A car dealership decreased the price of a certain car by 4% . The original price was $43,600 . write the new price in terms of the original price.

Answer:

a) [tex]\sigma_{\bar x} = 1.414[/tex]

b) [tex]\sigma_{\bar x} = 1.414[/tex]

c) [tex]\sigma_{\bar x} = 1.414[/tex]

d) [tex]\sigma _{\bar x} = 1.343[/tex]

Step-by-step explanation:

Given that:

The random sample is of size 50 i.e the population standard deviation  =10

Size of the sample n = 50

a) The population size is infinite;

The standard error is determined as:

[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]

[tex]\sigma_{\bar x} = 1.414[/tex]

b) When the population size N= 50000

n/N = 50/50000 = 0.001 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]

[tex]\sigma_{\bar x} = 1.414[/tex]

c)  When the population size N= 5000

n/N = 50/5000 = 0.01 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]

[tex]\sigma_{\bar x} = 1.414[/tex]

d) When the population size N= 500

n/N = 50/500 = 0.1 > 0.05

So; the finite population of the standard error is applicable in this scenario;

Therefore;

The standard error is determined as:

[tex]\sigma _{\bar x} = \sqrt{\dfrac{N-n}{N-1} }\dfrac{\sigma}{\sqrt{n} } }[/tex]

[tex]\sigma _{\bar x} = \sqrt{\dfrac{500-50}{500-1} }\dfrac{10}{\sqrt{50} } }[/tex]

[tex]\sigma _{\bar x} = 1.343[/tex]

Answer:

5

Step-by-step explanation:

We have x-2 = 5

x-2 = 5 we separate parenthesis.

x(-2) = 5(+2)

x = 7

We can check this as what the x-2 is saying is  7-2 = 5

Answer:

Since it is an equilateral triangle,

Perimeter = 3s = 3 x side

=> 15 = 3 X (x - 2)

=> 15 = 3(x - 2)

=> 15 = 3x - 6

=> 3x = 15 + 6

=> 3x = 21

=> x = 21/3

=> x = 7

When x = 7,

=> Side = 7 - 2 = 5 inches

Since, it is an equilateral triangle all sides are of 5 inches each.

Answer:

1674 ft²

Step-by-step explanation:

Area S = 65*30

Area A = (65 - x)(30 - x) = (65 - 3)(30 - 3) = 62*27= 1674 ft²

Answer: Y is less than or equal to 65 and X + y= less than or equal to 95

Answer:

2

Step-by-step explanation:

1. Divide by four

2. two of the fours will cancel out leaving you to divide 4 by - 2 which is 2

Answer:

give $20 to each person

Step-by-step explanation:

Answer:

Maths keeps one mentally active. The total surface of a hemisphere = 3(pi)r^2. So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.

Step-by-step explanation:

hope this helps you :)

Answer:

The total surface of a hemisphere = 3(pi)r^2.

So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.

Answer:

The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they are willing to pay more for the service, or they are not. Customers are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

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

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

40% of the customers are willing to pay more for the service.

This means that [tex]p = 0.4[/tex]

Now we have selected 10 customers randomly.

This means that [tex]n = 10[/tex]

What are the expected value and standard deviation

[tex]E(X) = np = 10*0.4 = 4[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.4*0.6} = 1.55[/tex]

The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.

Answer:

x = 75

Step-by-step explanation:

Assuming the angles are equal  ( bisected means divided in half)

2x-5 = 145

Add 5 to each side

2x-5+5 = 145+5

2x = 150

Divide by 2

2x/150/2

x = 75

Answer:

x=75

Step-by-step explanation:

∠BAD is bisected by AC and measurement of BAC is equal to 2x - 5 and measurement of CAD is equal to 145. Since they are bisected, they are equal and the solution is shown below:

m ∠ BAC = m ∠ CAD

2x - 5 = 145 , transpose -5 to the opposite side such as:

2x = 145 + 5 , perform addition of 145 and 5

2x = 150

2x / 2 = 150 / 2 , divide both sides by 2

x = 75

The answer is 75 for the x value.

Answer:

  x = -1/5, x = 1

Step-by-step explanation:

Maybe you want to find x.

Subtract the right side and collect terms.

  6x^2 +4x^2 -6x -4 -(2x -2) = 0

  10x^2 -8x -2 = 0

  5x^2 -4x -1 = 0 . . . . . . divide by 2

  (5x +1)(x -1) = 0 . . . . . . factor

Solutions are the values of x that make these factors zero:

  5x +1 = 0   ⇒   x = -1/5

  x -1 = 0   ⇒   x = 1

Solutions are x = -1/5, x = 1.

Answer:

|5| = 5 and |2| = 2 and because 5 > 2, our answer is |5| > |2|.

