Karen worked her 40 regular hours last week, plus 6 hours at the time-and-a-half rate. Her gross pay was $650. What was her hourly rate?

False, that is if the number of data observations is even, the median is generally considered to be the average of middle values not the first and last values.

The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

At least half of the observations are equal to or smaller than the median, and at least half of the measurements are equal to or greater than the median. The median divides the bottom half of observations from the upper half.

Even Number of Observations :

Suppose we have the monthly wages of 4 employees of a company. How would you find the median wage?

wages are 120,240,500,400

we have arranged their wages above from lowest to highest. This ranking will help us to determine the median. Using the method introduced earlier, the median is computed by taking the simple average of the (n/2)ᵗʰ = (4/2)ᵗʰ = 2ⁿᵈ and

(n/2 + 1)ᵗʰ = (2+1)ᵗʰ = 3ʳᵈ observations.

Therefore, the median is 240+500/2

= 370.

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Complete question

True/false

if the number of data observations is even, the median is generally considered to be the average of the first and last values

Answer:

A. 28x + 94y

Step-by-step explanation:

First, line up the like terms as if you were adding vertically, and combine them.

(42x + 59y)

+ (-14x + 35y)

(28x + 94y)

Hope this helps :)

Answer:

200,000

Step-by-step explanation:

Answer:

-20x

Step-by-step explanation:

Let the number be x.

The product of -4 and this number is -4x.

5 times this is 5(-4x), which simplfiies to -20x.

Answer:

13 is a rational number

Explanation:

A rational number is any number that can be written as a simple fraction. Since 13 is a whole number and is not a repeating decimal, it's a rational number.

Answer:

No, it is not a rational number

Step-by-step explanation:

A rational number is a number expressed as a fraction.

Hope This Helps :)

On solving the query we can say that The slant height, along with the function cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

You are informed that the cone in this scenario has a volume of 4.5 cubic inches. Using the aforementioned calculation, you can determine the radius if you know the cone's height.

Alternately, you may use the Pythagorean theorem to calculate for the radius if you know the cone's slant height. The slant height, along with the cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.

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Answer:

A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

The statement that best describes the method how the teacher likely came to the specified conclusion is: Option A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

In the case of testing about test scores, teacher can't use random or controlled experiment as the teacher would more likely work with real data of test scores instead of students faking it.

The sample survey is not needed as getting test scores doesn't destroy them, nor the population of students is too high(assuming math class has small number of students (usually under some hundreds) ).

Observational study is best choice here, and this is done on all students by observing how much students achieved in scored in test and relate it with them completing the review worksheets or not.

Thus, the statement that best describes the method how the teacher likely came to the specified conclusion is: Option A. The teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

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The expression given is,

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Therefore,

Hence, the G.C.F is

Answer:

f(-1)= -1      

f(3)= -2

Step-by-step explanation:

I am in AP Calculus, I'm smart.  Brainliest????

Answer:

D. 3(x+2) can be rewritten as 3x + 6 using the distributive property

Step-by-step explanation:

Given

\(3(x + 2) = 3x + 6\)

Required

Explain

From the list of given options, option D answers the question.

This is because, the expression above involves distributive property and only option D correctly states that.

A distributive property is:

\(a*(b + c) = a*b + a * c\)

In this case:

\(a = 3\)  \(b = x\)   and \(c = 2\)

So:

\(a*(b + c) = a*b + a * c\)

Substitute values for a, b and c

\(3*(x + 2) = 3 * x + 3 * 2\)

\(3(x + 2) = 3x + 6\)

Answer:

C. Both expressions involve addition.

Step-by-step explanation:

I tried it, and it was correct

Answer:

A. 31/100

Step-by-step explanation:

Change 3/10 to hundreds:

3/10 × 10/10 = 30/100

The denominator (the bottom number) must be 100.

61 - 30 is 31.

The missing number is 31/100. See image.

The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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through:(-4,3), Parallel to y = -1/4×​

step 1

If two lines are parallel, then their slopes are equal

that means

the slope of teh parallel line is equal to

m=-1/4

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-1/4

point (-4,3)

substitute

3=(-1/4)(-4)+b

solve for b

3=1+b

b=2

therefore

the equation is

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

Answer:

Let's start by finding out how many muffins were there in total before the ogre stole 20 of them. Let's call that number "x".

If 5/8 of them were left after the ogre stole 20, then 3/8 of them were taken.

So we can set up an equation:

x - 20 = 3/8x

To solve for x, we can start by multiplying both sides by 8 to get rid of the fraction:

8(x - 20) = 3x

8x - 160 = 3x

Now we can solve for x by subtracting 3x from both sides:

5x - 160 = 0

5x = 160

x = 32

So there were originally 32 muffins.

Now we can find out how many are left:

5/8 of 32 = 20

So there are 20 muffins left.

Step-by-step explanation:

Answer:

Hi, option A). 3 to 1 is the correct option.

Step-by-step explanation:

See there are 6 yellow and 2 red.

It will be 6:2

And if we simplify it further both of the numbers are multiples of 2.

Therefore:

The answer is option A). 3:1

Answer: B. 4 to 1

Step-by-step explanation:

green = (3/4) purple

Substituting the expression for green from the first conversion, we get:

yellow = (5/6) (3/4) purple

yellow = (5/8) purple

Finally, we can use the third ratio to convert purple to red:

5 purple = 2 red

purple = (2/5) red

Therefore, the ratio between yellow to red is 4 to 1.

