A salesperson works 40 hours per week at a job where she has two options for being paid. Option A is an hourly wage of ​$28. Option B is a commission rate of ​5% on weekly sales. How much does she need to sell this week to earn the same amount with the two​ options?

Answer:

x = 29

Step-by-step explanation:

Given:

m<PQS = 107°

m<RQS = 49°

m<PQR = (2x)°

Required:

Value of x

Solution:

m<RQS + m<PQR = m<PQS (angle addition postulate)

Plug in the values

49 + 2x = 107

Subtract 49 from each side

2x = 107 - 49

2x = 58

Divide both sides by 2

x = 58/2

x = 29

Answer:

a) The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of \(Z = \frac{X - \mu}{\sigma}\), in which \(\mu\) is the mean and \(\sigma\) is the standard deviation.

b) We have to find X when Z has a p-value of \(\frac{a}{100}\), and X is given by: \(X = \mu - Z\sigma\), in which \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Mean \(\mu\), standard deviation \(\sigma\)

a. Find the probability of a pregnancy lasting X days or longer.

The probability of a pregnancy lasting X days or longer is given by 1 subtracted by the p-value of \(Z = \frac{X - \mu}{\sigma}\), in which \(\mu\) is the mean and \(\sigma\) is the standard deviation.

b. If the length of pregnancy is in the lowest a​%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

We have to find X when Z has a p-value of \(\frac{a}{100}\), and X is given by: \(X = \mu - Z\sigma\), in which \(\mu\) is the mean and \(\sigma\) is the standard deviation.

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

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Answer:

3311 mililiters

Step-by-step explanation:

1 L = 1 liter = 1000 mililiters

3.311L = 3.311 liters = 3.311*1000 = 3311 mililiters

The sales tax on this computer in 62 dollars and 93 cents

The given parameters

Price = $899

Tax rate = 7%

The sales tax on this computer in dollars and cents is calculated as

Sales tax = Price * Tax rate

This gives

Sales tax = $899 * 7%

Evaluate

Sales tax = $62.93

Hence, the sales tax on this computer in 62 dollars and 93 cents

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Answer:

4-2(16x+8)^1/3=-8

-2(16x+8)^1/3=-12

(16x+8)^1/3=6

16x+8=216

16x=208

x=13

Checking if x=13 is an extraneous solution:

4-2[16(13)+8]^1/3=-8
4-2(208+8]^1/3=-8

4-2(216)^1/3=-8

4-2(6)=-8

4-12=-8

-8=-8

Not an extraneous solution.

Answer:

A

Step-by-step explanation:

-3 + 20 = 17 degrees

Answer:

5

Step-by-step explanation:

it is the only non-multiple of 3 and 4

Answer:

4x - 5y = -18

Step-by-step explanation:

y+2=4/5(x+7)

5(y + 2) = 5 × 4/5(x + 7)

5y + 10 = 4x + 28

5y = 4x + 18

4x - 5y = -18

The area of the ΔABC is 98 cm²

In a triangle, we can use the sine formula to find the area of the triangle when we know one angle and the two side lengths opposite and adjacent to that angle.

Area of ΔABC = (1/2) bc sinA

Substitute b = 28 cm, c = 14 cm, and m∠A = 30° into the formula:

Area of ΔABC = (1/2) × 28cm × 14cm × sin 30°

Area of ΔABC = 98 cm²

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The value of the side length x is equal to 14 using the trigonometric ratio of sine.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

sin45 = 7√2/x {opposite/hypotenuse}

√2/2 = 7√2/x {sin45 = √2/2}

x = 7√2 × 2/√2 {cross multiplication}

x = 7 × 2

x = 14

Therefore, the value of the side length x is equal to 14 using the trigonometric ratio of sine.

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Answer:

c

Step-by-step explanation:

Answer:

\(x=\{-\frac{1}{2} ,\:0\}\)

Step-by-step explanation:

\(f(x) =-2x^2 -x\\plug \: f(x) =0\\0= -2x^2 -x\\2x^2 + x = 0\\x(2x+1) = 0\\\therefore x =0 \: or \: 2x+1 = 0\\\therefore x =0 \: or \: 2x = -1\\\\\therefore x =0 \: or \: x = -\frac{1}{2} \\\\x=\{-\frac{1}{2} ,\:0\}\)

The total cost of all the items he wants to buy with the applied discount and before tax is $9.9.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Bashir has a loyalty card good for a 10% discount at his local hardware store.