Answer:

|5|

Step-by-step explanation:

5 is greater than 2

Answer:

-9

Step-by-step explanation:

5x+8-3x = -10

Combine like terms

2x+8 = -10

Subtract 8 to both sides

2x = -18

Divide both sides by 2

x = -9

Answer:

-9

Step-by-step explanation:

5x + 8 - 3x = -10

Combine like terms

2x + 8 = -10

Subtract 8 to both sides

2x = -18

Divide both sides by 2

x = -9

Answer:

[tex]81\pi[/tex]

Step-by-step explanation:

[tex]Area = \pi * r^{2} \\\pi *9^{2} =81\pi[/tex]

Answer:

81 π

Step-by-step explanation:

formula is radius squared times pi or π so the answer would be 9x9=81 and you said to leave in terms of π so the answer is 81 π.

Answer: a) S'(1) = 136; S'(2) = 104; S'(4) = 76;

b) S''(1) = -38; S''(2) = -26; S''(4) = -2

Step-by-step explanation:

a) S' means first derivative;

[tex]\frac{d}{dt}[/tex](6t³ - 45t² +180t +130) = 6t² - 50t + 180

S'(1) = 6.1² - 50.1 + 180

S'(1) = 136

S'(2) = 6.2² - 50.2 + 180

S'(2) = 104

S'(4) = 6.4² - 50.4 + 180

S'(4) = 76

b) S'' is the second derivative of S:

[tex]\frac{d^2}{dt^2}[/tex](6t² - 50t + 180) = 12t - 50

S''(1) = 12.1 - 50

S''(1) = -38

S''(2) = 12.2 - 50

S"(2) = -26

S"(4) = 12.6 - 50

S"(4) = -2

c) Derivative is the rate of change of a function. The first derivative is the slope of the tangent line to the graph if the function in a determined point, while the second derivative measures how the rate of change is changing.

Analysing the values, we can conclude that the sales of the product after t months is decreasing at a rate of 12.

Answer:

2,748.5

Step-by-step explanation:

Answer:

thank uuu

Step-by-step explanation:

Question Correction

A group of neighbors are constructing a community garden that is 80 meters wide and 40 meters long. The top two vertices are plotted below at (10, 70) and (90, 70). What are the coordinates for the bottom two vertices of the garden?

Answer:

(10,30) and (90,30)

Step-by-step explanation:

The community garden is 80 m wide and 40 m long.

The top two vertex are plotted at: (10, 70) and (90, 70).

Horizontal Distance =90-10=80

This serves as the Width of the garden.

Since the length is 40m, the bottom two vertex can be derived by the transformation: (x,y-40).

(x,y-40)-->(10, 70)=(10,30); and

(x,y-40)-->(90, 70)=(90,30)

The coordinates for the two bottom vertices are (10,30) and (90,30).

Answer:

i think is 30$

Step-by-step explanation:

Answer:

B. $15.00

Step-by-step explanation:

Think about it this way:

3 = 1.50

6 = 3.00

8 = 4.00

12 = 6.00

If you divide each of the first numbers by the second, you'll get 2.

This means that every doughnut costs $0.50.

From there you just multiply .5 by 30

  30

x  .5

15

30 Donuts would cost 15 dollars.

Ok so the above is a little bit more of a complicated way to do it, but it'll be more efficient for a similar, but more difficult problem. The general goal of these problems is to find out what 1 of the item would cost. In this case it's $0.50, but you need to find that out in all of these problems.

brainliest is appreciated.

Answer:

80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Step-by-step explanation:

We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;

Hours of TV per week (X): 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.

Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;

                                P.Q. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean number of hours of TV watched per week = [tex]\frac{\sum X}{n}[/tex] = 9.65

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]  = 4.61

            n = sample of people = 20

           [tex]\mu[/tex] = true average number of hours of TV watched per week

Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.

So, 80% confidence interval for the true average, [tex]\mu[/tex] is ;

P(-1.33 < [tex]t_1_9[/tex] < 1.33) = 0.80  {As the critical value of t at 19 degrees of

                                               freedom are -1.33 & 1.33 with P = 10%}  

P(-1.33 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.33) = 0.80

P( [tex]-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

P( [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.80

80% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.33 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.33 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                         = [ [tex]9.65-1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] , [tex]9.65+1.33 \times {\frac{4.61}{\sqrt{20} } }[/tex] ]

                                         = [8.28 hours, 11.02 hours]

Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Answer:

$61.12

Step-by-step explanation:

Price of the Video game = $69.99

Discount = 18%

Discount price = 18% of $69.99

                         = $69.99*18/100

                         = $12.6

Price after Discount = Price - Discount price

                                  = $69.99 - $12.6

                                  = $57.39

Sales tax = 6.5% applied to the discounted price

                = 6.5% of $57.39

sales tax in dollars = $57.39 * 6.5/100

                               = $3.73

The amount he pays for the game = $57.39 + $3.73

                                                          = $61.12

Answer:

The relation between battery capacity and time is:

[tex]Y=0.05t+0.2[/tex]

The graph is attached.

Step-by-step explanation:

We will graph the charged capacity of the battery in function of time.

The rate of charge is constant, so we can conclude the relation is linear.

At time t=0, the battery capacity is at 0.2 (or 20%).

