Need help on adding polynomials

Answer:

(a) There are 12 values in the data set which are greater than or equal to 10 and less than or equal to 19.

(b) There are 12 values in the data set which are greater than or equal to 30 and less than or equal to 39.

(c) There are 7 values in the data set which are greater than or equal to 40 and less than or equal to 49.

Step-by-step explanation:

We are given a set of data that is summarized by the stem and leaf plot below;

Steam Leaf

1  0 0 2 4 4 4 7 8 8 8 8 9

2  2 2 5 5 7 8

3  3 4 4 5 5 5 6 6 6 7 9 9

4  3 3 3 5 5 7 9

This shows that the data values are: 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19, 22, 22, 25, 25, 27, 28, 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39, 43, 43, 43, 45, 45, 47, 49.

(a) From the data above, the number of values in the data set which are greater than or equal to 10 and less than or equal to 19 is 12, i.e; 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19.

(b) From the data above, the number of values in the data set which are greater than or equal to 30 and less than or equal to 39 is 12, i.e; 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39.

(c) From the data above, the number of values in the data set which are greater than or equal to 40 and less than or equal to 49 is 7, i.e; 43, 43, 43, 45, 45, 47, 49.

Answer:5,9

Step-by-step explanation:

x-3y= -3x +3y=9

collect like terms

-3x will go to x and it will turn to

x+3x And -3y will go to +3y and it will turn to

×+3x=+3y+3y=9

solving time.

x+3x is 4x

3y +3y =6y

4x+6y =9

remove the 4x for now.

6y divided by 9.

3 in 6 is 2 and 3 in 9 is 3.

therefore 4x =2=9

4/2=2

2x=9.

4and half is the answer

Answer:

x = 3

y = 2

Step-by-step explanation:

x - 3y = -3

x + 3y = 9

Solve for x in the second equation.

x = 9 - 3y

Pu x as 9 - 3y in the first equation and solve for y.

9 - 3y - 3y = -3

9 - 6y = -3

-6y = -12

y = 2

Put y as 2 in the second equation and solve for x.

x = 9 - 3(2)

x = 9 - 6

x = 3

Answer:

2

Step-by-step explanation:

Let

P = percentage of those that text and drive

S = percentage of those that do not text and drive

P + S = 1

S = 1 - P

S = 1 - 0.52

S = 0.48

The expected number would be:

1/0.48 = 2.08

Which is approximately 2.

Therefore the expected number of people the police officer would expect to pull over until she finds a driver not texting is 2.

The number of people should a police officer expect to pull over until she finds a driver NOT texting while driving is; 2 people

A geometric random value is one that gives a discrete time as to the the first success of an event.  

Now, we are told that it is estimated that 52% of drivers text while driving. Thus, the success is a driver that is not texting, and the probability (p) is 0.52.

This means that the expected value of a geometric random variable is expressed as 1/p.  

Therefore, In this question;

geometric random variable = 1/0.52

⇒ 1.923 ≈ 2

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Answer:

gdk

Step-by-step explanation:

Answer:

a. P-value = 0.1589

b. P-value = 0.0016

Step-by-step explanation:

a. This is a hypothesis test for the difference between populations means.

The claim is that the two types of steel have different true average fracture toughness values.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The significance level is α=0.05.

The sample 1, of size n1=100 has a mean of 60.7 and a standard deviation of 1.  The sample 2, of size n2=100 has a mean of 60.5 and a standard deviation of 1.

The difference between sample means is Md=0.2.

[tex]M_d=M_1-M_2=60.7-60.5=0.2[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{100}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{100}}=\sqrt{0.02}=0.1414[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.1414}=\dfrac{0.2}{0.1414}=1.4142[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=100+100-2=198[/tex]

This test is a two-tailed test, with 198 degrees of freedom and t=1.4142, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t>1.4142)=0.1589[/tex]

As the P-value (0.1589) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

b. As the sample size changes, the standard error and the degress of freedom change.

