A department store purchases a dress for $80. To sell the dress to customers, the price is marked up by 19%. You hand the clerk $110. How much change will you get back?a. $30.00b. $15.20c. $95.20d. $14.80

Answer:

Blend of Whole bean coffee used = 22.5 Ib

Blend of Half bean Coffee used = 2.5 lb

Correction in statement:

The problem statement is missing information. The proper statement is as follows:

Seattle Star blends whole bean coffee worth $3 per pound with half bean coffee worth $3.5 per pound to get 25 pounds of a coffee blend worth $3.05 per pound. How many pounds of each type of coffee does she use?

Step-by-step explanation:

Whole Bean Coffee = $3

Half Bean Coffee = $ 3.5

Amount of whole bean coffee in Pounds (lbs) = Y

Mixture amount of whole bean and half bean blend = 25 lbs

Amount of half bean coffee = 25-Y (lbs)

Total blended mixture = $3.05

Cost of mixture = Cost of whole bean coffee used + Cost of half bean coffee used

3.05 (25) = 3Y + 3.5 (25-Y)

76.25 = 3Y + 87.5 - 3.5 Y

76.25 - 87.5 = 3Y - 3.5Y

- 11.25 = - 0.5 Y

or

0.5 Y = 11.25

Y=[tex]\frac{11.25}{0.5}[/tex]

Y= 22.5 lb

Which is the amount of whole bean coffee.

Amount of half bean coffee = 25-Y = 25- 22.5 = 2.5 lb

So,

Blend of Whole bean coffee used = 22.5 lb

Blend of Half bean Coffee used = 2.5 lb

Answer:

Length of poster is 9 inches and width of the poster is 3 inches.

Length of banner is 10 inches and width of the banner is 2 inches.

Step-by-step explanation:

Given:

Perimeter of Banner =24 in.

Perimeter of poster = 24 in.

we need to find the dimensions of poster and banner.

First we will find the dimension of poster.

Now Given:

A rectangular poster is 3 times as long as it is wide.

Let the Width of poster be [tex]'p'[/tex].

Length of the poster = [tex]3p[/tex]

Perimeter of poster = 24 in.

But perimeter of poster is equal to twice the sum of length and width.

framing in equation form we get;

[tex]2(p+3p)=24\\\\2(4p)=24\\\\8p=24\\\\p=\frac{24}{8} = 3\ in.[/tex]

Now width of poster = 3 inches

Length of the poster = [tex]3p = 3\times3 =9\ inches[/tex]

Hence Length of poster is 9 inches and width of the poster is 3 inches.

Now we will find the dimension of Banner.

Now Given:

A rectangular banner is 5 times as long as it is wide.

Let the Width of Banner be [tex]'b'[/tex].

Length of the banner = [tex]5b[/tex]

Perimeter of banner = 24 in.

But perimeter of banner is equal to twice the sum of length and width.

framing in equation form we get;

[tex]2(b+5b)=24\\\\2(6b)=24\\\\12b=24\\\\b=\frac{24}{12} = 2\ in.[/tex]

Now width of banner = 2 inches

Length of the banner = [tex]5b = 5\times2 = 10\ inches[/tex]

Hence Length of banner is 10 inches and width of the banner is 2 inches.

The width and length of the rectangular poster are 3 inches and 9 inches, respectively. The width and length of the rectangular banner are 2 inches and 10 inches, respectively. Both were calculated by setting up equations using the perimeter formula for rectangles.

The problem is to determine the lengths and widths of a rectangular poster and a rectangular banner, both having the same perimeter of 24 inches. The poster's length is 3 times its width, while the banner's length is 5 times its width. We'll set up two separate equations for their perimeters and solve for the width and length of each.

Let w be the width of the poster. Then the length is 3w. The perimeter is given by P = 2l + 2w, where P is the perimeter and l is the length. This gives us:

24 = 2(3w) + 2w -> 24 = 6w + 2w -> 24 = 8w -> w = 3 inches

Therefore, the length of the poster is 3w = 9 inches.

Let x be the width of the banner. Then the length is 5x. Again using the perimeter formula, we get:

24 = 2(5x) + 2x -> 24 = 10x + 2x -> 24 = 12x -> x = 2 inches

Therefore, the length of the banner is 5x = 10 inches.

