In the first year if ownership, a new car lose 20% of its value. If a car lost $4,200 value in the first year, how much did the car originally cost?

Answer:

Step-by-step explanation:

The associative property lets you move parentheses in a sum or product. That is, it doesn't matter which sum or product you compute first.

The commutative property lets you swap the order of operands in a sum or product.

The identity property says the operation using the identity element gives the original value, unchanged.

Answer:

Step-by-step explanation:

Answer:

Here are the formulas

Cube/Rectangular Prism:

Volume = Length*width*height

Surface area = 2(wl+hl+hw)

Lateral area= Area of vertical faces

Base area = length*width

Regular hexagonal prism:

Volume : (3sqrt3/2)*a^2*h

Surface Area  = 6ah+3sqrt(3)a^2

lateral area: 6ah

base area = 3sqrt(3)s^2/2

Triangular prism

Volume: The volume of a triangular prism can be found by multiplying the base times the height.

Surface area: A triangular prism has three rectangular sides and two triangular faces. To find the area of the rectangular sides, use the formula A = lw, where A = area, l = length, and h = height. To find the area of the triangular faces, use the formula A = 1/2bh, where A = area, b = base, and h = height.

Etc.

Answer:

Step-by-step explanation:

First, "boxes of two sizes" means we can assign variables:

  Let x = number of large boxes

       y = number of small boxes

 "There are 115 boxes in all"    means    x + y = 115      [eq1]

Now, the pounds for each kind of box is:

    (pounds per box)*(number of boxes)

So,

  pounds for large boxes     +    pounds for small boxes      =    4125 pounds

                 "the truck is carrying a total of 4125 pounds in boxes"

        (50)*(x)                   +              (25)*(y)                  = 4125    [eq2]

It is important to find two equations so we can solve for two variables.

Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2.  Let's solve for x:

   x = 115 - y          [from eq1]

    50(115-y) + 25y = 4125             [from eq2]

     5750 - 50y  + 25y = 4125           [distribute]

     5750 - 25y = 4125

      -25y = -1625

         y = 65             [divide both sides by (-25)]

 There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

  x = 115 - y

  x = 115 - 65

  x = 50

  There are 50 large boxes.

Check (very important):

Is   50+65 = 115   ?       [eq1]

         115 = 115   ?yes

Is  50(50) + 25(65) = 4125   ?

     2500 + 1625 = 4125   ?

       4125 = 4125   ? ye

Answer:

When x = -1/4 and when x = -15/4

Step-by-step explanation:

The x intercept will be when f(x)=0, so

0 = 4|x+2| -7

7 = 4|x+2|

|x+2|=7/4 here you have to cases

case 1

x+2=7/4

x=7/4-2

x=-1/4 = -0.25

case 2

x+2 = -7/4

x = -2-7/4

x = -15/4 = -3.75

Answer:

For the given data, the mean is 50.8, the median is 51, and the mode is 52.

For the sample with this error, the mean is 48.7, the median is 51, and the mode is 52.

For the sample with this value removed, the mean is 43.2, the median is 50, and the mode is 52.

Step-by-step explanation:

We are given the following set of sample data below;

18, 26, 30, 42, 50, 52, 52, 76, 78, 84.

The formula for calculating mean is given by;

         Mean  =  [tex]\frac{\text{Sum of all data values}}{\text{Total number of observations}}[/tex]

                     =  [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 76+ 78+ 84}{10}[/tex]  

                     =  [tex]\frac{508}{10}[/tex]  =  50.8

For calculating median, we have to observe that the number of observations (n) in our data is even or odd, i.e;

                    Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                    Median  =  [tex]\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}[/tex]

Now, here in our data the number of observations is even, i.e. n = 10.

So, Median  =  [tex]\frac{(\frac{n}{2})^{th}\text{ obs.} +(\frac{n}{2}+1)^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{(\frac{10}{2})^{th}\text{ obs.} +(\frac{10}{2}+1)^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{5^{th}\text{ obs.} +6^{th}\text{ obs.} }{2}[/tex]

                    =  [tex]\frac{50+52 }{2}[/tex]  =  51

A Mode is a value that appears the maximum number of times in our data.

In our data, the value 52 is appera]ing maximum number of times, i.e. 2 times which means that mode of our data is 52.

