Twice the difference of a number and 9 is 3. Use the variable b for the unknown number.

Answer:

3/2

Step-by-step explanation:

3/8 ÷ 1/4

Copy dot flip

3/8 * 4/1

12/8

Divide top and bottom by 4

3/2

Answer:

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft

Answer:

Height = 4 feet

Step-by-step explanation:

To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree

But the tree is 32 feet tall but on shadow it's 160

So lemme determine how long I'll be in my shadow first

Distance away from tree= 140 feet

Length of shadow cast by tree

= 160 feet

Length of shadow= 160-140

Length if shadow= 20 feet

My height= x

X/20= 32/160

X= 20*32/260

X = 4 feet

Height = 4 feet

Answer:

3 weeks

Step-by-step explanation:

6 quarts = 12 pints

12 divided by 3 = 4

Step-by-step explanation:

1 quart = 2 pints

6 quarts = 2 x 6 = 12 pints

12 ÷ 4 = 3

He can have 3 weeks

Answer:

[tex]\huge\boxed{y = 8}[/tex]

Step-by-step explanation:

-4x + 3y = 12

Given that x = 3

-4 (3) + 3y = 12

-12 + 3y = 12

Adding 12 to both sides

3y = 12+12

3y = 24

Dividing both sides by 3

y = 8

Answer:

y =8

Step-by-step explanation:

-4x + 3y = 12

Let x = 3

-4(3) +3y = 12

-12+3y = 12

Add 12 to each side

-12+12+3y =12+12

3y =24

Divide each side by 3

3y/3 = 24/3

y =8

Answer: -10

Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.

1. -4+2(-3)

2. -4+(-6)

3.-4-6

4.-10

Answer:

8

Step-by-step explanation:

-b + 2y

if

b = 4

and

y = 3

then:

-b + 2y = -4 + 2*6 = -4 + 12

= 8

Answer:

-7.

Step-by-step explanation:

g(x) = x^2 - 6x - 7

g(2) = 2^2 - 6(2) - 7

= 4 - 12 - 7

= -8 - 7

= -15

f(x) = x + 8

f(-15) = (-15) + 8

= 8 - 15

= -7

Hope this helps!

Step-by-step explanation:

42 is your answer according to bodmas

area of Arc subtending [tex]360^{\circ}[/tex] (i.e. the whole circle) is $\pi r^2$

so area of Arc subtending $\theta^{\circ}$ is, $\frac{ \pi r^2}{360^{\circ}}\times \theta^{\circ}$

$\theta =72^{\circ}$ so the area enclosed by one such arc is $\frac{\pi (10)^272}{360}$

abd there are 2 such arcs, so double the area.

[tex] \LARGE{ \underline{ \boxed{ \rm{ \purple{Solution}}}}}[/tex]

For solving this question, Let's know how to find the area of a sector in a circle?

[tex] \large{ \boxed{ \rm{area \: of \: sector = \frac{\theta}{360} \times \pi {r}^{2} }}}[/tex]

Here, Θ is the angle of sector and r is the radius of the circle. So, let's solve this question.

We have,

By using formula,

⇛ Area of shaded region = 2 × Area of each sector

⇛ Area of shaded region = 2 × Θ/360° × πr²

⇛ Area of shaded region = 2 × 72°/360° × 22/7 × 10²

⇛ Area of shaded region = 2/5 × 100 × 22/7

⇛ Area of shaded region = 40 × 22/7

⇛ Area of shaded region = 880/7 inch. sq.

⇛ Area of shaded region = 125.71 inch. sq.

☄ Your Required answer is 125.71 inch. sq(approx.)

━━━━━━━━━━━━━━━━━━━━

Answer:

Use the student t distribution

Step-by-step explanation:

Here is the formula

t = (x - u) ÷(s/√N)

From the information we have in the question:

n = 150

s = 550

x = 3400

u = mean = 2400

= 3400 - 2400÷ 500/√150

= 1000/44.9

= 22.27

At 0.05 significance level, df = 149 so t tabulated will be 1.65.

Answer:

The​ z-score for 1880 is 1.34.

The​ z-score for 1190 is -0.88.

The​ z-score for 2130 is 2.15.

The​ z-score for 1350 is -0.37.

And the z-score of 2130 is considered to be unusual.

