Translate the English phrase into an algebraic expression: the quotient of y and 5.

Answer:

Step-by-step explanation: 6.140

Answer: 13/12 times 12/4 is the answer

The average balance of the account is $1126.37.

An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Consider the table that shows the balance (in dollars) of a bank account for three months.

Months            Account Balance

1                       $1285.12

2                       $961.36

3                       $1132.63

As we are aware, the following formula for the mean or average of any set of data:

Mean, [tex]\overline X=\frac{\sum X}{n}[/tex]

where,  ∑X is the sum of all the observations in the data and n  is the number of observations in the data

Therefore, the average balance in the account is:

[tex]Average{~}balance=\frac{1285.12+961.36+1132.63}{3}[/tex]

[tex]Average{~}balance=\frac{3379.11}{3}[/tex]

Average balance = $ 1126.37

So, the account's average balance is $1126.37.

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The complete question is mentioned below:

The table shows the balance (in dollars) of a bank account each month for three months. What is the average balance of the account?

Table:

Month 1, account balance: $1285.12

Month 2, account balance: $961.36

Month 3, account balance: $1132.63

The average balance of the account is $1126.37

Average: An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Consider the table that shows the balance (in dollars) of a bank account for three months.

Months            Account Balance

1                       $1285.12

2                       $961.36

3                       $1132.63

As we are aware, the following formula for the mean or average of any

set of data,

Mean,

where,  ∑X is the sum of all the observations in the data and n  is the number of observations in the data

Therefore, the average balance in the account is,

Average balance of the account = $ 1126.37

So, the account's average balance is $1126.37

The complete question is mentioned below,

The table shows the balance (in dollars) of a bank account each month for three months.

Table:

Month 1, account balance: $1285.12

Month 2, account balance: $961.36

Month 3, account balance: $1132.63

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Answer:

£30

Step-by-step explanation:

Elvis is paying for 2/3 of 3 kg, so the cost is:

[tex]\frac{2}{3}(45)=30[/tex]

Answer:

The mean will move to the left as more affordable vehicles are introduced.

Step-by-step explanation:

It is given that a car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next 10 years.

We need to find how will the distribution be affected if he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years.

Now, let us understand what is meant by mean;

What is the Mean ?

The mean of a set of data is its average value.

Further, It is given that the car salesman sells cars with prices ranging from $5,000 to $45,000.

Additionally, the salesperson has noticed that a lot of students are searching for vehicles around $5,000.

If he chooses to sell vehicles as well and anticipates selling 200 of them over the following ten years,

The histogram will deviate from its mean if cards with values less than $5,000 are also included in the data set.

The mean will move to the left as more affordable vehicles are introduced.

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Step-by-step explanation:

The function f was shifted 8 units to the right to obtain g.

Answer:

[tex]\large\text{$y=ke^{\frac{1}{3}x^3+x}$}[/tex]

Step-by-step explanation:

Given differential equation:

[tex]\large\text{$\dfrac{\text{d}y}{\text{d}x}=y(x^2+1)$}[/tex]

Rearrange the equation so that all the terms containing y are on the left side, and all the terms containing x are on the right side:

[tex]\large\text{$\implies \dfrac{1}{y}\;\text{d}y=(x^2+1)\;\text{d}x$}[/tex]

Integrate both sides, remembering to add the constant of integration (C):

[tex]\large\begin{aligned}\implies \displaystyle \int\dfrac{1}{y}\;\text{d}y & =\int(x^2+1)\;\text{d}x\\\ln y & = \dfrac{1}{3}x^3+x+\text{C}\end{aligned}[/tex]

Rewrite C as ln k:

[tex]\large\text{$\implies \ln y = \dfrac{1}{3}x^3+x+\ln k$}[/tex]

Solve for y, applying:

[tex]\large\text{$ \implies e^{\ln y} =e^{\frac{1}{3}x^3+x+\ln k}$}[/tex]

[tex]\large\text{$ \implies y=e^{\ln k} \cdot e^{\frac{1}{3}x^3+x}$}[/tex]

[tex]\large\text{$\implies y=ke^{\frac{1}{3}x^3+x}$}[/tex]

Integration rules

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $\frac{1}{x}$}\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.1 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\\\(where $n$ is any constant value) \end{minipage}}[/tex]

Answer:

[tex]{ \tt{ \frac{dy}{dx} = y( {x}^{2} + 1) }} \\ [/tex]

