​Paul buys a ping pong table that has an original price of $350. He uses a coupon code to get a 20% discount off of the original price. He is then charged a 6%​ tax on the discounted price. What is the final cost for Paul's ping pong table?

Critical value with 35 degrees of freedom at 0.05 Los = 2.030

Given information,

Departmental liabilities have a mean and standard deviation that are unknown for the population. What t-score should be used to establish a 95% confidence interval estimate for the population mean if a random sample of 36 departments is utilized to estimate the mean liabilities?

Here,

By assuming a 95% confidence interval and by considering the t-value we have,

Therefore;

Critical value at 0.05 Los with 35 degrees of freedom =2.030

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The solution for y in the expression is y = -53 and y = 63

From the question, the expression is given as

y = 5 ± 58

We start by expanding the expression

So, we have the following representation

y = 5 - 58 and y = 5 + 58

Evaluate the sum and the difference of the like terms in the above expression

So, we have the following representation

y = -53 and y = 63

Hence, the solution is

y = -53 and y = 63

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Answer:

A. 20,000 is 10% of 200,000, so the percentage of the purchase price is 10%.

B. 90,000 is 45% of 200,000, so the percentage of the 90,000 down payment is 45%.

The probability of obtaining at least 1 false positive if the number of employees is 500 is 0.5

Probability

In the statistics concept, the probability refers the possible number of way of happening the particular event.

Given,

A test for a certain drug has a 0.1% probability of producing a false positive.

Here we need to find  the probability of obtaining at least 1 false positive if  a company hired 500 drug-free employees.

In the given question, we have the following values,

=> number of employees = 500

=> Probability of false positive = 0.1%

So, the probability of obtaining at least 1 false positive is calculated as,

=> 500 x 0.1/100

=> 5 x 0.1

=> 0.5

Therefore, the probability of obtaining at least 1 false positive is 0.5.

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If Shen produced and Manuel consumed one additional bottle of water, total surplus would be $2

The law of supply and demand combines two fundamental economic ideas that describe how changes in the price of a resource, commodity, or product affect its supply and demand.

Supply grows as the price rises, but demand drops. In contrast, as the price falls, supply is constrained and demand is increased.

Demand and supply levels for different prices can be displayed as curves on a graph. The intersection of these curves symbolizes the process of price discovery in the marketplace, as it indicates the balance, or market-clearing price, at which demand equals supply.

According to the law of demand, demand for a good or resource will decrease as its price increases and increase as its price decreases.

How to solve?

Price ------ Quantity Supplied ----- Quantity Demanded

2 --------------------- 1 ------------------------- 3

4 --------------------- 2 ------------------------ 2

6 --------------------- 3 ------------------------ 1

4 (quantity supplied = quantity demanded = 2)

4 ($7>$4 and $5>$4, $3<$4<$5, area above price line but under curve if price line was at $4, $7-$4=$3, $5-$4=$1, $3+$1=$4); 4 ($1<$4 and $3<$4, $3<$4<$5, area below price line and under curve if price line at $4, $4-$1=$3, $4-$3=$1, $3+$1=$4); 8 ($4 from consumer surplus + $4 from producer surplus)

fall (equilibrium = 2, 2-1=1, Shen: quantity supplied = 1 -> $2, Manuel: quantity demanded = 1 -> $6, total surplus = producer surplus + consumer surplus = ($4-$1)+($7-$4)=$6, $8>$6)

rise (equilibrium = 2, 2+1=3, Manuel: quantity demanded = 3 -> $2, Shen: quantity supplied = 3 -> $6, total surplus = consumer surplus + producer surplus = ($3-$2)+($7-$6)=$2, $8>$2, $6>$2)

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Answer:

5(v-1)/9

Step-by-step explanation:

(2/9v) - (-1/3v + 5/9)

To find the opposite of -1/3v + 5/9, find the opposite of each term.

2/9v  - (-1/3v) - 5/9

The opposite of -1/3v is 1/3v.

2/9v + 1/3v - 5/9

Combine 2/9v and 1/3v to get 5/9v

5/9v - 5/9

(1) It will take 17.8 hours for Sam's family to get to Chicago, Illinois .

(2) Rohan's family will take 17.9 hours to arrive in Chicago, Illinois .

In the question ,

it is given that ,

For Sam's Family ,

total distance to be covered is = 1157  miles ,

the average speed is given to be = 65 mph .

By the formula of Speed , Distance and Time ,

we get ,

65 = 1157/t

t = 1157/65

t = 17.8 hours .

For Rohan's family ,

total distance to be covered is = 1250  miles ,

the average speed is given to be = 70 mph ,

By the formula of Speed , Distance and Time ,

we get ,

70 = 1250/t

t = 1250/70

t = 17.9 hours

Therefore , Sam's family will take 17.8 hours and Rohan's family will take 17.9 hours .

