A bank compares two proposals to increase the amount that its credit card customers charge on their cards. (The bank earns a percentage of the amount charged, paid by the stores that accept the card). Proposal A offers to eliminate the annual fee for customers who charge $2,400 or more during the year. Proposal B offers a small percent of the total amount charged as a cash rebate at the end of the year. The bank offers each proposal to an SRS of 150 of its existing credit card customers. At the end of the year, the total amount charged by each customer is recorded. Here are the summary statistics:
Group n x s
A 150 $1,987 $392
B 150 $2,056 $413
A) Do the data show a significant difference between the mean amounts charged by customers offered the two plans?
B) The distributions of amounts charged are skewed to the right, but outliers are prevented by the limits that the bank imposes on credit balances. Do you think that skewness threatens the validity of the test? Explain.

Answer:

k = -0.1

Step-by-step explanation:

An ordered pair is in the form (x,y)  We can use the x and y from the point (-30,3) to find k

y = kx  We will replace x with -30 and y with 3

3 = (-30)k  divide both sides by -30

-0.1 = k  or \(\frac{-1}{10}\) in the fraction form

Answer:

1.8

Step-by-step explanation:

The value of f(x)=2x is -4 times the value of function f(x)=-0.5x.

Given two functions f(x)=-0.5x and f(x)=2x.

We are required to find a way how to form f(x)=-0.5x to f(x)=2x.

Function is like the relationship between two or more variables that are expressed in equal to form. The values that we are entering in the function are known as part of domain and the values that we get from the function are known as part of codomain or range of the function.

f(x)=-0.5x

Multiply the function by -4.

f(x)=-4*(0.5x)

=2x

Hence the value of f(x)=2x is -4 times the value of function f(x)=-0.5x.

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Answer: -65

Step-by-step explanation:

g(-6) = -6 - 61 + 2 = -65

Step-by-step explanation:

you are missing out on the second bracket but;

to solve this; substitute -6 in for x

g(-6) = -6 - 61 + 2

= -65

Answer: 5,211 dollars

Step-by-step explanation: Our first approch to this is to find the number of Gala and Honeycrisp(HC) Trees are there.

We are given the number of total trees (81 trees) and the ratio between Gala and HC trees  (5 to 4). This means for every set of 9 trees, 5 will be Gala and 4 will be HC. We can create the equation

9x = 81

5x = number of gala trees

4x = number of HC trees

x represents the number of sets of 9 trees so in this case, there will be 9 sets if you solve for x.

9x = 81

divide both sides by 9

x = 9

We can plug this back into the 2 other equations that represent the number of each tree so

5(9) = 45 gala trees,

4(9) = 36 HC trees

This makes sense since 45+36 = 81 so it adds up

Now to find the amount of money just take the amount of each trees we have and multiply it by the pounds each tree made then multiply it by the price each pound makes.

45 gala trees * 25 pounds * 1.52 dollars = 1,710 dollars

and

36 HC trees * 25 pounds * 3.89 dollars = 3,501 dollars

Finally, add both of them up to get the total profit

1,710 + 3,501 = 5211 dollars

Answer:

the quotient is is 115.915 and the remainder is 495

Step-by-step explanation:

Hope it helps you

Mark my answer as brainlist

have a nice day

Answer:

x > -5, so the correct answer is C.

9514 1404 393

Answer:

  s ≤ 4(0.20×80)

Step-by-step explanation:

The maximum Jason spends each week is 0.20 × $80. Then the amount (s) he spends in 4 weeks will be less than or equal to 4 times this product.

  s ≤ 4(0.20×80)

Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

Step-by-step explanation:

\(3\left(x-4+1\cdot \:b\right)=8\)

\(\mathrm{Divide\:both\:sides\:by\:}3\)

\(\frac{3\left(x-4+1\cdot \:b\right)}{3}=\frac{8}{3}\)

\(\mathrm{Simplify}\)