Step-by-step explanation:

The complete question is: A standardized​ exam's scores are normally distributed. In recent​ years, the mean test score was 1464 and the standard deviation was 310. The test scores of four students selected at random are ​1880, 1190​, 2130​, and 1350. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The​ z-score for 1880 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1190 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 2130 is nothing. ​(Round to two decimal places as​ needed.) The​ z-score for 1350 is nothing. ​(Round to two decimal places as​ needed.) Which​ values, if​ any, are​ unusual? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice. A. The unusual​ value(s) is/are nothing. ​(Use a comma to separate answers as​ needed.) B. None of the values are unusual.

We are given that the mean test score was 1464 and the standard deviation was 310.

Let X = standardized​ exam's scores

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean test score = 1464

           [tex]\sigma[/tex] = standard deviation = 310

S, X ~ Normal([tex]\mu=1464, \sigma^{2} = 310^{2}[/tex])

Now, the test scores of four students selected at random are ​1880, 1190​, 2130​, and 1350.

So, the z-score of 1880 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                      =  [tex]\frac{1880-1464}{310}[/tex]  = 1.34

The z-score of 1190 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                =  [tex]\frac{1190-1464}{310}[/tex]  = -0.88

The z-score of 2130 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                =  [tex]\frac{2130-1464}{310}[/tex]  = 2.15

The z-score of 1350 =  [tex]\frac{X-\mu}{\sigma}[/tex]

                                =  [tex]\frac{1350-1464}{310}[/tex]  = -0.37

Now, the values whose z-score is less than -1.96 or higher than 1.96 are considered to be unusual.

According to our z-scores, only the z-score of 2130 is considered to be unusual as all other z-scores lie within the range of -1.96 and 1.96.

Answer: 600 students.

Step-by-step explanation:

Ok, we start with 15,000 students.

40% of them had tuition, so the actual number of them that had tuition is:

15,000*0.40 = 6,000.

Now we want to find the number of students that studied math and science.

50% only studied math,

30% only studied science

10% studied other subjects.

So 50% + 30% + 10% did NOT studied both math and science

90% is the percentage that did not study math and mathematics as well as science, then the other 10% did.

Then, out of the 6,000 students that had tuition, 10% studied math and science, the total number is:

6,000*0.10 = 600

Answer:

d. 30

Step-by-step explanation:

The computation of the 35th percentile of this data set is shown below:

Before that first we have to series the number in ascending number

S. No          Numbers

1                       26

2                      29

3                      30

4                      30

5                      31

6                      32

7                      34

8                      35

9                       36

Now use the formula

Here n = 9

Percentile = 100

[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]

= 3.5th

= 3th + 0.5 (4th - 3th)

= 3th + 0.5 (30 - 30)

= 3th + 0

= 30

Answer: g = w + 8    g=w-2

Step-by-step explanation:

We could represent the word phrases by the equations.

g = w + 8  

g = w - 2  

Answer:

g = w + 8

g = w - 2

Step-by-step explanation:

Assuming that g and w exists, then we can show the relation as described:

"Variable g is 8 more than variable w."

g = w + 8

"Variable g is also 2 less than w."

g = w - 2

These are the two equations of the described relationship between g and w.

Note that g could not actually exist in the real number system:

g = w + 8

g = w - 2

w + 8 = w - 2

w - w = -2 - 8

0 != -10

This is impossible within the real number system.

Cheers.

Answer:

We conclude that no more than 10% of its microwaves need repair during the first five years of use.

Step-by-step explanation:

We are given that a maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use.

In a random sample of 50 microwaves that are 5 years old, 12% needed repairs.

Let p = population proportion of microwaves who need repair during the first five years of use.

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 10%      {means that no more than 10% of its microwaves need repair during the first five years of use}

Alternate Hypothesis, [tex]H_A[/tex] : p > 10%     {means that more than 10% of its microwaves need repair during the first five years of use}

The test statistics that will be used here is 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 microwaves who need repair during the first 5 years of use = 12%

           n = sample of microwaves = 50

So, the test statistics =  [tex]\frac{0.12-0.10}{\sqrt{\frac{0.10(1-0.10)}{50} } }[/tex]

                                    =  0.471

The value of z-test statistics is 0.471.

Now, at a 0.04 level of significance, the z table gives a critical value of 1.751 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 0.471 < 1.751, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that no more than 10% of its microwaves need repair during the first five years of use.

