A machine sales person earns a base salary of $40,000 plus a commission of $300 for every machine he sells. How much income will the sales person earn if they sell 50 machines per year?

Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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A measure of goodness of fit for the estimated regression equation is the residual standard error (RSE)

It is a measure of goodness of fit for the estimated regression equation. It measures the average amount that the response variable (y) deviates from the estimated regression line, in the units of the response variable.

The RSE is calculated as the square root of the sum of squared residuals divided by the degrees of freedom. A smaller RSE indicates a better fit of the regression line to the data.

It represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the model. The value of R-squared ranges from 0 to 1, with higher values indicating a better fit of the model to the data.

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Answer:

I know that the angle is 57

Step-by-step explanation:

Answer:

13) First blank: 2 Second blank: 5

14) First blank: 7 Second blank: 5

15) First blank: -11 Second blank: -2

16) First blank: 4 Second blank: 3

17) First blank: -3 Second blank: -8

18) First blank: -2 Second blank:6

The speed of the car, in kilometers per hour, at the time the brakes are first applied, for which the braking distance is less than 20 meters, could be 20 km/h and 30 km/h.

According to the given formula, the braking distance (d) is equal to 200 times the square of the speed of the car (s). To find the speeds at which the braking distance is less than 20 meters, we need to solve the inequality d < 20. Substituting the formula, we get 200\(s^{2}\)< 20. Dividing both sides of the inequality by 200 gives \(s^{2}\) < 0.1. Taking the square root of both sides, we have s < √0.1. Evaluating this value, we find that s is less than approximately 0.316. Converting this value to kilometers per hour, we get s < 0.316 * 60 = 18.96 km/h. Thus, any speed below 18.96 km/h will result in a braking distance less than 20 meters. However, since the options provided are discrete values, the closest speeds that satisfy the condition are 20 km/h and 30 km/h. Therefore, the possible speeds at which the braking distance is less than 20 meters are 20 km/h and 30 km/h.

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The volume of the prism is determined as  1,416 m³ and the surface area of the prism is 664.8 m².

The volume of the prism is determined from the product of base area and slant height of the prism.

Base of the prism, A = ¹/₂bh = ¹/₂ x 12 x 20 = 120 m²

Volume = AL

where;

L² = (12/2)² + (20.3/2)²

L² = 6² + 10.15²

L² = 139.0225

L = 11.8 m

V = AL

V = 120 x 11.8 = 1,416 m³

A = bh + pL

A = (12 x 20) + 11.8(12 + 12 + 12)

A = 664.8 m²

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Answer:

150

Step-by-step explanation:

It's very simple

C=100

L=50

CL=150

Answer:

150

Step-by-step explanation:

There are seven symbols that are used in the Roman Numeral system.

Answer:

d) population is divided into similar groups and a SRS is chosen from each group.

Step-by-step explanation:

Stratified random sampling

can be regarded as "proportional random sampling" and is method of sampling which entails division of a population to more simpler sub- groups, this sub- groups are regarded as " strata". This strata are been formed on the basis of shared attributes of the members. This attribute could be educational attainment as well as income. It should be noted that stratified random sample is population is divided into similar groups and a SRS is chosen from each group.

Answer:

Simple Intrest answer would be: $551.25

A=450(1+(0.075x3))

Compound Intrest answer would be: $559.03

Answer: Yes it is an expression

Step-by-step explanation:

half of a number or we can write it as x2, so it is an expression.

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Suppose ;

\(the \: angle \: = \: x\)

Thus the supplementary of x is :

\(180 - x\)

_________________________________

x angle measures 4° more than its supplementary ;

So :

\(x - (180 - x) = 4\)

\(x - 180 + x = 4\)

\(2x - 180 = 4\)

Add sides 180

\(2x - 180 + 180 = 4 + 180\)

\(2x = 184\)

Divided sides by 2

\( \frac{2}{2}x = \frac{184}{2} \\ \)

\(x = 92\)

Thus the angles measures

are : 92° and 88°

DONE....

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Answer:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Since the line given in the question is parallel to y = 1/4x + 7, we know that the line has a slope of m = 1/4.

To find the equation of the line that passes through (4,-1), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).

Therefore, the equation of the line passing through (4,-1) and parallel to y = 1/4x + 7 is:

y - (-1) = 1/4(x - 4)

y + 1 = 1/4x + 1

This is the equation of a line passing through (4,-1) and parallel to y = 1/4x + 7.

Answer:

-11.1

12°F= -11.1°C

Sorry if I'm late to answering..

The temperature of Alaska in degree celsius will be -11.11°C.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example, kilo gram to gram.

Given the temperature of Alaska 12° F.

Since we know,

°C = 5/9(°F - 32)

Given that.

°F → 12°F

So,

°C = 5/9(12 - 32)

°C = 5/9(-20)

°C = -11.11

Hence "The temperature of Alaska in degree celsius will be -11.11°C".

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Answer:

Step-by-step explanation:

There are 7 months in the year that have thirty-one days.

These months are January, March, May, July, August, October, and December.

There are seven months in the Gregorian calendar that have thirty-one days: January, March, May, July, August, October, and December.

This pattern of months with 31 days followed by months with fewer days repeats throughout the year.

This pattern was established by the Roman calendar, which had ten months totaling 304 days in a year.

The months of January and February were later added by King Numa Pompilius to align the calendar with the lunar year.

The months of January and February initially had 29 and 28 days respectively, but in 45 BC, Julius Caesar added one day to January and one day to August, which was originally a 30-day month, to make them both 31-day months.

In the Gregorian calendar, which is the most widely used calendar in the world, January, March, May, July, August, October, and December all have 31 days.

