Find the value of x.

Start by distributing the 2 through both terms inside the parentheses.

This gives us 2x + 14 + x = 20.

Now subtract 14 from both sides to get 2x + x = 6.

Now combine like terms on the left to get 3x = 6.

Now, dividing both sides by 3, we find that x = 2.

You just need to integrate 3 times:

[tex]f'''(t)=t^{1/2}-9\cos t[/tex]

[tex]f''(t)=\displaystyle\int f'''(t)\,\mathrm dt=\frac23 t^{3/2}-9\sin t+C[/tex]

[tex]f'(t)=\displaystyle\int f''(t)\,\mathrm dt=\frac4{15} t^{5/2}+9\cos t+Ct+D[/tex]

[tex]f(t)=\displaystyle\int f'(t)\,\mathrm dt=\frac8{105} t^{7/2}+9\sin t+\frac C2 t^2+Dt+E[/tex]

Step-by-step explanation:

18:27

=18/27

=2/3 or 2:3

Answer:

(a) Yes, the data suggest that females are more likely to graduate from high school than males.

(b) A 95% confidence interval for the difference in the graduation rates between females and males is [0.024, 0.404] .

Step-by-step explanation:

We are given that a survey of over 25,000 Americans aged between 18 and 24 years revealed the following: 88.1% of the 12,678 females and 84.9% of the 12,460 males had high school diplomas.

Let [tex]p_1[/tex] = population proportion of females who had high school diplomas.

[tex]p_2[/tex] = population proportion of males who had high school diplomas.

(a) So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex]    {means that females are less or equally likely to graduate from high school than males}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1 > p_2[/tex]     {means that females are more likely to graduate from high school than males}

The test statistics that will be used here is Two-sample z-test statistics for proportions;

                        T.S.  =    ~  N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of females having high school diplomas = 88.1%

[tex]\hat p_2[/tex] = sample proportion of males having high school diplomas = 84.9%

[tex]n_1[/tex] = sample of females = 12,678

= sample of males = 12,460

So, the test statistics =  

                                    =  7.428  

The value of the standardized z-test statistic is 7.428.

Now, at a 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 7.428 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that females are more likely to graduate from high school than males.

(b) Firstly, the pivotal quantity for finding the confidence interval for the difference in population proportion is given by;

                        P.Q.  =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex]  ~  N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of females having high school diplomas = 88.1%

[tex]\hat p_2[/tex] = sample proportion of males having high school diplomas = 84.9%

[tex]n_1[/tex] = sample of females = 12,678

[tex]n_2[/tex] = sample of males = 12,460

Here for constructing a 95% confidence interval we have used a Two-sample z-test statistics for proportions.

So, 95% confidence interval for the difference in population proportions, ([tex]p_1-p_2[/tex]) is;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                      of significance are -1.96 & 1.96}    

P(-1.96 < [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < 1.96) = 0.95  

P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95  

P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < ([tex]p_1-p_2[/tex]) < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95

95% confidence interval for ([tex]p_1-p_2[/tex]) = [[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] , [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ]

= [ [tex](0.881-0.849)-1.96 \times {\sqrt{\frac{0.881(1-0.881)}{12,678}+\frac{0.849(1-0.849)}{12,460}} }[/tex] , [tex](0.881-0.849)+1.96 \times {\sqrt{\frac{0.881(1-0.881)}{12,678}+\frac{0.849(1-0.849)}{12,460}} }[/tex] ]

= [0.024, 0.404]

Therefore, a 95% confidence interval for the difference in the graduation rates between females and males is [0.024, 0.404] .

(c) The assumptions and conditions necessary for the above inferences to hold are;

Answer: trapezoid

Step-by-step explanation: A trapezoid is a quadrilateral

with exactly one pair of parallel sides.

Also, quadrilaterals are two-dimensional shapes.

So it's impossible that's its 3-d.

