suppose a normal distribution has a mean of 38 and a standard deviation of 2. What is the probability that a data value is between 36 and 43? Round your answer to the nearest 10th of a percent.

Answer:

C. [tex]x\geq 55000[/tex]

Step-by-step explanation:  

Let x be the total monthly sales.

We have been given that a salesperson earns a salary of $700 per month plus 2% of the sales. The salesperson want to have a monthly income of at least $1800.  

This means that 700 plus 2% of total monthly sales should be greater than or equal to 1800. We can represent this information in an equation as:

[tex]700+(\frac{2}{100})x\geq 1800[/tex]

[tex]700+0.02x\geq 1800[/tex]

Let us solve our inequality to find the monthly sales (x).

Subtract 700 from both sides of our inequality.

[tex]700-700+0.02x\geq 1800-700[/tex]

[tex]0.02x\geq 1100[/tex]

Divide both sides of inequality by 0.02.

[tex]\frac{0.02x}{0.02}\geq \frac{1100}{0.02}[/tex]

[tex]x\geq \frac{1100}{0.02}[/tex]

[tex]x\geq 55000[/tex]

Therefore, the total monthly sales must be greater than or equal to 55,000 and option C is the correct choice.

The relationship between the year and the number of cinema sites can be expressed with the linear equation y = -300x + 608300, where y is the number of cinema sites and x is the year. This equation was derived by calculating the slope and y-intercept using the points provided.

The subject of the question falls into the domain of mathematics, specifically algebra. We are given two points on a line where the x-axis is the year and the y-axis represents the number of cinema sites. The two points are (2000, 8300) and (2004, 7100).

First, we need to calculate the slope, m: m = (y2 - y1) / (x2 - x1) = (7100 - 8300) / (2004 - 2000) = -1200 / 4 = -300.

The slope, -300, is the rate of change suggesting the number of cinemas decreases by 300 each year.

The equation of the line, or the linear equation, will be in the form y = mx + b. We now need to find the y-intercept (b) by substituting one of our points into the equation and solving for b.

If we use the point (2000, 8300): 8300 = -300*2000 + b. Solving for b gives b = 8300 + 600000 = 608300.

Therefore, the equation describing the relationship between the year and the number of cinema sites is y = -300x + 608300.

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Answer:

(<1 and <3) (<2 and <4) (<3 and <6)

Step-by-step explanation:

1 and 3 are corresponding equal angles

If one and three are equal, so are 2 and 4 since they are supplementary to equal angles.

6 and 7 are supplementary but not equal.

3 and 6 are equal angles because they are alternate interior angles.

Answer:

the answer if am not wrong would be C.n+5

Step-by-step explanation:

Answer:

$30

Step-by-step explanation:

Mark up is the profit on cost. if the pair of jeans was $45 after a 50% markup

Let the price of the jeans before the markup be p then;

p + 50%p = 45

1.5p =45

p = 45/1.5

p = 30

The price before mark up was $30, while the mark up or profit  is $15. This shows 50% of the price before mark up.

Answer:

97.8%

Step-by-step explanation:

110 is 2 standard deviations above the mean (6+6 = 12)

12+98 = 110

Looking at the standard deviation curve

P(x< or = to 110)  = 1 - P(x>110)

We can find the probability that x>100 by adding  anything above 2 standard deviations above the curve.

P(x>110) = 2.1+.1 = 2.2%

P(x< or = to 110)  = 1 - P(x>110)

                                = 1- 2.2%

                                = 1- .022

                                  = .978

                               = 97.8 %

Answer:

0.975

Step-by-step explanation:

A P E X

Answer:

The correct options are A: x+8 and C: x+2.

Step-by-step explanation:

We are given the following expression and we are to factorize it:

[tex]x^2+10x+16[/tex]

We are to find such factors that when multiplied they give a result of 16 (1 x 16 = 16) and when added they give a result of 10.

The two such factors of 16 are positive 2 and positive 8.

Factorizing the given expression to get:

[tex]x^2+10+16\\\\x^2+2x+8x+16\\\\x(x+2)+8(x+2)\\\\(x+2)(x+8)[/tex]

Therefore, the two binomial factors of the given expression [tex]x^2+10x+16[/tex] are (x+8) and (x+2).

Answer: x+6 x+2

tell me if I’m wrong because I put x+8 and x+2 and got it wrong it told me it was x+6 and x+2

The inverse function of f(x) = (x - 5)² for x greater or equal to 5 is g(x) = sqrt(x) + 5.

