What factoring method should be used to factor a polynomial with four terms?​

Answer:

2

Step-by-step explanation:

a10=a1+(n-1)d

15=-3+(10-1)d

15+3=9d

d=2

Answer:

B.

Step-by-step explanation:

Volume of the model of moon = 4/3(πr³)

= 4/3(π)(1)³

= 4.2 feet³

Volume of cylinder = πr²h

= (3.14)(0.5)²(0.5)

= 0.39 feet³

Cylindrical clay boxes to be used = 4.2/0.39

=10.7 ≈ 11

Answer:0.92

Step-by-step explanation:

Given

[tex]57\%[/tex] of Population is vaccinated

So, Probability of a person being vaccinated is [tex]P=0.57[/tex]

and simultaneously , probability of not vaccinated is [tex]1-P[/tex]

[tex]=1-0.57=0.43[/tex]

Now, Probability that atleast one of them has been vaccinated is given by

[tex]=1-P(\text{None of them is vaccinated})[/tex]

[tex]=1-0.43\times 0.43\times 0.43[/tex]

[tex]=1-0.0795[/tex]

[tex]=0.92[/tex]

Answer:

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

Step-by-step explanation:

Step(i):-

Given  57 % of the people have been vaccinated

p = 57% =0.57

q = 1-p =1-0.57 = 0.43

n = 3

[tex]P(X=r) = n_{C_{r} } p^{r} q^{n-r}[/tex]

Step(ii):-

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1) = P( x =1) + P(x =2)+P(x=3)             [tex]P(X\geq 1) = 3_{C_{1} } (0.57)^{1} (0.43)^{3-1} + 3_{C_{2} } (0.57)^{2} (0.43)^{3-2} + 3_{C_{3} } (0.57)^{3} (0.43)^{3-3}[/tex]

[tex]P(X\geq 1) = 3 (0.57) (0.43)^{2} + 3 (0.57)^{2} (0.43) + 1 (0.57)^{3} (0.43)^{0}[/tex]

               =  0.316179 + 0.419121 +0.185193

            = 0.920493

Final answer:-

The probability that AT LEAST ONE of them has been vaccinated

P( X ≥1)  = 0.920493

Answer:

The calculated value t = 2.038< 2.145 at 0.05 level of significance

Null hypothesis is accepted

There is the average rate is less than  μ ≤ 4

Step-by-step explanation:

Step(i):-

The Population of the mean 'μ' =4

sample size   'n' = 16

sample mean 'x⁻' = 4.53

given sample standard deviation 's' = 1.04

level of significance  α = 0.05

Step(ii):-

Null hypothesis:H₀ : There is no significance difference between two means

Alternative hypothesis : H₁: There is significance difference between two means

Test statistic

                    [tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n} } }[/tex]

                   [tex]t = \frac{4.53-4}{\frac{1.04}{\sqrt{16} } }[/tex]

                t = 2.038

Degrees of freedom ν = n-1 = 16-1 =15

t₀.₀₂₅ = 2.145

Conclusion:-

The calculated value t = 2.038< 2.145 at 0.05 level of significance

Null hypothesis is accepted

There is the average rate is less than  μ ≤ 4

Answer:

21829787.23 joules

Step-by-step explanation:

The recycling will require 6%energy if initial energy, let's say x.

94% of x will be used to power a 100W TV for 3 hours

X = (100*3*60*60)/0.94

X = 1148936.17 joules.

To make 19 aluminum cans ,

It will take 1148936.17*19

= 21829787.23 joules

Answer:

$ 1,946.00  

Step-by-step explanation:

Average income per year=total income per month/12 months

total income=average income for first 4 months*4+ total income for 8 months

Let x represent total income total income for remaining 8 months

$1780.75=($1450.25*4+x)/12

$1780.75*12=$5,801+x

$21,369==$5,801+x

x=$21,369-$5,801

x=$15,568

The average income for the remaining eight months=x/8=$15568/8 =$1,946.00  

The average income for the remaining 8 months is $ 1,946.00  

Answer:

24

Step-by-step explanation:

There are 4 options for the first reindeer.

After the first reindeer is selected, there are 3 options left for the second reindeer.

After the second reindeer is selected, there are 2 options left for the final reindeer.

The number of possible permutations is:

₄P₃ = 4×3×2 = 24

Answer:

3003 ways

Step-by-step explanation:

We are in a combination or permutation exercise, the difference between them is if the order matters (permutations) or does not matter (combinations),

in this case the order does not matter, since they only ask us for the ways to choose 10 of 15 roller coasters, therefore it would be a combination:

nCr = n! / (r! * (n-r)!

we know that n = 15 and r = 10, we replace:

15C10 = 15! / (10! * (15-10)!

15C10 = 3003

In other words, there are 3003 ways to choose 10 of the 15.

