At the beginning of the year, a sporting goods store had $250,000 worth of inventory. The store’s buyers purchased an additional $115,000 worth of inventory during the year. At year’s end, the value of the inventory was $185,000. What was the store’s cost of goods sold?

Final answer:

The total distance the spaceship traveled is 5/6 of a light-year, which was obtained by adding 3/4 and 1/12 light years together after finding a common denominator for the fractions.

Explanation:

The student's question is about calculating the total distance a spaceship travels based on two separate distances given in light years. To find this total distance, we will perform an addition of the two distances.

First, the spaceship traveled 3/4 of a light-year to a space station. Then, it traveled an additional 1/12 of a light-year to a planet.

To get the total distance traveled, we simply add the two distances:

To add these fractions, we need a common denominator, which is 12 in this case:

Now, when we add these fractions, we get:

We can simplify this fraction to:

Therefore, the spaceship traveled a total of 5/6 of a light-year.

Answer: Option 'd' is correct.

Step-by-step explanation:

Since we have given that

Researcher A :

Mean = 12.4

Standard deviation = 9

sample size = 30

So, the standard error is given by

[tex]\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{9}{\sqrt{30}}\\\\=1.643[/tex]

Researcher B:

Mean = 12.4

Standard deviation = 9

Sample size = 40

So, the standard error is given by

[tex]\dfrac{\sigma}{\sqrt{n}}\\\\=\dfrac{9}{\sqrt{40}}\\\\=1.423[/tex]

Sample B has smaller standard error than sample A because the sample size was larger than A.

Hence, Option 'd' is correct.

Answer:

$ 9287.45

Step-by-step explanation:

Since, the amount formula in compound interest,

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where,

P = principal amount,

r = rate per period,

n = number of periods per year,

Here, P = $ 5,000, r = 7% = 0.07, t = 9 years, n = 2 (semiannual in a year),

Thus, the amount after 9 years,

[tex]A=5000(1+\frac{0.07}{2})^{18}[/tex]

[tex]=5000(1+0.035)^{18}[/tex]

[tex]=5000(1.035)^{18}[/tex]

= $ 9287.45

Answer:

S=12+7D

Step-by-step explanation:

Linear relationships.

The initial amount of money Ethan has is $12. Each day, he adds up $7 to his savings. At a given day D after his initial funding, he will have added $7D, and he will have in his piggy bank

S=12+7D

For example, on the day D=30 he will have

S=12+7(30)=$222

Final answer:

Bob's consumer surplus after a tax is $4, and Lisa's is $1, making the total consumer surplus for both after the tax $5.

Explanation:

Consumer surplus is the difference between the value a consumer places on a good and what they actually pay. Before the government levies a tax, Bob's consumer surplus for a movie ticket is the difference between his valuation of $10 and the market price of $5, which is $5. Lisa's consumer surplus is the difference between her valuation of $7 and the market price of $5, which is $2.

After the government implements a $1 tax on movie tickets, increasing the price to $6, Bob's consumer surplus becomes $4 ($10 - $6), and Lisa's consumer surplus is now $1 ($7 - $6). Thus, the total consumer surplus for Bob and Lisa after the tax is implemented is $5 ($4 for Bob and $1 for Lisa).

Answer: 0.2

Step-by-step explanation:

We know that , the probability density function for uniform distribution is given buy :-

[tex]f(x)=\dfrac{1}{b-a}[/tex], where x is uniformly distributed in interval [a,b].

Given : The time to process a loan application follows a uniform distribution over the range of 8 to 13 days.

Let x denotes the time to process a loan application.