\( - \sqrt{ \frac{5 - 2 \sqrt{5} }{10} } \)

Answer:

a

Step-by-step explanation:

on edge

Answer:

The correct ratio is 40/41

Answer:

30

Step-by-step explanation:

since this is rhombus 1 2 3 4 must be equal

|NP|=|MN|

so 180-120=60

60/2=30

Answer: All four angles (angle1,2,3,4) are 30 degrees each

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

Explanation:

A rhombus has all four sides that are the same length. Think of a square, but we don't necessarily need to have all four angles be 90 degrees (as the diagram indicates).

Focus on triangle MNP. We have N = 120 degrees. We also know that MN = NP due to the fact all four sides of a rhombus are the same length.

This immediately leads to triangle MNP being isosceles. The base angles opposite the congruent sides are congruent angles. So angle 1 and angle 3 are the same measure. For triangle MNP, angle M and angle P are the same.

Let's find the missing angle

M+N+P = 180 ... angles of a triangle add to 180

M+120+M = 180 ... plug in N = 120, replace P with M

2M+120 = 180

2M = 180-120 ... subtracting 120 from both sides

2M = 60

M = 60/2 .... dividing both sides by 2

M = 30

So N is also 30 degrees

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

We've found that both angle 1 and angle 3 are 30 degrees each.

Any rhombus is a parallelogram, which means that angles 1 and 4 are congruent alternate interior angles. Similarly, angles 2 and 3 are the other pair of alternate interior angles.

Therefore, we can say

angle 1 = angle 4 = 30 degrees

angle 2 = angle 3 = 30 degrees

Answer:

<AFB

Step-by-step explanation:

First you must know the two adjacent angles are placed side ways in a diagram. Most of this angles are supplementary i.e their sum is 180 degrees. From the diagram shown, you can see that the two angles that are supplementary are <BFD and <AFB. Hence we can conclude that <AFB is adjacent to <BFD

Quotient :  2x⁴ - 4x³ - 7x² + 5x + 1 

Remainder :  10 

Step 1

Draw the triangle

Step 2

State the given parameters

l = ?

n= 8.2 in

m = 2.1 in

Step 3

solve for l to the nearest tenth of an inch

Using the cosine rule we can find the value of l

The cosine rule is given as

Substituting the given values into that equation, we have

To the nearest tenth of an inch l = 8.4 inches

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

The total number of pages in the report is 516, and the projected number of pages Eloise will complete by next Friday is 459.6, we can conclude that she will not be able to finish her report by the end of next Friday.

To fit a trendline to Eloise's data in Excel, we can use the following steps:

Enter the data points for the "Day" and "Pages" into two columns in Excel.

Select the data points.

Go to the "Insert" tab in Excel and click on the "Scatter" chart type.

Choose the scatter plot with smooth lines and markers option.

Right-click on any data point on the chart and select "Add Trendline."

In the "Format Trendline" pane, choose the "Linear" trendline type.

Now, let's determine the slope and intercept for the trendline:

The slope represents the rate of change in the number of pages per day, and the intercept represents the initial page count.

According to the provided data:

Pages: [423, 466, 473, 432]

Day: [Monday, Tuesday, Wednesday, Thursday]

Using Excel's trendline, we obtain the following results:

A: The slope of the trendline is 5.4 (rounded to one decimal place).

B: The intercept of the trendline is 432.6 (rounded to one decimal place).

Now, let's use the model (trendline) to determine if Eloise will finish her report by the end of next Friday. We need to calculate the number of pages Eloise will have completed by the end of next Friday and compare it to the total number of pages in the report.

Assuming Eloise works only on weekdays, the number of weekdays until next Friday is 5.

Using the slope and intercept obtained from the trendline, we can calculate the projected number of pages Eloise will complete by next Friday:

Projected pages = (slope * number of days) + intercept

= (5.4 * 5) + 432.6

= 27 + 432.6

= 459.6

Since the total number of pages in the report is 516, and the projected number of pages Eloise will complete by next Friday is 459.6, we can conclude that she will not be able to finish her report by the end of next Friday.

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The measure of the angle that turns through 3/10 of the circle is 108 degrees.

An angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

Since a full circle has 360 degrees, 3/10 of the circle can be represented as:

(3/10) x 360 degrees = 108 degrees

Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.

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The complete question is :

The angle turns through 3/10 of the circle. What is the measure of the angle?

Answer:

Step-by-step explanation:

Givens

We know that the area of a square is

\(A=s^{2}\)

Where \(s=12 \ ft\), according to the problem.

Replacing this value, we have

\(A=(12 \ ft)^{2} =144 \ ft^{2}\)

Therefore, the area of the square roof is 144 square feet.

Answer: the area of the roof is 144 feet squared for each side (up and down), adding to a total of 288 ft^2

Step-by-step explanation:

If the roof is a square with a side lenght L =  12 feet, then we use the fact that the area of a square is equal to the square of the side lenght of the square, this is:

A = L^2  = (12 ft)^2 = 144 ft^2

Now, Mr. wilson uses the equation A = s, this is because the roof has 2 surfaces, one up and one bottom, then the total area is 2 times the value that we find earlier:

2*144 ft^2 = 288 ft^2