A bank is investigating ways to entice customers to charge more on their credit cards. (Banks earn a fee from the merchant on each purchase, and hope to collect interest from the customers, as well.) A bank selects a random group of customers who are told their "cash back" will increase from 1% to 2% for all charges above a certain dollar amount each month. Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225. Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189. A level C = 95% confidence interval for \mu_1\:-\:\mu_2μ 1 − μ 2 is approximated by Group of answer choices (62.2, 113.8) (86.2, 120.5) (10.3, 23.8) (55.6, 67.8)

Question:

The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?

Answer:

The value of t is reduced by 6 when the value of r is increased by 4

Step-by-step explanation:

Given

[tex]2t + 3r + 6 = 0[/tex]

Required

What happens when r is increased by 4

[tex]2t + 3r + 6 = 0[/tex] -------- Equation 1

Subtract 2t from both sides

[tex]2t + 3r + 6 - 2t = 0 - 2t[/tex]

[tex]3r + 6 = - 2t[/tex] --- Equation 2

When r is increased by 4, equation 1 becomes

[tex]2T + 3(r+4) + 6 = 0[/tex]

Note that the increment of r also affects the value of t; hence, the new value of t is represented by T

Open bracket

[tex]2T + 3r+12 + 6 = 0[/tex]

Rearrange

[tex]2T + 3r+6 +12 = 0[/tex]

Substitutr -2t for 3r + 6 [From equation 2]

[tex]2T -2t +12 = 0[/tex]

Make T the subject of formula

[tex]2T = 2t - 12[/tex]

Divide both sides by 2

[tex]\frac{2T}{2} = \frac{2t - 12}{2}[/tex]

[tex]T = t - 6[/tex]

This means that the value of t is reduced by 6 when the value of r is increased by 4

Answer:

A

Step-by-step explanation:

Well first find the proportion of the sector of the major Arc(shaded area) and then Multiply by area of the circle πr²

Answer:

John is 9.21 km form the school.

Step-by-step explanation:

John leaves school to go home. His bus drives 6 kilometres north and then goes 7 kilometres west. It is required to find John's distance from the school. It is equal to the shortest path covered or its displacement. So,

[tex]d=\sqrt{6^2+7^2} \\\\d=9.21\ km[/tex]

So, John is 9.21 km form the school.

The building height is 32 feet.

Let us consider that building height is x feet.

From attached diagram shown below,

Two triangles are formed.

Apply law of similarity of triangles.

Corresponding sides are in equal proportion.

                  [tex]\frac{x}{24}=\frac{12}{9} \\\\9x=12*24\\\\x=\frac{12*24}{9}=32 feet[/tex]

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Answer:

The vertex is at (-8,-3)

Step-by-step explanation:

The function is of the form

y = a|x-h| + k  where (h,k) is the vertex

f(x) = |x+ 8|– 3

f(x) = |x - - 8|– 3

The vertex is (-8,-3)

Answer:

Savannah

Step-by-step explanation:

Emery has solved it incorrectly;

x = 100

The volume of any cylinder is

V = pi*r^2*h

where r is the radius and h is the height. We are keeping r = 2 the same the entire time, as the first part of the instructions indicate. In contrast, h is allowed to vary or change based on the values shown in the table.

If h = 1, then,

V = pi*r^2*h

V = pi*2^2*1

V = pi*4

V = 4pi

So you'll write "4pi", without quotes of course, in the V column next to h = 1. This first row shows a height of 1 leads to a volume of 4pi.

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

Then if h = 2, we have,

V = pi*r^2*h

V = pi*2^2*2

V = pi*8

V = 8pi  ... this is written in the second box

and finally if h = 3, we would say,

V = pi*r^2*h

V = pi*2^2*3

V = pi*12

V = 12pi .... and this is placed in the third box

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

The values of V we got were: 4pi, 8pi, 12pi

This is for h = 1,2 and 3 respectively in that order.

The sequence 4,8,12 is linear because we are adding 4 each time. More specifically, it fits the equation y = 4x where x = 1,2,3. Think of y = 4x as y = 4x+0 and that fits the slope intercept form y = mx+b.

Answer:

There are 55 sweets in total.

Step-by-step explanation:

The total number of sweets is t.

Henry, Brian and Colin share some sweets in the ratio 6:4:1.

This means that Henry earns [tex]\frac{6}{6+4+1} = \frac{6}{11}[/tex] of the total(t).

