Chrissy currently has a credit card that charges 15% interest. She usually carries a balance of about $500. What will her total annual interest be with her current card?

Answer:

(C) y = 3x

Step-by-step explanation:

Directly proportional relation is one in which the value of x and y gets increases or decreased in same proportion.

example of such relation can be y = kx

where k is the constant of proportionality which depicts by how much value of  y will change in response to change of x.

_______________________________________________

now in the option

A and B

y= 9 , y =1/5

value of y is constant and does not depend on other variable. it value will remain same.

for y = x+4

value of y increases with x but it does not increase proportionally.

let see an example for x =1 , y = 1+4 = 5

x =2 , y = 2+4 = 6

(1,5)  and (2,6) are not proportionally changing also this equation is not of form y = kx

thus, it is incorrect option.

_______________________________

(C) y = 3x

here equation is form y =kx .  in place of k there is 3

let see an example for x =1 , y = 3*1 = 3

x =2 , y = 3*2 = 6

(1,3)  and (2,6) are  proportionally changing (1/3 = 2/6) also this equation is  of form y = kx

thus, it is correct option.

Answer:

C

Step-by-step explanation:

Given

x + 10 = 3(x - 1)² ← expand (x - 1)² using FOIL

x + 10 = 3(x² - 2x + 1) ← distribute

x + 10 = 3x² - 6x + 3 ← subtract x + 10 from both sides

0 = 3x² - 7x - 7 → C

Answer:

Step-by-step explanation:

Answer:

[tex]\boxed{\ 123 \ dollars\ }[/tex]

Step-by-step explanation:

its value decreases at a rate of 2% each month

in 2 years there are 12*2=24 months

so the Samsung worth [tex]200(0.98)^{24}\\[/tex]

it gives 123 rounded to the nearest dollar

Answer:

$123

Step-by-step explanation:

initial price= $200

value decrease rate= 2% = 0.98 times a month

time = 2 years

current value= $200*0.98²⁴= $123

Answer:

618

Step-by-step explanation:

l x w

34x5

14x27

5x14

618

Answer:

51 1/3 hours

Step-by-step explanation:

Multiply the amount of sleep per day (7 1/3) by the number of days in a week (7), to get the total amount of sleep (51 1/3 hours)

Answer:

the third answer i am pretty sure because my brother is learning this and he told me and he has As

Step-by-step explanation:

if yo need any more help please tell me please mark as brainliest i only got it twice

Answer:

5 inches is 5 times as big as 1 inch

Answer: Option D.

Step-by-step explanation:

Here we see the cross-section of a cone when it is cut by a plane that is parallel to the base of the cone.

As the plane is parallel to the base, we expect to see a figure that has the same shape as the base ( a circle) (you can think that over the plane we have a smaller cone, and the base of that cone also must be circular)

So the correct option is D.

Answer:

4, 8, 16,64 and 4096.

Step-by-step explanation:

We are already given: [tex]4096=2^{12}[/tex]

To determine other whole numbers that can be raised to a power to obtain 4096, we apply the product rule of indices.

Product Rule of Indices: [tex]a^{xy}=(a^x)^y[/tex]

Now 12 can be factored in the following ways where one of the terms must be a perfect square:

[tex]2^{12}=(2^2)^6=4^6\\\\2^{12}=(2^6)^2=64^2\\\\2^{12}=(2^4)^3=16^3\\\\2^{12}=(2^3)^4=(8^2)^2=8^{2*2}=8^4\\\\2^{12}=(2^{12})^1=4096^1 $(This is the trivial case)[/tex]

Therefore, the other whole numbers that can be raised tp a power to obtain 4096 are: 4, 8, 16, 64 and 4096.

Answer:

Step-by-step explanation:

Hello!

So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.

Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.

The hypotheses are:

H₀: The variables are independent.

H₁: The variables are not independent.