Answer:

Dα/dt   = 0.079 degree/sec

Step-by-step explanation:

From problem statement, is easy to see, that if point A is ubicated at the top of the telescope,  the shoreline is directly below the woman ( point B), and the point where the boat is, which is at distance x from shoreline  is point C. These three point  shape a right triangle with angle α (the angle of the telescope).

So we have

tan α  =  x/250    

Differentiating both sides of the equation we get

D (tan α)/dt    =  ( 1/250)* Dx/dt

sec² α Dα/dt  =  ( 1/250)* Dx/dt  

we already know that    Dx/dt   = 20 feet/sec

sec² α Dα/dt  =  20/250   ⇒     sec² α Dα/dt  = 0.08  

Dα/dt   =  0.08 / sec² α

Then

tan α  =  20/250  = 0,08        α   = arctan 0.08      α  ≈ 5⁰

Dα/dt   =  0.08/ sec² α  

From tables we get    cos  5⁰  =  0.9961  then

1/ 0.9961  = 1.003

sec α  = 1.003      and     sec²  α   =   1.0078

Dα/dt   =  0.08/ sec² α    ⇒   Dα/dt   =  0.08/1.0078

Dα/dt   = 0.079 degree/sec

The change of position of the boat results in a change of the angle of the telescope, which can be calculated using related rates. With known factors such as the speed of the boat and its distance from shore, the rate of change of the telescope's angle can be found using the principles of trigonometry and calculus.

This question is about related rates in calculus.  Related rates describe the relationship between different rates of change that are connected to each other. In this case, the changing position of the boat creates a change in the angle of the telescope.

We know the woman is watching a boat that is approaching a shoreline directly below her at 20 feet per second, and we are asked to find the rate that the angle of the telescope is changing when the boat is 250 feet from shore. Here is a way of visualizing it:

Let D be the distance of the boat from the base of the cliff and θ the angle that the telescope makes with the horizontal. We are given that D(t) decreases at 20 feet per second and that when D(t) = 250, we want to know what is dθ/dt.

By using trigonometry, we can find a relationship between D and θ. Specifically, tan(θ) = 250/D, so by implicit differentiation, (sec^2(θ)) * dθ/dt = -250/D^2 * dD/dt. From the given data, dD/dt = -20 and D = 250, so substitute them into the equation and evaluate θ using the tan–1(1) to obtain dθ/dt.

https://brainly.com/question/29181502

#SPJ6

Answer:

23

Step-by-step explanation:

We can check all the possibilities.

It is not necessary to consider y>16, because in this case, 16#y=16 as 16 is too small to be split in  y  parts.

Now, 1,2,4, 8 and 16 are factors of 16. When you divide 16 by any of the previous integers, the remainder is zero so we discard these.

When y=3, 16=5(3)+1, 16#3=1 so we add y=3. From this, 16=3(5)+1 thus 16#5=1 and we add y=5.

We discard y=6 as 16#6=4 (using that 16=6(2)+4). We also discard y=7 because 16=2(7)+2 then 16#7=2.

For y=9,10,11,12,13,14, when dividing the quotient is one so 16#y=16-y>1 and these values are discarded. However, we add y=15 because 16=15(1)+1 and  16#15=1.

Adding the y values, the sum is 3+5+15=23.

Tan(Angle) = Opposite leg / Adjacent leg

Tan(A) = 5/7

A = Arctan(5/7)

A = 35.54 degrees.

Answer:

A.  35.54

Step-by-step explanation:

To find the angle A in the diagram above, we will simply use angle formula, we will check and see which angle formula will be best fit to use.

The formulas are;

SOH CAH TOA

sin Ф  =  opposite /   hypotenuse

cos Ф  =  adjacent / hypotenuse

tan Ф   =  opposite / adjacent

Looking at the figure given, since we are to find angle A, then our adjacent is 7 and the opposite is 5.

since we are given both opposite and adjacent, then the best formula to use for this is  tan Ф

tan Ф  =  opposite / adjacent

opposite =  5  and adjacent =7

we will go ahead and insert our values

tan A   =   5/7

tan A    = 0.71429

To get the value of tan A, we will simply take the [tex]tan^{-1}[/tex]  of both-side

