Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x.

Answer:

The null hypothesis is rejected.

There is enough evidence to support the claim that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.

Test statistic t=-40.91

P-value = 0

Step-by-step explanation:

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

The claim is that the true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=-10\\\\H_a:\mu_1-\mu_2< -10[/tex]

The significance level is 0.05.

The sample 1 (AISI 1064), of size n1=126 has a mean of 102.8 and a standard deviation of 1.2.

The sample 2 (AISI 1078), of size n2=126 has a mean of 121.3 and a standard deviation of 2.

The difference between sample means is Md=-18.5.

[tex]M_d=M_1-M_2=102.8-121.3=-18.5[/tex]

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

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.2^2}{126}+\dfrac{2^2}{126}}\\\\\\s_{M_d}=\sqrt{0.011+0.032}=\sqrt{0.043}=0.2078[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-18.5-(-10)}{0.2078}=\dfrac{-8.5}{0.2078}=-40.91[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-2=126+126-2=250[/tex]

This test is a left-tailed test, with 250 degrees of freedom and t=-40.91, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-40.91)=0[/tex]

As the P-value (0) 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 true average strength for the 1078 grade exceeds that for the 1064 grade by more than 10 kg/mm^2.

Answer:

z = -17.67 + i3.43

Step-by-step explanation:

Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -

z = 18( cos169 + isin169 ),

z = r(cos Ф + i sin Ф)

Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -

sin169 is positive, while cos169 is negative, thus -

a = -17.6692893021...,

b = 3.43456191678...

Rectangular Form, z = -17.67 + i3.43

Hope that helps!

Answer:

Population Mean = 29.33

Population Standard Deviation = 26.13

The samples of size 2 with replacement and their respective means and standard deviations

1) (66, 66)

Mean = 66.00, Standard deviation = 0.00

2) (66, 15)

Mean = 40.50. Standard deviation = 36.06

3) (66, 7)

Mean = 36.50. Standard deviation = 41.72

4) (15, 15)

Mean = 15.00. Standard deviation = 0.00

5) (15, 66)

Mean = 40.50. Standard deviation = 36.06

6) (15, 7)

Mean = 11.00. Standard deviation = 5.66

7) (7, 7)

Mean = 7.00. Standard deviation = 0.00

8) (7, 66)

Mean = 36.50. Standard deviation = 41.72

9) (7, 15)

Mean = 11, Standard deviation = 5.66

The sampling distribution of sample means is (66, 40.5, 36.5, 15, 40.5, 11, 36.5, 7, 11)

Mean of sampling distribution = 29.33

Standard deviation of sampling distribution = 18.48

The population mean and the mean of sampling distribution are both equal to 29.33

The standard deviation of the population (26.13) is higher than that of the sampling distribution (20.66).

Step-by-step explanation:

Complete Question

For the following situation, find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population. Find the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population. (Round to two decimal places.)

The number of dvds rented by each of the three families in the past month is 66, 15, 7. Use a sample size of 2.

Solution

For the population

Mean = (Σx)/N

Σx = Sum of all the variables = 66 + 15 + 7 = 88

N = Number of variables = 3

Mean = (88/3) = 29.33

Standard deviation =  σ = √[Σ(x - xbar)²/N]  

x = each variable

xbar = mean = 29.33

N = number of variables  = 3

Σ(x - xbar)² = (66 - 29.33)² + (15 - 29.33)² + (7 - 29.33)² = 2048.6667

σ = √(2048.6667/3) = 26.13

Noting that the for the samples,

Mean = (Σx)/N

Standard deviation =  σ = √[Σ(x - xbar)²/(N-1)]

The possible samples of size 2 possible from this distribution with replacement and their respective means and standard deviations include

(66, 66)

Mean = 66.00, Standard deviation = 0.00

(66, 15)

Mean = 40.50. Standard deviation = 36.06

(66, 7)

Mean = 36.50. Standard deviation = 41.72

(15, 15)

Mean = 15.00. Standard deviation = 0.00

(15, 66)

Mean = 40.50. Standard deviation = 36.06

(15, 7)

Mean = 11.00. Standard deviation = 5.66

(7, 7)

Mean = 7.00. Standard deviation = 0.00

(7, 66)

Mean = 36.50. Standard deviation = 41.72

(7, 15)

Mean = 11, Standard deviation = 5.66

The sampling distribution of sample means is (66, 40.5, 36.5, 15, 40.5, 11, 36.5, 7, 11)

The mean and standard deviation of sampling distribution

Mean = (66+40.5+36.5+15+40.5+11+7+36.5+11)/9 = (264/9) = 29.33

Standard Deviation = 18.48

The population mean and the mean of sampling distribution are both equal to 29.33

The standard deviation of the population (26.13) is higher than that of the sampling distribution (18.48).