Answer:

A. trapezoid

Step-by-step explanation:

Answer:

-2s is ur answer

hope it helps u

Answer:

Step-by-step explanation:

2s+(−4s)

Combine 2s and −4s to get −2s.

−2s

Answer:

C

Step-by-step explanation:

-27 -(-38)

when you subtract a negative it turns into addition

-27+38

Answer:

c) -27 +38

Step-by-step explanation:

the reason is because when a number is in parentheses, especially if they are negatives, they become the opposite which in this case is + so -(-38) can be the same as saying -1 × -38 and since they are both negatives, the sign becomes positive and it's just 38 while the 27 isn't affected because there's nothing in front of it I hope I helped.

Answer:

Option (2)

Step-by-step explanation:

Domain of a function is represented by the set of x-values (Input values) and Range of the function is represented by the set of y-values (Output values)

From the graph attached,

Given function is,

[tex]f(x)=\frac{x^2-x-6}{x+2}[/tex]

Domain of this function will be {x ∈ R | x ≠ -2}

[Since, point x = -2 doesn't lie on the given graph]

Range of the function will be {y ∈ R | y ≠ -5}  

Therefore, Option (2) will be the correct option.

Answer:

the correct answer is A

Step-by-step explanation:

just did it on edg

Answer:

11n

Step-by-step explanation:

The expression is 7n + 4n. Since 7n and 4n are like terms (they both are variables with n), we can combine them so the expression becomes 7n + 4n = 11n.

Answer:

a. 7(3) - 20 = 1°

b. 9 cm

c. Aly is correct

Step-by-step explanation:

Answer:

a. ZWY

b. 9cm

c. Aly's solution is correct

Step-by-step explanation:

a. YW bisects the whole angle, thus angle XWY and angle ZWY are same

NOTE: REMEMBER TO WRITE THE LETTER ACCORDINGLY

b. the two triangles are congruent by AAS (angle-angle-side) thus the two legs of the the triangles are also congruent. when one is 9cm, the other is also 9cm.

c. Since the triangles are congruent, their sides also congruent.

 7x-20=2x-5

 7x-2x=-5+20

     5x=15

       x=3

This is same as Aly's solution

Answer:

C. [tex]cos^2A -sin^2A[/tex]

Step-by-step explanation:

Given:

[tex]cos2A[/tex]

To find:

The given expression is equivalent to:

A. [tex]sin^2A-cos^2A[/tex]

B. [tex]sin^2A+cos^2A[/tex]

C. [tex]cos^2A -sin^2A[/tex]

D. [tex]cosA-sinA[/tex]

Solution/Proof:

First of all, let us have a look at the compound angle formula for [tex]cos(X+Y)[/tex].

Compound angle means in which there is sum of two angles given.

In the above we are having X+Y i.e. sum of two angles X and Y. So it is compound angle.

The compound angle formula for cosine is given as:

[tex]\bold{cos(X+Y)=cosXcosY-sinXsinY}[/tex]

Here, let us put X = Y = A

[tex]cos(A+A)=cosAcosA-sinAsinA\\\Rightarrow \bold{cos(2A)=cos^2A-sin^2A}[/tex]

So, cos2A is equivalent to [tex]cos^2A -sin^2A[/tex].

Correct answer is:

Option C. [tex]cos^2A -sin^2A[/tex]

Answer:

$3.

Step-by-step explanation:

All you have to do is 9/3 = 3.

Answer:

Step-by-step explanation:

Hello !

Using the cross multiplication method, which of the following is the solution to 21/(x+4) = 7/(x+2)?

21(x + 2) = 7(x + 4)

21x + 42 = 7x + 28

21x - 7x = 28 - 42

14x = -14

x = -14/14

x = -1

Answer:

3/(x+2)= x+1

Step-by-step explanation:

21/7=3

x/x= x

4/2=2

Answer:

765

Step-by-step explanation:

Hello, please consider the following.