So the probability distribution function of x for interval[8,13] will be :-

[tex]f(x)=\dfrac{1}{13-8}=\dfrac{1}{5}[/tex]

Now , the probability that a randomly selected loan application takes longer than 12 days to process will be :-

[tex]\int^{13}_{12}\ f(x)\ dx\\\\=\int^{13}_{12}\dfrac{1}{5}\ dx\\\\=\dfrac{1}{5}[x]^{13}_{12}\\\\=\dfrac{1}{5}(13-12)=\dfrac{1}{5}=0.2[/tex]

Hence, the probability that a randomly selected loan application takes longer than 12 days to process = 0.2

The probability a loan application takes no longer than 12 days is 0.1666

Let x = time to process a loan application

for a uniform distribution (8, 13)

[tex]f(x) = \frac{1}{6} ; 8 < x < 13[/tex]

The probability is

[tex]Pr[x > 12] = \int\limits^1^3_1_2 {f(x)} \, dx = 1/6\int_1_2^1^3 dx = \frac{13-12}{6} = 1/6[/tex]

The probability a loan application takes no longer than 12 days is 0.1666

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Answer:

The length of the altitude is 9.3 yards and

The area of the triangle Δ UVW is 139.3 yd².

Step-by-step explanation:

Given

WU = 22 yd

WV = 30 yd

∠ UWV = 25°

To Find:

Altitude, UM = ?

area of the Δ UVW = ?

Construction:

Draw UM perpendicular to WV, that is altitude UM to WV.

Solution:

In right triangle Δ UWM if we apply Sine to angle W we get

[tex]\sin W = \frac{\textrm{side opposite to angle W}}{Hypotenuse}\\ \sin W=\frac{UM}{UW} \\[/tex]

substituting the values we get

[tex]\sin 25 = \frac{UM}{22}\\0.422 = \frac{UM}{22} \\UM = 0.422\times 22\\UM = 9.284\ yd[/tex]

Therefore, the altitude from U to WV is UM = 9.3 yd.(rounded to nearest tenth)

Now for area we have formula

[tex]\textrm{area of the triangle UVW} = \frac{1}{2}\times Base\times Altitude \\\textrm{area of the triangle UVW} = \frac{1}{2}\times VW \times UM\\=\frac{1}{2}\times 30\times 9.284\\ =139.26\ yd^{2}[/tex]

The area of the triangle Δ UVW is 139.3 yd². (rounded to nearest tenth)

Answer: option 1 is the correct answer

Step-by-step explanation:

Number of times for which the die was rolled is 360. It means that our sample size, n is 360.

The probability of rolling a 5 or a 6 is 1/3. It means that probability of success,p = 1/3. The probability of failure,q is

1 - probability of success. It becomes

1 - 1/3 = 2/3

The formula for standard deviation is expressed as

√npq. Therefore

Standard deviation = √360 × 1/3 × 2/3

= √80 = 8.9443

Standard deviation is approximately 8.9

Answer: 68C2 = 2278

Step-by-step explanation:

Answer:

t=5.20s

Step-by-step explanation:

I think that is the expression because it say he purchases two bags, all the bags are 5.20 so he brought two bags which are school bag and one hand bag the formula I used was y=mx+b but in these case I had to put t=5.20x. I hope this really helped you..

Answer:

Step-by-step explanation:

Anthony purchases two bags. The price of all bags is $5.20

Anthony purchases one school bag and one hand bag. It means that he purchased one handbag and one school bag for a total cost of $5.20

Let s represent the number of school bags and

Let h represent the number of hand bags.

An expression that represents the total cost,T, of the bag will be

T = s + h

Since total cost = $5.20

Then,

5.20 = s + h

Answer:

27.71

Step-by-step explanation:

Using Google, we can find that if we plug in the area, a, the formula for the area of the triangle is [tex]\frac{\sqrt{3} }{4} a^{2}[/tex]. Plugging it in, we get [tex]\frac{\sqrt{3} }{4} * 64[/tex] = 27.71 (approximately)

Area of an equilateral triangle that has sides that are [tex]8[/tex] inches long is equal to [tex]\boldsymbol{16\sqrt{3}}[/tex] square inches

A triangle is a polygon that consists of three sides and three angles.

An equilateral triangle is a triangle in which all sides are equal and all angles are equal.