- Simplify by collecting each term according to its corresponding d

[tex]{ \tt{ \frac{dy}{y} = ( {x}^{2} + 1) \: dx}} \\ [/tex]

- Integrate both sides;

[tex]{ \tt{ \int \frac{1}{y} \: dy = \int ( {x}^{2} + 1) \: dx }} \\ \\ { \tt{ ln(y) = \frac{1}{3} {x}^{3} + x + c }}[/tex]

- To make y the subject, you must remove the natural log;

[tex]{ \tt{ log_{e}(y) = \frac{1}{3} {x}^{3} + x + c }} \\ \\ { \tt{y = {e}^{( \frac{1}{3} {x}^{3} + x + c) } }} \\ [/tex]

Answer:

C. =

Step-by-step explanation:

This is because 18% is 18/100. You could find the answer one of two ways. Divide by two or multiply by 2.

The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?

The side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].

By using geometry we answer this question.

Geometry is nothing but  the branch of mathematics which deals with measurements of shapes.

Here, we take the scale from a playground to this drawing as "a" and The scale from the same playground to another drawing as "b".

First, we see the scale from a playground to this drawing.

[tex]\frac{a}{l}= \frac{1}{5}[/tex]

[tex]l=5a[/tex]

Now we see the scale from the same playground to another drawing.

[tex]\frac{b}{l} =\frac{1}{8}[/tex]

[tex]b=\frac{l}{8}\\[/tex]

Here, l=5a then

[tex]b=\frac{5a}{8}[/tex]

Therefore, the side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].

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Answer:

28.26 inches^2

Step-by-step explanation:

The area of a circle is given by the formula [tex]A = \pi r^2[/tex].
We know that the diameter of the circle is 6 inches, therefore, its radius 3 inches (the radius is exactly one half of the circle's diameter).

Substituting into the formula

[tex]A = \pi r^2 \\ \\\to A = \pi \times 3^2 \\ \\\to A = \pi \times 9 = 28.26[/tex]

The inequality using interval notation are (-7, -4).

An interval is represented on a number line using interval notation.

For the given expression;

-7 < x < -4

As, x > -7; x is not equal to -7.

x < -4; here also x is not equal to -4.

So, the is a condition of open interval where both vales are not taken.

Thus, the intervals are written as; (-7, -4).

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Using proportions, it is found that the cat has to go 9/16 further to reach the gate.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

An entire distance is represented by the proportion of 1 = 100%. The cat has gone 7/16 of the distance, hence the fraction corresponding to the remaining distance that he has to go is given by:

1 - 7/16 = 16/16 - 7/16 = 9/16.

Hence the cat has to go 9/16 further to reach the gate.

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[tex]\displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\hspace{5em}\stackrel{\textit{L'Hopital's rule}}{\lim_{x\to 44}~\cfrac{ ~~ \frac{d}{dx}[\sqrt{x+5}-7] ~~ }{\frac{d}{dx}[x-44]}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{d}{dx}[\sqrt{x+5}-7]\implies \cfrac{1}{2}(x+5)^{-\frac{1}{2}}(1)\implies \cfrac{1}{2\sqrt{x+5}} \\\\\\ \cfrac{d}{dx}[x-44]\implies 1 \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{x\to 44}~\cfrac{\sqrt{x+5}-7}{x-44}\implies \lim_{x\to 44}~\cfrac{ ~~ \frac{1}{2\sqrt{x+5}} ~~ }{1}\implies \lim_{x\to 44}~\cfrac{1}{2\sqrt{x+5}}\implies \cfrac{1}{2\sqrt{44+5}} \\\\\\ \cfrac{1}{2\sqrt{49}}\implies \cfrac{1}{2(7)}\implies \cfrac{1}{14}[/tex]

[tex] \bf\longrightarrow \large\frac{ \frac{ \frac{a( {r}^{4} - 1)}{ \cancel{r - 1}} }{a( {r}^{2} - 1) } }{ \cancel{r - 1}} = 10 \\ [/tex]

[tex]\bf\longrightarrow {r}^{4} - 1 = {10r}^{2} - 10[/tex]

[tex]\bf\longrightarrow {r}^{4} - {10r}^{2} + 9 = 0[/tex]

[tex]\bf\longrightarrow \: {a}^{2} - 10 {a}^{2} + 9 = 0[/tex]

[tex]\bf\longrightarrow \: a = \frac{10± \sqrt{100 - 36} }{2} = \frac{10±8}{2} [/tex]

r = 3 or r = 1 but r ≠ 1

[tex]\therefore[/tex] r = 3

[tex]\bf\longrightarrow \: a_3 = 54 \\ \bf\longrightarrow \: a {r}^{2} = 54 \\ \bf\longrightarrow \: a = \frac{54}{9} = 6[/tex]

The yearly interest rate percentage is 7%

The rate of interest can be found dividing the interest and  the product of the principal and time period which can be written as

R = I / PT

where R is the Rate of interest

          I is the Interest

          P is the Principal amount

          T is the time period.

