Suppose that the base salary of a salesperson is $30,000 per year. The salesperson gets an additional $50 for every sale. Let x represents the number of sales. How can we model the scenario with a linear function? How many items does the salesperson need to sell to earn $50,000

Answer:

$122.9

Step-by-step explanation:

Given data

Principal= $114

Rate= 3.9%

Time= 2 years

The amount in the account is given as

A=P(1+rt)

substitute

A=114(1+0.039*2)

A=114(1+0.078)

A=114(1.078)

A=$122.9  

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

Answer: 1256.63706

Step-by-step explanation: A=(π20)2

The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.

To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:

Area = (1/2) * r^2 * (θ - sinθ)

Where:

r is the radius of the circle (r = 20 in your case).

θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).

Let's calculate it:

θ = 47° * (π / 180) ≈ 0.8203 radians

Now, plug these values into the formula:

Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))

Area ≈ (1/2) * 400 * (0.8203 - 0.7317)

Area ≈ (1/2) * 400 * 0.0886

Area ≈ 17.72 square units

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Answer:

3

Step-by-step explanation:

z/12=18/72      z/12=1/4  z=3

Answer:

The answer is z=3

Step-by-step explanation:

hope this helps

z/12 = 18/72

72z=216

To find z divide both sides by 72

72z/72=216/72

z=3

Answer:

tells us the rate of change of y relative to x. If the slope is 2, then y is changing twice as fast as x; if the slope is 1/2, then y is changing half as fast as x, and so on.

Step-by-step explanation:

In other words, if the line is near vertical then y is changing very fast relative to x.

Answer:

angle xdq= 90-49= 41

angle uxd= 180-41= 139

Step-by-step explanation:

A right angle equals 90 degrees.

90-49 = angle xdq = 41 degrees

49 + 90 + x = 180

angle x = 41

180-41 = angl uxd = 139

Answer:

the second one(20)

Step-by-step explanation:

If you pretend 20 is x, you solve the equation by pluging in x (20) into the equation and it gives you 70, 70 is what the big part is and 70+20 is 90, which is the size of a 90degree side.

4(20)-10

80-10

70

70+20=90

Answer: The answer to this question is 20 degrees

Step-by-step explanation:

So, you know that it's a straight line, which is 180 degrees. The angle on the very left is 90 degrees because it's a right angle.

So that means (x + 10) + x = 90 degrees because 180 - 90 = 90

Solve that equation for x:

x + 4x - 10 = 90

5x = 100

x = 20

So, your final answer is 20 degrees

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

x \ge 24/19

Step-by-step explanation:

(20x+6\right)\ge \:x+30

20x+6\ge \:x+30

20x\ge \:x+24

19x\ge \:24

divide both sides by 19

\frac{19x/{19\ge24/19

x\ge 24/19

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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Answer:

Sorry for the $ sign, I meant that pound sign, my computer doesn't have that sign, sorry. So just bear with me, the math is all the same.

The next one is $45+$22.5 = $67.5 for 100 ml. We can then form ratios:

55:80

67.5:100

We can then divide the first ratio by 80 on both of the sides. So we will get

0.688:1

And do the same with second but for 100

0.675:1

So since we are not counting discount on the 80 ml bottle, the best choice is the 50ml bottle with the discount one.

Answer:

105 minutes

Step-by-step explanation:

The pond is a prism. Its volume is the area of the trapezoidal base (the front and back faces) multiplied by the height (the 1 m edge).

Area of base of pond (front face) = (1/2)(B + b)h

Base = (1/2)(1.5 m + 0.6 m)(2 m)    [Here, height is the height oif the trapezoid, so it is 2 m]

Base = 2.1 m²

Volume = Base × Height

Volume = 2.1 m² × 1 m    [Here, height is the height of the prism, so it is 1 m]

Volume = 2.1 m³

The volume of the upper 30 cm (= 0.3 m) of the pond is:

V = LWH

V = 2 m × 1 m × 0.3 m

V = 0.6 m³

The volume of water decreased 0.6 m³ in 30 minutes.

In 60 minutes, it would decrease by 1.2 m³.

60 minutes = 1 hour

The flow rate is 1.2 m³ / hour.

The total volume of the pond is 2.1 m³.

Emptying out the pond completely means removing 2.1 m³ of water at the flow rate of 1.2 m³/hour.

flow rate = volume/time

time × flow rate = volume

time = volume / flow rate

time = 2.1 m³ / 1.2 m³/hour = 1.75 hour

time = 1.75 hour × 60 minutes/hour = 105 minutes

Answer: 105 minutes

Using the z-distribution, the z-statistic would be given as follows:

c) z = -2.63.

At the null hypothesis we test if the means are equal, hence:

\(H_0: \mu_D - \mu_C = 0\)

At the alternative hypothesis, it is tested if they are different, hence:

\(H_1: \mu_D - \mu_C \neq 0\)

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{s}\)

In which \(\mu = 0\) is the value tested at the null hypothesis.

Hence:

\(z = \frac{\overline{x} - \mu}{s}\)

\(z = \frac{-2 - 0}{0.76}\)

z = -2.63.

Hence option B is correct.

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Answer:

19 is D and question20 is 7

Step-by-step explanation:

Answer:

1, D

2, 7

Step-by-step explanation:

1,sqr root of 39 = 6.24499799

2, cuz 49 is perfect sqr 7*7 = 49

The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Answer:

O a=0

Step-by-step explanation:

1. Let the variable be x, which will be the weight of each box.

2. The equation would be total = weight of each box multiplied by the number of boxes and then that gets added to the 7 pounds

52 = 4x + 7

3. 52 = 4x + 7

Subtract 7 from both sides:

45 = 4x

Divide both sides by 4:

X = 45/4

X = 11.25

4. The weight of each care package was 11.25 pounds.

Answer:

Mechanical Keyboard

The type of keyboard that Shelley is most likely to use is a mechanical keyboard. The correct option is a.