Now, suppose the value 76 in the data is mistakenly recorded as 55 instead of 76. For the sample with this error,

            New Mean  =   [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 55+ 78+ 84}{10}[/tex]  

                                =  [tex]\frac{487}{10}[/tex]  =  48.7

Now, suppose the value 76 in the original sample is inadvertently removed from the sample. For the sample with this value removed,

            New Mean  =   [tex]\frac{18+ 26+ 30+ 42+ 50+ 52+ 52+ 78+ 84}{9}[/tex]  

                                =  [tex]\frac{432}{10}[/tex]  =  43.2

            So, Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                                 =  [tex](\frac{9+1}{2})^{th} \text{ obs.}[/tex]

                                 =  [tex]5^{th} \text{ obs.}[/tex] = 50

Answer:

D.

Step-by-step explanation:

Since opposite angles of a quadrilateral inscribes in a circle add up to 180°

So,

<P + <N = 180°

2x+2x-12 = 180°

4x = 180+12

4x = 192

Dividing both sides by 4

x = 48

Now

<P = 2(48)

<P = 96

Now

<N = 2(48)-12

<N = 96-12

<N = 84

Answer:

Step-by-step explanation:

Let us assume that x is normally distributed. The sample size is greater than 30. Since the the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 50

σ = 7

n = 36

If x is within 0.5 of the population mean, it means that x is between (50 - 0.5) and (50 + 0.5)

the probability is expressed as

P(49.5 ≤ x ≤ 50.5)

For x = 49.5

z = (49.5 - 50)/(7/√36) = - 0.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.334

For x = 49.5

z = (50.5 - 50)/(7/√36) = 0.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.666

Therefore,

P(49.5 ≤ x ≤ 50.5) = 0.666 - 0.334 = 0.332

Answer:

3

I used to be an olimpic runner and I ran the 400 all the time and I did cross country

Answer:

4

Step-by-step explanation:

ur welcome hopefully this helps

Answer:

a)Randomization condition: Satisfied, as the subjects were randomly selected.

10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).

Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.

b) The 90% confidence interval for the population proportion is (0.68, 0.70).

Step-by-step explanation:

a) Evaluating the necessary conditions:

Randomization condition: Satisfied, as the subjects were randomly selected.

10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).

Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.

[tex]n(1-p)=4,726\cdot (1-0.69)=4,726\cdot 0.31=1,465>10[/tex]

b) We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.69.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.69*0.31}{4726}}\\\\\\ \sigma_p=\sqrt{0.000045}=0.007[/tex]

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.007=0.01[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.69-0.01=0.68\\\\UL=p+z \cdot \sigma_p = 0.69+0.011=0.70[/tex]

The 90% confidence interval for the population proportion is (0.68, 0.70).

Answer:

[tex]2043.67[/tex]

Step-by-step explanation:

Hundredths is at 2 decimal places.

The thousandths place is higher than 5, so add 1 to the hundredths place.

Answer:

2043.67

Step-by-step explanation:

If you’ve ever rounded a number, you would know that if it’s 5 or higher, round it up, and if it’s 4 or lower, round it down. In this case, the second decimal place reads ’6’ which is higher that 5, so we round up. The rest of the numbers stay the same

2043.67

Step-by-step explanation:

multiple 6 by 9 then 2 by 5 then subtract them

Answer:

44

Step-by-step explanation:

(6*9) - (2*5)

54 - 10

44

Answer:

The steps Erin has to take for the reconciliation of her account and activities is as follows: Select the reconciled transactions, Select Batch actions, and Modify the selected ones.

Step-by-step explanation:

Solution

Since Erin could not detect any matches for the transactions she has entered before and enrolled, she needs to take the following processes to reconcile back all her credit activities which is stated below:

Process 1 :Select the reconciled transactions

Process 2 :Batch Actions

Process 3: Modify Selected

From the process stated above Erin can first of all choose the reconciled transactions, after that she can select the batch actions and lastly modify the ones that was selected with the aim of putting or adding them back in the account reconciliation.

4 for 16 would be written as 4/16.

Dividing both numbers by 4 it is simplified to 1/4

4 ounces for every 16 ounces can be written as:

[tex]\displaystyle \frac{4}{16} =\frac{1}{4}[/tex]

As a ratio, it can be expressed as:

[tex]1:4[/tex]

Answer:

[tex] - 45[/tex]

[tex]2.25( - 2) = - 45 \\ - 45[/tex]

Answer:

x = 5

Step-by-step explanation:

52 = y since they are the base angles of an isosceles triangle and the base angles are equal

The sum of the angles of a triangle are 180

52+y+14x+6 =180

Substitute for y

52+52+14x+6 = 180

Combine like terms

110 + 14x = 180

Subtract 110 from each side

110+14x-110 = 180-110

14x =70

Divide by 14

14x/14 = 70/14

x =5

            ∠FGK and ∠FGH               Im pretty sure its right

A ray is a half-infinite line. The pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.