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{500}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{500}}=\sqrt{0.004}=0.0632[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.0632}=\dfrac{0.2}{0.0632}=3.1623[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=500+500-2=998[/tex]

This test is a two-tailed test, with 998 degrees of freedom and t=3.1623, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t>3.1623)=0.0016[/tex]

As the P-value (0.0016) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the two types of steel have different true average fracture toughness values.

Answer:

n²+1

2n²

Step-by-step explanation:

We can see that 2, 5, 10, and 17 becomes 1, 4, 9, and 16 when we subtract 1.

So it adds 1. The nth will be n² + 1.

2, 8, 18, and 32 is the double of n². 1, 4, 9, and 16 are their half.

So the nth term becomes 2n².

The value of the equation is

a) The nth term of the equation is Aₙ = n² + 1

b) The nth term of the equation is Bₙ = 2n²

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 ,

a)

Let the nth term of the equation be represented as Aₙ

Now , the sequence is

P = { 2 , 5 , 10 , 17 , .. }

when n = 1 , P₁ = 2

when n = 2 , P₂ = 5

So , the equation for the nth term is Aₙ = n² + 1

b)

Let the nth term of the equation be represented as Bₙ

Now , the sequence is

Q = { 2 , 8 , 18 , 32 , .. }

when n = 1 , P₁ = 2

when n = 2 , P₂ = 8

So , the equation for the nth term is Bₙ = 2n²

Hence , the equations are solved

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Answer:

-2

Step-by-step explanation:

To find the slope: Rise/Run

You go 2 steps down for every step you go right.

Your rise is -2 and your run is 1.

So your slope is -2.

Answer:

-2

Step-by-step explanation:

Get two points that intersect that line.

(1, 5) and (2, 3)

Find the rise and run.

As we can see to get from (1,5) to (2,3), we have to go to the right by 1 and go down by 2 (in this case the movement is -2 steps).

rise/run

-2/1 = -2

Answer:

(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]

Step-by-step explanation:

Volume of fluid in the tank =1000 gallons

Initial Amount of Salt in the tank, A(0)= 30 pounds

Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.

Rate In=(concentration of salt in inflow)(input rate of brine)

[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]

The resulting mixture is pumped out at the same rate, therefore:

Rate Out =(concentration of salt in outflow)(output rate of brine)

[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]

Therefore:

The rate of change of amount of salt in the tank,

[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]

Answer:

[tex]-14x^4+71x^3-61x^2+30x-6[/tex]

Step-by-step explanation:

All we are doing is distributing each number of the 1st equation to the 2nd equation to get our answer. Once we do so, we combine like terms and we get our answer.

Answer:

B. 486

Step-by-step explanation:

3^4 = 3 × 3 × 3 × 3 = 81

2^0 = 1

6^1 = 6

Find the product.

81 × 1 × 6

= 486

Answer:

option B; 486

Step-by-step explanation: 3 raised to the power 4 can be written as 3*3*3*3, 2 raised to 0 is 1( any number raised to to the power 0 is 1), 6 raised to 1 is the number itself( means that 6 is only repeated or mentioned once).

so, 3*3*3*3*1*6=486

Your question is not complete, however, I have provided answers to it by suggesting that the question goes like this;

Twelve different video games showing drug use were observed. The duration times of drug use​ (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 85​sec, what does df​ denote, and what is its​ value

Answer:

df denote degree of freedom.

degree of freedom df is 11.

Step-by-step explanation:

what does df​ denote?

df denote degree of freedom

To find it value,

we have twelve different video games showing drug use, then, it means that the sample size "n" is 12

the degree of freedom is 1 < n ( i.e, one less than sample size)

df = n -1 = 12 -1 = 11

So, degree of freedom df is 11.

Note; use your sample size to solve the question as I don't know the exact value you were given. Thanks.

Answer:

2.598 and -2.598.