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The expected value of the product of the numbers on the marbles is

6.

Given:

There are 5 marbles numbered 1 through 5 in a bag.

Suppose if two different marbles are taken out at random.

what is the expected value of the product of the numbers on the marbles = ?

5C 2  =  10

So we have ten possible sums

1 + 2  = 3       2 + 3  = 5      3  + 4  =  7      4 + 5  =  9

1+ 3  =  4       2 + 4  = 6      3 +  5  =  8

1 + 4 =  5       2 + 5 =  7

1 + 5  = 6

Expected value  =

3 *  Prob of occurence  + 4 * Prob of occurence + 5*Prob of occurence + 6 * Prob of occuence +7 * Prob of occurence   + 8 * Prob of occurence  + 8 * Prob of occurence

3 (1/10)  + 4(1/10) + 5(2/10) + 6(2/10)  + 7 (2/10) + 8 (1/10) + 9(1/10)  =

3/10  + 4/10  + 10/10  + 12/10 + 14/10  + 8/10 + 9/10 =  

60/10

= 6

Hence we get the required answer.

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The values of a, b and c in the mixed fractions are 1, 5 and 9 respectively.

The fractions are mixed fractions . let's convert it to improper fraction be we simplify its.

A mixed fraction is a whole number and a proper fraction combined. Improper fractions are defined as fractions for which the numerator is greater than the denominator.

Therefore, let's solve the fractions as follows:

[tex]3\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]

[tex]3\frac{1}{2} = \frac{7}{2}[/tex]

[tex]2\frac{1}{4} = \frac{9}{4}[/tex]

Therefore,

[tex]\frac{7}{2} (\frac{4}{9} ) = \frac{28}{18} = 1\frac{10}{18} = 1\frac{5}{9}[/tex]

Hence,

a = 1

b = 5

c = 9

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The probability that the cost will be between $250 and $470 is 0.7354.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

Automobile repair costs continue to rise with the average cost now at $367 per repair.†

Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88.

We have to find the probability that the cost will be between $250 and $470.

P( 250 < x < 470 ) = P( x <470 ) - P( x < 250 )

P( x < 470 ) = NORMDIST( 470 , 367, 88, 1 ) = 0.8272

P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183

P( 250 < x < 470 ) = 0.8272 - 0.09183 = 0.7354

P( 250 < x < 470 ) = 0.7354

Hence, the probability that the cost will be between $250 and $470 is 0.7354.

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The triangles when enlarged by a scale factor of 3 the final image is at the coordinates: (7, 3), (5, 3), and (7, 7)

The coordinates of the preimage are

(5, 3), (4, 3), and (5, 5)

translate to the origin

= (5 - 3, 3 - 3), (4 - 3, 3 - 3), and (5 - 3, 5 - 3)

= (2, 0), (1, 0), and (2, 2)

dilate about the origin

2 * { (2, 0), (1, 0), and (2, 2) }

(4, 0), (2, 0), and (4, 4)

translate back to usual position

(4 + 3, 0 + 3), (2 + 3, 0 + 3), and (4 + 3, 4 + 3)

(7, 3), (5, 3), and (7, 7)

Therefore the image is at (7, 3), (5, 3), and (7, 7)

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Using the area formula, we know that the width of the pan is 18 inches.

An area is a unit of measurement used to describe a region's size on a flat or curved surface.

While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

So, the width of the pan will be:

We know that:

The length of a rectangular pan is exactly 4/3 the width.

The pan's total surface area is 432in².

Formula: Area = 432 = length*width = w*4w/3

Now, calculate the width as follows:

Formula: Area = 432 = length*width = w*4w/3

4w^2/3 = 432

w^2 = 432*3/4 = 324

w = 18

Therefore, using the area formula, we know that the width of the pan is 18 inches.

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Complete question:
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.2. What is the width of the cake pan

Answer: B. 18 in

Step-by-step explanation:

You will get this answer using the Area formula, which is A-lw

Answer:

Step-by-step explanation:

Chose 2 points (-3,6) and (0,8)

Using slope formula;   m=( y2 - y1 ). / ( x2 -x1)

m=(8-6)/(0+3)  = 2/3

slope 2/3 and y intercept is 8 because the  line cuts the y axis at (0,8)

the equation of the line is: y=2/3(x) + 8

Step-by-step explanation:

"with replacement". that means any pulled ball is returned into the bag, and we have the full 7+3 = 10 balls to pull from every time.

remember, a probability is always

desired cases / totally possible cases

(a) 2 back will be red. I understand this, that exactly 2 balls will be red (not fewer, not more).