[tex]tan^{-1}[/tex]   tan A  =   [tex]tan^{-1}[/tex]  0.71429

                A    =  35.54

Therefore angle A is 35.54

Answer: a - 4.512 hours

b - 1.94 hours

Step-by-step explanation:

Given,

a) A(t) = 10 (0.7)^t

To determine when 2mg is left in the body

We would have,

A(t) = 2, therefore

2 = 10(0.7)^t

0.7^t =2÷10

0.7^t = 0.2

Take the log of both sides,

Log (0.7)^t = log 0.2

t log 0.7 = log 0.2

t = log 0.2/ 0.7

t = 4.512 hours

Thus it will take 4.512 hours for 2mg to be left in the body.

b) Half life

Let A(t) = 1/2 A(0)

Thus,

1/2 A(0) = A(0)0.7^t

Divide both sides by A(0)

1/2 = 0.7^t

0.7^t = 0.5

Take log of both sides

Log 0.7^t = log 0.5

t log 0.7 = log 0.5

t = log 0.5/log 0.7

t = 1.94 hours

Therefore, the half life of the drug is 1.94 hours

Answer:

Justin spends $14.24 on gas to travel to work.

Step-by-step explanation:

Given:

Average speed at which Justin goes to work = 65 miles/hour

Time taken by Justin to arrive at work = 1 hour and 30 minutes = 1.5 hours [As 30 minutes =0.5 hours]

Distance he can travel per gallon of gas = 25 miles.

Cost of per gallon of gas = $3.65

Solution:

We first determine the distance Justin travels to work.

Distance = [tex]Speed\times time[/tex]

Distance = [tex]65\times 1.5 = 97.5\ miles[/tex]

Using unitary method to find the amount of gas required to cover the distance.

If 25 miles is covered in 1 gallon of gas

Then 1 mile will be covered in = [tex]\frac{1}{25}[/tex] gallons of gas

So, to cover 97.5 miles gas required = [tex]\frac{1}{25}\times 97.5=3.9[/tex] gallons of gas.

Using unitary method to find the cost of 3.9 gallons of gas.

Cost of 1 gallon of gas = $3.65

So, cost of 3.9 gallons of gas will be = [tex]\$3.65\times 3.9=\$14.235\approx\$14.24[/tex] (Answer)

Answer:

six raised to the one twelfth power

Step-by-step explanation:

The cubed root of 6/the fourth root of 6 equals (6^1/3)/(6^1/4)

6^((1/3)-(1/4))

6^((4-3)/12)

6^1/12

The simplified form of the expression is six raised to the one twelfth power

Given the expression

According to indices, this expression can also be written as:

Using the law of indices;

[tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex]

Applying this expression will give:

[tex]=\dfrac{6^{1/3}}{6^{1/4}} \\= 6^{1/3-1/4}\\=6^{4-3/12}\\=6^{1/12}[/tex]

Hence the simplified form of the expression is six raised to the one twelfth power

Learn more on indices here: https://brainly.com/question/8952483

Answer:

15 students visited both museums.

Step-by-step explanation:

Operations With Sets

Sets are a collection of elements. Some sets have elements in common with other sets. These elements are said to be in their intersection. If we know the number of elements in the set A and in the set B, and also the total number of elements in both sets, we can say

[tex]N(A\bigcup B)=N(A)+N(B)-N(A\bigcap B)[/tex]

where [tex]N(A\bigcup B)[/tex] is the total number of elements, N(A) and N(B) are the number of elements in A and B respectively, and [tex]N(A\bigcap B)[/tex] is the number of elements in their intersection. If we wanted to know that last number, then we isolate it

[tex]N(A\bigcap B)=N(A)+N(B)-N(A\bigcup B)[/tex]

Let A= Students who visited the museum of natural history

B=Students who visited the natural air and space museum

We know [tex]N(A)=18, N(B)=22, N(A\bigcup B)=25,\ so[/tex]

[tex]N(A\bigcap B)=18+22-25=15[/tex]

Answer: 15 students visited both museums.

Note: We are assuming no students didn't visit at least one museum

The set theory in Mathematics implies that 15 out of the 25 students must have visited both the Museum of Natural History and Natural Air and Space Museum, since these students are counted twice when you add the students who visited each museum separately.

The problem asked is: When 25 students went to Washington DC, 18 of them visited the Museum of Natural History and 22 visited the Natural Air and Space Museum. How many students visited both museums?

