I need help on 4,5,6, and 7.

a. What percent of people earn less than $40000?

Solution: Let S be the random variable of a salary of employee (in $), S ~ N(50000,20000). Then the random

variable X =−50000

20000

~N(0,1).

( < 40000) = ( <

40000 − 50000

20000 ) = ( < −0.5) = (−0.5) = 0.3085375.

Here Φ(x) denotes the cumulative distribution function of a standard normal distribution.

Answer: 31%.

b. What percent of people earn between $45000 and $65000?

Solution:

(45000 < < 65000) = (

45000 − 50000

20000 < <

65000 − 50000

20000 ) = (−0.25 < < 0.75)

= (0.75) − (−0.25) = 0.7733726 − 0.4012937 = 0.3720789.

Answer: 37%.

c. What percent of people earn more than $70000?

Solution:

( > 70000) = ( >

70000 − 50000

20000 ) = ( > 1) = 0.8413447.

Answer: 84%.

By converting the salary amounts to Z-scores and checking a standard normal distribution table, the percentages of people earning less than $40,000, between $45,000 and $65,000, and more than $70,000 are approximately 30.85%, 37.21%, and 15.87%, respectively.

In this question, we are dealing with what is known as a 'normal distribution' in statistics. The properties of a normal distribution allow us to calculate the percentages requested. First, we need to convert each salary to a 'Z-score'. A z-score will tell us how many standard deviations away from the mean the salary lies.

a) For $40,000, the Z-score will be (40000-50000)/20000, yielding -0.5. Looking up this Z-score in a standard normal distribution table, or using a calculator equipped with normal distribution functions, we find that roughly 30.85% of employees would earn less than $40,000.

b) For the range $45,000 to $65,000: the Z-scores will be -0.25 and 0.75 respectively. These correspond to about 40.13% and 77.34%. The percentage of people earning between these amounts would be 77.34% - 40.13% = 37.21%.

c) For over $70,000: the Z-score is 1.0 which corresponds to around 84.13%. Therefore, the percentage earning more than $70,000 is 100% - 84.13% = 15.87%

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The answer is 10x+8y-12 if the problem was -6x - 12 + 8y + 16x because you added an extra negative at the start.

Answer:

The length of the rectangle is 25 km

Step-by-step explanation:

Let

x ----> the length of rectangle

y ----> the width of rectangle

we know that

The perimeter of rectangle is

[tex]P=2(x+y)[/tex]

we have

[tex]P=68\ km[/tex]

so

[tex]68=2(x+y)[/tex]

simplify

[tex]34=(x+y)[/tex]---- > equation A

[tex]x=3y-2[/tex] ---> equation B

substitute equation B in equation A and solve for y

[tex]34=(3y-2)+y[/tex]

[tex]34=4y-2[/tex]

[tex]4y=34+2[/tex]

[tex]4y=36[/tex]

[tex]y=9\ km[/tex]

Find the value of x

[tex]x=3(9)-2=25\ km[/tex]

therefore

The length of the rectangle is 25 km

Answer:

20

Step-by-step explanation:

2x^2-y

x = 3 and y = -2

So then we have 2*3^2--2 which equals 20.

The solution to the algebraic expression 2x² - y for  x= 3 and y=-2. is: 22

An algebraic expression in mathematics is defined as an expression which is made up of variables and constants, along with algebraic operations

We are given the algebraic expression as:

2x² - y for  x= 3 and y=-2.

Thus, plugging in 3 for x and -2 for y in the given equation and we have:

2(3)² - (-2)

= (2 * 9) + 4

= 18 + 4

= 22

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Answer:

x=-3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(x−6)+6=5x−6

(3)(x)+(3)(−6)+6=5x+−6(Distribute)

3x+−18+6=5x+−6

(3x)+(−18+6)=5x−6(Combine Like Terms)

3x+−12=5x−6

3x−12=5x−6

Step 2: Subtract 5x from both sides.

3x−12−5x=5x−6−5x

−2x−12=−6

Step 3: Add 12 to both sides.

−2x−12+12=−6+12

−2x=6

Step 4: Divide both sides by -2.

−2x

−2

=

6

−2

x=−3

Answer: x = -3

Step-by-step explanation:

1. Distribute the 3 into the parenthesis

     3x - 18 + 6 = 5x - 6

2. Combine like terms (on the left side of the equation

    3x - 12 = 5x - 6

3. Add 6 to both sides to get rid of the -6 on the right side

    3x - 6 = 5x

4. Subtract 3x from both sides to get rid of the 3x from the left side

    -6 = 2x

5. Divide both sides by 2

    -3 = x    

Final answer:

The numbers 68.75, 5.894, 634.9201, and 89.99 when rounded to one decimal place become 68.8, 5.9, 634.9, and 90.0 respectively.