to get exactly 2 red balls we get 2 red balls and 4 black balls.

the probability for such a single event is

7/10 × 7/10 × 3/10 × 3/10 × 3/10 × 3/10 = 49×81/1000000 =

= 0.003969

because the probably to get a red ball (one from 7 out of 10) is 7/10.

the probability to get a black ball is 3/10.

how many different such single events are possible ?

as many as there are combinations to pick 2 out of 6 :

C(6, 2) = 6! / (2! × (6-2)!) = 6! / (2 × 4!) =

= 6×5 / 2 = 3×5 = 15

so, the probability to get exactly 2 red balls is

15 × 0.003969 = 0.059535 ≈ 0.05954

(b)

the probability of all 6 balls being black is

3/10 × 3/10 × 3/10 × 3/10 × 3/10 × 3/10 =

= 3⁶/1000000 = 0.000729 ≈ 0.00073

(c)

"at least 4 black balls" means exactly 4, or exactly 5, or exactly 6 balls are black.

that means we need to calculate all 3 probabilities and add them (non-overlapping "or"-cases means addition of probabilities, "and" cases mean multiplication as above).

to get exactly 4 black balls (= 4 black balls and 2 red balls) is the same as (a) : 0.059535

to get exactly 5 black balls (= 5 black balls and 1 red ball) in one specific constellation is

3⁵/10⁵ × 7/10 = 243×7/1000000 = 0.001701

and we have C(6, 5) possible constellations

C(6, 5) = 6! / (5! × (6-5)! = 6! / 5! = 6

the total probability to get exactly 5 black balls is

6 × 0.001701 = 0.010206

to get exactly 6 black balls is (b) : 0.000729

the probability to get at least 4 black balls is

0.059535 + 0.010206 + 0.000729 =

= 0.07047

Using the definition of covariance, Cov(Y(1)Y(2))= 0. From the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2)). So, it can be concluded that Uncorrelated variables need not be independent.

Given joint probability function of Y(1) and Y(2), is

p(Y(1)*Y(2)) = 1/3, for (y(1)*y(2)) = (- 1, 0), (0, 1), (1, 0)

So Y(1), takes random variable -1,0,1.

And Y(2) takes random variable 0,1.

Y(2)|Y(1)      -1               0             1

0                  1/3            0             1/3

1                   0               1/3           0

From the table:

The marginal probability function of Y(1) is;

P(Y(1)=y(1)) = ∑P(Y(1)=y(1)), y(1)= -1,0,1. That is;

Y(1)=y(1)                      -1                   0               1

P(Y(1)=y(1))                  1/3                 1/3             1/3

From the definition of expectation,

E[y(1)]= [tex]\Sigma_{y_{1}}[/tex] y(1)P(Y(1)=y(1))

E[y(1)]= -1(1/3)+0(1/3)+1(1/3)

E[y(1)]= -1/3+0+1/3

E[y(1)]= 0

The marginal probability mass function of y(2) is

P(Y(2)=y(2)) = ∑P(y(1)y(2)), y(2)= 0,1. That is;

Y(2)=y(2)                    0               1

[tex]P_{Y(2)}[/tex](y(2))                  2/3             1/3

Now E[y(2)]= [tex]\Sigma_{y_{2}}[/tex] y(2)P(Y(2)=y(2))

E[y(2)]= 0(2/3)+1(1/3)

E[y(2)]= 1/3

And

E[y(1)y(2)]= [tex]\Sigma_{y_{1}}\Sigma_{y_{2}}[/tex] y(1)y(2)P(y(1)y(2))

E[y(1)y(2)]= -1(0)(1/3)+0(1)(1/3)+1(0)(1/3)

E[y(1)y(2)]= 0

From the definition of covariance.

The Cov(Y(1)Y(2))= E[Y(1)Y(2)]-E[Y(1)E[Y(2)]

Cov(Y(1)Y(2))= 0-1/3 (0)

Cov(Y(1)Y(2))= 0

The Cov(Y(1)Y(2))=0, implies that the two variables are uncorrelated. But from the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2))

Hence, it can be concluded that Uncorrelated variables need not be independent.

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The total cost for a team of 10 player in a baseball league is $978.5.

For the stated question,

The cost of each equipment for each player is-

Thus,

Total cost for each player =  $50. 95  + $20. 95  +  $25. 95

Total cost for each player = $97.85

Total number of player in a baseball league = 12

Total cost for team = 10 x $97.85

Total cost for team = $978.5

Thus, the total cost for a team of 10 player in a baseball league is $978.5.

