Find the slope of each line defined below and compare their values.​

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:

Step-by-step explanation:

The estimated cost is ...

  $14000 +12600 +6200 = $32800

The actual cost is ...

  $13860 +12420 +6500 = $32780

The variance is the difference between actual cost and predicted cost:

  $32,780 - 32800 = -$20.

It is favorable when actual costs are lower than predicted.

Answer:

50

Step-by-step explanation:

There are 434 different ways to distribute 15 identical stuffed animals among six children so that each child receives at least one but no more than three stuffed animals.

1. Define the generating function for distributing stuffed animals to each child as:

 [tex]\[ (x + x^2 + x^3)^6 \][/tex]

  This represents the options for each child receiving 1, 2, or 3 stuffed animals, and there are 6 children.

2. Expand the generating function using the binomial theorem:

  [tex]\[ (x + x^2 + x^3)^6 = \binom{6}{0}x^0 + \binom{6}{1}x^1 + \binom{6}{2}x^2 + \binom{6}{3}x^3 + \binom{6}{4}x^4 + \binom{6}{5}x^5 + \binom{6}{6}x^6 \][/tex]

  Simplify to:

  [tex]\[ 1 + 6x + 21x^2 + 56x^3 + 126x^4 + 252x^5 + 462x^6 \][/tex]

3. The coefficient of [tex]\( x^{15} \)[/tex] in the expansion represents the number of ways to distribute 15 stuffed animals among six children.

4. Identify the terms that contribute to [tex]\( x^{15} \)[/tex]:

  [tex]\[ 56x^3 + 126x^4 + 252x^5 \][/tex]

5. Add the coefficients:

  56 + 126 + 252 = 434

Therefore, there are 434 different ways to distribute 15 identical stuffed animals among six children so that each child receives at least one but no more than three stuffed animals.

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

The school uses 23,070 pieces of paper in all.

Here's an explanation:

It is already given that the school uses 13,270 pieces of white paper. Then it says that there are 7,570 fewer pieces of blue paper than white paper. So if you subtract 7,570 from 13,270, you get that the school used 5700 pieces of blue paper. Then it says that there are 1,600 fewer pieces of yellow paper than blue paper. So when you subtract 1,600 from 5,700, you get that the school used 4,100 pieces of yellow paper. So if you do 13,270+5,700+4,100, you get that the school used 23,070 pieces of paper in total.

The school uses a total of 23,070 pieces of paper, which is calculated by adding 13,270 pieces of white paper, 5,700 pieces of blue paper, and 4,100 pieces of yellow paper.

The school used 13,270 pieces of white paper. It is stated that they use 7,570 fewer pieces of blue paper than white paper, which means they used 13,270 - 7,570 = 5,700 pieces of blue paper. For yellow paper, they use 1,600 fewer pieces than blue paper, which means they use 5,700 - 1,600 = 4,100 pieces of yellow paper. To get the total number of pieces of paper the school used, you would add all these together: 13,270 white paper pieces + 5,700 blue paper pieces + 4,100 yellow paper pieces = 23,070 pieces of paper in total.

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Answer:

  12

Step-by-step explanation:

The degree of the polynomial is 12, so the theorem tells you it has 12 zeros.

Answer:

[tex]\displaystyle 12[/tex]

Step-by-step explanation:

You base this off of the Leading Coefficient's degree.

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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:

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:

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:

$ 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:

[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.

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The complete question is written below:

While on vacation, Enzo sleeps 115% as long as he does while school is in session. He sleeps an average of s hours per day while he is on vacation. Which of the following expressions could represent how many hours per day Enzo sleeps on average while school is in session?

A.1.15s

B.s/1.15

C.100/115s

D.17/20s

E.(1.15-0.15)s

Answer:

B. [tex]\dfrac{s}{1.15}[/tex]

Step-by-step explanation:

Let the hours per day slept while school is in session be [tex]x[/tex].

Given:

Hours slept per day on vacation = [tex]s[/tex]

Enzo sleeps 115% as long in vacation as he does in school. Therefore, as per question,

[tex]s=115\%\ of\ x\\\\s=\frac{115}{100}x\\\\s=1.15x\\\\x=\dfrac{s}{1.15}[/tex]

Hence, the number of hours Enzo sleeps while school is in session is given as:

[tex]x=\dfrac{s}{1.15}[/tex]

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: 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:

  50 cm²

Step-by-step explanation:

The area of a trapezoid can be figured from the formula

  A = (1/2)(b1 +b2)h

Filling in the given numbers and doing the arithmetic, we get ...

  A = (1/2)(10.2 +9.8)(5) = 50 . . . . square centimeters

The area is 50 cm².

