I’ll mark Brainlyist to the correct answer

Rewrite 8 log3 x^7 in a form that does not use exponents.
8log3 x^7 = ( )log3 x

Answer:

[tex] P(X=3)[/tex]

And we can use the probability mass function and we got:

[tex]P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091[/tex]

Then the probability that all three have a smart phone is 0.091

Step-by-step explanation:

Let X the random variable of interest "number of students with smartphone", on this case we now that:

[tex]X \sim Binom(n=3, p=0452)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X=3)[/tex]

And we can use the probability mass function and we got:

[tex]P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091[/tex]

Then the probability that all three have a smart phone is 0.091

Answer:

[See Below]

Step-by-step explanation:

Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]

'm' is the slope

(x1, y1) is a coordinate point.

Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points (-1,5) and (3,-3).

[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]

The slope of the line is -2.

I will use (-1,5) as the point:

[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]

Slope intercept is: [tex]y=mx+b[/tex]

'm' - Slope

'b' - y-intercept

We can use the point slope equation to convert it into slope intercept form:

[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]

Standard form is [tex]Ax+By=C[/tex]

Using out slope intercept form equation:

[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]

Complete Question:

A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.

Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.

(a) Find the interest that will be owed after 4 months

(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months

Answer:

a) Interest that will be owed after 4 months , I = $131.48

b) Amount owed by the restaurant after 4 months = $16231.48

Step-by-step explanation:

Note that the question instructs not to round any intermediate computations except the final answer.

Annual rate = 2.45%

Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]

R = 0.20416666666%

Time, T = 4 months

Interest, [tex]I = \frac{PRT}{100}[/tex]

[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]

b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)

Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)

Amount owed by the restaurant after 4 months = 16100 + 131.48

Amount owed by the restaurant after 4 months = $16231.48

Answer:

[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|[/tex]

Step-by-step explanation:

Cost of a bowl of salad = $5.00

Cost of a slice of pizza = $2.00

If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation:

Next, we make P the subject of the equation above.

2P=E-5S

[tex]P=\dfrac{E-5S}{2} \\P=0.5(E-5S)[/tex]

Therefore, The quantity of pizza he buys can be represented by the equation:

When E=$40, we are required to complete the table below.

[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&\\40.00&4&\\40.00&&0\end{array}\right|[/tex]

When S=0, E=$40

From P=0.5(E-5S)

P=0.5(40-5(0))=20

When S=4, E=$40

P=0.5(40-5(4))

=0.5(40-20)

=0.5*20

=10

When P=0, E=$40

P=0.5(E-5S)

0=0.5(40-5S)

40-5S=0

5S=40

S=8

Therefore, the completed table is:

[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|[/tex]

[tex]9+(-2)\\9-2\\=7[/tex]

[tex]-6+(-3)\\-6-3\\=-9[/tex]

[tex]4+(-9)\\4-9\\=-5[/tex]

Answer:

see below

Step-by-step explanation:

9 + -2 =

9 -2 = 7

-6 + -3

-6 - 3 =-9

4 + - 9

-9 +4 = -5

Answer:

[tex]-15.11[/tex]

Step-by-step explanation:

[tex]-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11[/tex]

Answer:

-15.11

Step-by-step explanation:

-12.48+2.99-5.62=

-9.49 - 5.62= - (9.49+5.62)=-15.11

Answer:

The probability that applicants would you expect to have scores of 600 or above = 0.0401 or 4%

Step-by-step explanation:

Explanation:-

Let "x" Scores are normally distributed

Given  mean of the Population = 460

standard deviation of the population = 80

Let X = 600

[tex]Z = \frac{x -mean}{S.D} = \frac{600-460}{80} =1.75[/tex]

The probability that applicants would you expect to have scores of 600 or above

P( X≥600) = P( Z≥ 1.75)

                = 1- P( Z≤1.75)

               = 1- ( 0.5 + A(1.75)

              =  1- 0.5 - A(1.75)

              = 0.5 - 0.4599 (from Normal table)

              = 0.0401

The probability that applicants would you expect to have scores of 600 or above = 0.0401 or 4%

Answer:

[tex]x\le \:9[/tex]

Step-by-step explanation:

[tex]5x\le 45[/tex]

[tex]\frac{5x}{5}\le \frac{45}{5}[/tex]

[tex]x\le \:9[/tex]

Answer:

B

Step-by-step explanation:

We divide the entire inequality by 5 to get rid of the coefficient of x. The ≤ stays the same so we get x ≤ 9.

Answer:

Volume: 1080

Surface area: 654

Step-by-step explanation:

Part A:

How to solve surface Area: 2×(9×15 + 9×8 + 15×8)

How to solve volume: 9x15x8

Part B:

Surface Area

Part C:

Volume

Hope this helps

Answer:

A. [tex](2b+7)^2[/tex]

Step-by-step explanation:

[tex]4b^2 +28b + 49\\=(2b)^2 + 2\times 2b\times 7 + (7)^2\\=(2b+7)^2[/tex]

Answer:

[tex]1\ inch = 2\ feet[/tex]

Step-by-step explanation:

Given:

[tex]Real\ tank\ measurement\ = 24\ feet[/tex]

[tex]Scale\ measurement\ = 12\ inches[/tex]

Required:

Scale Ratio.