Brian earns [tex]\frac{4}{11}[/tex] of the total.

Colin earns [tex]\frac{1}{11}[/tex] of the total

Henry gets 25 more sweets than Colin.

Henry earns [tex]\frac{6t}{11}[/tex]

Colin earns [tex]\frac{t}{11}[/tex]

So

[tex]\frac{6t}{11} = \frac{t}{11} + 25[/tex]

Multiplying everything by 1

[tex]6t = t + 275[/tex]

[tex]5t = 275[/tex]

[tex]t = \frac{275}{5}[/tex]

[tex]t = 55[/tex]

There are 55 sweets in total.

Answer:  h = -(16t + 3)(t - 2)

               h(0) = 6

               h(1) = 19

               h(2) = 0

Step-by-step explanation:

Factor the equation by finding two numbers whose

product = a×c and sum = b, then replace the b value with those two numbers and factor the equation.

h = -16t² + 29t + 6      

 a=-16   b=29   c=6           a×c = -96      b = 29      

                                      32 × -3 = 96          32 + (-3) = 29

h = -16t² + 32t    -3t + 6

h = -16t(t - 2)      -3(t - 2)

h = (-16t - 3) (t - 2)

h = -(16t + 3)(t - 2)

h(0) = -[16(0) + 3] [0 - 2]

      = -(3)(-2)

      = 6  

h(1) = -[16(1) + 3] [1 - 2]

      = -(19)(-1)

      = 19  

h(2) = -[16(2) + 3] [2 - 2]

      = -(35)(0)

      = 0  

The right answers are:

Hope it helps.

please see the attached picture for full solution

Good luck on your assignment

Answer:

  $140

Step-by-step explanation:

You can add up the prices to find the total. Most of us find it easier to multiply the price by the number of items.

  cost of 2 shirts = (2)($25.00) = $50

  cost of 4 pants = (4)(22.50) = $90

The total was $50 +90 = $140.

Answer:

6.18% of the class has an exam score of A- or higher.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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, we have that:

[tex]\mu = 80, \sigma = 6.5[/tex]

What percentage of the class has an exam score of A- or higher (defined as at least 90)?

This is 1 subtracted by the pvalue of Z when X = 90. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{90 - 80}{6.5}[/tex]

[tex]Z = 1.54[/tex]

[tex]Z = 1.54[/tex] has a pvalue of 0.9382

1 - 0.9382 = 0.0618

6.18% of the class has an exam score of A- or higher.

Answer:

A. Only the mode makes sense since the data is nominal.

Step-by-step explanation:

Hello!

The objective of the study was to determine if deficiency of carbon dioxide in the soil affects the phenotype of peas.

The variable of study is X: Phenotype of a pea grown in soil with carbon dioxide deficiency.

Possible values of Phenotype codes:

1= smooth-yellow

2= smooth-green

3= wrinkled-yellow

4= wrinkled-green

The absolute frequencies for each phenotype are:

f(1)= 3

f(2)= 4

f(3)= 6

f(4)= 1

n= 14

a) Mean:

X[bar]= (∑xifi)/n= [(1*3)+(2*4)+(3*6)+(4*1)]/14= 33/14= 2.357= 2.36

The average value is always within range of definition of the variable but it does not necessarily correspond to an observation.

b) Median:

To determine the value that corresponds to the median you have to calculate its position:

For even samples the position is:

PosMe= n/2= 14/2= 7

Then you have to arrange the data from least to greatest, in this case, starting from the first category, you have to determine where the seventh observation is within the observed absolute frequencies. The phenotype that corresponds to the 7th observation is 2= smooth-green.

Me= 2= smooth-green.

c) Mode:

The mode corresponds to the most observed category/ value of the variable, i.e. the category with the most observations is 3= wrinkled-yellow

Md= 3= wrinkled-yellow

d) Midrange: (1 + 4)/2= 2.5

e)

As you can see the variable is qualitative and categorical. Even if all central tendency measurements can be calculated, truth is that the only one that shows any valuable information regarding the data set is the mode.

I hope this helps!

Answer:

x=-1/39

Step-by-step explanation:

Answer:

  -7

Step-by-step explanation:

To find the differences in a sequence, subtract the term before:

  -15 -(-8) = -7

  -22 -(-15) = -7

These differences are the same, so constitute the "common" difference.

The common difference of the sequence is -7.

Answer:

This can be written as d + 16 because plus means addition.

