Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(x) = x−1⁄3 (x − 12)

first we writte the information they are giving to us:

For company A:

initial fee = $90

rent per mile = $2

For combany B:

initial fee = $50

rent per mile = $3

Now for company A the equation that represent the charge in one mile will be: (where n is the number of miles)

And for company B:

Now to determine the number miles driven, that would make the cost of each company the same, we have to make A = B

and finaly we can solve for n

so if they drive for 40 miles the will pay the same

Answer:

what graph?

Step-by-step explanation:

By the knowledge on absolute values, functional theory and rigid transformations and given that the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, {\displaystyle |x|=x} if x is a positive number, and {\displaystyle |x|=-x} if x is negative, and {\displaystyle |0|=0}.

here, we have,

According to the image attached herein,

the function f(x) is an absolute value and the function g(x) results from translating f(x) in +x direction, representing a kind of rigid transformation as Pythagorean distance at every point of the function is conserved.

There, we can define the function g(x) as follows:

g(x) = f(x - k), for k > 0     (1)

By the knowledge on absolute values, functional theory and rigid transformations

and given that

the function f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

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The solutions will be (x-2)(x+1), (3x+5)(5x+2) and (x+1)(x-1) respectively using factorization.

A number or other mathematical object is factorized or factored in mathematics by writing it as the product of numerous factors, typically smaller or simpler things of the same kind.

18) 8x³-8x²-16x = 0

Taking 8x common we get,

8x(x²-x-2) = 0

x²-x-2 = 0×8x

x²-(2-1)x-2 = 0

x²-2x+x-2 = 0

x(x-2)+1(x-2) = 0

(x-2)(x+1) = 0

Hence, the factors are (x-2)(x+1).

19) 15x³+31x²+10x = 0

Taking x as common as we get,

x(15x²+31x+10) = 0

Factorize 15x²+31x+10=0

15x²+(25+6)x+10=0

15x²+25x+6x+10=0

5x(3x+5)+2(3x+5)=0

(3x+5)(5x+2)=0

Hence the factors are (3x+5)(5x+2).

20) x³-x=0

Taking x as common as we get,

x(x²-1)=0

x²-1=0

(x+1)(x-1)=0

Hence the factors are (x+1)(x-1).

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What is the solution of the equation [tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1[/tex] ?

x=4

How is the given equation solved?

[tex]\frac{2}{3}(x-1) -\frac{1}{5} (2x-3)=1\\\\\frac{2}{3} x-\frac{2}{3} -\frac{2}{5} x+\frac{3}{5}=1\\\\\frac{2}{3} x-\frac{2}{5}x =1+\frac{2}{3}- \frac{3}{5}\\\\\text{Taking LCM},\\\\\frac{10x-6x}{15} =\frac{15+10-9}{15} \\\\4x= 16\\\\x=4[/tex]

What is solving an equation?

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let x is the random variable that represents the speed of car.

probability that x is higher than 100 :

for x=100:

so,

probability =total area - area of the left of (z=1)

and the area of the left of z=1 is 0.8413 (from normal distribution)

The function is given by:

The three quantities are zero then it follows:

Option D is correct.

The intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Increased or decreased functions are two categories of functions. Consequently, a function increases when the y-values grow, while a function decreases when the y-values decrease.

The graph indicates the y-values increase in the x-intervals from -∞  to 0 and from 3.5 to ∞. You can express that a function is increasing in the following ways using interval notation:  (-∞, 0) U (3.5, ∞).

The graph, on the other hand, is decreasing: (0, 3.5)

Hence, the intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)

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EXPLANATION

Let's see the facts:

We can use the Law of Cosines to calculate the unknown value:

Replacing terms:

Isolating x:

Answer is x=6.