[tex]10x^2+100x+1000=10(x^2+10x+100)\\\\=10((x+5)^2-25+100)\\\\=10(x+5)^2+750[/tex]

So, a = 10, b = 5, c = 750 and the sum is 765.

Thank you

Answer:

380 square inches

Step-by-step explanation:

Step 1

We find the Surface Area of the Rectangular Prism

The Rectangular Prism has the dimensions of Length × Width × Height = 8 inches by 9 inches by 10 inches

Surface Area of a Rectangular Prism = 2(WL+ HL + HW)

Where W = Width = 9 inches

L = Length = 8 inches

H = Height = 10 inches

Surface Area of the Rectangular Prism = 2(9 × 8 + 10 × 8 + 9 × 10)

= 2(72 + 80 + 90)

= 2(242)

= 484 square inches.

Step 2

Find the area of the Rectangular shaped wrapping paper

The wrapping paper has dimensions :

2 feet by 3 feet

We have to convert to inches first

1 foot = 12 inches

2 feet = 2 × 12 inches = 24 inches

3 feet = 3 × 12 inches = 36 inches

Area of the Rectangular shaped wrapping paper = Length × Width

= 24 inches × 36 inches

= 864 square inches

Step 3

We calculate the amount of square inches of wrapping paper left.

The Amount left over = Area of Rectangular wrapping paper - Area of Rectangular prism

= 864 square inches - 484 square inches

= 380 square inches.

Therefore, the square inches of wrapping paper left over is 380 square inches.

Answer:

Step-by-step explanation:

In a single - sampling plan, when a decision on acceptance / rejection of the lot  is made on the basis of  only one sample, Then , the acceptance plan is said to be a single sampling plan. The single sampling plan is known as the most common and easiest sampling plan

The following symbol representation can be written as follows:

a. N    →   Lot size   from which the sample is drawn

b. n    →    sample size

c. c    →     acceptance number

d. d   →    number of defectives in the sample

For example:

if we take a  randomized sample of  size 'n' from the Lot size.

The next step will be to inspect all items in the sample to find the defectives 'd'

The decision rule is that:

If  the number of defectives is less than or equal to acceptance number, then answer is YES i.e d ≤ c, Then ,  we accept the Lot

If the number of defectives is not less than or equal to acceptance number, then the answer is NO . Then , we reject the Lot.

So if we reject, we either do 100% inspection or return the lot to the supplier.

In a double sampling plan , the decision on acceptance/rejection  of the Lot is based on two samples.

The following symbol representation can be written as follows:

a. n1    →  number of size of sample 1

b. n2    → number of size of sample 2

c. c1    →  acceptance number for sample 1

d. c2    →  acceptance number for sample 2

e. d1    →  number of defectives in sample 1

f. d2   →  number of defectives in sample 2

Answer: Joseph Kabila

Step-by-step explanation:

Answer:

Joseph Kabila

Step-by-step explanation:

[tex]\$1562.52[/tex]

The unitary method is a methodology for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value. The unitary method is used to calculate the value of a single unit from a given multiple.

Number of books sold last month [tex]=1364[/tex]

Total amount earned [tex]=\$1579.16[/tex]

So,

Price of each book [tex]=\frac{1579.16}{1364}[/tex]

                                [tex]=\$1.16[/tex]

Number of books sold this month [tex]=1347[/tex]

Total amount earned [tex]=1.16\times 1347[/tex]

                                   [tex]=\boldsymbol{\$1562.52}[/tex]

Find out more information about unitary method here:

https://brainly.com/question/12116123?referrer=searchResults

Answer:

$12 the hour

Step-by-step explanation: $360 divided by 30 is 12, meaning he will need to make a minimum of 12 an hour to support his family.