Answer:

The probability that at least, one of the four children the couple has is a boy is 0.8.

Step-by-step explanation:

Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..

Note that it is possible to have the following for 4 children:

1. 4 boys, 0 girls

2. 3 boys, 1 girl

3. 2 boys, 2 girls

4. 1 boy, 3 girls

5. 0 boys, 4 girls.

To have at least, one boy, out of the 5 options, only 4 is possible.

1. 4 boys, 0 girls.........YES

2. 3 boys, 1 girl ...........YES

3. 2 boys, 2 girls.........YES

4. 1 boy, 3 girls.............YES

5. 0 boys, 4 girls..........NO

The probability is therefore,

(Probability of event = 4) ÷ (Total possible outcome = 5)

P = 4/5 = 0.8

Answer:

x = -10

Step-by-step explanation:

(x - 3) - 2(x + 6) = -5

Distribute

x-3 -2x-12 = -5

Combine like terms

-x -15 = -5

Add 15 to each side

-x-15+15 = -5+15

-x=10

Multiply each side by -1

x= -10

Answer:

c

Step-by-step explanation:

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

Hi there! :)

Answer:

Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

To solve, we will need to set up a system of equations:

Let x = # of dramas, y = # of comedies, and z = # of documentaries:

Write equations to represent each person:

Gina:

x + y + z = 11

Sam:

2x + 3y + 2z = 27

Robby:

x + 2y + 2z = 19

Write the system:

x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Begin by subtracting the third equation from the second:

2x + 3y + 2z = 27

x + 2y + 2z = 19

-----------------------

x + y = 8

If x + y = 8, plug this into the first equation:

(8) + z = 11

z = 11 - 8

z = 3

We found the # of documentaries Gina rented, now we must solve for the other variables:

Subtract the top equation from the third. Substitute in the value of z we solved for:

x + 2y + 2(3) = 19

x + y + (3) = 11

-------------------------

y + 3 = 8

y = 5

Substitute in the values for y and z to solve for x:

x + 5 + 3 = 11

x + 8 = 11

x = 11 - 8

x = 3.

Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Answer:

B- x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Step-by-step explanation:

I took the quiz

Using concepts of circles, it is found that the angle measure of each slice is of 72º.

--------------------------------------------

--------------------------------------------

5 equal slices, thus:

[tex]\frac{360}{5} = 72[/tex]

The angle measure of each slice is of 72º.

A similar problem is given at https://brainly.com/question/16746988

Answer:

154.2

Step-by-step explanation:

143 plus

156 plus

172 plus

133 plus

167 = 771

divide by 5 equals 154.2

Answer:

49

Step-by-step explanation:

With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.

[tex]5x+3+8x-4=90[/tex]

Combine like terms:

[tex]13x - 1 = 90[/tex]

Add 1 to both sides:

[tex]13x = 91[/tex]

Divide both sides by 13:

[tex]x = 7[/tex]

Hope this helped!

Answer:

x = 7

Step-by-step exxplanation:

5x + 3 + 8x - 4 = 90

5x + 8x = 90 - 3 + 4

13x = 91

x = 91/13

x = 7

probe:

5*7 + 3 + 8*7 - 4 = 90

35 + 3 + 56 - 4 = 90

Answer: Will continue to rise

Step-by-step explanation:

Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.

The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.

This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.

Answer:

EDGE 2021

Step-by-step explanation:

1) 4%

2) Increase

Answer:

Step-by-step explanation:

Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.

So, to answer the first question, [tex]6^2[/tex] is a perfect square.

(a,b,c) is a Pythagorean triple means the following

[tex]a^2+b^2=c^2[/tex]

Here, it means that

[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]

Thank you.

Answer:

Its B

Step-by-step explanation:

Answer:

[tex]( - \sqrt{3} \: an d \: 1)[/tex]

Answer:  A)  g(x) = 3x - 14

Step-by-step explanation:

Solve the equation for y and replace y with g(x):

y - 3x = -14

y        = 3x - 14

  g(x) = 3x - 14

Answer:

Show that the statement is true for n=1

Step-by-step explanation:

Hey,

Show that the statement is true for n=1

You can check my other answer there which explains a little bit more the ideas.

https://brainly.com/question/17162256

thank you