Explanation:

The student is asking for rounding to one decimal place. Here is how you round the given numbers:

Answer:

Option C) |2x| > 6 is correct.

Step-by-step explanation:

Consider the provided solution set:

{x ⎸x > 3 or x < –3}

Now check which options are correct.

Option A) |2x| < 6

[tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]

[tex]-6<2x<6[/tex]

[tex]-3<x<3[/tex]

Thus, the option is incorrect.

Option B) |2x| ≥ 6

[tex]\mathrm{If}\:|u|\:\ge \:a,\:a\:>\:0\:\mathrm{then}\:u\:\le \:-a\:\quad \mathrm{or}\quad \:u\:\ge \:a[/tex]

[tex]2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6[/tex]

[tex]2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6[/tex]

Thus, the option is incorrect.

Option C) |2x| > 6

[tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]

[tex]2x<-6\quad \mathrm{or}\quad \:2x>6[/tex]

[tex]x<-3\quad \mathrm{or}\quad \:x>3[/tex]

Thus, the option is correct.

Option C) |2x| ≤ 6

[tex]\mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a[/tex]

[tex]2x\ge \:-6\quad \mathrm{and}\quad \:2x\le \:6[/tex]

[tex]x\ge \:-3\quad \mathrm{and}\quad \:x\le \:3[/tex]

Thus, the option is incorrect.

Hence, Option C) |2x| > 6 is correct.

Answer:

Step-by-step explanation:

The simplified version of 127/30 is 4 7/30 (mixed number)

127/30 is basically 127 divided by 30, so if you divide 127 by 30, you get 4 and a remainder of 7. WAIT! That's not where I stop. The quotient is the whole number, the remainder is the numerator, and the divisor is the denominator. Therefore, the simplified version of 127/30 is 4 7/30.

Answer:

4  7/30

Step-by-step explanation:

This is an improper fraction.

30 goes into 127 four times with 7 left over.

You place 7 over the original denominator of 30

7/30 is a reduced fraction so ...

4 and 7/30 is your answer.

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Answer:

See explanation

Step-by-step explanation:

Let x be the number of hours per week Nando is brisk walking  and y be the number of hours per week Nando is  biking at a moderate pace.

For the first month, he needs to exercise at most five hours per week, then

[tex]x+y\le 5[/tex]

Brisk walking burns about 350 calories per hour, then it burns 350x calories per x hours.

Biking at a moderate pace burns about 700 calories per hour, then it burns 700y calories per y hours.

Nando must burn at least 2,000 calories per week, so

[tex]350x+700y\ge 2,000[/tex]

You get the system of two inequalities:

[tex]\left\{\begin{array}{l}x+y\le 5\\ 350x+700y\ge 2,000\end{array}\right.[/tex]

The attached graph shows the solution set to this system of inequalities. In this diagram, red region represents the solution set to the first inequality, blue region represents the solution set to the second inequality and their intersection is the solution set to the system of two inequalities.

Answer:

112

Step-by-step explanation:

The number is 112 if Five-eighths of a number decreased by twelve is the same as one-half of the number increased by two the answer is 112.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

Five-eighths of a number decreased by twelve is the same as one-half of the number increased by two.

Let x be the number:

From the question:

(5/8)x - 12 = (1/2)x + 2

The above equation is a linear equation in one variable:

After solving:

(5/8)x - (1/2)x =  12 + 2

(5-4)x/8 = 14

x = 14×8

x = 112

Thus, the number is 112 if Five-eighths of a number decreased by twelve is the same as one-half of the number increased by two the answer is 112.

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Answer:

3,9,and 36

Step-by-step explanation:

small=x

median=3x

big=12x

x+3x+12x=48

16x=48

x=3

3=small

3*3=9  (median)

9*4=36(big)

3+9+36 = 48

The problem is solved by setting up and solving an equation where 'x' represents the length of the first piece. The three pieces of the wire measure 3ft, 9ft, and 36ft respectively.

The question is about finding the length of each piece of a 48ft wire when it's divided into 3 pieces, with each piece having a specific relative length. Let's denote the length of the first piece as 'x'. According to the problem, the second piece is three times as long as the first one, so it's '3x', and the third is four times as long as the second, so it's '4*3x', which simplifies to '12x'.

Combining all these pieces, we get the total length of the wire: x + 3x + 12x = 48ft. This simplifies to 16x = 48ft. Finally, solving for 'x', we find that x = 48ft / 16 = 3ft. Therefore, the three pieces of the wire measure 3ft, 9ft, and 36ft respectively.

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Among the given options, "-0.1" is not a possible R-value. R-values represent the thermal resistance of a material, and they are always positive values.

R-values are used to measure the ability of a material to resist the flow of heat, and a higher R-value indicates better insulation. Therefore, values like 1.75, 0.2, and -0.5 could potentially be R-values, with 1.75 and 0.2 being good insulators and -0.5 indicating a poor insulator. However, a negative value like -0.1 does not make physical sense in the context of R-values.