Length of a side of an equilateral triangle [tex](l)=8[/tex] inches

Area of an equilateral triangle [tex](A)=\boldsymbol{\frac{\sqrt{3}}{4}l^2}[/tex]

                                                        [tex]=[/tex][tex]\boldsymbol{\frac{\sqrt{3}}{4}(8)^2}[/tex]

                                                       [tex]=\boldsymbol{16\sqrt{3}}[/tex] square inches

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Answer:1) $40x 2)$80x 3) 500units 4)b

Step-by-step explanation:

For the cost function, which is the amount used for production, we are told to use x and number of canoes produced, and canoe is produced at $40 per canoe, multiplying both

So production cost is $40x

And each canoe is sold at $80 per canoe, multiplying with no of canoes

so revenue is $80x

The break even cost happens when the amount of money put into the business equals the amount of revenue got, so total amount of money put into the business is the addition of the fixed cost and production cost of the canoes which is $20,000 + $40x (1)

And the revenue cost is 80x (2)

So equating (1) and (2) together, we find the value of x to reach the break even point

20000 + 40x = 80x

20000 = 80x - 40x

20000 = 40x

20000/40 = x

x = 500 units

I've already explained the answer to 4 being option b, because that's the fact we used to solve the amount of units to produce and sell to reach the break even point

Answer:

  y - 285 = 45(x - 3)

Step-by-step explanation:

The given point is (hours, fee) = (3, 285), and the slope is given as 45 per hour.

The point-slope form of the equation for a line is ...

  y - k = m(x - h) . . . . . . . for a slope m and a point (h, k)

Using the given values, and letting x stand for the number of hours, the equation is ...

  y - 285 = 45(x - 3)

Answer:

y - 285 = 45(x - 3)

Step-by-step explanation:

Answer:

The answer to your question is [tex]f(x) = \sqrt{x+ 4}[/tex]

Step-by-step explanation:

                                           f(x) = x² - 4

Process

1.- Change f(x) for y

                                           y = x² - 4

2.- Change "x" for "y" and "y" for "x".

                                           x = y² - 4

3.- Make "y" the object of the equation

                                          y² = x + 4

                                          [tex]y = \sqrt{x+ 4}[/tex]

4.- Change "y" for f(x)

                                          [tex]f(x) = \sqrt{x+ 4}[/tex]

Question is Incomplete, Complete question is given below,

Murphy loves pistachio nuts. Every Saturday morning, she walks to the market and buys some. Last week, she bought two pounds and paid $7.96, and this week she bought only one-half pound and paid $1.99. What the unit rate for pistachio nuts?

Answer:

The unit rate for pistachio nuts is $3.98.

Step-by-step explanation:

Given;

Price of 2 pounds of pistachio nuts = $7.96

We need to find the price of 1 pound of pistachio nuts.

To find the same we will use the unitary method,

Hence ,

Price of 1 pound of pistachio nuts = [tex]\frac{\$7.96}{2} = \$3.98[/tex]

Also given:

Price of half pound of pistachio nuts = $1.99

We need to find the price of 1 pound of pistachio nuts.

To find the same we will use the unitary method,

Hence ,

Price of 1 pound of pistachio nuts = [tex]\$1.99\times 2 = \$3.98[/tex]

Hence, The unit rate for pistachio nuts is $3.98

The solution to the system of equations represents the break-even point for the production and sale of sweatshirts, indicating the number of units that must be sold to cover production costs.

The solution of the system of equations y=35x and y=-0.05(x-400)^2+9,492 represents the break-even point where the money collected from selling x number of sweatshirts equals the money spent to produce those sweatshirts. In this context, solving the system means finding the number of sweatshirts (x) that need to be sold at $35 each to exactly cover the production costs described by the second equation.

This involves first substituting the expression for y from the first equation into the second equation, then solving for x to find the exact point where income equals expenses. Once x is found, it can be plugged back into either equation to verify the break-even amount of money (y).