So, Each good he buys at (100 - 10)% = 90% of the value before tax.

He wants to buy some items that cost $11  before the discount and tax.

Therefore the amount he has to pay is,

= (90/100)×11.

= $9.9

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Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

84π mm^2

Step-by-step explanation:

formula for circumference is 2πr where r is the radius of circle

Given,The circumference of the base of a cylinder is 24π mm

Thus,

2πr= 24π mm

=> r = 24π mm/2π = 12 mm

________________________________________

A similar cylinder has a base with circumference of 60π mm.

radius for this cylinder will be

2πr= 60π mm

r =   60π mm/2π = 30mm

______________________________________________

Given

The lateral area of the larger cylinder is 210π mm2

lateral area of cylinder is given by  2πrl

where l is the length of cylinder

thus,

r for larger cylinder = 30mm

2π*30*l  = 210π mm^2

=> l = 210π mm^2/2π*30 = 3.5 mm

___________________________________________

the lateral area of the smaller cylinder

r = 12 mm

l = 3.5 mm as both larger and smaller cylinder are same

2πrl  =  2π*12*3.5 mm^2 = 84π mm^2 answer

Answer:

33.6pi mm2 is the correct answer

edge 2021

Step-by-step explanation:

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2.

What is the lateral area of the smaller cylinder?

17.1π mm2

33.6π mm2

60π mm2

84π mm2

Step-by-step explanation:

Y= m x+ C

m (slope ) = 2 - (_3) / 0 _( - 9 )

= 5 / 9

( O, 2 ) Satisfying equation

2= 5/9 ( 0) + C

C= 2

So eq. is

y= 5/ 9 X + 2

Answer: It would cost $47.3 to fill the same tank in 2010

Step-by-step explanation:

In 1970

Total cost to fill the tank = $6

Cost per capacity of tank = $0.36

Capacity of tank = Total cost / Cost per capacity of tank

Capacity = 6/0.36

Capacity = 16.6

Therefore

In 2010

Cost per capacity of tank = $2.84

And we now know it capacity = 16.6

Total cost to fill the tank = 2.84 * 16.6

Total cost = $47.3

Hope this helps have a awesome day ❤️✨

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

In response to the given question, we can state that Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.

Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.

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9514 1404 393

Answer:

  3×10^8 m/s

Step-by-step explanation:

The desired speed is ...

  \(\dfrac{\dfrac{9.45\times10^{15}\text{ m}}{\text{yr}}}{\dfrac{3.15\times10^7\text{ s}}{\text{yr}}}=\dfrac{9.45}{3.15}\times10^{15-7}\text{ m/s}=\boxed{3.00\times10^8\text{ m/s}}\)

__

Your calculator can help you figure this out.

A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.

In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.

Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).

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Answer:

it’s D dotted line with shading below

Step-by-step explanation:

i got it on my quiz

Answer:

f(6) = 12

Step-by-step explanation:

We are given the following function:

\(f(x) = x^2 - 5x + 6\)

Evaluate the function f(6).

This is \(f(x)\) when \(x = 6\). So

\(f(6) = 6^2 - 5(6) + 6 = 36 - 30 + 6 = 12\)

f(6) = 12 is the answer.

Answer:

\(1\frac{2}{3}\)

Step-by-step explanation:

\(2\frac{1}{2} * \frac{2}{3}\)

\(\frac{5}{2} *\frac{2}{3}\)

\(\frac{10}{6}\)

\(\frac{5}{3}\)

\(1\frac{2}{3}\) .....final answer.

Answer:

7.0m

Step-by-step explanation:

=2h ×2w

=2(1.5m)+2(2.0m)

=7.0m

Answer:

You will have .38 feet left of string

Step-by-step explanation:

Just subtract the numbers

Have a good day!

Answer:

0.38

Step-by-step explanation:

4.25-3.87=0.38

Answer: the answer is C $912.

Step-by-step explanation: The interest on the loan is calculated as follows:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the length of the loan in years. Substituting the given values, we get:

Interest = $800 x 0.14 x 1

Interest = $112

Therefore, the total amount to be repaid is the sum of the principal and the interest, which is:

Total amount = Principal + Interest

Total amount = $800 + $112

Total amount = $912