α: 0.05

[tex]X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~X_{(r-1)(c-1)}[/tex]

r= total number of rows

c= total number of columns

i= 1, 2 (categories in rows)

j=1, 2, 3 (categories in columns)

To calculate the statistic you have to calculate the expected frequencies for each category:

[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]

[tex]O_{i.}[/tex] Represents the marginal value of the i-row

[tex]O_{.j}[/tex] Represents the marginal value of the j-column

[tex]E_{11}= \frac{O_{1.}*O_{.1}}{n}= \frac{21*40}{120}= 7[/tex]

[tex]E_{12}= \frac{O_{1.}*O_{.2}}{n}= \frac{21*40}{120}= 7[/tex]

[tex]E_{13}= \frac{O_{1.}*O_{.3}}{n}= \frac{21*40}{120}= 7[/tex]

[tex]E_{21}= \frac{O_{2.}*O_{.1}}{n}= \frac{99*40}{120}= 33[/tex]

[tex]E_{22}= \frac{O_{2.}*O_{.2}}{n}= \frac{99*40}{120}= 33[/tex]

[tex]E_{23}= \frac{O_{2.}*O_{.3}}{n}= \frac{99*40}{120}= 33[/tex]

[tex]X^2_{H_0}= \frac{(7-7)^2}{7} + \frac{(5-7)^2}{7} + \frac{(9-7)^2}{7} + \frac{(33-33)^2}{33} + \frac{(35-33)^2}{33} + \frac{(31-33)^2}{33} = 1.385= 1.34[/tex]

Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:

[tex]X^2_{(c-1)(r-1);1-\alpha }= X^2_{2; 0.95}= 5.991[/tex]

Decision rule:

If [tex]X^2_{H_0}[/tex] ≥ 5.991, reject the null hypothesis.

If [tex]X^2_{H_0}[/tex] < 5.991, do not reject the null hypothesis.

The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.

At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.

I hope this helps!

Answer:

Bacterial infection

Step-by-step explanation:

Antibiotics are most effective against bacterial infections.

Answer:

Bacterial infection

Antibiotics are most effective against bacterial infections

Answer:

y = 12 + 6x

y = 12x

Step-by-step explanation:

From the information provided, the following equations are derived:

y = 12 + 6x    ------- Eqn 1

y = 12x          ------- Eqn 2

Since Eqns 1 and 2 have the same subject, we equate them to solve for x. We have:

12x = 12 + 6x

Putting like terms together, we have:

12x - 6x = 12 ⇒ (12 - 6)x = 12

6x = 12 ⇒ x = 2

x = 2

Substitute x into Eqn 1 or 2

Eqn 1

y = 12 + 6x

y = 12 + 6(2) = 12 + 12

y = 24

Eqn 2

y = 12x

y = 12(2)

y = 24

It means that it will take Ms. Ironperson and Mr. Thoro 2 days apiece to produce the same number of posters at the current rate (which is 24 posters). Both Ms. Ironperson and Mr. Thoro will individually take 2 days to produce 24 Avenger posters apiece.

Answer:

there are 86,400 seconds in one day

Answer:

Sqrt(13)

Step-by-step explanation:

d = sqrt(3^2 + 2^2) = sqrt (13)

Answer:

c) descriptive statistics

Correct. When we present information without any type of hypothesis we are describing the information

Step-by-step explanation:

We know that we are presenting historical information without any hypothesis and we need to find the right term, let's analyze one by one

a) predictive statistics

False. We can't predict if we are using historical information because predict is for the future and that not applied here.

b) prescriptive statistics

False. This term not exists in reality the most similar term is prescriptive analytic who analyze a series of scenarios fr an information given

c) descriptive statistics

Correct. When we present information without any type of hypothesis we are describing the information

d) inferential statistics

False. If we don't have any hypothesis we can't apply any inferential study and for this case is not the correct option

uhh there is no such thing because -1 isn't a perfect square.

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

Name the probabilities:

p₁ = 0.02,   p₂ = 0.07,   p₃ = 0.91

q₁ = 1-p₁ = 0.98 ,   q₂ = 1-p₂ = 0.93 ,   q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

A.

The function will follow multinomial distribution:

[tex]f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})[/tex]

Substitute the values and make a table.

TABLE IN ATTACHMENT

B.

We calculate marginal distribution by:

[tex]P (X=x)=[/tex] ∑ [tex]P(X=x,Y=y)[/tex]

[tex]fx(x)[/tex] can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

The mathematic expectation E is the sum of product of each possibility with its probabiity.