Hope this Helps!!!

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.

Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.

Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.

The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.

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Answer:

c

Step-by-step explanation:

Answer:

all squares are quadrilaterals

Answer:

-Population is DeVry statistics students - Sample is 128 DeVry statistics students.

Step-by-step explanation:

First of all, population is defined as a set of all elements while sample includes some or all those of elements, whereas, sample never includes more elements when compared to population.

Hence, we select sample from the population.

Now, in this question, the survey include 128 DeVry statistics students. Thus, these 128 statistics students would be a sample while total number of Devry statistics students will be the population.

83% is the sample statistic because it gives us numerical information about the sample.

Thus, we can conclude that;

-Population is DeVry statistics students - Sample is 128 DeVry statistics students.

Answer:

[tex]\large \boxed{\text{-1.8$^{\circ}$F/1000 ft}}[/tex]

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

[tex]\begin{array}{cccc}\textbf{Alt/1000 ft} & \textbf{B.p.$/^{\circ}$F} & \Delta\textbf{B. p}& \Delta\textbf{B.p/1000 ft}\\0 & 212.0 & & \\& &-0.9 & -1.8\\0.5 & 211.1 & & \\& &-0.9 & -1.8\\1.0 & 210.2 & & \\& &-1.8 & -1.8\\2.0 & 208.4 & & \\& &-1.8 & -1.8\\3.0 & 206.6 & & \\& &-1.8 & -1.8\\4.0 & 204.8 & & \\& &-0.9 & -1.8\\4.5 & 203.9 & & \\\end{array}[/tex]

[tex]\text{ The change in boiling point per thousand feet of altitude is $\large \boxed{\textbf{-1.8$^{\circ}$F/1000 ft}}$}[/tex]

Answer:

Answer:

Step-by-step explanation:

Identify the changes (Δ) in each consecutive pair of x-values and y-values, then calculate the corresponding values of Δy/Δx

Your working table should look like the one below.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The fire department property is 2 units in height. 2 units from the line y=3 can be on the line y=5, or on the line y=1.

There are no answer choices with y=5, so the appropriate choices are those with C and D having the x-coordinates of B and A, respectively, and y=1.

  C(1, 1), D(4, 1)

Answer:

In improper form your solution will be [tex]\frac{90}{7}[/tex]. As a mixed fraction it will be [tex]12\frac{6}{7}[/tex].

Step-by-step explanation:

The first thing we want to do here is to simplify this expression. After doing so, " a " and " b " should be multiplied to result in a possible improper fraction,

[tex]\left(81x^{\frac{2}{7}}\right)\:\left(2/9x^{\frac{3}{7}}\right)\:[/tex] - Apply exponential rule " [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] "

= [tex]81\cdot \frac{2}{9}x^{\frac{2}{7}+\frac{3}{7}}[/tex] - Combine fractions [tex]\frac{2}{7}[/tex] and [tex]\frac{3}{7}[/tex]

= [tex]81\cdot \frac{2}{9}x^{\frac{5}{7}}[/tex] - Multiply the fractions, and simplify further

= [tex]\frac{162x^{\frac{5}{7}}}{9}[/tex] = [tex]18x^{\frac{5}{7}}[/tex] - This is out simplified expression

Now that we have this simplified expression, we can see that a = [tex]18[/tex], and b = [tex]\frac{5}{7}[/tex]. Therefore, multiplying the two we should receive the improper fraction as follows,

[tex]18 * \frac{5}{7}[/tex] = [tex]\frac{90}{7}[/tex] - Note that this is in improper form. If you want your solution in a mixed fraction, it will be [tex]12\frac{6}{7}[/tex].

