What is DC ?

Enter the answer in the box.

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:

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:

As a fraction, the answer is 3/4

In decimal form that is equivalent to 0.75, which converts to 75%

===============================================

Work Shown:

13 red

13 green

13 yellow

13 blue

13+13+13+13 = 52 total

52 - 13 = 39 non-blue

--------

There are 39 non-blue candies out of 52 total.

39/52 = 3/4 is the probability, as a fraction, that we pick a non-blue candy.

3/4 = 0.75 = 75%

Answer:

Since the person took one piece of candy it would be 3/4 of candy. I think

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:

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:

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.

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:

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: 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: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: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:

x - y =  -  0.25 cups.

Step-by-step explanation:

Let x :  The number of cups of water Ashley is supposed to use

    y :  The  number of cups of water she actually uses

The actual measurement of water for 1 glass lemonade = 3/ 4 cup

So, the measurement of water for 5 glass lemonade  

=  5 x ( Measure of water for 1 glass) = [tex]5 \times (\frac{3}{4})[/tex]

The amount of water Ashley actually uses for 5 glass lemonade  = 4 cups

⇒  [tex]x = 5 \times (\frac{3}{4})[/tex]  = 3. 75 cups

   and   y = 4 cups

So, x - y = 3.75 cups  - 4 cups = -0.25 cups.

Hence, she used the amount 0.25 cups water extra while making 5 glass lemonades according to the given recipe.

To find x-y, subtract the amount of water Ashley actually uses from the amount she is supposed to use.

To find the value of x-y, we need to find the difference between the amount of water Ashley is supposed to use (x) and the amount of water she actually uses (y).

The recipe calls for 3/4 cup of water. Since Ashley wants to make five times the amount of lemonade, she needs to use 5 times the amount of water, which is 5 times 3/4 = 15/4 cups of water.

However, Ashley mistakenly uses 4 cups of water, so y = 4. Therefore, x-y = 15/4 - 4.

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

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:

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

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

Answer:

Volume of the silo is 7772 cubic ft.

Step-by-step explanation:

Given:

A grain Silo is cylindrical in shape.

Height  (h) = 44 ft.

Diameter (d) = 15 ft.

[tex]\pi  = 3.14[/tex]

We need to find the Volume of silo.

We will first find the radius.

Radius can be given as half of diameter.

hence Radius (r) = [tex]\frac{d}{2} =\frac{15}{2}=7.5ft.[/tex]

Since Silo is in Cylindrical Shape we will find the volume of cylinder.

Now We know that Volume of cylinder can be calculate by multiplying π with square of the radius and height.

Volume of Cylinder = [tex]\pi r^2h = 3.14\times(7.5)^2\times44 = 7771.5 ft^3[/tex]

Rounding to nearest whole number we get;

Hence,Volume of Silo is [tex]7772 \ ft^3[/tex].

The volume of the cylindrical grain silo with a diameter of 15 ft and a height of 44 ft is approximately 7,853 cubic feet.

The volume of a cylindrical grain silo can be found using the formula V = πr²h, where V is volume, π (pi) is approximately 3.14, r is the radius of the cylinder, and h is the height.

To calculate the volume, you first need to find the radius by dividing the diameter by two. The diameter is given as 15 ft, so the radius is 15 ft / 2 = 7.5 ft. Using the volume formula, the volume V is:

π × (7.5 ft)² × 44 ft

Performing the multiplication:

3.14 × (7.5 ft × 7.5 ft) × 44 ft

3.14 × 56.25 ft² × 44 ft = 7,853 ft³ (to the nearest whole number)

Therefore, the volume of the silo is approximately 7,853 cubic feet.

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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) C(x) = 15000/x + 6x +80

b) Domain of C(x)  { R x>0 }

Step-by-step explanation:

We have:  

Enclosed area = 1500 ft²   = x*y      from which     y  =  1500 / x    (a) where x is perpendicular to the river

Cost = cost of sides of fenced area perpendicular to the river  + cost of side parallel to river + cost of 4 post then

Cost = 10*y + 2*3*x + 4*20 and accoding to (a)  y = 1500/x

Then

C(x)  = 10* ( 1500/x ) + 6*x + 80

C(x) = 15000/x + 6x +80

Domain of C(x)  { R x>0 }

The function for the cost of the project depending on x, a side perpendicular to the river, is C(x) = $15000/x + $6x + $80. The domain of this function, representing all possible lengths of x, is from 0 to the square root of 1500, exclusive on the lower end, inclusive on the upper end.