[tex]E(X)=[/tex]∑ [tex]xP(X=x)[/tex]

Find E(X):

[tex]E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)[/tex]

[tex]E(X)=0.06[/tex]

Condition probability states:

[tex]P(A|B)=\frac{P(A,B)}{P(B)}[/tex]

It can also be written as:

[tex]f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}[/tex]

Where [tex]f_x(1)\\[/tex] = 0.057624

Calculate the quotient:

[tex]Y|_{x=1}[/tex] = 0 ,  [tex]f_{Y|_X=1[/tex] = 0.862245

[tex]Y|_{x=1}[/tex] = 1 ,  [tex]f_{Y|_X=1[/tex] = 0.132653

[tex]Y|_{x=1}[/tex] = 2 ,  [tex]f_{Y|_X=1[/tex] = 0.000510

[tex]Y|_{x=1}[/tex] = 3 ,  [tex]f_{Y|_X=1[/tex] = 0

Find the dependency:

[tex]f_{XY}(y)=f_X(x)f_Y(y)[/tex]

We found that

[tex]f_{Y|_X=1[/tex] = 0.862245

Calculate [tex]f_Y(1)[/tex] from summing the column from the table

[tex]f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141[/tex]

Which are not equal.

Conclusion:

X and Y are NOT Independent

Answer:

The second choice.

Step-by-step explanation:

Answer:

The amount of heat lost by the aluminum is 31,500 J

Step-by-step explanation:

Given;

mass of aluminum, m =  500 g

initial temperature of the aluminum, θ₁ = 100° C

final temperature of the aluminum, θ₂ = 30°C

specific heat capacity of water, C = 4.18 J/g °C

specific heat capacity of aluminum , C = 0.90 J/g

Heat lost by the aluminum is equal to heat gained by the water.

The amount of heat lost by the aluminum, is calculated as;

Q = MCΔθ

Q = 500 x 0.9 (100 - 30)

Q = 500 x 0.9 x 70

Q = 31,500 J

Therefore, the amount of heat lost by the aluminum is 31,500 J

4+6=10+6=16+6=22+6=28...

I hope it is helpful for everyone

Answer:

[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]

And we can find this probability with this difference

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]

And we can find the difference with the normal standard distirbution or excel:

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]

Step-by-step explanation:

Let X the random variable that represent the hotel room cost of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(202,70)[/tex]  

Where [tex]\mu=202[/tex] and [tex]\sigma=70[/tex]

We are interested on this probability

[tex]P(210<X<290)[/tex]

The z score formula is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the formula we got:

[tex]P(210<X<290)=P(\frac{210-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{290-\mu}{\sigma})=P(\frac{210-202}{70}<Z<\frac{290-202}{70})=P(0.114<z<1.26)[/tex]

And we can find this probability with this difference

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)[/tex]

And we can find the difference with the normal standard distirbution or excel:

[tex]P(0.114<z<1.26)=P(z<1.26)-P(z<0.114)=0.896-0.545=0.351[/tex]

Complete question is:

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer:

Probability = 0.0277

Step-by-step explanation:

We are given;

Mean: μ = 32

Standard deviation;σ = 7

Random sample number; n = 34

To solve this question, we would use the equation z = (x - μ)/(σ/√n) to find the z value that corresponds to 29.7 grams of fat.

Thus;

z = (29.7 - 32)/(7/√34)

Thus, z = -2.3/1.200490096

z = -1.9159

From the standard z table and confirming with z-calculator, the probability is 0.0277

Thus, the probability to select 34 fish whose average grams of fat per pound is less than 29.7 = 0.0277

Answer:

[tex]4x -y = 5[/tex]

And if we rewrite this expression we got:

[tex] y= 4x -5[/tex]

If the system have just one solution then we need the slope different and for this reason we can discard the options:

y = 4x-5

-2y = -8x - 10 equivalent to y =4x+5

2y = 8x - 10  equivalent to y = 4x -5

And then the correct answer would be:

y=-4x + 5

Step-by-step explanation:

For this case we have the following equation given:

[tex]4x -y = 5[/tex]

And if we rewrite this expression we got:

[tex] y= 4x -5[/tex]

If the system have just one solution then we need the slope different and for this reason we can discard the options:

y = 4x-5

-2y = -8x - 10 equivalent to y =4x+5

2y = 8x - 10  equivalent to y = 4x -5

And then the correct answer would be:

y=-4x + 5

Answer:

A: y = –4x + 5

Step-by-step explanation:

I got it right on Edge

Answer:

  x = 8

Step-by-step explanation:

The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...