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Answer:

do the area of the triangle formula the base × height ÷ 2

38 to the power of 5 is written as 38^5

When a number is raised to a power, multiply that number by itself the number of the power:

38 x 38 x 38 x 38 x 38 = 79,235,168

Answer:

10

Step-by-step explanation:

x×4/5=8

x=8×5/4

x=10

Answer:

The correct answer is 10.

Step-by-step explanation:

One of the ways to find this answer is the following:

If 4/5 represent 8 pounds, it means that every fifth is two pounds.

If the total amount is five fifths, it is necessary to perform the following multiplication:

2 * 5 = 10, so it is the correct answer.

[tex]\frac{-12}{-4}[/tex] is 3.

Answer:

-12/-4 is 3

Step-by-step explanation:

hope this helps !!

Answer:

320+40=360

Step-by-step explanation:

8(40+5)

320+40=360

Answer:

320+40=360

Step-by-step explanation:

First you split 45 to 40 and 5

45= 40+5

Next you multiply each piece of 45 by 8

(40x8)+ (5x8)

Simplify

320+40

Solve

320+40=360

Answer:

6 hours

Step-by-step explanation:

234.50-50.00=184.50

184.50/30.75=6

6 hours

Answer:

7x + 9 ≥ 30

x ≥ 3

Step-by-step explanation:

7x + 9 ≥ 30

7x ≥ 21

x ≥ 3

Final answer:

The inequality 7x + 9 ≥ 30 represents the description given, and the solution is x ≥ 3, meaning any number greater than or equal to 3 satisfies the inequality.

Explanation:

The inequality that represents the description 'nine more than seven times a number (x) is at least thirty' is written as 7x + 9 ≥ 30.

To solve this inequality:

Therefore, the solution to the inequality is that x must be a number greater than or equal to 3.

Answer:

100.

Step-by-step explanation:

118 rounded to the nearest hundred is 100

When rounding 118 to the nearest hundred, we look at the tens digit (which is 1 in this case). Since this digit is less than 5, we round down to the nearest hundred. Therefore, 118 rounded to the nearest hundred is 100.

Answer:

3.5

Step-by-step explanation:

15 - 8 = 7

7 / 2 = 3.5

Answer:

a. 81.9

b. 144.7

c. 110.2

d. 48

Step-by-step explanation:

a. 120/109.2 = 90/x

x = 81.9

b. 45.6/120 = 55/x

x = 144.7

c. 304.8/96 = 350/x

x = 110.2

d. 109.2/45.6 = 115/x

x = 48

8:

q/6 + p

12/6 + 10

2 + 10

12

10:

15 - m/p

15 - 3/10

14.7

12:

p - 2/qp

7 - 2/(4)(7)

7 - 2/28

7 - 1/14

6.928

Answer:

0.820

Step-by-step explanation:

7 is above five so round to the nearst tenth

Answer:

58,000,000 km

Step-by-step explanation:

the hair thing is just to throw you off

The average distance from the Sun to the planet Mercury is approximately 58 million kilometers, which also translates to 0.39 astronomical units (AU). Mercury's orbit varies from 46 million kilometers at its closest to 70 million kilometers at its farthest from the Sun due to its elliptical orbit.

Distance from the Sun to Mercury

The average distance from the Sun to Mercury is about 58 million kilometers. This distance is known as the semimajor axis of Mercury's orbit. Since Mercury's orbit has a high eccentricity of 0.206, its actual distance from the Sun can vary significantly. The closest point, or perihelion, is about 46 million kilometers, and the farthest point, or aphelion, is about 70 million kilometers. The concept of astronomical unit (AU) is used as a standard measure within the solar system, defined as the average Earth-Sun distance, which is about 150 million kilometers or 1 AU. Consequently, Mercury's average distance from the Sun can also be expressed as 0.39 AU.

Answer:

toward the outside

Step-by-step explanation:

The plasma membrane is composed of the phospholipid bilayer and cholesterol.The phospholipids have a head and two tails.The head is water loving, hence it is termed as polar/hydrophilic.The tails are nonpolar/ water fearing/hydrophobic.Both inside and outside the cell, water is vital thus the phospholipid line up in two layers where the head points outwards and the tails hidden in the middle.

Answer:

to the middle

Step-by-step explanation:

Answer:

17720 feet

Step-by-step explanation:

5.4 km × (1 mile / 1.609 km) × (5280 feet / mile) ≈ 17720 feet

Answer:

17,720.32

Step-by-step explanation:

Divide 5.4 by 1.609 x 5,280 = 17,720.32

Answer:

405

Step-by-step explanation:

45% of 900

=(45/100) . 900

=405