Answer:

the answer you are looking for is D 778

Step-by-step explanation:

I think there should be 5 capsicums because

4 times onions = 5 x 4 = 20

Then 5 capsicums = 20 + 5 = 25

Answer:

A large pizza has toppings of capsicum and onion. In total there are 36 pieces of both on the pizza .If there are 5 times as many onions pieces as capsicum pieces,how many of each vegetable are there on the pizza?

Step-by-step explanation:

Can you please help with this one

f(3x - 1) = 6x - 1

Rewrite 6x - 1 as a function of 3x - 1:

6x - 1 = 6x - 2 + 1 = 2(3x - 1) + 1

That is,

f(3x - 1) = 2(3x - 1) + 1

which means

f(x) = 2x + 1

and so

f(0) = 2*0 + 1 = 1

Answer:  B) Scott sold 1 van

Step-by-step explanation:

A₂,₃ represents:  matrix A - 2nd row - 3rd column

The second row is Scott and and the 3rd row is Vans

If you look at Scott - Vans, you will see that Scott sold 1 van.

Answer:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): [tex]\mu \geq 2000[/tex]

Alternative hypothesis (H1): [tex]\mu <2000[/tex]

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no

Step-by-step explanation:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): [tex]\mu \geq 2000[/tex]

Alternative hypothesis (H1): [tex]\mu <2000[/tex]

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no

Answer:

P = 8000

t = 2

I = p × r × t

400 = 8000 × r/100 × 2

r = 400/160 per year

r = 40/16 = 2.5 %

Answer:

Yes, [tex]\frac{3}{4}[/tex] is a solution of the inequality.

Step-by-step explanation:

Solution of an inequality is given by the values of the variable t ≥ [tex]\frac{2}{3}[/tex]

Or t ≥ 0.67

If a solution of this inequality is t = [tex]\frac{3}{4}[/tex]

Or t = 0.75

Since, on a number line 0.75 > 0.67

Therefore, [tex]\frac{3}{4}[/tex] will be a solution of the inequality.

Answer:

-1.

Step-by-step explanation:

The standard form of a line can be written y = mx + b where m is the slope.

y = x + 5 can be written as y = 1x + 5 which shows that the slope is 1.

If the slope of a line  is m then the slope of a line perpendicular to it is -1/m.

So the required slope is -1/1 = -1.

Answer:

-1

Step-by-step explanation:

the line is exactly opposite like a mirror image when it is perpendicular,

so the gradient of the first line is 1 (because there is no number beside x, the gradient would be 1), that means the opposite of 1 would be -1.

The answer is -1

Answer:

The Probability that the product is shipped out is 0.7283

Step-by-step explanation:

Here, we are given that, a product passes through 6 tests before it is shipped out and a product is shipped out only if it passes all the first 3 tests and at least 1 of the remaining 3 tests.

We have P(pass)= 0.9, is the Probability of passing any test.

Which implies, P(fail)= 1- 0.9= 0.1

We have to find the Probability that the product is shipped out.

P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests) •••••••••••(i)

We can take the product as the tests are Independent.

Now, let us obtain

P(it passes first 3 tests ) = P(pass)*P(pass)*P(pass)

=P(pass)]^3 = (0.9)^3 = 0.729

Hence, P( it passes first 3 tests)= 0.729 •••••••(ii)

Now,

P(passes at least 1 of the remaining 3 tests)

= 1-P(fails all the 3 remaining tests)

= 1-(0.1)^3 = 1 - 0.001 = 0.999

Hence,

P(passes atleast 1 of the remaining 3 tests)=0.999 ••••••••(iii)

Now, substituting the 2nd and 3rd equations in the first equation, we have;

P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests)

= (0.729)*(0.999)

= 0.728271

= 0.7283

Answer:

Which statements?

Step-by-step explanation:

Can you write the statements please?

Answer:

Brainelist~~~!!!

Step-by-step explanation:

4c=3

c=3/4

c=0.75

The solution of the linear equation 4·c = 3, obtained by solving for the variable c is; c = 3/4

A linear equation is an equation that can be expressed in the form; y = m·x + c

The equation 4·c = 3 is a linear equation

In order to solve the equation 4·c = 3 for the variable c, the variable c needs to be isolated to one side of the equation, by dividing both sides of the equation by 4 as follows;

4·c = 3

(4·c)/4 = 3/4

c = 3/4

Therefore, the solution of the equation, 4·c = 3 is; c = 3/4

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Answer: idk

Step-by-step explanation:

idk