Every column have 7 bricks

There are 8 columns,

Then there are

8x7 = 56 bricks + another 7 bricks = 63 bricks

Divide now 63 between 10

63/10 = 6 tens + 3 ones

ANSWER IS

6 TENS 3 ONES

Answer:

y + 4 = -6 (x - 8)

Step-by-step explanation:

Change the equation to the slope intercept form for a line

x - 6y 5 = 0  Add 5 to both sides

x - 6y = 5  Subtract x from both sides

-6y = -x + 5  Divide both sides by -6

y = [tex]\frac{1}{6}[/tex] c  - [tex]\frac{5}{-6}[/tex]  Your slope is [tex]\frac{1}{6}[/tex]

A perpendicular slope is the opposite reciprocal of [tex]\frac{1}{6}[/tex], that would be -6

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])  Plug is -4 for [tex]y_{1}[/tex] and 8 for [tex]y_{1}[/tex]

y - -4) -6(x-8)

y + 4= -6 (x -8)

Answer:

Step-by-step explanation:

square kilometre (km 2): 1,000,000    hectare: 10,000

Unit: Area in m 2                                   square meter: SI Unit

There exist more distinctions and classifications for different types of

trapezoids, but their areas are still calculated in the same manner using the

following equation: area = b 1 + b 2 2 × h where b1 and b2 are the bases. h is the height, or perpendicular distance between the bases The Farmer and his Daughter – Ramping Endeavors

Concept

To solve the question you will use the associative property.

a . ( b + c ) = a . b + a . c

The expressions that is equivalent to 5 .(3 + 7) = 5 . 3 + 5 . 7 , ( 3 + 7 ) 5 , 5 . (

Fi

ANSWER

EXPLANATION

We want to write the sentence as an inequality.

We have:

The sum of 3 times a number n and 8 is at most 16.

3 times a number n is 3 * n i.e. 3n

Adding that to 8 would yield:

3n + 8

That is at most 16.

This means that it is less than or equal to 16.

That is:

If  an automatic machine inserts mixed vegetables into a plastic bag.  the probability of selecting four packages that are underweight is: 0.000000390625

Probability can be defined as the tendency or likelihood that an event will happen.

We would be making use of multiplication rule to determine the probabiliy that four packages are underweight.

Given :

Underweight = 2.5 % or 0.025

Hence,

Now let find the probability that  P (all four underweight) :

P(all four underweight) = ( 0.025 ) ( 0.025 ) ( 0.025 ) ( 0.025 )

P(all four underweight) = 0.000000390625

Therefore we can conclude that the probability is  0.000000390625.

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The domain will be x ≥ 3 for f(x)=√x-3 and g(x)=1-x².

In case a function f gives a way to effectively create a single value y utilizing for that reason a value for x at that point that chosen x-value is said to have a place to the domain of f. there are some conditions to be checked such as denominators cannot equal 0, radicands of even roots can't have a negative value, logarithms can as it was being taken of positive values. Since we are given that f[tex]\sqrt{x-3}[/tex] and g(x)=1-x², for g(x)  since it's a polynomial function its domain had to be real numbers, whereas for f(x) is all positive and real numbers.

for the given  condition (f•g)(x)

=> (f•g)(x)= f(x)*g(x)

=> (f•g)(x) = √(x-3) * (1 - x²)

=>(f•g)(x) = √(x-3)-x²(√x-3)

So the domain for (f•g)(x) will be all positive real numbers x≥3 x ∈ [3,∞)

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Solution

Using Z score calculator

P(x>Z) = 0.04093

The The 3 ratios are;

A=60: 84

F=90:126

H=5:7

Answer

SOLUTION

Problem Statement

The question gives us an expression to simplify and we are to simplify by finding the product. We are also asked to find the degree of the polynomial as well

Method

We simply need to expand the bracket to solve this question. But the degree of the polynomial is gotten by assessing which term in the final expression has the highest power. If the expression has a term with its highest power being 3, then the degree of the polynomial is 3.

With this information, let us begin solving.

Implementation

1. Expanding the expression:

Expanding the polynomial, we have:

2. Degree of the polynomial:

From the above result, we can see that the highest degree of n in all the terms is 3, therefore, the degree of the polynomial is 3

Final answer

According to the solving the  Polynomial  Standard Form of the given equation is :

3x^2-7x-17.