Answer:

B) x < 22.5; Sam has fewer than 22.5 minutes left to finish running.

Step-by-step explanation:

For this case we have the following inequality:

From here, we define the variable x.

x: number of minutes remaining to finish the race.

From here, we clear the value of x.

We have then:

 Therefore, Samuel has less than 22.5 minutes to finish the race in the estimated time.

Answer:

x < 22.5; Sam has fewer than 22.5 minutes left to finish running.

x < 22.5; Sam has fewer than 22.5 minutes left to finish running.

For this case we have the following inequality:

From here, we define the variable x.

x = number of minutes remaining to finish the race.

From here, we clear the value of x.

We have then:

Therefore, Samuel has less than 22.5 minutes to finish the race in the estimated time.

The major examples of social inequality include income gap, gender inequality, health care, and social class. In health care, some individuals receive better and more professional care compared to others.

Learn more about inequality here: brainly.com/question/25275758

#SPJ2

Answer:

  see attached for a graph

Step-by-step explanation:

When g(x) is transformed to

  f(x) = f(x -h) +k

The graph of g(x) is translated h units right and k units up.

__

Here, the function g(x) = x^2 is transformed to ...

  f(x) = g(x -3) +12 = (x -3)^2 +12

Then the graph of f(x) is the graph of g(x)=x^2 translated 3 units right and 12 units up.

(1) Suppose x = 32.12353535... . Then 100x = 3212.353535... and 10000x = 321235.353535... .

Subtracting these gives

10000x - 100x = 321235.353535... - 3212.353535...

9900x = 321235 - 3212

9900x = 318023

x = 318023/9900

(2) By the same process as above, we start with

x = 2.333...

y = 4.151515...

Then

10x = 23.333...

==>  10x - x = 23.333... - 2.333...

==>  9x = 23 - 2

==>  x = 21/9

and

100y = 415.151515...

==>  100y - y = 415.151515... - 4.151515

==>  99y = 415 - 4

==>  y = 411/99

After this, we get

x + y = 2.333... + 4.151515...

==>  x + y = 21/9 + 411/99

==>  x + y = 231/99 + 411/99

==>  x + y = 642/99 = 214/33

Answer:

3 pack of hot dogs and 2 pack of buns 24

Step-by-step explanation:

hot dogs come in packs of 8

burns came in packs of 12

what is the least number of each you can buy in order to have a equal number of hot dogs and buns

so to get equal number

we have to look for the LCM of 8 and 12 = 24

therefore the packs will be equal to product

hot dogs come in packs of 8 = 8*3 = 24

burns came in packs of 12 = 12 *2 = 24

therefore, 3 pack of hot dogs and 2 pack of buns 24

Answer:

The slope of the line is -7/8

When the point (7, –4) is used, the point-slope form of the line is

y+4=(-7/8)(x-7)

The slope-intercept form of the line is y=(-7/8)x+(17/8)

Step-by-step explanation:

Answer:

The equation is y=1/2x+5

Step-by-step explanation:

Answer:

y=1/2x+5

Step-by-step explanation:

I learned this last year. I know this is the answer

Answer:

PO = 20

Step-by-step explanation:

They are equidistant from the centre

PG = GO

x-4=1/2x+3

Multiplying both sides by 2

2(x-4)=x+6

2x-8=x+6

2x-x = 6+8

x = 14

Now

PO = 14-4+7+3

PO = 10+10

PO = 20

Answer:

A homeowner has to pay phone bill, home insurance, cable bill, internet bill

Step-by-step explanation:

If the homeowner doesn't pay these then they won't get to continue using it until they pay for it again.

Answer:

The answer should contain any four of the following:

utility fees

association fees

private mortgage insurance (PMI)

title insurance

homeowners insurance

property taxes

Step-by-step explanation: This is the PLATO answer.

Answer: itz 780

Step-by-step explanation:

Answer:

1 5/6 gallons

Step-by-step explanation:

1. 5 1/2 = 11/2 gallons

2. She uses: 1/3 x 11/2 = 11/6 gallons

3. so: 11/6 = 1 5/6 gallons

I'M MARIE!!!

Answer:

The probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is P=0.68.

Step-by-step explanation:

For a uniform distribution, any value within the minimum and maximum value have the same probability. Outside that interval, the probability is 0.