Given values are

P = $5,875

 I = $1,675

 T = 4 years

Then,

R = I/PT

   = 1,645/(5,875 x 4)

   = 1645 / 23500

   = 0.07

The Yearly interest rate percentage is

 =0.07 x 100

 = 7%

Therefore, the yearly rate percentage is 7%

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Answer:

Step-by-step explanation:

go

After rounding, we can say that there are about 1,140 candles in the 22 packets.

First let's get the exact number, and then round it as we need to do.

We know that each packet contains 52 candles, and there are 22 packets, so the total number of candles is given by the product between these two values, which gives:

C = 52*22 = 1,144 candles.

Now we want to round it to the nearest ten, to do so, we need to look at the digit at the right of the tens unit (in this case the ones digit) and see, if it is 5 or more, we round up, if it is 4 or less, we round down.

We can see that it is a 4, so we round down here:

C = 1,140

There are about 1,140 candles in the 22 packets.

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Answer:

its 4

Step-by-step explanation:

Answer:

y = 2/3x + 9

Step-by-step explanation:

The equation of a line is defined as y = mx + b

with m being the slope, and b being he intercept.

So to figure out the equation for the line with a slope of 2/3 and an intercept of 9, we can just plug those values into our line equation!

So take y = (slope)*x + *(intercept)

and plug your values in and you get...

y = 2/3 * x + 9

Answer: the answers for the quiz are

1. What is the slope (rate of change) of the line in the graph show below? Answer is A. -2

2. Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1). Answer is D. 4/3

3. constant of variation of -4y=8x  answer is B. -2

4 the value of y when x=10 answer is B. 30

5. the equation for the line with slope 2/3 and y-intercept 9 answer is C. y=2/3x+9

6 is the equation in slope intercept form for the line that passes through the points (1, -3) and (3, 1) answer is D. y=2x-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

                           [tex]\displaystyle\\\boxed {M_{AB}=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2} ) }[/tex]

1) E(-5,-3)      F(3,7)      M(x,y)=?

[tex]\displaystyle\\M(x,y)=(\frac{-5+3}{2} ),\frac{-3+7}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{4}{2} )\\\\ M(x,y)=(-1,2)\\\\Thus, \ M(-1,2)[/tex]

2) L(-8,11)     N(-3,12)      M(x,y)=?

[tex]\displaystyle\\M(x,y)=(\frac{-8+(-3)}{2} ,\frac{11+12}{2} )\\\\M(x,y)=(\frac{-11}{2},\frac{23}{2})\\\\ M(x,y)= (-5.5,11.5)\\\\Thus, M(-5.5,11.5)[/tex]

3) A(-4,6)    B(2,4)    M(x,y)=?

[tex]\displaystyle\\M(x,y)=(\frac{-4+2}{2},\frac{6+4}{2})\\\\ M(x,y)=(\frac{-2}{2},\frac{10}{2})\\\\ M(x,y)=(-1,5)\\\\ Thus,\ M(-1,5)[/tex]

Answer:

only D is negative on the leading term

Step-by-step explanation:

even roots bounce at (0,0)

negative leading coefficient: initial graph descending to right, curve up

4 local extremes means remaining 5 degree of the function

Step-by-step explanation:

when a line intersects with 2 (or more) parallel lines, the angles at the intersection points are the same for each parallel line.

therefore,

5 + 10x = 85

10x = 80

x = 8

so, B is the right answer option.

Answer:

6.  ∠PVU = 58°

7.  y = 74°

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ ∠USP + ∠PSV = 180°

⇒ 148° + ∠PSV = 180°

⇒ 148° + ∠PSV - 148° = 180° - 148°

⇒ ∠PSV = 32°

The interior angle of a rectangle at each vertex is 90°.

⇒ ∠VPS = 90°

Interior angles of a triangle sum to 180°.