Answer:

12

Step-by-step explanation:

Answer:

[tex]x = 2a[/tex]

Step-by-step explanation:

Required

Represent twice a number is x as an algebra

Given that the number is a;

Then

[tex]Twice\ a\ number = 2 * a[/tex]

[tex]Twice\ a\ number = 2a[/tex]

Also,

[tex]Twice\ a\ number = x[/tex]

So, we have that

[tex]x = 2a[/tex]

Hence, the algebraic representation of the given parameters is

[tex]x = 2a[/tex]

Answer:

Commutative Property of Addition: a + b = b + a

Step-by-step explanation:

The Commutative Property of Addition implies that even on changing the order of addition the final result (i.e. the sum) remains the same.

a + b = b + a

Suppose a = 5 and b = 6, then:

a + b = 5 + 6 = 11

b + a = 6 + 5 = 11.

Thus, a + b = b + a.

a + b + c= a + c + b = b + a + c = c + a + b

Suppose a = 4, b = 3 and c = 6, then:

a + b + c = 4 + 3 + 6 = 13

a + c + b = 4 + 6 + 3 = 13

b + a + c = 3 + 4 + 6 = 13

c + a + b = 6 + 4 + 3 = 13.

Thus, a + b + c= a + c + b = b + a + c = c + a + b.

Answer:

Probabilty of selecting a blue marble if one marble is drawn

= 0.3529

Step-by-step explanation:

A bag contains 4 red marbles, 6 blue marbles, and 7 green marble.

Total number of marbles

=4 red+ 6 blue+7 green

= 17 marbles in total

Probabilty of selecting a blue marble if one marble is drawn

= Number of blue marble/total number of marble

Probabilty of selecting a blue marble if one marble is drawn

= 6/17

Probabilty of selecting a blue marble if one marble is drawn

= 0.3529

Answer: Hi!

The equation for inverse proportion is x y = k or x = k/ y.

When finding the value of the constant k, you can use the known values and then use this formula to calculate all of the unknown values.

Hope this helps!

Answer:

Step-by-step explanation:

Given that:

A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data.

To obtain the geometric mean of the untransformed data,

X = set of numbers

N = number of observations

Arithmetic mean if transformed data = 1.65

Log(Xi).... = transformed data

Arithmetic mean = transformed data/ N

Log(Xi) / N = 1.65

(Πx)^(1/N), we obtain the antilog of the aritmétic mean simply by raising 10 to the power of the Arithmetic mean of the transformed data.

10^1.65 = 44.668359

Answer:

The probability the die chosen was green is 0.9

Step-by-step explanation:

From the information given :

A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4.

SO, the probability of obtaining 4 in a single throw of a fair die is:

P (4  | red dice) =  [tex]\dfrac{1}{6}[/tex]

P (4 | green dice) =  [tex]\dfrac{3}{6}= \dfrac{1}{2}[/tex]

A die is selected at random and rolled four times.

When the die is selected randomly; the probability of the first die must be equal to the probability of the second die =  [tex]\dfrac{1}{2}[/tex]

The probability of two 1's and two 4's in the first dice can be calculated as:

[tex]= \begin {pmatrix} \left\begin{array}{c}4\\2 \end{array}\right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]

[tex]=\dfrac{4!}{2!(4-2)!}\times (\dfrac{1}{6})^4[/tex]

[tex]=\dfrac{4!}{2!(2)!}\times (\dfrac{1}{6})^4[/tex]

[tex]=\dfrac{4\times 3 \times 2!}{2!(2)!}\times (\dfrac{1}{6})^4[/tex]

[tex]=\dfrac{12}{2 \times 1}\times (\dfrac{1}{6})^4[/tex]

[tex]= 6 \times (\dfrac{1}{6})^4[/tex]

[tex]= (\dfrac{1}{6})^3[/tex]

[tex]= \dfrac{1}{216}[/tex]

The probability of two 1's and two 4's in the second  dice can be calculated as:

[tex]= \begin {pmatrix} \left\begin{array}{c}4\\2 \end{array}\right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