Then, for a uniform distribution within a and b, the probability P(X>c), being z<c<b is:

[tex]P(X>c)=\dfrac{b-c}{b-a}[/tex]

For our case, with a uniform distribution within 0 and 7 minutes, the probability that a randomly selected passenger has a waiting time greater than 2.25 minutes is:

[tex]P(t>2.25)=\dfrac{7-2.25}{7-0}=\dfrac{4.75}{7}=0.68[/tex]

78% means 78/100=0.78

Answer:

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

Step-by-step explanation:

Perpendicular => So, it will have a slope of a negative reciprocal to this slope

Slope = m = 1/2

Now,

Point = (x,y) = (0,1)

So, x = 0 and y = 1

Putting this in slope-intercept equation to get b

=> [tex]y = mx+b[/tex]

=> 1 = (1/2)(0) + b

=> b = 1

Now putting m and b in the slope intercept equation to get the required equation

=> [tex]y = \frac{1}{2} x+1[/tex]

Answer:

y = \frac{1}{2} x+1

Step-by-step explanation:

Answer:

Area of the rectangle = 1056 square units

Step-by-step explanation:

Rectangle published could be dissected into nine different squares with different sizes.

Area of the squares with different measure of sides will be,

For side length = 1 unit

Area of the square = (Side)²

= 1²

= 1 square units

For side length = 4 units

Area of the square = 4² = 16 units²

For side length = 7 units

Area of the square = 7² = 49 units²

For side length = 8 units

Area of the square = 8² = 64 units²

For side length = 9 units

Area of the square = 9² = 81 square units

For side length = 10 units

Area of the square = 10² = 100 square units

For side length = 14 units

Area of the square = 14² = 196 square units

For side length = 15 units

Area of the square = 15² = 225 square units

For side length = 18 units

Area of the square = 18² = 324 square units

Total area of the rectangle by adding these 9 squares

= 1 + 16 + 49 + 64 + 81 + 100 + 196 + 225 + 324

= 1056 square units

Answer:

87.49% probability that the sample average was less than 375 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 359, \sigma = 90.4, n = 42, s = \frac{90.4}{\sqrt{42}} = 13.95[/tex]

What is the probability that the sample average was less than 375 days?

This is the pvalue of Z when X = 375. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{375 - 359}{13.95}[/tex]

[tex]Z = 1.15[/tex]

[tex]Z = 1.15[/tex] has a pvalue of 0.8749.

87.49% probability that the sample average was less than 375 days

Answer:

We conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.

Step-by-step explanation:

We are given that in a certain school district, it was observed that 24% of the students in the element schools were classified as only children

However, in the special program for talented and gifted children, 119 out of 415 students are only children.

Let p = proportion of only children in the special program.

So, Null Hypothesis, [tex]H_0[/tex] : p = 24%      {means that the proportion of only children in the special program is equal to the proportion for the school district}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 24%     {means that the proportion of only children in the special program is significantly different from the proportion for the school district}

The test statistics that would be used here One-sample z-test for proportions;

                                T.S. =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of only children in the special program = [tex]\frac{119}{415}[/tex] = 0.29

           n = sample of students = 415

The hypothesized population proportion for this test is 0.24.

So, the test statistics  =  [tex]\frac{0.29-0.24}{\sqrt{\frac{0.24(1-0.24)}{415} } }[/tex]  

                                     =  2.385

The value of z test statistic is 2.385.

Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of only children in the special program is significantly different from the proportion for the school district.

Answer:

Best: 42/60 free throws

Second Best: 39/60 free throws

Third Best: 33/60 free throws

Step-by-step explanation:

Answer:

Step-by-step explanation:

here ,

6x +238 = 3x+178 ( vertically opposite angles are equal)

so 6x - 3x = 178 -238

3x =-60

x =-60/3

x=-20

hope it helps / please mark me as the brainliest..

Answer:

x= -20

Step-by-step explanation:

The 2 angles are opposite each other. Therefore, they are vertical angles and congruent. We can set them equal to each other and solve.

6x+238=3x+178

To solve the equation, we want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

First, subtract 3x from both sides

6x-3x+238=3x-3x+178

6x-3x+238=178

3x+238=178

Next, subtract 238 from both sides

3x+238-238=178-238

3x=178-238

3x=-60

Finally, divide both sides by 3.

3x/3= -60/3

x=-60/3

x= -20

The easiest way to solve this problem is by calculating the areas of all the sides and adding them together.

Step 1; Calculate the area of the rectangular front & back

A = 2 * (l * w)

  = 2 * (25 * 10)

Step 2; Calculate the area of the rectangular sides

A = 2 * (1 * w)

  = 2 * (55 * 10)

= 1100 ft^2

Answer:

27

Step-by-step explanation:

39+4=43

27, 31, 35, 39, 43

Answer:

27

Step-by-step explanation:

When you add u subtract 39 from 43 u will get 4

Therefore u will subtract 4 from 39 to get the third number which is 35 then subtract 4 from it to get the second number which is 31 then subtract another 4 to get the first number that's 27

Answer:

V=3

Step-by-step explanation:

2(v-1)+8=6(2v-4)

2V-2+8=12v-24(calculate)

2v+6=12v-24(move terms)

2v-12v=-24-6(collect like terms)

-10v=-30(devide both sides by-10)

V=3

hi I hope this helps.