Part A) What is the cost of 14.6 gallons of gasoline at $2.70 per gallon? Part B) Explain the steps you would take to solve this problem.

Answer:

x(6 + 8x²) or 6x + 8x³.

Step-by-step explanation:

"The square of x" can be represented by x² and 8 times that would be 8 * x² or 8x². The sum of 6 and 8x² can be represented by 6 + x² and the product of x and 6 + x² can be represented by x * (6 + 8x²) or x(6 + 8x²) which simplifies to 6x + 8x³.

Answer:

14x * x^2

Step-by-step explanation:

So you just have to read very carefully on these questions.

the product of x and the sum of 6 and 8

x times 6+8= x times 14= 14x

Product= multiply

Sum= add

that answer times the square of x

x^2

=14x times x^2

Answer:

142

Step-by-step explanation

Answer:

[tex]\huge \boxed{\mathrm{10.3 \ units}}[/tex]

Step-by-step explanation:

To solve for CD, we can create a right triangle.

Where CD becomes the hypotenuse.

The length of the base of the triangle is 9 units.

The length of the height of the triangle is 5 units.

Apply Pythagorean theorem to solve for the hypotenuse.

[tex]\sf hypotenuse = \sqrt{(base )^2 +(height )^2 }[/tex]

[tex]c=\sqrt{9^2 +5^2 }[/tex]

[tex]c=\sqrt{106}[/tex]

[tex]c \approx 10.29[/tex]

Step-by-step explanation:

[tex]15( \frac{11\pi}{6} ) \\ 15 \div 3 = 5 \\ 6 \div 3 = 2 \\ = 5( \frac{11\pi}{2} )[/tex]

[tex]11 \times 5 \\ = \frac{55\pi}{2} [/tex]

Answer: C. The size of a business is​ ordinal-scaled because it has values that can be used as an order or rank of a categorical variable.

Step-by-step explanation: Ordinal variables are simply categorical in nature just like nominal variables, however, the difference exists in the fact that ordinal labels posses an ordered rank or level unlike nominal variables. Though the extent or width of the difference between these labels cannot be ascertained. In the scenario above, size of businesses are labeled qualitatively with labels such as : small, medium and large. This labels depicts and follow a certain order with small being the least, then medium, then large. Telling us large businesses are superior in size to small and medium and medium is superior to large. Though the extent of the difference cannot be accurately ascertained.

Answer:

{3x-2}+4=10

Step-by-step explanation:

Answer:

There is no sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

We are given;

n = 27 bags

Sample mean;X = 402 gram

Population mean;μ = 404 gram

Variance = 676

We know that, standard deviation(σ) = √variance

Thus;

σ = √676

σ = 26

The hypotheses are;

Null hypothesis; H0: μ = 404

Alternative hypothesis; HA: μ < 404

Let's find the z-score from the formula;

z = (X - μ)/(√σ/n)

z = (402 - 404)/√(26/27)

z = -2.04

From the z-distribution table attached, we have a p-value of 0.02068

This is less than the significance value of 0.01 and thus we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled

Answer:

I believe the answer is 4,000 times larger.

Step-by-step explanation:

8*10⁷ = 80000000

2*10⁴ = 20000

20000*4000 = 80000000

Answer:

The rectangle has a width of 4 and a height of 8

Step-by-step explanation:

Let the height of the rectangle be H and the width be W.

We know the height of the rectangle is twice the width, so:

H = 2W

The area of a rectangle, A, is given by A = W * H, so in this case:

32 = W * 2W

32 = 2W²

W² = 16

W = 4

Knowing that the width is 4, the height must be 8. This gives us an area of 32.

Answer:

Twelve tickets cost $30 --> True

Thirty tickets cost $12 --> False

Each additional costs $2.50 --> True

The table is a partial rep --> True

ordered pairs --> False

Step-by-step explanation:

Twelve tickets cost $30 --> True, you can literally see that in the table

Thirty tickets cost $12 --> False, 30 is not in the table so you don't have that information. Besides, $12 is an unlikely low value for so many tickets.

Each additional costs $2.50 --> True, you can see the difference in the TotalCost column to be consistently 2.50.

The table is a partial rep --> True, values below 11 are not shown for example.

ordered pairs --> False --> Then the x value should be first, e.g., (11, 27.50), since the cost y is a function of the number x.

Answer:

144 square inches.