Mechanical keyboards offer a considerably more comfortable typing experience, as well as a plethora of customization options in terms of style and feel, and they're also more durable and easier to repair.

Mechanical keyboards often require only a half-press of a key to transmit a signal to your computer, allowing for faster and easier typing.

Here a mechanical keyboard will be used because she is an assistant and uses a desktop computer for scheduling appointments. She would not use tablets and laptops or virtual keyboards.

Therefore, the correct option is a. Mechanical keyboard.

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The statements are always true will be m∠2 + m∠3 + m∠5 = 180°, m∠2 + m∠3 = m∠6, and m∠5 + m∠6 =180°. Then the correct options are C, D, and E.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

By the condition, the equations are given as,

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠3 = m∠6

m∠5 + m∠6 =180°

The statements are always true will be m∠2 + m∠3 + m∠5 = 180°, m∠2 + m∠3 = m∠6, and m∠5 + m∠6 =180°. Then the correct options are C, D, and E.

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The cost of the topsoil needed to fill the flower bed is $588.75.

A rectangular flowerbed measures 3 meters by 5 meters.

The bed must be dug out and filled with topsoil to a depth of 0.5 meters.

To find:

a) The volume of the topsoil needed to fill the flowerbed.

Volume of topsoil = length × breadth × height of flowerbed

= 3 m × 5 m × 0.5 m= 7.5 m³

Therefore, the volume of topsoil needed to fill the flowerbed is 7.5 cubic meters.

Now, let us calculate the cost of the topsoil needed.Cost of 1 meter of topsoil

To calculate the volume of topsoil required to fill the flower bed, you can use the cuboid volume formula:

Volume = Length x Width x Depth

Length = 3 meters

Width = 5 meters

Depth = 0.5 meters

Substituting the values ​​into the resulting formula:

Volume = 3 meters x 5 meters x 0.5 meters

Volume = 7.5 cubic meters

The volume of topsoil required for Bed 7.5 cubic meters.

b) To calculate the cost of topsoil required, the volume of topsoil should be multiplied by the cost per meter.

The cost is $78.50 per meter, so you can calculate the cost as follows:

cost = volume * cost per meter

Plug the value into the formula:

cost = 7.5 cubic yards * $78.50/ meters

cost = $588.75

= $78.50Cost of 7.5 meters of topsoil

= 78.5 × 7.5= $588.75

Therefore, the cost of the topsoil needed is $588.75.

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I am pretty sure it is B. Sorry if I am wrong

Answer:

y=2/7x

Step-by-step explanation:

trust me pls

Answer:

900 meters long

Step-by-step explanation:

Toby is riding his bicycle at 15 m/s. If it takes him 60 seconds to get to the end of the street. What was the length of the street?

at 15 meters per second for 60 seconds:

= time * speed

60* 15= 900 meters traveled,

so the street is 900 meters long.

Answer:

its B

Step-by-step explanation:

I calaulated all the numbers

The 95% confidence interval for the difference between the two proportions is (0.056, 0.164)

Here, we are given that from the sample information for people under 18-

n₁  =  500

x₁ =  180

⇒ p₁  =  180/ 500    

p₁  =  0.36    

then,  

q₁  =  1 -  p₁    

q₁ =  0.64

Similarly, from the sample information for people over 18, we have-

n₂  =  600

x₂  =  150

⇒ p₂  =  150 / 600  

p₂ =  0,25  

then,

q₂  =  1 - p₂  

q₂ =  1 - 0.25  

q₂ = 0,75

Now, we conduct a hypothesis test as follows-

Null hypothesis (H₀) ⇒  p₁  =  p₂

Alternative Hypothesis (Hₐ) ⇒ p₁  ≠  p₂

Confidence interval =  95 %    

⇒ significance level (α) = 5 %  

α  =  0.05  

and α/ 2  =  0.025  

⇒ z at 95% significance level = 1.96 (from z tables)

Now, we calculate z statistic-

z(s)  =  (p₁ - p₂) / EED

EED = √[(p₁*q₁)n₁  +  (p₂*q₂)/n₂]

EED = √[( 0.36*0.64)/500  +  (0.25*0.75)/600]

EED = √[0.00046  +  0.0003125]

EED = 0.028

and (p₁  -  p₂) = 0.36 - 0.25  

= 0.11

Therefore,

z(s)  =  0.11 / 0.028

z(s) = 3.93

we can see that  z(s) > 1.96

⇒ z(s) is in the rejection region for H₀

Thus, we reject H₀. We can´t support the idea of equals means

Now, CI at 95 %  = (p₁ - p₂) ±  z(c) * EED

CI = (0.11 ± 1.96 * 0.028)

CI = (0.11 ± 0.054)

CI =  (0.056, 0.164)

Thus, the 95% confidence interval for the difference between the two proportions is (0.056, 0.164)

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Your question was incomplete. Check for missing content below-

Q1. Let P, represent the proportion under and p, the proportion over the age of 18. The null hypothesis is:_____.

Q2. The 95% confidence interval for the difference between the two proportions is:____.

Answer:

1008

Step-by-step explanation:

The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units

For two triangles to be similar, the corresponding sides of the triangles must be in proportion

Having said  that

The side AC corresponds to the side AC in the other triangle

The length BC is calculated as

BC/9 = 25/15

Express as products

So, we have

BC = 9 * 25/15

Evaluate the products

BC = 15

Hence, the length of BC is 15 units

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Answer:

3

Step-by-step explanation:

Prime factorization

60 = 2 x 2 x 5 x 3  

9  15  and 6   are NOT prime numbers !