The function f(x) = (x - 5)² for x greater or equal to 5 has a specific inverse function denoted as g(x). To find the inverse of a function, one typical solution is to replace f(x) with y, swap x and y, and solve for y. Here, it means writing y = (x - 5)², changing it to x = (y - 5)², and solving for y.

The solved y function is g(x) = √(x) + 5 (where sqrt indicates a square root), ensuring the range for x is greater than or equal to 5 to adhere to the original function constraints.

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Answer:

187.69 cm

Step-by-step explanation:

We have that the maximum area allowed for the painting = 3003.04 [tex]cm^{2}[/tex].

Also, the width of Carmen's painting = 16 cm.

It is required to maximum length of Carmen's painting that will be eligible to take part in the competition.

Let the maximum length of the painting = L cm.

Since, Area of a rectangle = length of the rectangle × width of the rectangle.

i.e. 3003.04 = L × 16

i.e. [tex]L=\frac{3003.04}{16}[/tex]

i.e. L = 187.69 cm

Hence, the length of the painting should not exceed 187.69 cm in order to be eligible to participate in the competition.

Answer:

Number of chores done by Janie are 5.

Step-by-step explanation:

Janie's allowance per week is $3.

For each chore she earns $2.

Now we assume that number of chores in a week she does = c

Then total earning from chore = $2 × c

So for the purchase of CD total earning this week inequality will be

⇒ 3 + 2c [tex]\geq[/tex]13

⇒ 2c [tex]\geq[/tex] 13-3

⇒ c [tex]\geq[/tex] 10÷2

⇒ c [tex]\geq[/tex] 5

Answer:

A)84 – 73 = 11 miles

Step-by-step explanation:

On Tuesday she drove 84 miles  (rounding to the nearest mile)

On Monday she drove 73 miles (rounding to the nearest mile)

Tuesday's mileage - Mondays miles = difference in miles

84-73 = 11 miles

Answer: A. 84 – 73 = 11 mi

Answer: Length of each of rope will be 9.93 feet.

Step-by-step explanation:

Since we have given that

Length of rope that Emma brandy and Damien will cut = 29.8

Number of jumps = 3

According to question, each of the three jumps ropes will be the same length l.

Length of rope can be attained by dividing the length of rope with number of jumps.

so, length of each rope will be

[tex]l=\frac{\text{Length of rope}}{\text{Number of jumps cut into }}\\\\=\frac{29.8}{3}\\\\=9.93\ feet[/tex]

Hence, Length of each of rope will be 9.93 feet.

Answer: After 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.      

Step-by-step explanation:

Let after x year from the first year Eric sees that investment R's value exceeded investment Q's value.

Investment Q has a value of $ 500 at the end of the first year and increases by $ 45 per year.

Thus, after x year from the first year the total amount of  Investment Q,

500 + 45 x

Similarly, after  x year from the first year the total amount of  Investment R,

⇒ [tex]400(1+\frac{10}{100} )^x = 400(1.1)^x[/tex]

Thus,  [tex]500 + 45 x = 400(1.1)^x[/tex]

By plotting the equations in the graph,

We get,  x = -6.178 or 8.069

But year can not be negative,

Therefore, x = 8.069

Thus, Approx after 8 year from the first year Eric will see that investment R's value exceeded investment Q's value.

Answer: it’s 10 I’m 100% sure

Answer: (b) x = -7, x = 2, x = 4

Step-by-step explanation:

Remainder Theorem is used to determine if a given value is a root.

It is stated that (x + 7) is a root ⇒ x + 7 = 0  ⇒ x = -7

We can confirm this by plugging in x = -7 and getting a value of 0.

f(x) = 5x³ + 5x² - 170x + 280

f(-7) = 5(-7)³ + 5(-7)² - 170(-7) + 280

      = -1715 + 245 + 1190 + 280

     = 0

CONFIRMED that x = -7 is a zero!

Next, let's try x = 2

f(2) = 5(2)³ + 5(2)² - 170(2) + 280

      = 40 + 20 - 340 + 280

     = 0

CONFIRMED that x = 2 is a zero!

Lastly, let's try x = 4

f(4) = 5(4)³ + 5(4)² - 170(4) + 280

      = 320 + 80 - 680 + 280

     = 0

CONFIRMED that x = 4 is a zero!