Answer:

(-2, 2)

Step-by-step explanation:

Well first you would have to graph both inequalities.

y = mx + b

b is the y-axis intercept

m is the slope

Answer:

Co-ordinates of point N is (3,-6)

Step-by-step explanation:

Given point:

Endpoint K(7,-2)

Mid-point of segment KN (5,-4)

Let endpoint [tex]N[/tex] have co-ordinates [tex](x_2,y_2)[/tex]

Using midpoint formula:

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are co-ordinates of the endpoint of the segment.

Plugging in values to find the midpoint of segment KN.

[tex]M=(\frac{7+x_2}{2},\frac{-2+y_2}{2})[/tex]

We know [tex]M(5,-4)[/tex]

So, we have

[tex](5,-4)=(\frac{7+x_2}{2},\frac{-2+y_2}{2})[/tex]

Solving for [tex]x_2[/tex]

[tex]\frac{7+x_2}{2}=5[/tex]

Multiplying both sides by 2.

[tex]\frac{7+x_2}{2}\times 2=5\times 2[/tex]

[tex]7+x_2=10[/tex]

Subtracting both sides by 7.

[tex]7+x_2-7=10-7[/tex]

∴ [tex]x_2=3[/tex]

Solving for [tex]y_2[/tex]

[tex]\frac{-2+y_2}{2}=-4[/tex]

Multiplying both sides by 2.

[tex]\frac{-2+y_2}{2}\times 2=-4\times 2[/tex]

[tex]-2+y_2=-8[/tex]

Adding both sides by 2.

[tex]-2+y_2+2=-8+2[/tex]

∴ [tex]y_2=-6[/tex]

Thus co-ordinates of point N is (3,-6)

Answer:

Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))

1. R is reflexive if for each element a∈B, aRa.

2. R is symmetric if satisfies that if aRb then bRa.

3. R is transitive if satisfies that if aRb and bRc then aRc.

Then, our set B is [tex]\{1,2,3,4\}[/tex].

a) We need to find a relation R reflexive and transitive that contain the relation [tex]R1=\{(1, 2), (1, 4), (3, 3), (4, 1)\}[/tex]

Then, we need:

1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,

2. Observe that

Therefore [tex]\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(4,1),(4,2)\}[/tex] is the smallest relation containing the relation R1.

b) We need a new relation symmetric and transitive, then

and the analysis for be transitive is the same that we did in a).

Observe that

Therefore, the smallest relation containing R1 that is symmetric and transitive is

[tex]\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}[/tex]

c) We need a new relation reflexive, symmetric and transitive containing R1.

For be reflexive

For be symmetric

For be transitive

Then, the smallest relation reflexive, symmetric and transitive containing R1 is

[tex]\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}[/tex]

To find the smallest relation containing given pairs with specific properties, we add missing pairs and ensure all existing pairs satisfy the required properties.

a. To find the smallest relation that is reflexive and transitive, we need to add any missing pairs that would make the relation reflexive and ensure that all existing pairs satisfy the transitive property. In this case, the relation already contains (1, 2), (1, 4), (3, 3), and (4, 1). To make it reflexive, we add (2, 2) and (4, 4). To satisfy the transitive property, we need to add (1, 1), (2, 4), (3, 1), and (4, 2). Therefore, the smallest relation that is reflexive and transitive is {(1, 1), (1, 2), (1, 4), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4)}.

b. To find the smallest relation that is symmetric and transitive, we need to add any missing pairs that would make the relation symmetric and ensure that all existing pairs satisfy the transitive property. In this case, the relation already contains (1, 2), (1, 4), (3, 3), and (4, 1). To make it symmetric, we need to add (2, 1) and (4, 4). To satisfy the transitive property, we need to add (1, 1), (2, 4), (3, 1), and (4, 2). Therefore, the smallest relation that is symmetric and transitive is {(1, 1), (1, 2), (1, 4), (2, 1), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4)}.

c. To find the smallest relation that is reflexive, symmetric, and transitive, we need to add any missing pairs that would make the relation reflexive, symmetric, and ensure that all existing pairs satisfy the transitive property. In this case, the relation already contains (1, 2), (1, 4), (3, 3), and (4, 1). To make it reflexive, we add (2, 2) and (4, 4). To make it symmetric, we need to add (2, 1). To satisfy the transitive property, we need to add (1, 1), (2, 4), (3, 1), and (4, 2). Therefore, the smallest relation that is reflexive, symmetric, and transitive is {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 4)}.