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: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

The solution of p is given by the equation p = 2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

17 - 2p = 2p + 5 + 2p   be equation (1)

Adding 2p on both sides , we get

2p + 2p + 2p + 5 = 17

On simplifying , we get

6p + 5 = 17

Subtracting 5 on both sides , we get

6p = 17 - 5

6p = 12

Divide by 6 on both sides , we get

p = 12 / 6

p = 2

Therefore , the value of p is 2

Hence , the solution is p = 2

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Answer:

Estimated 5 hours

Step-by-step explanation:

780 miles = 12 hours

1 mile = 0.0154hr (3s.f)

325 miles = 0.0154 × 325

= 5.01hr

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:

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:

Step-by-step explanation:

The increase in the number of books sold each year follows an arithmetic progression, hence it is linear.

The formula for the nth term of an arithmetic progression is expressed as

Tn = a + (n - 1)d

Where

Tn is the nth term of the arithmetic sequence

a is the first term of the arithmetic sequence

n is the number of terms in the arithmetic sequence.

d is the common difference between consecutive terms in the arithmetic sequence.

From the information given,

a = 500 (number of books in the first year.

T5 = 1000 (the number of books at 2014 is)

n = 5 (number of terms from 2010 to 2014). Therefore

T5 = 1000 = 500 + (5 -1)d

1000 = 500 + 4d

4d = 500

d = 500/4 =125

The linear function that represents the number of yearbooks sold per year will be

T(n) = 500 + 125(n - 1)

The correct linear function that represents the number of yearbooks sold per year is [tex]\( f(t) = 100t + 500 \)[/tex], where [tex]\( t \)[/tex] is the number of years since 2010.

To determine the linear function, we need to find the slope (rate of change) and the y-intercept (initial value) of the function.

 Given that in 2010, 500 yearbooks were sold, we can denote this point as (0, 500) since 0 years have passed since 2010. This gives us the y-intercept of the function.

 Next, we look at the year 2014, where 1000 yearbooks were sold. This is 4 years after 2010, so we can denote this point as (4, 1000).

 The slope of the line (m) is calculated by the change in the number of yearbooks sold divided by the change in time (years). So, we have:

[tex]\[ m = \frac{1000 - 500}{4 - 0} = \frac{500}{4} = 125 \][/tex]

 This means that the number of yearbooks sold increases by 125 each year.

 Now, we can write the linear function using the slope-intercept form [tex]\( f(t) = mt + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

 Substituting the values we have:

[tex]\[ f(t) = 125t + 500 \][/tex]

However, to make the function more general and to avoid dealing with fractions, we can express the slope as a multiple of 100. Since 125 is the same as [tex]\( \frac{5}{4} \times 100 \)[/tex], we can rewrite the function as:

[tex]\[ f(t) = \frac{5}{4} \times 100t + 500 \][/tex]

 Simplifying this, we get:

[tex]\[ f(t) = 100t + 500 \][/tex]

 This function represents the number of yearbooks sold each year, where [tex]\( t \)[/tex] is the number of years since 2010. For example, in 2011 (t=1), the function would predict [tex]\( f(1) = 100(1) + 500 = 600 \)[/tex] yearbooks sold.

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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The critical values for a Chi-square distribution with 80% confidence level and sample size of 15 (thus 14 degrees of freedom) are: χ2L = 18.475 and χ2R = 8.897.

The question is asking for the critical values for a Chi-square distribution which can be found using Chi-square tables usually found in statistics textbooks or online. The critical values refer to the boundary values for the acceptance region of a hypothesis test.

When trying to find the critical values for an 80% confidence level with 14 degrees of freedom (since degrees of freedom = n - 1 for sample, thus 15 - 1 = 14), you need the 90th percentile for the χ2L and the 10th percentile for the χ2R (since α = 20%, then α/2 = 10%).

Using a Chi-square table for these percentiles, we get:

χ2L = 18.475

χ2R = 8.897

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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: Charlie have to drive at a speed of 80miles per hour in order to reach there on time.

Step-by-step explanation:

At 4pm Charlie realizes he has half an hour to get to his grandmothers house for diner. Knowing that the time he has left is 30 minutes and the distance to his grandmother's place is 40 miles, the only thing that he can control is his speed

Speed = distance travelled / time taken

40/0.5 = 80 miles per hour

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:

ΔNAS≅ΔSEN by SSA axiom of congruency.

Step-by-step explanation:

Consider ΔNAS and ΔSEN,

NS=SN(Common ie . Both are the same side)

SA=NE( Given in the question that SA≅ NE)

∠SNA=∠NSE( Due to corresponding angle property where SE ║ NA)

Therefore, ΔNAS ≅ΔSEN by SSA axiom of congruency.

∴ NA≅SA by congruent parts of congruent Δ. Hence, proved.

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.