  4 +7x = 60

  7x = 56 . . . . . . subtact 4

  x = 8 . . . . . . . . .divide by 7

Answer: 7/6

Step-by-step explanation:

If he is writing sixths, then we have multiples of 1/6.

this is:

0*(1/6) = 0

1*(1/6) = 1/6

.

.

.

5*(1/6) = 5/6 (the numer he wrote at the left of 1)

6*(1/6) =  6/6 = 1

7*(1/6) = 7/6

So the number next to 1, (at the right of 1) must be 7/6.

You also can find it by adding 1/6 to 1.

1/6 + 1 = 1/6 + 6/6 = 7/6.

Answer:

[tex]7/6[/tex]

Explanation:

[tex]1/6 \approx 0.16666[/tex]

[tex]2/6 \approx 0.33333[/tex]

[tex]3/6 = 0.5[/tex]

[tex]4/6 \approx 0.66666[/tex]

[tex]5/6 \approx 0.83333[/tex]

[tex]6/6=1[/tex]

[tex]7/6 \approx 1.16666[/tex]

Answer:

u=6

Step-by-step explanation:

One rule in algebra is what you do to one side, you do it to other side. So if you multiply a number in one side, multiply the same number in other side. Here in this question, you are trying to find the value of the variable u. Variable is called so because the value of it varies depending on different question. Here u is going to be a constant number which when multipled by 3 and then subtracted by 3 equals 15.

So first step is we try to get constants on one side. So we add 3 on both sides to get rid of 3 on left.

3u - 3 + 3= 15+3

3u= 18

Now we divide by 3 on both sides to get u by itself.

3u/3 = 18/3

u= 6

Answer:

y = -z/2 - x/2

Step-by-step explanation:

2y + 5x – z = 4y + 6x

-5x. -5x

2y - z = 4y + x

+z. +z

2y = 4y + z + x

-4y -4y

-2y = z + x

÷-2. ÷-2

y = -z/2 - x/2

Answer:

a) 56.82

b) 64

c) there is no mode

d) 57

e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless

Step-by-step explanation:

The first thing is to organize the data from least to greatest:

15 24 29 38 41 64 72 74 76 93 99

a) the mean would be the average of the data, thus:

m = (15 + 24 + 29 + 38 + 41 + 64 + 72 + 74 + 76 + 93 + 99) / 11

m = 56.82

b) the median is the data of half, when the data is organized, in this case the value of half would be the sixth data that is 64.

c) the mode is the value that is most repeated, therefore as none is repeated there is no mode.

d) the midrange is the average between the minimum value and the maximum value:

mr = (15 + 99) / 2

mr = 57

e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless

Answer:

480

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

The sample shows the scores for the combined three-part SAT.

Raw data in first attachment.

a.

To arrange the data in a frequency table using class intervals you have to determine the number of intervals you want to use and calculate their width. In this case, the width is given and so is the lower limit of the first interval, you calculate the successive limits by adding the width. The lower limit of the next interval will be the upper limit of the previous one:

1) 800 + 200= 100

First interval [800; 1000)

2) 1000 + 200

Second interval

[1000; 1200)

And so on until you reach the maximum value of the data set,

[1200; 1400)

[1400; 1600)

[1600; 1800)

[1800; 2000)

[2000; 2200)

Then you have to order the data from least to greatest and count how many observations correspond to each value, this way you'll determine the observed frequency for each interval.

Table and histogram in second attachment.

b.

As you can see in the histogram, this distribution is symmetrical centered in the interval [1400; 1600) and there are no outliers observed.

c.

Values around 1400-1600 are the most common ones while scores around 800-1000 or 2000-2200 are more uncommon, in this sample it seems the probability to obtain a perfect score for the combined three-part SAT is extremely low.

I hope you have a nice day!