A half-infinite line (also known as a half-line) with one of the two points and is commonly used to represent a ray. It is assumed to be infinite.

A straight line has an angle of measurement of 180°. And a 90° angle is made when two lines are perpendicular to each other.

As we can see the line EGH is a straight line, and FG is another line that is perpendicular to line EH, therefore, it will form two angles measuring 90°. These angles will be ∠FGE and ∠FGH.

Hence, the pairs of non-overlapping angles that share a ray to make a right angle are ∠FGE and ∠FGH.

Learn more about Ray:

https://brainly.com/question/17491571

Answer:

Step-by-step explanation:

Let "a" and "b" represent the costs of one apple and one banana, respectively. Then the purchases can be written ...

  4a +b = 1.40

  7a +b = 2.00

Subtracting the first equation from the second gives ...

  (7a +b) -(4a +b) = (2.00) -(1.40)

  3a = 0.60 . . . . simplify

  a = 0.20 . . . . . .divide by 3

Using this in the first equation, we have ...

  4(0.20) +b = 1.40

  b = 0.60 . . . . . subtract 0.80

The cost of an apple is £0.20; the cost of a banana is £0.60.

Answer:

The probability that the student is in high school and has visited a foreign country is 0.18.

Step-by-step explanation:

We are given that in a survey of students, 60% were in high school and 40% were in middle school.

Of the high school students, 30% had visited a foreign country.

Let the Probability that students were in high school = P(H) = 60%

Probability that students were in middle school = P(M) = 40%

Also, let F = event that students had had visited a foreign country

So, Probability that high school students had visited a foreign country = P(F/H) = 30%

Now, probability that the student is in high school and has visited a foreign country is given by = Probability that students were in high school [tex]\times[/tex] Probability that high school students had visited a foreign country  

            =  P(H)  [tex]\times[/tex]  P(F/H)

            =  0.60  [tex]\times[/tex]  0.30

            =  0.18 or 18%

Answer:

The original price of the fan is $35.71

Step-by-step explanation:

Since Griffin’s General Store is having a 30% off sale on fans, it simply means that fans are paying for (100%-30%)= 70%.

Let the original price be x;

Therefore, 70% of x equal to $25;

[tex]\frac{70}{100}x=25[/tex]

70/100x = 25

0.7x = 25

[tex]x = \frac{25}{0.7}[/tex]

x = 35. 71

Hence, The original price of the fan is $35.71

Answer:

$35.71

Step-by-step explanation:

The statement indicates that Robert paid $25 for a fan and that it had a 30% discount. To be able to determine the original price, you have to divide the the price with the discount by the result of 1 minus the discount.

Original price= 25/(1-0.3)

Original price= 25/0.7

Original price= 35.71

According to this, the answer is that the original price of the fan is $35.71.

Answer:

112

Step-by-step explanation:

Difference between each 4,8,7,5,1

Add numbers next to each other in pairs = 12

So 12-1= 11 and

101+11=112

Answer:

80 milk chocolates

Step-by-step explanation:

Probability of choosing a dark chocolate= number of dark

chocolate/number of total

chocolate

But the probability of choosing dark chocolate= 2/9

The number of dark chocolate= 24

Total chocolate= number of dark

chocolate/probability

of choosing dark

chocolate

Total chocolate= 24/(2/9)

Total chocolate=( 24*9)/2

Total chocolate= 108

Number of milk chocolate= total- dark

Number of milk chocolate

= 108-28

= 80

Answer:

Step-by-step explanation:

no          x                y                   xy                               x²

1           2300         74             170200                      5290000

2          1800          73             131400                      3240000

3          2500         70             175000                     6250000

4          2700         66             178200                     7290000

5          2000         63             126000                     4000000

6          1700          62             105400                     2890000

7           1500         52              78000                      2250000

8           2700        68              183600                    7290000

Total   17200         528           1147800                   38500000

Mean of x is

[tex]\bar x = \frac{17200}{8} =2150[/tex]

Mean of y is

[tex]\bar y = \frac{528}{8} =66[/tex]

From the table above

we find [tex]\hat B_1[/tex]

