tex]x\rightarrow -\infty[/tex], [tex]f(x) \rightarrow 0[/tex]

Range is [tex](0, \infty)[/tex]

For y- intercept, x = 0

Putting x = 0, we get y = 3

y- intercept is 3

This means initial value of the coin is $3

The graph of the function has been attached here

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The answer of the given multiplication is 19.2, 1.7, 15.93 and 0.0512 respectively.

To find the answer, we will simply multiply the given numbers.

i) 3.2 × 6 = 19.2

ii) 8.5 × 0.2 = 1.7

iii) 2.7 × 5.9 = 15.93

iv) 0.32 × 0.16 = 0.0512

Hence, the answers is 19.2, 1.7, 15.93 and 0.0512 respectively.

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