To solve a system of equations by elimination, make the coefficients of one variable equal. Subtract one equation from the other to solve for one variable, then substitute this solution into one of the original equations to solve for the other variable. In this case, the solution to the given system of equations is x = 3, y = 6.

In mathematics, specifically in algebra, the method of elimination is used to solve a system of simultaneous equations. Your equations are:

To solve this system by elimination, we need to make the coefficients of y in both equations equal by multiplying if necessary. We can obtain this by multiplying the first equation by 2:

4x - 2y = 0
3x - 2y = -3

Next, we subtract one equation from the other to eliminate y:

4x - 3x = 0 - (-3) => x = 3

To find y, substitute x = 3 into the first equation:

2*3 - y = 0 => y = 2*3 = 6

So, the solution to the system of equations is x = 3, y = 6.

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[tex]a_1=-2\\\\a_n=3\cdot a_{n-1}\\-----------------------------------\\a_1=-2\\\\a_2=3\cdot a_{2-1}=3\cdot a_1\to a_2=3(-2)=-6\\\\a_3=3\cdot a_{3-1}=3\cdot a_2\to a_3=3(-6)=-18\\\\a_4=3\cdot a_{4-1}=3\cdot a_3\to a_4=3(-18)=-54\\\\a_5=3\cdot a_{5-1}=3\cdot a_4\to a_5=3(-54)=-162\\\\a_6=3\cdot a_{6-1}=3\cdot a_5\to a_6=3(-162)=-486\\\\Answer:\ \boxed{-2,\ -6,\ -18,\ -54,\ -162,\ -486}[/tex]

If a, b and c are the lengths of the sides of a triangle then

if a ≤ b ≤ c, then a + b > c.

A) 10, 14, 26

10 + 14 = 24 < 26   INCORRECT  :(

B) 10, 14, 16

10 + 14 = 24 > 16  CORRECT :)

C) 10, 10, 14

10 + 10 = 20 > 14  CORRECT :)

D) 8, 10, 14

8 + 10 = 18 > 14   CORRECT :)

E) 5, 10, 14

5 + 10 = 15 > 14   CORRECT :)

F) 2, 10, 14

2 + 10 = 12 < 14   INCORRECT :(

Options B, C, D and E are correct answers.

Given that, a triangle has two sides of lengths 10 and 14.

We need to find what value could the length of the third side be and check all that apply.

Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

Now, from the given options:

A) 10, 14, 26

10 + 14 = 24 < 26 the triangle can not be formed

B) 10, 14, 16

10 + 14 = 24 > 16 the triangle can be formed

C) 10, 10, 14

10 + 10 = 20 > 14 the triangle can be formed

D) 8, 10, 14

8 + 10 = 18 > 14 the triangle can be formed

E) 5, 10, 14

5 + 10 = 15 > 14 the triangle can be formed

F) 2, 10, 14

2 + 10 = 12 < 14 the triangle can not be formed

Therefore, options B, C, D and E are correct answers.

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Answer:

d. The bonds will earn $26.40 more than the stocks.

Step-by-step explanation:

Assuming, the rates are uniform for 6 years.

Stock in Ombor Medical Supplies earns a return of 5.3% annually, so $1000 will yield annually;

[tex]0.053\times1000=53[/tex] dollars

Total amount in 6 years will become = [tex]53\times6=318[/tex] dollars

Bonds issued by Ombor Medical Supplies earns a return of 4.1% annually, so $1400 will yield annually;

[tex]0.041\times1400=57.40[/tex] dollars

Total amount in 6 years will become = [tex]57.40\times6=344.40[/tex] dollars

We can see that bonds have high yield than stocks.

So, difference amount is = [tex]344.40-318=26.40[/tex] dollars.

Therefore, The bonds will earn $26.40 more than the stocks.

Answer:

it is d

Step-by-step explanation:

i took the edu test :)

Step-by-step explanation:

We are asked to write a system of equations using our given information.

Let x be number of small dogs and y be number of large dogs.

We have been given that paws at play made a total of $1,234 grooming 22 dogs, which means that number of small dogs and large dogs is 22. We can represent this information as:

[tex]x+y=22...(1)[/tex]  

We have been given that paws at play charges $43 to groom each small dog and $75 for each large dog. So the total grooming charges for grooming x small and y large dogs will be 43x+75y, that is equal to total charges for grooming $1234.