\(x-4+b=\frac{8}{3}\)

\(\mathrm{Subtract\:}b\mathrm{\:from\:both\:sides}\)

\(x-4+b-b=\frac{8}{3}-b\)

\(\mathrm{Simplify}\)

\(x-4=\frac{8}{3}-b\)

\(\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\)

\(x-4+4=\frac{8}{3}-b+4\)

\(\mathrm{Simplify}\)

\(x=-b+\frac{20}{3}\)

\(\\ \rm\Rrightarrow 3(x-4+b)=8\)

\(\\ \rm\Rrightarrow 3x-12+3b=8\)

\(\\ \rm\Rrightarrow 3x+3b=20\)

\(\\ \rm\Rrightarrow x+b=20/3\)

\(\\ \rm\Rrightarrow x=20/3-b\)

Answer:

A=3.1

B=3.2

Step-by-step explanation:

Answer:

0.2 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

4+2=6

6/3=2

3+1=4

4/2=2

2/2=1

Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

Let y = x + 22 and dy = dx, so the integral becomes

\(\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{25}^{31} \frac{\mathrm dy}{(y-1)\sqrt{y}}\)

Now let z = √y, so that z ² = y. Then 2z dz = dy, and the integral becomes

\(\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{\sqrt{25}}^{\sqrt{31}} \frac{2z}{(z^2-1)z} \\\\ = \int_5^{\sqrt{31}} \frac{2}{z^2-1}\,\mathrm dz\)

Expand the integrand into partial fractions:

\(\dfrac{2}{z^2-1} = \dfrac1{z-1}-\dfrac1{z+1}\)

Then we have

\(\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_5^{\sqrt{31}}\left(\frac1{z-1}-\frac1{z+1}\right)\,\mathrm dz \\\\ = \left(\ln|z-1|-\ln|z+1|\right)\bigg|_5^{\sqrt{31}} \\\\ =\left[\ln\left|\frac{z-1}{z+1}\right|\right]\bigg|_5^{\sqrt{31}} \\\\ =\ln\left(\frac{\sqrt{31}-1}{\sqrt{31}+1}\right) - \ln\left(\frac{4}{6}\right) \\\\ =\ln\left(32-2\sqrt{31}\right) - \ln\left(\frac23\right) \\\\ =\boxed{\ln\left(48-3\sqrt{31}\right)}\)

Answer:

The last one

Step-by-step explanation:

........................

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

The given equation x = 1 represents a horizontal lines that passes thourgh (1, 0).

Inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

As given in the question,

Amount Gabriela plans to save to buy a car = at least $5,600

Amount she already has = $2500

Amount she needs to save at least = $(5600 -2500)

                                                          =$3100

Plans to save each month =$500

Inequality to represents the number of months to save at least $5600

m ≥ 3100/500

⇒ m ≥ 6

Therefore, inequality represents number of months (m) it will take Gabriela to save at least $5,600 is m ≥ 6.

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Answer:

The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

\(\mu = 68, \sigma = 15\)

Middle 68.26% of the grades:

From the

50 - (68.26/2) = 15.87th percentile

To the

50 + (68.26/2) = 84.13rd percentile.

15.87th percentile:

X when Z has a pvalue of 0.1587. So X when Z = -1.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1 = \frac{X - 68}{15}\)

\(X - 68 = -1*15\)

\(X = 53\)

84.13rd percentile:

X when Z has a pvalue of 0.8413. So X when Z = 1.

\(Z = \frac{X - \mu}{\sigma}\)

\(1 = \frac{X - 68}{15}\)

\(X - 68 = 1*15\)

\(X = 83\)

The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.

Answer:X= 4 and -2/3

Step-by-step explanation:

Because of the absolute value sign you need to split this into 2

3x-5 = 7.   to     3x = 12    x = 4

-3x+5 = 7   -3x = 2.   x=-2/3

Answer:

Step-by-step explanation:

Dear student, the missing data in the given information includes that:

The past experience showcases that for 75% successful bids & 40% unsuccessful bids,  additional information is being requested by the agency.