To answer this, we need to understand the concept of the set theory in Mathematics. It helps us know the total number of students who visited both museums: we subtract the total number of students from the sum of students who visited each museum separately.

So, if we add those who visited the Museum of Natural History (18 students) and those who went to the Natural Air and Space Museum (22 students), we get 40. But we know there were only 25 students in total, implying that 15 students must have visited both museums since these students are counted twice in our sum. Therefore, 15 students visited both museums.

https://brainly.com/question/27333813

#SPJ12

Answer:

48

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total number of rows of squares in the quilt is 8. Each row contains 6 squares.

Since each square measures 1 foot on a side, the area of each square would be 1^2 = 1 foot^2

This means that each row contains six 1 foot^2. Since there are 8 rows, a triangle would be formed such that one of its sides is

6 × 1 foot == 6 feets and the other side would be

8 × 1 foot = 8 feets.

The area of the quilt in a square feet would be the area of the rectangle. It becomes

6 × 8 = 48 feets

Given the total weight of the hot air balloon as 210 kg, the envelope weighting half of this, the weight of the basket, which is 3/5 of the envelope, is calculated to be 63 kg.

To determine the weight of the basket attached to a hot air balloon, we can use the information that the envelope weighs  [tex]\frac{1}{2}[/tex]  of the total weight of the balloon and that the basket weighs [tex]\frac{3}{5}[/tex] of the envelope's weight. If the total weight of the hot air balloon will be 210 kg, then the envelope weighs 105 kg (which is [tex]\frac{1}{2}[/tex] of 210 kg). The weight of the basket can then be calculated as:

Weight of the balloon = 210 kg

Weight of the envelope = 210 * (1/2) = 105 kg

Weight of the basket = 105 * (3/5) = 63 kg

Therefore, the weight of the basket is 63 kg.

Answer:

Step-by-step explanation:

Total number of Pokemon cards that Tim has in his collection is 480

He arranges the cards in his album and each page of his album holds 12 cards.

The total number of pages in the album is 35. After he has filled his album completely, the total number of cards that the album would contain would be 35 × 12 = 420

Let x represent the number of Pokemon cards he has left. Therefore, the expression becomes

x + 420 = 480

x = 480 - 420 = 60

It is proportional because the relationship between gallons of gas and distance is constant and linear. The rate is 32 miles per gallon. You can also call 32 the slope of this linear relationship.

Answer:

(1, 10)

Step-by-step explanation:

Use midpoint formula.

Mₓ = (x₁ + x₂) / 2

3 = (5 + x) / 2

6 = 5 + x

x = 1

Mᵧ = (y₁ + y₂) / 2

9 = (8 + y) / 2

18 = 8 + y

y = 10

The coordinates of point D are (1, 10).

The coordinates of point D are (1, 10).

Midpoint, as the word suggests, means the point which lies in the middle of something.

Midpoint of a line segment means a point which lies in the mid of the given line segment.

Given; CD has endpoints C and D, with C at coordinates (5,8). CD has midpoint M at (3,9).

Using midpoint formula;

Mₓ = (x₁ + x₂) / 2

3 = (5 + x) / 2

6 = 5 + x

x = 1

Now, Mᵧ = (y₁ + y₂) / 2

9 = (8 + y) / 2

18 = 8 + y

y = 10

Hence, The coordinates of point D are (1, 10).

Learn more about midpoint here;

https://brainly.com/question/5127660

#SPJ2

Answer:

The answer to your question is

a) Poster             width = 3 in

                            lenght = 9 in

b) banner

                           width = 2 in

                           lenght = 10 in

Step-by-step explanation:

a) For the poster

   width = x

   lenght = 3x

Perimeter of a rectangle = 2base + 2 height

                                         = 2(x) + 2(3x) = 24

                                         2x + 6x = 24

                                         8x = 24

                                           x = 24/8

                                           x = 3

    width = 3 in

     lenght = 3(3) = 9 in

b) For the banner

    width = y

    lenght = 5y

Perimeter of a banner = 2 base + 2 height

                                        2 (y) + 2(5y) = 24

                                        2y + 10y = 24

                                        12y = 24

                                           y = 24/12

                                           y = 2

     width = 2 in

     lenght = 5(2) = 10 in

Answer:

The rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].