[tex]= \dfrac{4!}{2!(4-2)!} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

[tex]= \dfrac{4!}{2!(2)!} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

[tex]= 6 \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

[tex]= \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]

[tex]= \dfrac{9}{216}[/tex]

∴  The probability of two 1's and two 4's in both dies

= P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )

The probability of two 1's and two 4's  = [tex](\dfrac{1}{216} \times \dfrac{1}{2} )+ ( \dfrac{9}{216} \times \dfrac{1}{2})[/tex]

The probability of two 1's and two 4's  = [tex]\dfrac{1}{432}+ \dfrac{1}{48}[/tex]

The probability of two 1's and two 4's  = [tex]\dfrac{5}{216}[/tex]

Using Bayes Theorem; the probability that the die was green can be computed as follows:  

P(second die (green) | two 1's and two 4's )  = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's)

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216} }{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{\dfrac{1}{48} }{\dfrac{5}{216}}[/tex]

P(second die (green) | two 1's and two 4's )  =[tex]\dfrac{1}{48} \times \dfrac{216}{5 }[/tex]

P(second die (green) | two 1's and two 4's )  = [tex]\dfrac{9}{10}[/tex]

P(second die (green) | two 1's and two 4's )  = 0.9

∴

The probability the die chosen was green is 0.9

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ - 54w + 45}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{3 + 6( - 9w + 7)}[/tex]

Distribute 6 through the parentheses

⇒[tex] \sf{3 - 54w + 42}[/tex]

Add the numbers : 42 and 3

⇒[tex] \sf{ - 54w + 45}[/tex]

Hope I helped!

Best regards!!

Answer:

r≈2.05

Step-by-step explanation:

Answer:3

Step-by-step explanation:

Answer:

b= - 1.26317

a = 17.237

b. The selling price (in dollars) of a 7-year-old car

y =  8394.81 dollars

C.  For each additional year, the car decreases $ ___ in value.

1263.17 $ decreases per year

Step-by-step explanation:

Let y be the selling price in thousands and x be the age in years

Car         Age        Selling Price

             (years)           ($000)             XY                    X²  

                    X                 Y          

1                   9                  11.1              99.9                   81          

2                  5                  9.5              47.5                   25

3                 13                  4.4               57.2                 169

4                 17                  4.4               74.8                 289

5                 7                 8.06             56.42                49

6                1                   2.07            2.07                     1

7                  1                    0.6            0.6                      1

8                 14                  8.1              113.4                  196

9                12                   8.1              97.2                  144

10              17                    4.8             81.6                  289

11               4                     12.5           50                     16

12              4                      10.7            42.8                 16      

∑               97                    84.33          723.49            1276                

The estimated regression line of Y on X is

Y= a +bX

and the two normal equations are

∑ y= na + b∑X

∑XY= a∑X + b∑X²

Now

X`= ∑X/n = 97/12= 8.083

b= n∑XY - (∑X)(∑Y)/ n∑ X²- (∑X)²

b= 723.49 - (97)(84.33)/ 12(1276) - (97)²

b= -7456.52/ 5903

b= - 1.26317

a= Y`- b X`

a= 7.0275 - (-- 1.26317)8.083

a = 17.237

Y = 17.237  - 1.26317 X

y= - 1.26317 X + 17.237

b. The selling price (in dollars) of a 7-year-old car

y = - 1.26317 (7) + 17.237

y= 8.39481

y =  8394.81 dollars

C.  For each additional year, the car decreases $ ___ in value.

1.26317 *1000= 1263.17 $ decreases per year

Answer:

3(x^y(5x^2y-x³)+25x⁴))

Step-by-step explanation:

15x^2y²-3x^3y+75x⁴

From 15x^2y²-3x^3y only, 3x^y is the common factor

=> 3x^y(5x^2y-x³)+75x⁴

Taking the common factor of the latter expression, 3 shows to be the common factor of all the expression.

=> 3(x^y(5x^2y-x³)+25x⁴)