Answer:

  134 degrees

Step-by-step explanation:

Right so far. To find the numerical measure of the angle, you need to use x=7 in your expression for the angle measure:

  m∠STU = -27 +23(7) = 134 . . . degrees

Answer:

f so final percentage

= .91(.85)(.82) = .63427

or 63.427% of the original price

Step-by-step explanation:

Answer:

C. $172,000

Step-by-step explanation:

Calculation for the median value of the houses

The following data was given in the question:$172,000, $164,000, $142,000,

$159,000, $191,000, $124,000, and $146,000

The first step is to Arrange the above data in ascending order

$124,000,$142,000,$146,000,$159,000,

$164,000,$172,000,$191,000

Second step is to find the Median

The Median will be the mid value, which means that $159,000 is the mid value

Based on the information given in the question we were given that a public

assessor has determined that the value of each house is actually $13,000 higher than previously thought

Hence, the Median will be = $159,000+$13,000=$172,000

Therefore the median value of the houses will be $172,000

Answer:

The 99% confidence interval is = 0.37 +/- 0.070

= (0.300, 0.440)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 37% = 0.37

Number of samples n = 315

Confidence interval = 99%

z value(at 99% confidence) = 2.58

Substituting the values we have;

0.37 +/- 2.58√(0.37(1-0.37)/315)

0.37 +/- 2.58√(0.00074)

0.37 +/- 2.58(0.027202941017)

0.37 +/- 0.070183587825

0.37 +/- 0.070

= (0.300, 0.440)

The 99% confidence interval is = 0.37 +/- 0.070

= (0.300, 0.440)

Answer:

A) A = {RRR, LLL, SSS}

B) B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Step-by-step explanation:

A) All vehicles must go right, left or straight ahead (three possibilities):

A = {RRR, LLL, SSS}

B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):

B = {LRS. LSR, RLS, RSL, SLR, SRL}

C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:

C = {RRL, RRS, RSR, RLR, LRR, SRR}

D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):

D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:

D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}

F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.

C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}

G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:

C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}

Answer:

Prime number

Step-by-step explanation:

A prime number has 2 factors.

A composite number has more than 2 factors.

47 has the factors 1 and 47.

47 is a prime number.

Answer:

47 is prime.

Step-by-step explanation:

Its factors are 1 and 47.

If a number has only 2 factors, then it's prime.

Answer:

The solutions are a₁ = -4/19 i, a₂ = 4/19 i and a₃ = -1/4

Step-by-step explanation:

Given the equation 76a³+19a²+16a=-4, for us to solve the equation, we need to find all the factors of the polynomial function. Since the highest degree of the polynomial is 3, the polynomial will have 3 roots.

The equation can also be written as (76a³+19a²)+(16a+4) = 0

On factorizing out the common terms from each parenthesis, we will have;

19a²(4a+1)+4(4a+1) = 0

(19a²+4)(4a+1) = 0

19a²+4 = 0 and 4a+1 = 0

From the first equation;

19a²+4 = 0

19a² = -4

a² = -4/19

a = ±√-4/19

a₁ = -4/19 i, a₂ = 4/19 i (√-1 = i)

From the second equation 4a+1 = 0

4a = -1

a₃ = -1/4

Answer:

The general term is

Sn = -(-2)ⁿ.3¹⁻ⁿ

step by step Explanation:

we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

a = 4 /b

or ab = 4

Step-by-step explanation:

An inverse relation is given by

a = k/b where k is the constant

Rewriting

ab = k

12 * 1/3 = k

4 = k

a = 4 /b

or ab = 4

Answer:

probability of chosing a student that has a cat and a dog is 9/25

Step-by-step explanation:

And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16

This makes it

[ 3 ( 6 ( 9 ) 7 ) ]

3 + 6 + 9 + 7 = 25

Answer:

The correct option are  A and D

Step-by-step explanation:

Given that T is  a linear transformation it means the T can only modify the value of the scalars but can not modify the dependent(y) and the independent variables (x)

Considering the first option

    T(ax -by)

evaluating the above we get

   Tax - Tbx

=>   a T(x) - bT(y)

So we see that in this equation T only just modified the scalars so option A will always be true

   Considering option B

   [tex]T(a^2 x) = (T(ax))^2[/tex]

Comparing the RHS and the LHS of the equation we see that the independent variable has been modified from [tex]x \to x^2[/tex] hence option B is  false

 Considering option C

     T(x y) = T(x)T(y)

  Comparing the RHS and the LHS of the equation we see that the

The T modified both the independent variable and the independent variable hence C is  false

        Considering option D

    Comparing the RHS and the LHS of the equation we see that the

That there was no modification to the dependent and the independent variable  hence  

  option D is always  true

       Considering option E

      Comparing the RHS and the LHS of the equation we see that the

  For  RHS to be  true  z must not necessary be zero Hence option E is  false  

Answer:

Minimum 8 at x=0, Maximum value: 24 at x=4

Step-by-step explanation:

Retrieving data from the original question:

[tex]f(x)=x^{2}+8\:over\:[-1,4][/tex]

1) Calculating the first derivative

[tex]f'(x)=2x[/tex]

2) Now, let's work to find the critical points

Set this

[tex]2x=0\\x=0[/tex]    

0, belongs to the interval. Plug it in the original function

[tex]f(0)=(0)^2+8\\f(0)=8[/tex]

3)  Making a table x, f(x) then compare

x|  f(x)

-1 | f(-1)=9  

0 | f(0)=8   Minimum

4 | f(4)=24 Maximum

4) The absolute maximum value is 24 at x=4 and the absolute minimum value is 8 at x=0.    