To get the scale ratio, we simply divide the actual measurement by the scale measurement

This is done as follows:

[tex]Scale\ Ratio = \frac{Actual\ Measurement}{Scale\ Measurement}[/tex]

[tex]Scale\ Ratio\ = \frac{24\ feet}{12\ inches}[/tex]

[Divide numerator and denominator by 12]

[tex]Scale\ Ratio\ = \frac{2\ feet}{1\ inch}[/tex]

[Convert the above expression to ratio]

[tex]Scale\ Ratio = 2\ feet : 1\ inch[/tex]

The interpretation of this is that 1 inch on the scale measurement represent 2 feet on the actual measurements

Answer:

Step-by-step explanation:

The amount Lila and Wassim plan to save is ...

  (£13 +13)(9) = £234

__

The charges they expect to incur are a per-person charge and a tent pitch charge. Since they expect to stay 10 nights, the special rate means they will only be charged for 8 nights.

per-person charge

  per-person-per-night charge = (2 persons)(8 nights)(£6 per person-night)

  = £96

tent pitch charge

To determine the tent pitch area required, we need to find the area of the tent:

  A = LW = (4.2 m)(2.3 m) = 9.66 m²

This is less than 10 square meters, so we can expect the pitch charge to be £15 per night for 8 nights.

  tent pitch charge = (£15/night)(8 nights) = £120

So, the total of camp site charges is expected to be ...

  person charge + pitch charge = £96 +120 = £216

__

The expected savings exceeds the expected charges by ...

  £234 -216 = £18

Lila and Wassim will have enough saved, with £18 extra.

Answer:

(fog)(x) means that we have the function f(x) evaluated in the function g(x), or f(g(x)).

So, if f(x) = x^3 + 1 and g(x) = x - 2.

we have:

a) (fog)(0) = f(g(0)) = (0 - 2)^3 + 1 = -8 + 1 = -7

b) (gof)(0) = g(f(0)) = (0^3 + 1) - 2 = -1

c)  (fof)(1) = f(f(1)) = (1^3 + 1)^3 + 1 = 2^3 + 1 = 8 + 1 = 9

d) (gog)(1) = g(g(1)) = (1 - 2) - 2 = -1 -2 = -3

Answer:

A: x= -1 or x=3

B: Since the quadratic equation has two real solutions, the graph of the quadratic equation intercepts the x axis at (-1,0) and (3,0)

Step-by-step explanation:

x^2 -2x -3 =0

Factor

(x-3 )(x+1) =0

Using the zero product property

x-3 =0   x+1 =0

x=3  x=-1

The zeros are

(3,0) (-1,0)

It intersects the x axis at (3,0) (-1,0)

Answer:

The price per ounce should have been 1.25 per ounce

Step-by-step explanation:

The price per ounce should have been 1.25 per ounce

-google

(found it online)

XD - don't delete/report!

Answer:

1.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

its b on edge

Step-by-step explanation:

Answer: D. [tex]y+4=(x+2)[/tex]

Step-by-step explanation: Once you subtract [tex]4[/tex] from both sides, in order to solve for y (as the equation needs to be in the slope-intercept form, otherwise known as [tex]y=mx+b[/tex]), you end up with [tex]y=x-2[/tex], which is the right answer. It is the correct answer because the y-intecept shown in the equation matches what is on the graph, in addition to the fact that the slope is just [tex]x[/tex].

Answer:

[tex]0 \leq P( P_B) \leq 1[/tex]

[tex]P(P_B) = 0.17[/tex]

Step-by-step explanation:

From the given question:

The probabilities are assigned using the Subjective method.

Let the probability that his roommate will choose rock be  [tex]P(R_B) = 0.28[/tex]

Let the probability that his roommate will choose scissors be [tex]P(S_B) = 0.55[/tex]

∴

[tex]P(R_B) + P(S_B) +P(P_B) = 1[/tex]

[tex]0.28+ 0.55 + P(P_B) =1[/tex]

[tex]0.83 + P(P_B) = 1[/tex]

[tex]P(P_B) = 1 - 0.83[/tex]

[tex]P(P_B) = 1 -0.83[/tex]

[tex]P(P_B) = 0.17[/tex]

So;

[tex]0 \leq P( P_B) \leq 1[/tex]

[tex]P(P_B) = 0.17[/tex]

Answer:

Step-by-step explanation:

a) H0: μ = 10

Ha: μ ≠ 10

This is a two tailed test

n = 13

Since α = 0.01, the critical value is determined from the t distribution table. Recall that this is a two tailed test. Therefore, we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

The critical value is 3.012

The rejection region is area > 3.012

b) Ha: μ > 10

This is a right tailed test

n = 23

α = 0.1

We would reject the null hypothesis if the test statistic is greater than the table value of 1 - α