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Answer: Alternate exterior angles --> 1,8 and 2,7

Vertical angles --> 2,3 and 5,8

Corresponding angles --> 1,5 and 2,6

Alternate interior angles --> 3,6 and 4,5

Answer:

it would take him 4/7 of an hour

Step-by-step explanation:

Answer:7:20

Step-by-step explanation:

The solution of the algebraic equation for the cost of downloading a song for members is x = $0.95

Given that:

1. Peggy pays an annual fee of $10.75. Last year she downloaded 105 songs

2. Non-members pay $0.35 more per song download than members

3. Daniel is not a member of the club and downloaded 85 songs last year

Let x represent the cost of downloading a song for members

Thus, the cost of a song for Peggy will be x

From statement 2: the cost of a song for Daniel will be x+0.35

The algebraic equation for the total amount for Peggy will be:

A = 105x + 10.75

The algebraic equation for the total amount for Daniel will be:

A = 85(x+0.35)

If Daniel and Peggy both paid the same total amount, we can say:

105x + 10.75 = 85(x+0.35)

105x + 10.75 = 85x + 29.75

105x - 85x = 29.75 - 10.75

20x = 19

x = 19/20

x = 0.95

Thus, the cost of a song for member is $0.95

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Answer:

A

Step-by-step explanation:

describes a good place

Answer: 72

Step-by-step explanation: because 8 x 12 = 96  and 3 x 8 = 24  

96 - 24 = 72

A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes.

Sample sizes may be chosen in several ways:

Given in the question:

A sample size of n is needed.

n is found when M = 0.4.

95% Central interval

Z = 1.96

  M = z × σ /√n

⇒ 0.40 = 1.96 × 0.75 /√n

⇒ 0.40√n = 1.96 ×0.75

⇒ √n = 1.96 ×0.75/0.40

⇒ (√n)² = (1.96 ×0.75 / 0.40 )²

⇒ n = 14.6

Rounding up 14.6

n = 15

The sample size of 15 is needed.

Thus, A large sample size of 15 is necessary if the width of the 95% interval is to be 0.40

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The probability that a randomly selected jury of 12 people is all male is 2.01 × 10⁻⁵   .

In the question ,

it is given that ,

total number of people in the jury pool is 30 people ,

the total number of men in the jury pool is = 16 ,

total number of women in the jury pool is = 14 ,

So , 12 members can be selected from 30 people in ³⁰C₁₂ ways ,

So , total number of ways = ³⁰C₁₂ = 86493225 ways

and 12 male can be selected from 16 men in ¹⁶C₁₂ ways

= ¹⁶C₁₂ = 1820.

So , the probability of selecting 12 men is = 1820/86493225

= 0.00002104211

≈ 2.01 × 10⁻⁵

Therefore , the required probability is 2.01 × 10⁻⁵  .

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Answer:

Positive seven.

Step-by-step explanation:

Go past zero to normal seven.

Answer:positive 7

Step-by-step explanation:

Tn the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂

An assertion used in statistical inference experiments is known as the alternative hypothesis.

It is indicated by Ha or H1 and runs counter to the null hypothesis.

Another way to put it is that it is only a different option from the null.

An alternative theory in hypothesis testing is a claim that the researcher is testing.

The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge.

According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.

So, the new production method supposedly lowers the mean operating cost per hour.

The following are the hypothesis when comparing the average production costs of the new production method (μ₁) with the old production method (μ₂):

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

Therefore, in the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂

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After approximately 113 minutes, there will be only 40 bacteria remaining.

Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.

N(t) = N₀(1/2)^(t/T)

where N(t) = amount of substance remaining after time t

N₀ = initial amount of substance

t = time

T = half-life

If the sample begins with 500 bacteria, and after 16 minutes there are 350 bacteria, then

N₀ = 500, and N(t) = 350 when t = 16 minutes

Substitute the given values and solve for the half-life.

N(t) = N₀(1/2)^(t/T)

350 = 500(1/2)^(16/T)

T = 31.09 minutes

Using the formula, solve for t when n(t) = 40.

N(t) = N₀(1/2)^(t/T)

40 = 500(1/2)^(t/31.09)

t = 113.30 minutes

t ≅ 113 minutes

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By using the concept of arithmetic series, it can be calculated that

y - x = 1250

What is arithmetic series?

Arithmetic series are those series whose difference between two consecutive terms are same.

The odd integers forms an arithmetic series

For the sum of first 25 odd integer

First odd integer = 1

25th odd integer = 49

Sum of first 25 odd integers = [tex]\frac{25}{2}(1 + 49)[/tex] = 625

x = 625

For the sum of first 50 odd integers

First odd integer = 1

50th odd integer = 99

Sum of first 50 odd integers = [tex]\frac{50}{2}(1 + 99)[/tex] = 2500

Sum of next 25 odd integers = 2500 - 625 = 1875

y = 1875

y - x = 1875 - 625 = 1250

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