For part a, we can set up the function C(x) as follows:

Given that the area of the rectangle is 1500 sq. ft, the length of the side parallel to the river will be 1500/x.

Therefore, combining all these costs, your C(x) = $15000/x + $6x + $80.

As for part b, the domain of C(x) is the set of all possible values of x. Since x represents the length, it must be greater than zero but less than or equal the length of a side of the rectangular area where the length of the side is limited by the area of 1500 square feet. Hence, the domain of C is (0, sqrt(1500)].

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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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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:

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)

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:

x+2

Step-by-step explanation:

A factor of a polynomial can be thought of as the value of x at which the polynomial is equal to zero.

So, you can use the values in the options given and put them in the polynomial from the question.

for example: try, part a) x-1, here x=1 since the factor is x-1=0

put this value in the polynomial to see if it results to zero.

[tex](1)^3 + 3(1)^2 - 2(1) - 8\\ -6[/tex]

so this isn't the answer.

now try, part d) x + 2, here, x = -2

[tex](-2)^3 + 3(-2)^2 - 2(-2) - 8\\ 0[/tex]

you'll see this is the factor!

Answer:

  d.  x+2

Step-by-step explanation:

The question is essentially asking which of -2, -1, 1, 2 is a zero of the polynomial. All of them are plausible, because all are factors of -8, the constant term.

So, we don't have much choice but to try them. That means we evaluate the function to see if any of these values of x make it be zero.

±1:

The value 1 is easy to substitute for x, as it makes all of the x-terms equal to their coefficient. Essentially, you add all of the coefficients. Doing that gives ...

  1 +3 -2 -8 = -6

Similarly, the value -1 is easy to substitute for x, as it makes all odd-degree terms equal to the opposite of their coefficient. Here, ...

  f(-1) = -1 +3 -(-2) -8 = -4

Neither one of these values (-1, +1) is a zero of the polynomial, so choices A and B are eliminated.

__

(x-2):

To see if this is a factor, we need to see if x=2 is a zero. Evaluation of a polynomial is sometimes easier when it is written in Horner form:

  ((x +3)x -2)x -8

Substituting x=2, we get ...

  ((2 +3)2 -2)2 -8 = (8)2 -8 = 8 . . . not zero

This tells us there is a zero between x=1 and x=2, but that is not what the question is asking.

__

(x+2):

We can similarly evaluate the function for x=-2 to see if (x+2) is a factor.

  ((-2 +3)(-2) -2)(-2) -8 = (-4)(-2) -8 = 0

Since x=-2 makes the function zero, and it makes the factor (x+2) equal to zero, (x+2) is a factor of the polynomial.

So, the factor (x+2) is a factor of the given polynomial.

_____

I find that a graphing calculator answers questions like this quickly and easily. If you're allowed one, it is a handy tool.

Answer:

Glen uses 15.65 inches fabrics for headbands and 9.68 inches for each player

Explanation:

Given the fabric used are:

For headbands, 641.65 inches for 41 people (39 players and 2 coach)

Therefore, applying the concept of unitary method  

41 people = 641.65 inches

1 person = [tex]\frac{641.65}{41} inches[/tex]= 15.65 inches

For wristbands, 377.52 inches for 39 players

39 players = 377.52 inches

1 player = [tex]\frac{377.52}{39} inches[/tex] = 9.68 inches

Therefore, Glen uses 15.65 inches fabrics for headbands and 9.68 inches for each player

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:

A) Y=1/3x+6

Step-by-step explanation:

1. Subtract 6 from both sides.

-6 = 1/3 x

2. Divide 1/3 from both sides.

[tex] - 6 \div ( \frac{1}{3} ) = x[/tex]

x = -18

Answer: 68C2 = 2278

Step-by-step explanation:

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.