∴

For a bid to be successful, the chance is half

Thus, the prior probability P(successful) is;

P(successful) = \(\dfrac{50}{50+50}\)

P(successful) = 0.5

The conditional probability is:

\(P(request/successful)= \dfrac{P(request \& \ successful) }{P(successful)}\)

\(P(request/successful)= 0.75\)

To compute the posterity probability, we use the Naive Bayes Theorem:

So,

Let S = successful, Us = Unsuccessful; R = request:

Then;

\(P(S/R) = \dfrac{P(R/S) *P(S)}{[P(R/s)* P(S) +P(R/Us) *P(Us)]}\)

\(P(S/R) = \dfrac{0.75*0.5}{0.75* 0.5 +0.40 *0.5]}\)

\(P(S/R) = \dfrac{0.375}{0.375 +0.20} \\ \\ P(S/R) = \dfrac{0.375}{0.575}\)

P(S/R) = 0.65

Check the picture below.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{14}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{z} \end{cases} \\\\\\ z=\sqrt{ 14^2 - 8^2}\implies z=\sqrt{ 196 - 64 } \implies z=\sqrt{ 132 } \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{p}\\ a=\stackrel{adjacent}{21}\\ o=\stackrel{opposite}{\sqrt{132}} \end{cases} \\\\\\ p=\sqrt{ 21^2 + (\sqrt{132})^2}\implies p=\sqrt{ 441 + 132 } \implies p=\sqrt{ 573 }\implies p\approx 23.9\)

Answer:

\(x=3\sqrt{5}\)

Step-by-step explanation:

Right Triangles

Right triangles have one of its interior angles with a measure of 90°.

In right triangles the Pythagora's Theorem is satisfied.

Being c the longest side (hypotenuse), a and b the shorter sides (the legs), then:

\(c^2=a^2+b^2\)

We have modified the image to include some known data. Both triangles are congruent since they share one side, have a right angle, and have the same base length.

This means the value of x can be calculated as the hypotenuse of the triangle 3-6-x:

\(x^2=3^2+6^2=9+36=45\)

\(x=\sqrt{45}=\sqrt{9*5}\)

\(\boxed{x=3\sqrt{5}}\)

Answer:

2.33 units

Step-by-step explanation:

\(\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units\)

Answer:

y=2/3x -3

Step-by-step explanation:

y=mx+c

If the gradient(m) is the same then it's parallel.

The line passes through -3 so the y intercept(c) is -3

Answer:

Y=2/3x-9

Step-by-step explanation:

Y=mx+c

y=2/3x+c

Then substitute the coordinates

y=-3

x=9

-3=2/3*(9)+c

-3=6+c

Make c the subject by subtracting 6 from both sides.

-9=c

so the answer is

Y=2/3x-9

The bridge opening times when there are 60 minutes in an hour will be 45/60 and 10/60.

From the information, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge.

From the table, Colby is on the 3/4 hour. This will be:

= 3/4 × 60

= 45

Also, Wave Bridge will be:

= 1/6 × 60

= 10

Therefore, it's 45/60 and 10/60 because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.

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Complete question

On the Dell River, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge. Rename each of the two drawbridge opening times. There are 60 minutes in an hour, so use 60 as a common denominator. Then, rename each opening time using another common denominator

Bridge name:

1. Asher Cross

2. Colby

3. Rainbow

4. Red Bank

5. Wave

Time of Opening:

1. On the hour

2. On the 3/4 hour

3. On the 2/3 hour

4. On the 1/4 hour

5. On the 1/6 hour

Answer:

answer is c $14.40

Step-by-step explanation:

this is easy, sense you got a 20% discount you do 18 % 20 you get 3.6, so you do 18- 3.6 you get 14.40