Step-by-step explanation:

f(x) = 2 cos x + sin 2x

f'(x) = -2 sin x + 2 cos 2x = 0   for turning points.

cos 2x =  1 - 2 sin^2 x so we have

-2 sin x + 2 - 4 sin^2 x = 0

4sin^2 x + 2 sin x - 2 = 0

2(2 sin^2 x + sin x - 1) = 0

2(2sinx - 1)(sinx + 1) = 0

sin x  = 0.5, -1   when  f(x) is at a turning point.

x = π/6,  -π/2, 5pi/6

The second derivative is  2 cos x + 2 * -2 sin 2x

= 2 cos x - 4 sin 2x

When x = π/6, this is negative , when x = -π/2 it is positive

so x = π/6 gives a maximum f(x) and x = -π/2 gives 0 so this is a point of inflection

When x = π/6 , f(x) = 2.598

When x = 5pi/6,  f(x) = -2.598.

Answer:

Step-by-step explanation:

The null and alternative hypothesis that would seek to challenge this belief would be

Null hypothesis: u = 0.75

Alternative hypothesis: u =/ 0.75

The type of test to be used would be a one sample z test where one sample is drawn from the population and the mean engagement of students who become knowledgeable in the material is measured and tested in an experiment against the null hypothesis.

Answer:

divided by 6

Step-by-step explanation:

Given pattern

360,60,10

would it be add 60

lets

add 60 to each term

360 +60 = 420

but next term is 60, hence it incorrect choice

divided by 6

lets divide each term by 6

360/6 = 60 which is the next term in the series as well

60/6 = 10 which is also the next term in the series as well

hence divided by 6 is the correct option.

multiply by 6

multiply by 6 to each term

360 *60 = 21600

but next term is 60, hence it incorrect choice

subtract 60 from each term

360 -300 = 60 which is the next term in the series

60 -300 = -240 which is not same the next term in the series that is 10

hence this is incorrect choice

Answer:

nx^(n-1)

Step-by-step explanation:

Answer: 2.06

Step-by-step explanation:

Remember if the number is greater than 5 round up, if it is less than 5 don't round up.

After round off the number 2.0625 to its nearest hundredth, it is 2.06.

When we round to the nearest hundredth, we follow the rule that says:

The given number is 2.0625

In this number, the thousandth digit is 2 that is less than 5.

So we round down the hundredth place. The hundredth digit is 6 which remain 6 after rounding down.

So, the rounded number will be 2.06.

Hence, when we round 2.0625 to its nearest hundredth, it will be 2.06.

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Answer:

0.0066

Step-by-step explanation:

The x has a distribution that is approximately normal. For normal distribution the probability of x will be,

u = 12 and 18

P (12 [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 18)

P (- 2.3  [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 2.85 )

P (0.9912 - 0.9978)

= 0.0066

Answer:

3/4

Step-by-step explanation:

Use [tex]\frac{rise}{run}[/tex]. From the bottom red point, you have to go up 3 and left 4 to get to the top point. That's your answer.

Answer:

a =10% b=50% c=20% d=20%

Step-by-step explanation:

n(CuT)=n(C)+n(T)-n(CnT)

so n(CnT)=10%

for b

tea but not coffee =nonly(T)

=n(T)-n(TnC)

=50%

for c

only coffee=nonly(C)

=n(C)-n(CnT)

=20%

what is the question? if u give the question , I might help and edit this :)

Answer:

i think it's 70

Step-by-step explanation:

sorry if its wrong let me know plz

Answer:

12,780

Step-by-step explanation:

Initial population = 9000

grows 7% of 9000= 630 people in a year

after 6 yrs, number of added people = 630× 6=3780 ...... totally, population = 9000+ 3780

= 12,780

The population of the town after 6 years will be 13506.

Thus, the population of the town after 6 years will be 13506.

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Answer:

[tex]\boxed{<x = 17 degrees}[/tex]

Step-by-step explanation:

<EGB = 73 degrees (Vertically Opposite angles are congruent)

=> <x = 90-<EGB (Complementary angles)

=> <x = 90-73

=> <x = 17 degrees

Answer: A

Step-by-step explanation:

Answer: A.

Step-by-step explanation:

A composition of reflections over two parallel lines is equivalent to a translation.