Step-by-step explanation:

In mathematical language, the slope m of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Plugging (x₁, y₁) ⇒ (-7, 5) and  (x₂, y₂) ⇒ (3, 9) into the slope equation

[tex]m=\frac{9-5}{3-(-7)}[/tex]

[tex]m=\frac{4}{10}[/tex]

[tex]m=\frac{2}{5}[/tex]

So, the rate of change of the hiking trail is [tex]m=\frac{2}{5}[/tex].

Keywords: rate of change, slope, coordinates

Learn more rate of change from brainly.com/question/11884403

#learnwithBrainly

Answer:

Step-by-step explanation:

Here is an illustration of the problem:

             ----------------------------->|<------------------

            A                                  t                     J

Alex and Jo start from their separate homes and drive towards one another.  The t indicates the time at which they meet, which is the same time for both.  Filling in a d = rt table:

              d           =        r        x        t

Alex                              14                t

Jo                                   6                t

The formula for motion is d = rt, so that means that Alex's distance is 14t and Jo's distance is 6t.

                      14t                               6t

   ---------------------------------->|<------------------

   A                                       t                      J

The distance between them is 5 miles, so that means that Alex's distance plus Jo's distance equals 5 miles.  In equation form:

14t + 6t = 5 and

20t = 5 so

t = .25 hours or 15 minutes.

If they leave their homes at 3 and they meet 15 minutes later, then they meet at 3:15.

Answer:

Edie has a better deal since his final price is lower

Step-by-step explanation:

Cousin Edie drank all of Clark's egg nog . Edie finds a coupon for 50 cents off that can only be use at a local grocery store.Clark normally buys his egg nog at the supermarket.

The tax rate at both stores is 2.25%.

Clark buys the egg nog at $5.95 plus tax .

Edie buys the egg nog at $6.35 plus coupon plus tax.

After Edie applies the coupon , the final price is $( 6.35 - 0.50 ) = $5.85

Since the percentage of tax applied is the same, the deal with lower final price is better.

Hence, Edie has a better deal.

The price of each regular pizza is $8 and the price of each deluxe pizza is $10.

To find the price of each pizza, we need to set up a system of equations using the given information. Let's denote the price of a regular pizza as 'r' and the price of a deluxe pizza as 'd'. Using the first customer's order, we can write the equation: 7r + d = 74. Using the second customer's order, we can write the equation: 5r + d = 58. To solve this system of equations, we can subtract the second equation from the first equation to eliminate the 'd' variable: (7r + d) - (5r + d) = 74 - 58. Simplifying, we get 2r = 16, which gives us r = 8. Plugging this value back into the first equation, we find d = 10. Therefore, the price of each regular pizza is $8 and the price of each deluxe pizza is $10.

Answer: Here is the answer.

Step-by-step explanation:

Answer:

The exponential Function is [tex]20+12h=200[/tex].

Farmer will have 200 sheep after 15 years.

Step-by-step explanation:

Given:

Number of sheep bought = 20

Annual Rate of increase in sheep = 60%

We need to find that after how many years the farmer will have 200 sheep.

Let the number of years be 'h'

First we will find the Number of sheep increase in 1 year.

Number of sheep increase in 1 year is equal to Annual Rate of increase in sheep multiplied by Number of sheep bought and then divide by 100.

framing in equation form we get;

Number of sheep increase in 1 year = [tex]\frac{60}{100}\times20 = 12[/tex]

Now we know that the number of years farmer will have 200 sheep can be calculated by Number of sheep bought plus Number of sheep increase in 1 year multiplied by number of years  is equal to 200.

Framing in equation form we get;

[tex]20+12h=200[/tex]

The exponential Function is [tex]20+12h=200[/tex].

Subtracting both side by 20 using subtraction property we get;

[tex]20+12h-20=200-20\\\\12h=180[/tex]

Now Dividing both side by 12 using Division property we get;

[tex]\frac{12h}{12} = \frac{180}{12}\\\\h =15[/tex]

Hence Farmer will have 200 sheep after 15 years.

Answer:

The new crew and the experience crew working together can paint the apartment in 4 hours.

Step-by-step explanation:

Given:

Time taken by new crew of painters to paint an apartment = 12 hours

Time taken by experience crew of painters to paint an apartment = 6 hours

To find the time taken by them to  paint the apartment working together.