When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on. When x is the variable and ai are coefficients, the polynomial has the conventional form f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

f(x)= x-7

g(x)= 3x^2-7x-10

f(x)= x-7 by substituting in the value of  g into f.

f(3x^2-7x-10) =  (3x^2-7x-10)-7

                     = 3x^2-7x-17

According to the solving the slandered form of the given equation is :

3x^2-7x-17

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Answer:

B. radio stations stopped advertising

Answer:

As televisions became more affordable and advertisers flocked to the new medium, radio stations had to quickly adapt to the changing field. Stations stopped using live in-studio performances, instead playing less expensive recordings.

Step-by-step explanation:

In the 1950s, television surpassed radio as the most popular broadcast medium, and commercial radio programming shifted to narrower formats of news, talk, sports and music. Religious broadcasters, listener-supported public radio and college stations provide their own distinctive formats.

The arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The equation:

h = −8t(2t−6)

To find the total number of seconds the arrow will be in the air:

Plug h = 0

−8t(2t−6) = 0

t(2t−6) = 0

t = 0   or    t = 6/2

t = 0  or   t = 3 seconds

Thus, the arrow will be in the air for 3 seconds after 3 seconds the arrow hit the target.

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The graph that shows the relationship between the height of the bamboo and months planted is given as h = 5t + 10

Given that the graph shows the relationship between the height (h) of a bamboo plant after months it has been planted.

Let us assume that h is plotted on the vertical axis and months (t) is planted on the horizontal axis.

If the graph passes through the points (0, 0) and (2, 10), hence:

h - 10 = [(10 - 0)/(2 - 0)](t - 0)

h - 10 = 5(t)

h = 5t + 10

The graph is given as h = 5t + 10

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[tex]9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}[/tex]

Answer:

[tex]\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}[/tex]

[tex]\textsf{2.} \quad -8\sqrt{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]9\sqrt{56x^7y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 56 as 4·14:

[tex]\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 4 as 2²:

[tex]\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Simplify:

[tex]\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]

[tex]\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6[/tex]

Rewrite ⁷/₂ as 3 + ¹/₂

[tex]\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}[/tex]

Rearrange:

[tex]\implies 18\;x^3\;y^{6}\sqrt{14x}[/tex]

Given expression:

[tex]7\sqrt{32}-6\sqrt{72}[/tex]

Rewrite 32 as 16·2 and 72 as 36·2:

[tex]\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}[/tex]

Rewrite 16 as 4² and 36 as 6²:

[tex]\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}[/tex]

Simplify:

[tex]\implies 28\sqrt{2}-36\sqrt{2}[/tex]

[tex]\implies -8\sqrt{2}[/tex]

The ways to translate the figure include:

It doesn't change its orientation.

It also doesn't change its size or shape.

When a geometric figure glides up, down, left, or right on the coordinate plane, this is referred to as translation. The figure changes its location but not its orientation. It also retains its size and shape. When you translate a figure, you slide it left or right, up or down.

When you translate a figure, you slide it left or right, up or down. This indicates that the coordinates for the figure's vertices will vary on the coordinate plane. To graph a, make the same modification at each point. The variations in coordinates of a reflection can be used to identify it.

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y + 5x = 0 is the line's equation in point-slope form.

Given is a line with a slope of 0 and a point at (0, -10) on it. We must determine the line's point slope form equation.

The line's point-slope shape is  ( y -[tex]Y_{1}[/tex]  ) = m ( x - [tex]X_{1}[/tex]  ).

According to the query, slope (m) = 0 and

the line is going through ( [tex]X_{1}[/tex] , [tex]Y_{1}[/tex] ) = ( 0 , -10 )

∴ ( y - [tex]Y_{1}[/tex] ) = m ( x - [tex]X_{1}[/tex] )

y + 10 = 0 ( x - 0 )

y + 10 = 0

y + 5x = 0

As a result, the equation for the line in point-slope form will be

y + 5x = 0.

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Each sector is formed like a triangle with a circle base. The sum of all the bases should be equal to half the length of the circle's circumference, this is calculated with the following expression:

This is the base of the parallelogram.