Answer:

The probability no one delays or goes without medical care is 0.168;

The probability only one person delays or goes without medical care is 0.336.

Step-by-step explanation:

This problem can be modeled with a binomial random variable, with sample size n=8 and probability of success p=0.2.

The probability that exactly k Americans delay or go without medical care because of concerns about cost within the sample of eight individuals can be calculated as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{8}{k} 0.2^{k} 0.8^{8-k}\\\\\\[/tex]

The probability no one delays or goes without medical care (x=0) is:

[tex]P(x=0) = \dbinom{8}{0} p^{0}(1-p)^{8}=1*1*0.168=0.168\\\\\\[/tex]

The probability only one person delays or goes without medical care (x=1) is

[tex]P(x=1) = \dbinom{8}{1} p^{1}(1-p)^{7}=8*0.2*0.21=0.336\\\\\\[/tex]

Answer:  0.627 or 62.7 %

Step-by-step explanation:

The probability that shipment will be rejected P(rejected) = 1- probability that shipment will be accepted.

P(rejected)= 1-P(accepted)

P(accepted) is equal to probability when all 10 watches are not defective.

The probability that 1st one randomly selected watches are not defective is 51/60  (51 watches are not defective and 9 are defective)

The probability that 2-nd one randomly selected watches are not defective is  50/59 ( because the total number of the watches now is 1 unit less 60-1=59, and the total number of not defective watches is 1 unit less 51-1=50 units)

The probability that 3rd one randomly selected watches are not defective is 49/58  (49 watches are not defective total number of watches is 58)

Similarly P(4th)= 48/57  P(5th)=47/56   P(6th)=46/55  P(7th)=45/54

P(8th)=44/53  P(9th)=43/52  P(10th)=42/51

So P(accepted)= P(1st)*P(2nd)*P(3rd)*P(4th)*P(5th)*P(6th)*P(7th)*P(8th)*P(9th)*P(10th)=

=51*50*49*48*47*46*45*44*43*42/(60*59*58*57*56*55*54*53*52*51)=

= approx= 0.373

So P(rejected)=1-0.373=0.627

Answer:

$1,06

Step-by-step explanation:

Calculation for dividend per share of common stock for board of directors of Midwest Foods

First step is to find the amount of dividends due to the preferred shareholders

Using this formula

Total Dividend =Dividend- (Preferred stock *Per share of preferred stock )

Let plug in the formula

Total Dividend =$3,500,000-($300,000*$2.85)

Total Dividend =$3,500,000-$855,000

Total Dividend =$2,645,000

The second step is to find Dividend per share of common stock

Using this formula

Dividend per share of common stock=Total dividend/Shares of common stock

Let plug in the formula

Dividend per share of common stock=$2,645,000/$2,500,000

Dividend per share of common stock=$1.06

Therefore the dividend per share of common stock for board of directors of Midwest Foods will be $1.06

Answer:

The point estimate for the mean mpg of hybrid cars is 30 mpg.

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this problem, we have that:

Lower bound: 22

Upper bound: 38

Point Estimate:

(22 + 38)/2 = 30

The point estimate for the mean mpg of hybrid cars is 30 mpg.

Answer: 2

Step-by-step explanation:

The equation for slope is change in y / change in x, which is (-4-(-12))/(4-0) in this case. That is equal to 2.

The gradient of the line segment between the points (4,-4) and (0,-12) is 2.

We have to determine, the gradient of the line segment between the points (4,-4) and (0,-12).

The gradient and slope of the line segment between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by the following formula;

The gradient of the line segment = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Then, the gradient of the line segment between the points (4,-4) and (0,-12) is,

[tex]= \dfrac{-12-(-4)}{0-4}\\\\= \dfrac{-12+4}{-4}\\\\= \dfrac{-8}{-4}\\\\= 2[/tex]

Hence, The required gradient of the line segment between the points (4,-4) and (0,-12) is 2.

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Answer:

r = 982

Step-by-step explanation:

[tex]-25(r-989)=175\\-25r+24725=175\\-25r=-24,550\\25r=24,550\\r=982[/tex]