[tex]\hat B_1=\frac{\sum xy- \bar x \sum y}{\sum x^2- n \barx^2} \\\\=\frac{1147800-2150(528)}{38500000-8(2150)^2} \\\\=\frac{1147800-1135200}{38500000-36980000} \\\\=\frac{12600}{1520000} \\\\=0.008289[/tex]

so [tex]\hat b_0[/tex] is

[tex]\hat b_0=\bar y-\bar B_1 x\\\\=66-0.008289(2150)\\\\=66-17.82135\\\\=48.17865[/tex]

The line of regression is

The price x is 1900

[tex]\hat y =\hat B_0+\hat B_1x\\\\=48.17865+0.008289\times1900\\\\=48.17865+15.7491\\\\=63.928[/tex]

The line of regression is 63.928

Answer:

y=48.2+0.00829x;64

Step-by-step explanation:

Answer:

(-3,2) is not a solution.

Step-by-step explanation:

The solution of a linear inequality in two variables like [tex]Ax + By > C[/tex] is an ordered pair [tex](x, y)[/tex] that produces a true statement when the values of x and y are substituted into the inequality.

To find if (-3,2) is a solution of [tex]7x+9y>-3[/tex], you must substitute this point into the inequality.

                                                 [tex]7\left(-3\right)+9\left(2\right)>-3\\\\-21+18>-3\\\\-3>-3[/tex]

Because -3 is not greater than -3, (-3,2) is not a solution.

Answer:

No

Step-by-step explanation:

Khan academy

Hope this helps!! :)

Answer:

a) x = 30°

b) mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Question:

The complete question as found on Chegg website:

In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs

intercepted have the following ratio of measurements:

mRS : mST :MTU : mUR=1:4:4:3

(a) If mRS = x, then write an equation that could be used to solve for x

and find the value of x.

(b) State the measure of each of the four arcs.

mRS =

mST =

MTU

MUR =

Step-by-step explanation:

Find attached the diagram related to the question

mRS : mST : mTU : mUR = 1:4:4:3

Since mRS = x

Writing the ratios of the measure of angle in terms of mRS:

mST = 4× mRS = 4×x = 4x

mTU = 4× mRS = 4×x = 4x

mUR= 3× mRS = 3×x = 3x

The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)

mRS + mST + mTU + mUR = 360°

x + 4x + 4x + 3x = 360

12x = 360

x = 360/12

x = 30°

b) The measure of angle

mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Answer: (-∞, 2)∪(2, 3]∪(4, ∞)

Step-by-step explanation:

Domain is the allowed x values in the function. The numerator, x + 1 will be defined for all numbers. But that fraction wont be, the minute that fractions denominator is equal to zero, your entire function becomes undefined.

So lets figure out what number will make this undefined. Then we'll know the functions domain is everywhere but that x value.

Make x^2 - 6x + 8 = 0

What two numbers multiply to equal +8 but add to equal -6? Thats -4 and -2.

(x - 4)(x - 2) = 0 This means the function is undefined when x equals 4 and 2

(-∞, 2)∪(2, 3]∪(4, ∞)

Answer:

D Edg

Step-by-step explanation:

all real numbers except 2 and 4

Answer:

y=4x

Step-by-step explanation:

an independent variable is the variable  that is changed or controlled in an experiment or observation to test the effects on the dependent variable

a dependent variable is variable being tested and measured in a scientific experiment

in this case, the number of help desk tickets  closed out is dependent on the number of hours the individual works so y is the number of tickets closed (dependent variable). The number of tickets closed of will be 4 multiplied by the number of hours worked i.e. y=4x

Answer:

c

Step-by-step explanation:

you should divide the distance on time

so

33/6=5.5

26/4=6.5

60/8=7.5

17/2=8.5

you can see answer in this order in c

Answer:

Answer:

c

Step-by-step explanation:

you should divide the distance on time

so

33/6=5.5

26/4=6.5

60/8=7.5

17/2=8.5

you can see answer in this order in c

Step-by-step explanation:

Answer:

[tex]y=300(1+0.16)^x[/tex]

Step-by-step explanation:

 [tex]A= P(1+r )^t[/tex]

Where

A =final amount  = y

P=initial principal balance = $300

r=interest rate  = 16%= 0.16

t=number of time periods elapsed= x

Hence the equation to model his account balance/ final amount A (y) after time (x) years is

[tex]y=300(1+0.16)^x[/tex]