⇒ ∠PVS + ∠PSV+ ∠VPS = 180°

⇒ ∠PVS + 32° + 90° = 180°

⇒ ∠PVS + 122° = 180°

⇒ ∠PVS + 122° - 122° = 180° - 122°

⇒ ∠PVS = 58°

From inspection of the given diagram:

⇒ ∠PVU = ∠PVS

⇒ ∠PVU = 58°

Opposites sides of a rectangle are parallel.

Therefore, GF is parallel to AB:

⇒ ∠CFG = ∠CBA = 32°

Interior angles of a triangle sum to 180°.

⇒ ∠FGC + ∠GCF + ∠CFG = 180°

⇒ y + 74° + 32° = 180°

⇒ y + 106° = 180°

⇒ y + 106° - 106° = 180° - 106°

⇒ y = 74°

Every point in the interval [2, 6] has an equal probability of occurring, 1/(6 - 2) = 1/4. So the PDF of X is

[tex]f_X(x) = \begin{cases} \frac14 & \text{if } 2 \le x \le 6 \\ 0 & \text{otherwise} \end{cases}[/tex]

Compute the CDF by integrating the PDF.

• If [tex]x<2[/tex], we have

[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^x 0 \, dt = 0[/tex]

• If [tex]2\le x< 6[/tex], we have

[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^x \frac{dt}4 \\\\ ~~~~~~~~~~~~~~~~~ = 0 + \frac14 \int_2^x \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \frac{x-2}4[/tex]

• If [tex]x\ge6[/tex], we have

[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^6 f_X(t) \, dt + \int_6^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^6 \frac{dt}4 + \int_6^x 0 \, dt \\\\ ~~~~~~~~~~~~~~~~~ = 0 + 1 + 0 \\\\ ~~~~~~~~~~~~~~~~~ = 1[/tex]

Putting the pieces together, we find the CDF to be

[tex]\boxed{F_X(x) = \begin{cases} 0 & \text{if } x < 2 \\\\ \dfrac{x-2}4 & \text{if } 2\le x < 6 \\\\ 1 & \text{if } x\ge6 \end{cases}}[/tex]

Compute the expectation of X.

[tex]\Bbb E[X] = \displaystyle \int_{-\infty}^\infty x\,f_X(x)\,dx \\\\ ~~~~~~~ = \int_{-\infty}^2 0 \, dx + \int_2^6 \frac x4 \, dx + \int_6^\infty 0 \, dx \\\\ ~~~~~~~ = 0 + \frac{6^2 - 2^2}8 + 0 \\\\ ~~~~~~~ = \boxed{4}[/tex]

Answer:

2, 4 6, 8

Step-by-step explanation:

The counting numbers are the set of numbers: 1,2,3,4,... It follows that pattern forever.  No, 1/2 or .0745.

Answer:

2 4 6 8 is the answer for your question

The value of the given functions are:

(i) f + g = x² + x - 6

(ii) f - g = -x² + x - 4

(iii) f . g = x³ - 5x² - x + 5

(iv) f/g = ( x - 5)/(x +1)(x - 1)

(v) g(f(x)) = x² - 10x + 24

The two functions are given that

f(x) = x - 5

g(x) = x² - 1

We have to find

(i) f + g

f(x) + g(x) = ( x-5)  + (x² - 1)

                = x² + x -5 -1

               = x² + x -6

(ii) f - g

f(x) - g(x) = (x-5)- (x² - 1)

              = -x² + x -5 +1

              = -x² + x -4

(iii) f . g

f(x) . g(x) = (x-5)(x²-1)

              =x(x² - 1) -5(x² - 1)

              = x³ - x - 5x² + 5

              = x³ - 5x² - x + 5

(iv) f/g

f(x) / g(x) = (x-5) / ( x² - 1)

              = (x - 5) / (x+1)(x-1)

(v) g(f(x)) = - 1 + ( -5 + x )²

              = -1 + 25 + x² - 10x

              = x² - 10x + 24

Therefore we get the value of the function, (i) f + g = x² + x - 6, (ii) f - g = -x² + x - 4,(iii) f . g = x³ - 5x² - x + 5, (iv)f/g = ( x - 5)/(x +1)(x - 1), (v) g(f(x)) = x² - 10x + 24.

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The complete question is:

F(x)=x-5 and g(x)=x2 - 1 find (i) f + g , (ii) f-g, (iii) f. g (iv) f/g (v) g(f(x)).