The height of each triangle is the radius of the circle, therefore:

The area of the parallelogram is the product of the base and the height.

So the base is pi*r;

The height is r;

The area is pi*r².

Answer:  Choice A)   [tex]\boldsymbol{78.67\% \ \pm \ 9.46\%}[/tex]

======================================================

Explanation:

phat = 59/75 = 0.7867 = 78.67% approximately is the sample proportion

n = 75 is the sample size

Your teacher doesn't mention a confidence level, so I'll assume it's the default 95%.

Let's compute the margin of error at 95% confidence

E = z*sqrt(phat*(1-phat)/n)

E = 1.96*sqrt(0.7867*(1-0.7867)/75)

E = 0.0927 approximately

E = 9.27% approximately

Unfortunately the margin of error 9.27% isn't listed among the four answer choices, but let's change the z = 1.96 to z = 2 instead.

Recalculate the margin of error.

E = z*sqrt(phat*(1-phat)/n)

E = 2*sqrt(0.7867*(1-0.7867)/75)

E = 0.0946 approximately

E = 9.46% approximately

This margin of error is listed among the four answer choices.

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

We found that

The confidence interval in the format [tex]\text{phat} \ \pm \ \text{E}[/tex] is approximately [tex]78.67\% \ \pm \ 9.46\%[/tex] which points us to choice A as the answer.

Answer:

[tex]\textsf{a)} \quad 78.67\% \pm 9.46\%[/tex]

or d) None of the answers are correct.  (Please see notes below).

Step-by-step explanation:

P-hat is the probability that a given outcome will occur given a specified sample size.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{P-hat formula}\\\\$\hat{p}=\dfrac{X}{n}$\\\\where:\\\phantom{ww}$\bullet$ $\hat{p}$ is the probability. \\ \phantom{ww}$\bullet$ $X$ is the number of occurrences of an event. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula to find p-hat:

[tex]\implies \hat{p}=\dfrac{59}{75} =0.78666666...[/tex]

The critical value for a 95% confidence level using normal distribution is:

[tex]z=1.9600\;\;\sf (4\;d.p.)[/tex]

[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Margin of error}\\\\$ME=z \cdot \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$\\\\where:\\\phantom{ww}$\bullet$ $z$ is the critical value. \\ \phantom{ww}$\bullet$ $\hat{p}$ is the sample proportion. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]

Substitute the given values into the margin of error formula:

[tex]\implies ME=1.9600 \cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]

[tex]\implies ME=0.092715036...[/tex]

Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) is:

[tex]\implies \hat{p}\pm ME[/tex]

[tex]\implies 0.7867\pm 0.0927[/tex]

[tex]\implies 78.67\% \pm 9.27\%[/tex]

This result if not given in the list of answer options.  However, the final result depends on the accuracy of the z-score and p-hat used in the calculations.  

If we round the critical value to the nearest integer then:

[tex]\implies z=2[/tex]

Substitute the rounded z-value into the margin of error formula:

[tex]\implies ME=2\cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]

[tex]\implies ME=0.094607180...[/tex]

Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) using z = 2 is:

[tex]\implies 78.67\% \pm 9.46\%[/tex]

Note:  It is likely that this question required the critical value to be rounded to the nearest integer, however please note that this is not normal practice as it produces a different result, as evidenced above.

The value of the expression after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

Option D is true.

What is mathematical expression?

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

Given that;

The expression is;

''The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths.''

Now, We can write the expression in mathematical form as;

⇒ (- 1/8  j + 2/3) - (5/3 j + 9/12)

Solve the expression as;

⇒ - 1/8 j + 2/3 - 5/3 j - 9/12

⇒ - 1/8 j - 5/3 j + 2/3 - 9/12

⇒ j (-1/8 - 5/3) + 2/3 - 3/4

⇒ j (- 3 - 40)/24 + (8 - 9)/12

⇒ j (-43/24) + (- 1/12 )

This can be written as;

''negative 43 over 24 times j plus negative 1 over 12''

Therefore, The value of the expression after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

Option D is true.

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