Every minute that passes, an additional 5% percent of its capacity is charged. So we can say that at t=1, the battery capacity is 0.2+0.05=0.25 (or 25%).

We can calculate the slope of the linear function as:

[tex]m=\dfrac{\Delta Y}{\Delta t}=\dfrac{0.05}{1}=0.05[/tex]

Then, the relation between battery capacity and time is:

[tex]Y=0.05t+0.2[/tex]

Answer:

1. Number of classes used are 7 with 5 class interval.

Step-by-step explanation:

Note: See the attached files for the tables and answers to questions 2, 3, 4 and 5.

Answer:

y=3x-1

Step-by-step explanation:

you first find the gradient

(-7,-5). (-7,-2)

x¹ y¹ x² y²

gradient=y²-y¹

x²-x¹

-2+5

-7+7

3/1=3. gradient is 3

equation formula= y=mx+c

(among the two sets of value you were given use one eg I will use -7 and -2)

y-(-7)/x-(-2)=3

y+7/x+2=3

y+7=3(x+2)

y+7=3x+6

y=3x+6-7

y=3x-1

Answer:

[tex]75.6\%[/tex]

Step-by-step explanation:

Let B be the event of buying a basic model.

Given that P(B) = 41%

Let D be the event of buying a basic model.

Given that P(D) = 1 - 41% = 59%

Let E be the event of extended warranty.

Given that:

P(E [tex]\cap[/tex] B) = 31% and

P(E [tex]\cap[/tex] D) = 48%

P(E) = P(E [tex]\cap[/tex] B) [tex]\times[/tex] P(B) + P(E [tex]\cap[/tex] D) [tex]\times[/tex] P(D)

P(E) = 31% [tex]\times[/tex] 41% + 48% [tex]\times[/tex] 59% = 0.4103

To find: P(B/E)

Formula:

[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]

[tex]\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%[/tex]

So, the correct answer is [tex]75.6\%[/tex].

Answer:

C is the correct answer.

Step-by-step explanation:

The reason it is C is because pi/the symbol on top is irrational.

Hope you have a good rest of your day :)

Answer:

Mean of the binomial distribution  μ = 82.68

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 106 diamonds

The probability that the diamonds fail to qualify as "gemstone grade

p = 78% =0.78

We will use binomial distribution

Mean of the binomial distribution

                                       μ = n p

                                       μ = 106 × 0.78

                                       μ = 82.68

conclusion:-

Mean of the binomial distribution  μ = 82.68

Answer:

c>-13/10

Step-by-step explanation:

55c+13<75c+39

55c+13-75c<39

-20c+13<39

-20c<39-13

-20c<26

c>26/-20

c>-13/10

Answer:

18 meters.

Step-by-step explanation:

There is a constant acceleration for 3 seconds, reaching 4 m/s. This, when drawn on a velocity/time graph, creates a diagonal line. The area underneath this line, which is the distance it travels, is found by the following: 0.5(l*h), the formula used to find the area of a triangle.

0.5(3*4)=6m

There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.

0.5(2*4)=4m

Now, all that remains is a rectangle of height 2 and a length of 4, so we find the area of it.

2*4=8m

Finally, we add each of these up.

6m+4m+8m=18m

Sorry if the step by step process was poorly explained, I'm not the best at explaining. Hope this helped, though. :^)

The total distance traveled by the toy car is 18 meters.

Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.

For three seconds, there is a steady acceleration that reaches 4 m/s. This yields a diagonal line when drawn on a velocity/time graph. The following formula can be used to determine the region beneath this line, or the distance it travels:

The triangle area is calculated using the formula:-

A = 0.5(l x h).

A = 0.5(3 x 4)=6m

There is then a constant deceleration of 0.5m/s for 4 seconds. This does also create a diagonal line on a velocity/time graph, but it doesn't go down to 0. What I do is split it up so that a triangle and a rectangle are created from the shape made. The triangle has a height of 2, and a length of 4, so we use the same formula used before.

0.5(2 x 4)=4m

Now, all that remains is a rectangle of height 2 and a length of 4, so we find its area of it.

2 x 4 = 8m

Finally, we add each of these up.

6m+4m+8m=18m

Therefore, the total distance traveled by the toy car is 18 meters.

To know more about acceleration follow

https://brainly.com/question/23516420

#SPJ2

Answer:

160 units and $6400

Step-by-step explanation:

We have that the cost per x unit is: 20 * x + 0.25 * x ^ 2

the price per unit is 100, therefore revenue for each unit would be 100 * x

However:

profit = revenue - cost

p (x) = 100 * x - 20 * x - 0.25 * x ^ 2

for the maximum value profit we must derive and equal 0:

p '(x) = 100 - 20 - 0.5 * x

0 = 80 - 0.5 * x

0.5 * x = 80

x = 80 / 0.5

x = 160

Therefore, the maximum profit occurs when there are 160 units, replacing we have:

p (x) = 100 * 160 - 20 * 160 - 0.25 * 160 ^ 2

p (x) = 6400

that is to say that the $ 6400 is the maximum profit.