Solution:

Using unitary method to determine their 1 hour work.

In 12 hours the new crew can paint = 1 apartment

So,in 1 hours the new crew can paint = [tex]\frac{1}{12}[/tex] of the apartment

In 6 hours the experience crew can paint = 1 apartment

So,in 1 hour the experience crew can paint = [tex]\frac{1}{6}[/tex] of the apartment

Now, the new crew and the experience crew are working together.

So, in 1 hour, they can paint :

⇒ [tex]\frac{1}{12}+\frac{1}{6}[/tex]

Taking LCD = 12, we will add fraction.

⇒ [tex]\frac{1}{12}+\frac{2}{12}[/tex]

⇒ [tex]\frac{3}{12}[/tex]

Simplifying fraction we have:

⇒ [tex]\frac{1}{4}[/tex] of an apartment

Again using unitary method to determine the time taken by them working together to paint the whole apartment.

They can paint  [tex]\frac{1}{4}[/tex] of an apartment in 1 hour.

To paint 1 apartment they will take  = [tex]\frac{1}{\frac{1}{4}}=4[/tex] hours

Thus, the new crew and the experience crew working together can paint the apartment in 4 hours.

Answer:

[tex]P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}[/tex]

Step-by-step explanation:

In a coin toss the  probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

[tex]R=\frac{2n!}{m!*(2n-m)!}[/tex]

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of [tex]P_{case}=0.5^{2n}[/tex] so:

[tex]P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}[/tex]

For example, to toss 4 heads in 5 rounds:

[tex]P=\frac{10!}{4!*(10-4)!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7*6!}{4!*6!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7}{4!}*0.5^{10}[/tex]

[tex]P=\frac{10*9*8*7}{4!}*0.5^{10}=0.205[/tex]

Answer:

C. $144,200

Step-by-step explanation:

We have been given that a borrower's monthly interest payment on an interest-only loan at an annual interest rate of 7.3% is $877.

To find the loan amount, we will use simple interest formula.

[tex]I=Prt[/tex], where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

One month will be equal to 1/12 year.

[tex]7.3\%=\frac{7.3}{100}=0.073[/tex]

Upon substituting our given values in simple interest formula, we will get:

[tex]877=P*0.073*\frac{1}{12}[/tex]

[tex]877*12=P*0.073*\frac{1}{12}*12[/tex]

[tex]10524=P*0.073[/tex]

[tex]P*0.073=10524[/tex]

[tex]\frac{P*0.073}{0.073}=\frac{10524}{0.073}[/tex]

[tex]P=144164.3835616438356[/tex]

Upon rounding to nearest hundred, we will get:

[tex]P\approx 144,200[/tex]

Therefore, the loan amount was $144,200 and option C is the correct choice.

Final answer:

To calculate the loan amount based on a monthly interest payment and an annual interest rate, convert the rate to monthly and divide the payment by this rate. For a monthly payment of $877 at 7.3% annual interest, the loan amount is approximately $144,200.

Explanation:

To determine the loan amount of an interest-only loan given a monthly interest payment and an annual interest rate, follow these steps:

In this case, the annual interest rate is 7.3%, so the monthly interest rate is 7.3% / 12 = 0.6083%. The monthly interest payment is $877. Therefore, the loan amount can be calculated as follows:

$877 / 0.6083% = $877 / 0.006083 = $144,200.46

When rounded to the nearest hundred, the loan amount is $144,200.

The correct answer is C. $144,200.

Answer:

P(X1=1, X2=1) = 1/15

P(X1=1, X2=0) = 7/30

P(X1=0, X2=1) = 7/30

P(X1=0, X2=0) = 7/15

Step-by-step explanation:

Let Xi = 1 if the i-th white ball is selected. In this question the 3 white balls are marked 1,2 and 3.

We need to know the possible combination between X1 and X2 i.e. for the white ball 1 and 2 being chosen in the event.

We also need to note that the event is dependent which that after a ball is being chosen, it will not be put back hence affecting the probability of picking the next ball.

Consider all the possible combination between X1 and X2

a) both being chosen P(X1=1, X2=1)

= (3/10) x (2/9) = 1/15

Note that the first probability is the probability before any ball is being picked. The chances for ball white to be pick is 3/10 (3 white ball from the total 10 balls).