The remaining five months have fewer days, with February having 28 days most of the time, and 29 days in a leap year.

Knowing the number of days in each month is important for various reasons, such as planning events, scheduling appointments, and calculating pay periods.

There are several mnemonics used to remember the number of days in each month, such as "30 days hath September, April, June, and November, all the rest have 31, except February, with 28 days clear, and 29 in each leap year."

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Answer:

10/26

Step-by-step explanation:

out of 26 student 10 have a brother 8 people have only a brother and 2 people have both a sister and a brother. so you have 10/26

Answer:

x = 8 or f(x) = -4 or y = -4

Also:

Plz mark brainliest if this helped :)

Answer:

You'll have a closed circle at x = 2, and shading to the left

See the diagram below

=========================================================

Explanation:

The fractions here are 3/7 and 21/2. The denominators of which are 7 and 2 respectively. The LCD is 7*2 = 14.

If we multiply both sides by 14, then this will clear out the denominators and make the fractions go away.

So if we multiplied both sides by 14, then we have these steps

\(\frac{3}{7}(35x-14) \le \frac{21x}{2}+3\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}+3\right)\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}\right)+14*\left(3\right)\\\\6(35x-14) \le 147x+42\\\\\)

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

Let's isolate x

\(6(35x-14) \le 147x+42\\\\6(35x)+6(-14) \le 147x+42\\\\210x-84 \le 147x+42\\\\210x-147x \le 42+84\\\\63x \le 126\\\\x \le 126/63\\\\x \le 2\\\\\)

The graph of this will consist of a closed or filled in circle at x = 2. We shade to the left to represent numbers smaller than 2.

So either x = 2 or x < 2.

If we used an open hole at 2, then we wouldn't be including 2 (but we want to include this endpoint).

See the diagram below.

Answer:

500mph

Step-by-step explanation:

5784.4 miles --> estimates to 6000 miles

6000/12=500

500mph

Answer:

the base must have a minimum of 3 sides

Step-by-step explanation:

Answer:

It's 3

Step-by-step explanation:

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Hi there!

The answer is →\(15 \sqrt{3}\)←

(Check the attached image for the explanation)

Answer:

x= - 20

y= 6

Step-by-step explanation:

2x + 5y = -10

-2x + y = 46

if u solve it

it is 6y= 36 so y =6

and substitute y value into the equation:

-2x+ 6 = 46

-2x= 40

so x= -20

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

We know that Betrys is cooking for 8 people, and we know that a recipe for 2 people needs 10 ounces.

8 people is 4 times 2 people, then for 8 people you need 4 times 10 ounces, this is 4*10 oz = 40 ounces.

Now we can apply a change of units, remember that:

1 oz = 28 grams

Then the total amount she needs is:

40 oz = 40*28 g = 1,120 g

So she needs in total 1,120 grams, and in the balance, she already has 720 grams, so the amount that she needs is given by the subtraction:

1,120 g - 720g = 400

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

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The width of the box m = 5 units

The width of  the box = m units

Where m is a prime number

Height of the box = m+2 units

The length of the box = m -1 units

The volume of the box = 140 cubic units

The volume of the box = Length × width × height

140 = m × (m+2) × (m-1)

140 = (m^2 + 2m )(m-1)

140 = m^3 - m^2 + 2m^2 - 2m

140 = m^3 + m^2 - 2m

m^3 + m^2 - 2m - 140 = 0

We can split the equation by taking the common term outside

(m-5) (m^2 + 6m + 28) = 0

Therefore, one value of m = 5

5 is a prime number

Therefore, the value of m is 5

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Rate of diffusion will be more for right circular cylinder.

"Information available from the question"

In the question:

A sphere with a ratio of surface area to volume equal to 0. 15 m-1.

A right circular cylinder with a ratio of surface area to volume equal to 2. 2 m^-1.

Now, According to the question:

Before, answering the question, First we have to understand the effect of ratio of surface area to volume on the rate of diffusion.

The ratio of diffusion for a body having larger surface area as compared to the ratio of surface area to volume will be more than a body having less surface area, Mathematically it can be written as :

V x R {where V is the rate of diffusion and R is the ratio of surface area to volume}.

As per the question, the ratio of surface area volume for a sphere is given 0.15m^-1

The surface area to volume ratio for right circular cylinder is given 2.2m^-1.

Hence, it is obvious that the ratio is more for right circular cylinder. As the rate diffusion is directly proportional to the surface area to volume ratio.

Hence rate of diffusion will be more for right circular cylinder.

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The coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

Any equation of the form \(axx^{2} + bx + c = 0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

It is given that:

The quadratic equation is:

y = 9 + 18x - 3x²

To find the turning point:

Graph the above quadratic equation;

From the graph:

The maximum point from where the graph starts to decrease is (3,36)

Thus, the coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).

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Answer:

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

Step-by-step explanation:

Given the 2 equations

3x + \(\frac{1}{2}\) y = 3 → (1)

6x - y = 2 → (2)

Multiplying (1) by - 2 and adding to (2) eliminates the term in x, that is

- 6x - y = - 6 → (2)

Add (2) and (3) term by term to eliminate x

- 2y = - 4 ( divide both sides by - 2 )

y = 2

Substitute y = 2 into either of the 2 equations and solve for x

Substituting into (2)

6x - 2 = 2 ( add 2 to both sides )

6x = 4 ( divide both sides by 6 )

x = \(\frac{4}{6}\) = \(\frac{2}{3}\)

Solution is ( \(\frac{2}{3}\), 2 )

Answer:

I think is 50m.

Step-by-step explanation:

The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

\(((\bar p_{1} -\bar p_{2})\)±\(Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })\)

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±\(1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })\)

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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