We can represent this information as:  

[tex]43x+75y=1234...(2)[/tex]

Therefore, our desired system of equations is:

[tex]x+y=22...(1)[/tex]

[tex]43x+75y=1234...(2)[/tex]    

Answer:

Mr. Robins commision rate is 15%.

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

Mr robbins earns a commission on each airfare he books.

At the end of the day,he had booked $208.60 worth if airfare and earned $31.29.

Here

Part value = $31.29

Total value = $208.60

Put in the formula

[tex]Percentage = \frac{31.29\times 100}{208.60}[/tex]

[tex]Percentage = \frac{312900}{20860}[/tex]

Percentage = 15%

Therefore the  Mr. Robins commision rate is 15%.

Answer:$80.00

Step-by-step explanation:

APEX

Answer:

The amount of the earth’s surface covered by water is 2.12*10^8 greater than the amount of the earth’s surface covered by land.

Step-by-step explanation:

(Subtraction of scientific notation)

Earth’s surface covered by water- 3.61*10^8

Earth’s surface covered by land- 1.49*10^8

(3.61*10^8) - (1.49*10^8)

(3.61-1.49) *10^8

2.12*10^8

Hope this helps you out

Answer:

Taylor's new balance is  $ 185.57  .

Step-by-step explanation:

As given

Taylor has $97.23 and her checking account.

she uses debit card to spend $29 .74 .

Than

Balance in the account after uses debit card = $97.23 - $29.74

                                                                          = $ 67.49

As given

Then deposits $118.08 into her accounts.

Total balance of the account = $118.08 + $67.49

                                                 = $ 185.57

Therefore Taylor's new balance is  $ 185.57  .

Answer:

$185.57

Step-by-step explanation:

Answer:

option B

Step-by-step explanation:

the correct answer is option B

A Line, segment, or ray that bisects a segment at a right angle is Perpendicular bisector.

The slope of the is the rate of change of y-axis w r t to x-axis.

Midpoint is the center of any line segment.                    

An angle bisector is a line which bisects angle in equal proportion

Answer:

4 adult dinosaurs and 12 baby dinosaurs.

Step-by-step explanation:

Let the number of adult dinosaurs be x.

Number of baby dinosaurs = 3x

Number of paintings made by each baby dinosaur = 15

Number of paintings made by each adult dinosaur = 7

Total number of paintings made by 3x baby dinosaurs = Number of baby dinosaurs * Number of paintings made by each baby dinosaur

= 3x * 15

= 45x

Total number of paintings made by x adult dinosaurs = Number of adult dinosaurs * Number of paintings made by each adult dinosaur

= x * 7

= 7x

Total number of paintings made by both baby and adult dinosaurs = 45x + 7x

= 52 x

Again the problem says that the total number of paintings made  = 208

So, 52x = 208

Dividing both sides by 52

[tex]\frac{52x}{52}[/tex]  = [tex]\frac{208}{52}[/tex]

Cancelling out the 52's from the top and bottom on the left

x = 4

So, number of adult dinosaurs = 4

Number of baby dinosaurs = 3x = 3*4 = 12

A system of equations based on the information given can be used to find the number of baby and adult dinosaurs. The two equations are 1515b + 77a = 208208 and b = 33a. Solve these to find the number of each type of dinosaur.

This problem can be solved by setting up a system of equations. Let's denote the number of baby dinosaurs as 'b' and the number of adult dinosaurs as 'a'. Then, from the statement, we know two things:

By substituting the second equation into the first, we can determine the number of adult dinosaurs, and subsequently, the number of baby dinosaurs. Solving this would give us the solution needed.

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Answer:

Surface Area = 150

Step-by-step explanation:

The surface area of this triangular prism is the sum of area of all the sides.

Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)

Summing all these gives us the total surface area.

Total surface area = [tex]12+12+35+35+56=150[/tex]

**** The triangle shown is divided into half by the perpendicular line (3cm) to the base. So the base is divided in half (4 cm and 4 cm).

Now, we have a right triangle with one leg 4 cm and another leg 3 cm. How do we get the hypotenuse? We use Pythagorean Theorem. Which is:

[tex]leg^2+leg^2=hypotenuse^2\\3^2+4^2=hypotenuse^2\\25=hypotenuse^2\\hypotenuse=5[/tex]

Hence, the side length of the hypotenuse is 5 [used above in the calculation]