After 1 white ball being selected, that ball is not again out back into the urn making white ball 2 and total ball 9. Hence probability of picking another white ball is 2/9

b) only X1 chosen P(X1=1, X2=0)

= (3/10) x (7/9) = 7/30

After the white ball was picked, the probability of white not being pick again is the same as red being picked. Since there is still 7red balls and a total of 9 balls, the probability is 7/9

c) only X2 chosen P(X1=0, X2=1)

= (7/10) x (3/9) = 7/30

The white is not being picked first, making the probability of picking red is 7/10. Then the probability of white being picked is 3/9

d) both not chosen

P(X1=0, X2=0)

= (7/10) x (6/9) = 7/15

In other word only red being chosen. So the first probability is 7 red out of 10 balls (7/10), and the next red ball being picked next is 6/9

Answer:

Step-by-step explanation:

Last year, sales at a book store increased from $5,000 to $10,000. The amount by which it increased would be 10000 - 5000 = $5000

The percentage by which the sales increased would be

5000/5000 × 100 = 100%

This year, sales decreased to $5,000 from $10,000.The amount by which it decreased would be 5000 - 10000 = - $5000

The percentage by which the sales increased would be

5000/10000 × 100 = 50%

The problem can be solved by using a theorem from number theory stating that gcd(a, b) * lcm[a, b] = a * b. Applying this theorem with the given values leads us to solution where a = 210^2 and b = 210^2.

In this mathematics problem, we're given two positive integers, a and b, whose greatest common divisor (gcd) equals to 210, and the least common multiple (lcm) equals to 210^3.

It is a well-known theorem in number theory that for any two positive integers a and b, gcd(a, b) * lcm[a, b] = a * b. We can apply this theorem to our problem. Since we know the values for greatest common divisor and least common multiple, namely gcd = 210 and lcm = 210^3 = 210 * 210 * 210, we have:

210 * 210^3 = a * b

This can be simplified to a * b = 210^4. Since we're told that a < b, and both a and b must divide 210^4, the only possible values for a and b are a = 210^2 and b = 210^2, which respects the condition a < b.

https://brainly.com/question/34444516

#SPJ3

Answer:

(-2,-11)

Step-by-step explanation:

x = -2

y = -11

Answer:

B

Step-by-step explanation:

because, the closer the data points are to the x axis on a residual plot with no definite shape means that a linear model is appropriate for this data set

A linear model is appropriate because, the closer the data points are to the x axis on a residual plot with no definite shape. So, option B is correct.

A residual is a measure of how far away a point is vertically from the regression line.

It is the error between a predicted value and the observed actual value.

A residual plot is a graph that has data points that are all very close to the x-axis. It shows the residuals on the y axis and the independent variable on the x axis.

The goodness of fit of a linear model is depicted by the pattern of the graph of a residual plot. If each individual residual is independent of each other, they create a random pattern together.

When graphing the residual values you know if a linear model is an appropriate model for your data if the points in the residual plot are scattered.

A linear model is appropriate because, the closer the data points are to the x axis on a residual plot with no definite shape.

So, option B is correct.

Learn more about residual plot here;

brainly.com/question/2876516

#SPJ5

The question is missing a tabular data. So, it is attached below.

Answer:

The total cost for the party is $74.50.

Step-by-step explanation:

Given:

Lanes rented at regular cost = 4

Cost of 1 lane rented  at regular cost = $9.75

Cost of 1 lane rented for members = $7.50

Cost of 1 shoe rental at regular cost(non members) = $3.95

Cost of 1 shoe rental for members = $2.95

Since, lanes are rented at regular cost, we use unit rate at regular cost

So, cost of 4 lanes rented = [tex]4\times 9.75= \$ 39[/tex]

Now, out of 10 people who rented shoes, 4 are members. So, the number of non-members is given as:

Non members who rented shoes = 10 - 4 = 6

So, 4 members and 6 nonmembers rented shoes.

So, cost of 6 non members renting shoes = [tex]6\times 3.95=\$ 23.70[/tex]

Cost of 4 members renting shoes = [tex]4\times 2.95=\$ 11.80[/tex]

Total cost for the party is the sum of all the costs. This gives,

= 39 + 11.80 + 23.70

= 50.80 + 23.70

= $74.50

Therefore, the total cost for the party is $74.50.