Answer:

6 x 10⁶ or 6,000,000

Step-by-step explanation:

100 × (200 × 300)

100 x 60,000 → 6,000,000

6,000,000 → 6 x 10⁶

Hope this helps! :)

Step-by-step explanation:

[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

The quadratic formula is honestly the most straightforward way of solving here.

Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:

1) a=1, b=0, c=8

This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)

2) a=-9, b=4, c=-10

This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.

3) a=1, b=8, c=17

This reduces to x=(-4+i), (-4-i)

So those are the answers for each.

Please Refer to the screenshot. Hope this helps!

Answer:

y>3x -1 is the right answer

Answer:

percentage of interest = 22.6% (to one decimal place)

Step-by-step explanation:

actual price paid (including interest) = 429,   out of which

interest = 429-350 = 79

Percentage of interest out of actual price paid

= 79/429* 100%

= 22.6%

Answer:

b)  geometric

Step-by-step explanation:

Notice that each new term is derived by multiplying the previous term by 2.  Thus:  the first term is -2 and the common ratio is 2.  This is a geometric sequence.

Answer:

3

Step-by-step explanation:

minus the variable, 4-1 is 3.

Answer:

x = 5, AB=5, BC = 15

Step-by-step explanation:

AC = AB + BC (Segment Addition)

AC= 20, AB =x Bc = 3x,

20= x+3x 20=4x

x=5

AB=x, AB =5

BC=3x BC= 15

The segment addition postulate states gives the value of x as 5, given

that the sum of x and 3·x is 20.

Responses:

From the given diagram, we have;

[tex]\overline{AB}[/tex] = x

[tex]\overline{BC}[/tex] = 3·x

According to segment addition postulate we have;

[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 20 inches

Which gives;

x + 3·x = 20

Therefore;

4·x = 20

[tex]x = \dfrac{20}{4} = 5[/tex]

[tex]\mathbf{\overline{BC}}[/tex] = 3·x  

[tex]\mathbf{\overline{BC}}[/tex] = 3 × 5 = 15

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Answer:

50 liters

Step-by-step explanation:

Amount of salt in the 35% solution + amount of salt in the 70% solution = amount of salt in the 45% solution

0.35 x + 0.70 (20) = 0.45 (x + 20)

0.35 x + 14 = 0.45 x + 9

5 = 0.1 x

x = 50

The volume of the 35% solution is 50 L

Known parameter;

The percentage concentration of the salt solution with unknown volume = 35%

The percentage concentration of the 20 liters salt solution = 70%

The percentage concentration of the resulting solution = 45%

Unknown parameter;

The volume of the 35% salt solution

Strategy;

Let x represent the volume of the 35% salt solution that must be mixed  to obtain the 45% salt solution

Balance the masses of the salts before and after mixing

The mass of the salts before mixing = 70% × 20 L + 35% × x

The mass of the salt solution mixture after mixing = 45% × (20 L + x)

By conservation principles, we get;

70% × 20 L + 35% × x = 45% × (20 L + x)

0.7 × 20 L + 0.35 × x = 0.45 × (20 L + x)

14 L + 0.35·x = 9 L + 0.45·x

14 L - 9 L = 0.45·x - 0.35·x = 0.1·x

5 L = 0.1·x

x = 5 L/(0.1) = 5 L × 10 = 50 L

The volume of the 35% solution that must be mixed with the 70% salt solution x =  50 L

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Answer:

the area of the circle surrounding everything is 11^2pi=121pi=379.94

379.94-8^2pi=379.94-200.96=178.98

Answer:

  179.1 ft^2

Step-by-step explanation:

The radius of the centerline of the path is 8 ft + (3 ft/2) = 9.5 ft. Then the area of the path is the product of the width of the path and the circumference at that centerline radius:

  A = (3 ft)(2π(9.5 ft)) = 57π ft^2 ≈ 179.07 ft^2

The area of the path is about 179.1 square feet.

_____

If you use 3.14 instead of a more accurate value of π, the result will be an area of 178.98 ft^2.