1 - α = 1 - 0.1 = 0.9

The critical value is 1.319

The rejection region is area > 1.319

c) Ha: μ > 10

This is a right tailed test

n = 99

α = 0.05

We would reject the null hypothesis if the test statistic is greater than the table value of 1 - α

1 - α = 1 - 0.05 = 0.95

The critical value is 1.66

The rejection region is area > 1.66

d) Ha: μ < 10

This is a left tailed test

n = 11

α = 0.1

We would reject the null hypothesis if the test statistic is lesser than the table value of 1 - α

1 - α = 1 - 0.1 = 0.9

The critical value is 1.363

The rejection region is area < 1.363

e) H0: μ = 10

Ha: μ ≠ 10

This is a two tailed test

n = 20

Since α = 0.05, we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

The critical value is 2.086

The rejection region is area > 2.086

f) Ha: μ < 10

This is a left tailed test

n = 77

α = 0.01

We would reject the null hypothesis if the test statistic is lesser than the table value of 1 - α

1 - α = 1 - 0.01 = 0.99

The critical value is 2.376

The rejection region is area < 2.376

Answer:

130 women

Step-by-step explanation:

First set up a system of equations:

1.23W+2.50M=365.00

W+M=211

Using substitution you get:

1.25W+2.50(211-W)=365.00

Simplify:

-1.25W=-162.5

Divide:

W=130

Answer:

$23.64

Step-by-step explanation:

Each package of seeds cost $1.97, and Maire bought and planted 12 packages. You would do 12 x 1.97 to get 23.64

Answer:

$23.64

Step-by-step explanation:

$1.97 × 12

$23.64

Hope this helps...

Answer:

10 2/3π or 33.51

Step-by-step explanation:

the volume of a sphere is 4/3πr^3

if the sphere has a diameter of 4 the radius is half the diameter so it would be 2. 2^3 = 8 now multiply 8 by 4/3 to get 10 2/3. now multiply by pi to get 10 2/3 π or 33.5103 which rounds to 33.51

Answer:

32π/3 cubic cm

Step-by-step explanation:

Answer: £625,000

Step-by-step explanation:

Previous year's profit can be calculated as:

700000 / 1.12 = 625000

The profit that should make a year before should be  £625,000.

Given that

So the profit that should make a year before should be

[tex]= \frac{700,000}{(1 + 0.12)} \\\\= \frac{700,000}{(1.12)}[/tex]

=  £625,000

Therefore we can conclude that The profit that should make a year before should be  £625,000.

Learn more about the profit here: brainly.com/question/9281343

Answer:

980 intervals.

Step-by-step explanation:

For each interval, there are only two possible outcomes. Either it captures the population mean, or it does not. One interval is independent of other intervals. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

98% confidence interval

Has a 98% probability of capturing the population mean, so [tex]p = 0.98[/tex]

1000 intervals

This means that [tex]n = 1000[/tex]

How many of these 1000 intervals do you expect to capture the corresponding value of μ?

[tex]E(X) = np = 1000*0.98 = 980[/tex]

980 intervals.

Answer:

C. 7.5

Step-by-step explanation:

I took the quiz on EDGE

If the first term of the sequence is 120, then f(5) will be 7.5

The steps are as follow:

So if the first term of the sequence is 120, then f(5) will be 7.5

Learn more about recursively sequence here:

https://brainly.com/question/1275192

#SPJ2

Answer:

(7,-1)

Step-by-step explanation:

common rule for reflections across the origin; im guessing you meant a reflection across the line y=x since it goes through the origin too.

for this make sure to add this transformation:

(x,y) --> (-x,-y)

Answer:

Dataset A

We have the following results:

[tex] \bar X_A = 359.786[/tex]

[tex]s_A= 60.904[/tex]

[tex] CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2[/tex]

Dataset B

We have the following results:

[tex] \bar X_B = 1.791[/tex]

[tex]s_B= 0.635[/tex]

[tex] CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4[/tex]

Step-by-step explanation:

For this case we have the following info given:

A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312

B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41

We need to remember that the coeffcient of variation is given by this formula:

[tex] CV= \frac{s}{\bar X}[/tex]

Where the sample mean is given by:

[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]

And the sample deviation given by:

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

Dataset A

We have the following results:

[tex] \bar X_A = 359.786[/tex]

[tex]s_A= 60.904[/tex]

[tex] CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2[/tex]

Dataset B

We have the following results:

[tex] \bar X_B = 1.791[/tex]

[tex]s_B= 0.635[/tex]

[tex] CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4[/tex]

Answer:

(D)0.9836

Step-by-step explanation:

There are 365 days in a year.

Since each person has a different birthday:

Therefore,

P(4 randomly selected people all have different birthdays)

[tex]=\dfrac{365}{365} \times \dfrac{364}{365} \times \dfrac{363}{365} \times \dfrac{362}{365}\\\\=0.9836[/tex]

Answer:

Substitute the given value into the function and evaluate:

f(x)=6x

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Answer:

f(-11/5) = -5

Step-by-step explanation:

f(n) = 5n + 6

Let x = -11/5

f(-11/5) = 5*-11/5 +6

          = -11 +6

           = -5