Step-by-step explanation:

4*12*3=144

Answer:

[tex]Length = \frac{64}{3}m[/tex]

[tex]Width= \frac{32}{3}m[/tex]

Step-by-step explanation:

Given

[tex]Perimeter = 64m[/tex]

[tex]Length = 2 * Width[/tex]

Required

Determine the length and the width

Since the alley is rectangular, the perimeter is as follows;

[tex]Perimeter = 2 (Length * Width)[/tex]

Substitute 64m for Perimeter

[tex]64m = 2(Length + Width)[/tex]

Substitute 2 * Width for Length

[tex]64m = 2(Width+ 2 * Width)[/tex]

[tex]64m = 2(Width+ 2 Width)[/tex]

[tex]64m = 2(3 Width)[/tex]

[tex]64m = 6Width[/tex]

Divide both sides by 6

[tex]Width= \frac{64m}{6}[/tex]

[tex]Width= \frac{32}{3}m[/tex]

Recall that

[tex]Length = 2 * Width[/tex]

[tex]Length = 2 * \frac{32}{3}m[/tex]

[tex]Length = \frac{64}{3}m[/tex]

Answer:

The third option: (f°g)(x)=1.07(0.65x)=06955x

Step-by-step explanation:

The reason I chose this is because 0.65x is the discount price.  That's because 35% off is the same as 1.00-0.35 which equals 0.65.  After that you would multiply that discount price by 1.07 because you want the 7% sales tax added on to the discount price.  Therefore, I would choose the third option as my answer.

Answer:

y = In | cos(2x + c ) | + c

Step-by-step explanation:

y" + (y')^2 + 4 = 0

substituting u = y'

u' + u^2 + 4 = 0

hence : u' = - (u^2 + 4 )

       [tex]\frac{u'}{-(u^2 + 4)}[/tex] = 1 ------- (1)

integrating both sides of the equation 1

[tex]1/2 \int\limits^1_1 {\frac{2du}{(u^2+4)} } \, = x + c[/tex]

x + c = [tex]- \frac{1}{2} arc tan (\frac{u}{2} )[/tex]   hence  u = -2 tan(2x + c )

remember u = y'

y' = -2 tan(2x + c) ------ (2)

integrating both sides of the equation 2

y = ∫ [tex]\frac{-sin u}{cos u } du[/tex]

therefore Y = In | cosu | + c

 y = In | cos(2x + c ) | + c

Answer:

a) $4720

b) $5569.60

Step-by-step explanation:

Initial amount = $4000

Interest rate = 18% PA compounded

Amount after 1 year

Amount after 2 years

Answer:

In 4 hours.

Step-by-step explanation:

Just equate f(x) = g(x). So:

15x + 90 = 30x + 30

60 = 15x

x = 4 hours.

In 4 hours the amount of candy produced be the same for both machines.

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that A candy factory wants to compare a new machine to their current machine. Both machines produce y boxes of candy for every hour x. The current machine is represented by the equation f(x). The new machine is represented by the equation g(x). f(x) = 15x + 90 g(x) = 30x + 30.

The value of time will be calculated below:-

Just equate f(x) = g(x).

15x + 90 = 30x + 30

60 = 15x

x = 4 hours.

Therefore, In 4 hours the amount of candy produced is the same for both machines.

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A cluster is a small group of dots close together. An outlier is a single dot far away from the rest of the dots.

The above graph has a small cluster around y 6&7 and has an outlier at (9,5)

The answer should be D.

Answer:

The correct answer is D. This scatter plot has one cluster and one outlier.

Step-by-step explanation:

From looking at the scatterplot, the majority of the points are collected on the upper left side of the coordinate grid, creating a cluster.  This just means that these data points are located close to one another.

If we continue to look at the scatterplot, we can see that there is one data point at approximately (9, 5.25) that is very far from the other data points.  This point is considered to be an outlier because it does not follow the general trend of the other data points and changes the data analysis significantly if included in the calculations.

Hope this helped!

Answer:

13

Step-by-step explanation:

if y = 4, then 4 + 9 = 13

Answer:

[tex]\huge\boxed{13}[/tex]

Step-by-step explanation:

The given condition is:

=> y + 9

Given that y = 4

=> 4 + 9

=> 13

Answer:

Step-by-step explanation:

First we must understand that absolute value of a function returns both positive and negative function.

1) Given |x-6| = 5

For the positive value of the function:

x-6 = 5

Add 6 to both sides

x-6+6 = 5+6

x = 11

For the negative function:

-(x-6) = 5

Open the parentheses

-x+6 = 5

Subtract 6 from both sides

-x+6-6 = 5-6

-x = -1

x = 1

Hence x = 1, x = 11

2 ) Given |3x-7| = 12

For the positive value of the function:

3x-7 = 12

Add 7 to both sides

3x-7+7 = 12+7

3x = 19

x = 19/3

For the negative function:

-(3x-7) = 12

Open the parentheses

-3x+7 = 12

Subtract 7 from both sides

-3x+7-7 = 12-7

-3x = 5

x = -5/3

Hence x = 19/3, x = -5/3

3) Given |2x+9| - 10= 5

For the positive value of the function:

2x+9-10= 5

2x-1 = 5

Add 1 to both sides

2x-1+1 = 5+1

2x = 6

x= 3

For the negative function:

-(2x+9)-10 = 5

Open the parentheses

-2x-9-10 = 5

-2x-19 = 5

Add 19 to both sides

-2x-19+19 = 5+19

-2x= 24

x = -24/2

x= -12

Hence x = 3, x = -12

4) ) Given |5x-3|+12 = 4

For the positive value of the function:

5x-3+12= 4

5x+9 = 4

Subtract 9 from both sides

5x+9-9 = 4-9

5x = -5

x= -1

For the negative function:

-(5x-3)+12= 4

Open the parentheses

-5x+3+12 =4

-5x+15 = 4

Subtract 15 from both sides

-5x+15-15 = 4-15

-5x = -11

x = 11/5

Hence x = -1, x = 11/5

Answer:

I think it would be 8 and 1/3 inches long

Step-by-step explanation:

P.S. You spelled inches wrong

The circumference of a circle, which is another way of saying the perimeter of a circle, can be found using the formula 2πr.

Note that π represents the irrational number 3.14159... which

rounds to 3.14 and r represents the radius of the circle.

Therefore, since π = 3.14, another way of writing the formula

for the circumference of a circle is 2 · 3.14r or 6.28r.

Answer:

circumference = 2 π r

or

circumference = π d

Step-by-step explanation:

r = radius of a circle

d = diameter

therefore

circumference = 2 π r

or

circumference = π d

Answer:

(-4, 3)

Step-by-step explanation:

From the graph, it looks like the two lines intersect at pint (-4, 3).

Answer:

it is 3/3

Step-by-step explanation:

2 tan is 2/3 +cos is  1/4 +2/4

Answer:

[tex]Range=\left \{y|y\geq 5\right \}[/tex]

Step-by-step explanation:

Since given the expression, this represents graphically a parabola with arms pointing up, and a vertical translation of its vertex 5 units up, then the range of the function must be all the y values such that they are greater or equal to 5. This is written as:

[tex]Range=\left \{y|y\geq 5\right \}[/tex]

Answer:

z > -5/2

Step-by-step explanation:

Since both sides are divided by a negative number, the equality is switched.

10 - 4z < 20

(10 - 4z) - 10 < 20 - 10

-4z < 10

(-4z)/-4 < 10/-4

z > -5/2

The solution for z will be;

⇒ z ∈ (- 2.5 , ∞ )

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 10 - 4z < 20

Now,

Since, The inequality is,

⇒ 10 - 4z < 20

Solve for z as;

⇒ 10 - 4z < 20

⇒ 10 - 4z + 4z < 20 + 4z

⇒ 10 < 20 + 4z

⇒ 10 - 20 < 4z

⇒ - 10 < 4z

⇒ - 2.5 < z

⇒ z ∈ (- 2.5 , ∞ )

Thus, The interval notation is,

⇒ z ∈ (- 2.5 , ∞ )

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Answer:  7/12 + 2/3q

Step-by-step explanation:

[tex]\frac{11}{12} - \frac{1}{6}q + \frac{5}{6}q - \frac{1}{3}[/tex]     Combine like terms  subtract 1/3 from 11/12 and add -1/6q and 5/6q.

[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]  

[tex]-\frac{1}{6}q + \frac{5}{6} q = \frac{4}{6}[/tex]q = 2/3 q

Answer: (31.75%, 36.25%)

Step-by-step explanation:

Let p be the proportion of workers in this city who have full health insurance coverage.

As per given,

Sample size : n= 170

Number of workers who had full health insurance coverage.=578

i.e. sample proportion: [tex]\hat{p}=\dfrac{578}{1700}\approx0.34[/tex]

Also, z-score for 95% confidence level : 1.96

Formula to find the confidence interval for p :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]0.34\pm (1.96)\sqrt{\dfrac{0.34(1-0.34)}{1700}}[/tex]

[tex]=0.34\pm (1.96)\sqrt{0.000132}\\\\=0.34\pm (1.96)(0.011489125)\\\\\approx 0.34\pm0.0225\\\\=(0.34-0.0225,\ 0.34+0.0225)\\\\=(0.3175,\ 0.3625) =(31.75\%,\ 36.25\%)[/tex]

Hence, a 95% confidence interval for the true percent of workers in this city who have full health insurance coverage= (31.75%, 36.25%)

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]\displaystyle f'(0)=\lim_{x\rightarrow0} {\dfrac{f(x)-f(0)}{x-0}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1}{x}-k}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\dfrac{\sqrt{1+x}-1-kx}{x}}{x}}\\\\=\lim_{x\rightarrow0} {\dfrac{\sqrt{1+x}-1-kx}{x^2}}\\[/tex]

Thank you

Answer:

c. 134,847

Step-by-step explanation:

82,000 x (1.051)^10 = 82,000 x 1.64447456 = 134,847