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Answer:

A) c(x)=1.50+1.25x

Step-by-step explanation:

The fixed rate (constant) is 1.50 and 1.25 (variable) depending on the number of additional nights, that is, c (x) = 1.25 (x) +1.50 =1.50+1.25x

the answer would be A

Answer:11.396Ibs of nuts that cost $9.60/Ib and 9.014Ibs that cost $2.80/Ib

Step-by-step explanation:

First we find the cost of the supposed mixture we are to get by selling it $6.60/Ib which weighs 20.41Ibs

Which is 6.6 x 20.41 = $134.64

Now we label the amount of mixture we want to get with x and y

x = amount of nuts that cost $2.8/Ib

y = amount of nuts that cost $9.6/Ib

Now we know the amount of mixture needed is 20.41Ibs

So x + y = 20.41Ibs

And then since the price of the mixture to be gotten overall is $134.64

We develop an equation with x and y for that same amount

We know the first type of nut is $2.8/Ib

So for x amount we have 2.8x

For the second type of nut that is $9.6/Ib

For y amount we have 9.6y

So adding these to equate to $134.64

2.8x + 9.6y = 134.64

So we have two simultaneous equations

x + y = 20.41 (1)

2.8x + 9.6y = 57.148 (2)

We can solve either using elimination or factorization method

I'm using elimination method

Multiplying the first equation by 2.8 so that the coefficient of x for both equations will be the same

2.8x + 2.8y = 57.148

2.8x + 9.6y = 134.64

Subtracting both equations

-6.8y = -77.492

Dividing both sides by -6.8

y = -77.492/-6.8 =11.396

y = 11.396Ibs which is the amount of nuts that cost $9.6/Ib

Putting y = 11.396 in (1)

x + y = 20.41 (1)

x +11.396 = 20.41

Subtract 11.396 from both sides

x +11.396-11.396 = 20.41-11.396

x = 9.014Ibs which is the amount of nuts that cost $2.8/Ibs

To obtain the desired mixture, we set up a system of equations. However, there is no solution to this problem.

To find the amount of each type of nut needed to obtain the desired mixture, we can set up a system of equations.

Let x be the amount of the first type of nut (selling for $2.80/lb), and y be the amount of the second type of nut (selling for $9.60/lb).

We have the following equations:

Multiplying equation 1 by 2.80 and subtracting equation 2 from it, we can eliminate x and solve for y:

2.80x + 2.80y - (2.80x + 9.60y) = 56.16 - 6.60(20.4)

Simplifying the equation gives:

6.80y = 56.16 - 133.92

6.80y = -77.76

y = -77.76/6.80 ≈ -11.44

Since we cannot have a negative amount of nuts, the value of y is not valid.

Therefore, there is no solution to this problem. It is not possible to obtain a nut mixture with the given requirements.

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Answer:

Step-by-step explanation:

An arc is the length along the circumference of a circle that is bounded by 2 radii. I

A central angle in a circle has a measure of 180. This means that the arc subtends an angle of 180 degrees at the center of the circle.

The length of the arc is 8 inches

Formula for the length of an arc is expressed as

Length of arc = #/360 × 2πr

r = radius of the circle

Length of arc = 8 inches

# 180 degrees

π = constant = 3.14

Substituting,

8 = 180/360 ×2 × 3.142 × r

8 = 3.14r

r = 8/3.14 = 2.56 inches

Answer:

[tex]\displaystyle Mary\:and\:Neil[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 = \frac{7\frac{1}{2}}{3\frac{3}{4}}[/tex]

Two hours is much closer up three hours, so either way, they would still paint the room in time.

I am joyous to assist you anytime.

Final answer:

To maximize the enclosed area, each pig pen should have a length of 84 feet and a width of 168 feet.

Explanation:

To find the dimensions of the pig pens that will maximize the enclosed area, we can use the quadratic formula. Let's assume the length of each pen is 'x' feet. Since the two pens share a common side, the combined length of the pens will be '2x' feet. The total length of the fencing, including both sides and the common side, will then be '2x' + 'x' + 'x' = '4x' feet.

According to the problem, the total length of the fencing is 336 feet. Therefore, we can write the equation '4x = 336'. To find the value of 'x', we divide both sides of the equation by 4: 'x = 84'.

So, each pen should have a length of 84 feet and a width of 2x the length, which is '2 × 84 = 168' feet.

Final Answer:

The dimensions for each pig pen that would yield the maximum enclosed area are 84 feet in length and 56 feet in width.

Explanation:

To solve this optimization problem, we can use calculus. Let's denote:
- The length of each pig pen by L
- The width of each pig pen by W
- The total amount of fencing by P, which is 336 feet

Since the two pig pens share a common side, the amount of fencing will be used for 3 widths and 2 lengths. So our perimeter constraint is:
3W + 2L = P

Since we know P is 336 feet, we can write this as:
3W + 2L = 336

We want to maximize the area, A, of the two pens combined. Since the two pens are adjacent and identical, this area can be represented by:
A = 2 * (L * W)

We want to maximize A with respect to our constraint.
First, let's express L in terms of W using our perimeter constraint:
2L = 336 - 3W
L = (336 - 3W) / 2

Now, we can express the area solely in terms of W:
A = 2 * (L * W)
A = 2 * ((336 - 3W) / 2 * W)
A = (336W - 3W^2)

To maximize A, we take the derivative of A with respect to W and set it to zero:
dA/dW = 336 - 6W

Setting dA/dW to zero gives us:
336 - 6W = 0
6W = 336
W = 336 / 6
W = 56

Now we have the width of each pig pen. Next, we'll use the value of W to find L:
L = (336 - 3W) / 2
L = (336 - 3 * 56) / 2
L = (336 - 168) / 2
L = 168 / 2
L = 84

So the dimensions of each rectangular pen that will maximize the area with 336 feet of fencing are:
- Length (L) = 84 feet
- Width (W) = 56 feet

We should verify this solution is a maximum by checking the second derivative of the area function:
d²A/dW² = -6

Since the second derivative is negative, our critical point W = 56 feet corresponds to a maximum. Therefore, the dimensions for each pig pen that would yield the maximum enclosed area are 84 feet in length and 56 feet in width.

Answer:

24 boxes

Step-by-step explanation:

The processor knows that the standard deviation of box weight is 0.5 pound

[tex]\sigma = 0.5[/tex]

We are supposed to find How many boxes must the processor sample to be 95% confident that the estimate of the population mean is within 0.2 pound

Formula of Error=[tex]z \times \frac{\sigma}{\sqrt{n}}[/tex]

Since we are given that The estimate of the population mean is within 0.2 pound

So, [tex]z \times \frac{\sigma}{\sqrt{n}}=0.2[/tex]

z at 95% confidence level is 1.96

[tex]1.96 \times \frac{0.5}{\sqrt{n}}=0.2[/tex]

[tex]1.96 \times \frac{0.5}{0.2}=\sqrt{n}[/tex]

[tex]4.9=\sqrt{n}[/tex]

[tex](4.9)^2=n[/tex]

[tex]24.01=n[/tex]

Hence the processor must sample 24 boxes to be 95% confident that the estimate of the population mean is within 0.2 pound

To be 95% confident that the estimate of the population mean is within 0.2 pound, the processor must sample approximately 25 boxes, as the calculation using the sample size estimation formula indicates.

To determine how many boxes must be sampled to be 95% confident that the estimate of the population mean is within 0.2 pound, we use the formula for the sample size in estimation:

n = (Z·σ/E)^2

Where:

For a 95% confidence level, the z-score (Z) is approximately 1.96. Given that the population standard deviation (σ) is 0.5 pound and the desired margin of error (E) is 0.2 pound, the formula becomes:

n = (1.96· 0.5/0.2)^2

Calculating:

n = (1.96· 2.5)^2

n = (4.9)^2

n = 24.01

The processor must sample approximately 25 boxes (since we round up to the nearest whole number when it comes to sample size) to be 95% confident that the estimate of the population mean is within 0.2 pound.

Answer:

options 1,3,4 are functions.

Step-by-step explanation:

RULE: a relation is said to be a function if every element in the domain ( the numbers in the left side in the below sets) is related to only one number ( number on the right side in the below sets).

Let us check each option one by one:

1.   3           2

    9           1

   -4           7

    0          -2

here each number on the left side is mapped to or is related to one number only.

so this relation is a function

2.  7         1

    -5        2,3

     1         0

here, "-5" is mapped to two different numbers. so this relation is not a function.

3.  -2    -4

    2      4

    6      8

    -6    -8

here each number on the left side is mapped to or is related to one number only.

so this relation is a function

4.  1     3

   -1    3

   2    3

  -2    3

here each number on the left side is mapped to or is related to one number only.

so this relation is a function.

even if it is related to the same number, it doesn't matter.

it should follow the above given rule that's it.

Answer:

a.False

b.False

Step-by-step explanation:

a.Total possible outcomes of a die=1,2,3,4,5,6=6

Probability of getting an ace=[tex]\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]

Favorable cases=1

Probability of getting an ace=[tex]\frac{1}{6}[/tex]

A die is rolled three times .

We are given that the probability of getting at least one ace is

[tex]\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1}{2}[/tex]

There are using addition rule but it is not correct because addition rule used when the events are mutually exclusive .

The events are mutually exclusive when the events cannot occur at the same time.

Since it is possible to obtain one ace on more than one roll of a die.

Therefore, the events are not  mutually exclusive.

Hence, the given statement is false.

b.Total cases in one coin=2(H,T)

Number of cases in favor of head=1

The probability of getting on head=[tex]\frac{1}{2}[/tex]

The coin is tossed twice.

We are given that

If a coin is tossed twice ,the chance of getting at least on head is 100%.

There are using addition rule but it is not correct because addition rule used when the events are mutually exclusive .

The events are mutually exclusive when the events cannot occur at the same time.

Since it is possible to obtain head on both  tosses of coin.

Therefore, the events are not  mutually exclusive.

Hence, the given statement is false.

Both statements are false. For the dice rolls, the chance of getting at least one ace is calculated by finding the complementary probability. For the coin tosses, the chance of getting at least one head is 3 in 4, not 100%.

The question revolves around basic probability concepts applied to dice and coin tossing. Firstly, part (a) of the question is false. When a die is rolled three times, the chances of getting at least one ace (or a one) are not simply the sum of the individual probabilities. Events are independent, meaning the outcome of one roll doesn't affect the other.

The correct approach is to calculate the probability of not getting an ace in all three rolls (5/6 * 5/6 * 5/6) and subtract this from 1 to get the complementary probability of at least one ace.

For part (b), the statement is also false. When a coin is tossed twice, the chance of getting at least one head is not 100%. To find the correct probability, we can list all possible outcomes (HH, HT, TH, TT) and calculate that there is a 3 in 4 chance of getting at least one head.

Answer:

a one-unit increase

Step-by-step explanation:

In a simple regression model, the relationship between x and y can be represented by the equation y = ax+b, where

The slope term is the change in the mean value of y associated with a one-unit increase in x.