To make ends meet, Ms.
Farnsby works three jobs. Her total income last year was $48,000. Her income from teaching was just $6000 more than her income from house painting. Royalties from her textbook sales were one-seventh of the total money she received from teaching and house painting. How much did she make from each source last year?

The average of the increased set of numbers is 21

The average, also known as the arithmetic mean is found by adding together, the numbers in a set of numbers, and dividing the sum by the count of the numbers.

The average of the 5 numbers = 18

The amount by which the numbers are increased are as follows;

First number; Increased by one

Second number; Increased by two

Third number; Increased by three

Fourth number; Increased by four

Fifth number; Increased by five

Let a represent the first number, b the second number, c the third number, d, the fourth number, e, the fifth number, we get;

The increased numbers are; a + 1, b + 2, c + 3, d + 4, e + 5

The initial average can be presented as follows;

Initial average = [tex]\frac{a+b+c+d+e}{5} = 18[/tex]

The imncreased average becomes;

New average = [tex]\frac{(a+1)+(b+2)+(c+3)+(d+4)+(e+5)}{5} = \frac{a+b+c+d+e+15}{5}[/tex]

The new average = (a + b + c + d + e + 15)/5 = (a + b + c + d + e)/15 + 15/5

The term (a + b + c + d + e)/15 in the expression on the right for the new average is the initial average and is equivalent to 18, therefore;

(a + b + c + d + e)/15 = 18

The new average = (a + b + c + d + e)/15 + 15/5

(a + b + c + d + e)/15 + 15/5 = 18 + 15/5 = 18 + 3

The new average = 18 + 3 = 21

The average of the increased set of numbers (the new average) is 21

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The two rational numbers that result in the lowest product are given as follows:

18.5 and -12.4.

For the product of two rational numbers, we have that their signal is given as follows:

For the lowest product, we want a negative number, with the highest absolute value, hence we take the lowest negative and highest positive, as follows:

18.5 and -12.4.

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Check the picture below.

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(18^o)}{1.9}=\cfrac{\sin(59^o)}{j}\implies j=\cfrac{1.9\sin(59^o)}{\sin(18^o)}\implies j\approx 5.3~in[/tex]

Make sure your calculator is in Degree mode.

The length of side J is 5.6 inches.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To find the length of side J, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite to angles A, B, and C respectively:

a/sin(A) = b/sin(B) = c/sin(C)

In this case, we know that side K is 1.9 inches, and angles J and K are 59° and 18° respectively.

Let's use the law of sines to find the length of side J:

J/sin(59°) = 1.9/sin(18°)

J = (sin(59°)/sin(18°)) * 1.9

J ≈ 5.6 inches

(rounded to the nearest tenth of an inch)

Therefore,

The length of side J is approximately 5.6 inches.

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Answer:

8.4+3.5t

Step-by-step explanation:

8.4+3.5t

The area of a cross section perpendicular to one face is 16 square Inches and its perimeter is 16 inches.

The term perimeter in math is known as the total distance around the respective shape.

Here we know that the edge of a cube is 4 Inches.

Here we have to draw a sketch of a cube with side = 4 in as shown below..

Here we have to know that the shaded area is perpendicular to the right and left vertical faces of the cube, then the cross section is a square with each side equal to 4 in.

Hence the value of the area of the cross section is calculated as

=> 4*4 = 16 in²

And the value of the perimeter of the cross section is

=> 4+4+4+4 = 16 in.

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If a plumber has a very long piece of pipe that is used to run city water parallel to a major roadway. The length of the  longer piece of the pipe is: 172 ft.

Let x represent the longer piece

Let  x - 12   represent the shorter piece

So,

(3)(x - 12)  = 120  

Multiply both sides by 4/3

x - 12  = 120 (4/3)

x - 12  = 160      

Add 12 to both sides

x = 172 ft (longer piece)

Therefore the length of the longer piece is 172 ft.

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The correct question is:

A plumber has a very long piece of pipe that is used to run city water parallel to a major roadway. The pipe is cut into two sections. One section of the pipe is 12 ft. shorter than the other. If 3/4 of the length of the shorter pipe is 120 ft., how long is the longer piece of the pipe?

Answer:28

Step-by-step explanation:

5x5=25

25+3=28

Answer:

C. 28

Step-by-step explanation:

3 + 5^2

3 + 25 = 28

To write the equation of a line that is perpendicular to y = 2x - 5, we need to find the slope of the new line.

As we know, the slope of a line perpendicular to y = 2x - 5 is the negative reciprocal of the slope of y = 2x - 5, which is -1/(2) = -1/2.

To find the equation of the line in slope-intercept form (y = mx + b), we can use the point (2, -5) and the slope of -1/2.

We know that the point (2, -5) belongs to the line, so we can substitute these values into the equation:

y = -1/2x + b

-5 = -1/2(2) + b

-5 = -1 + b

b = -4

So, the equation of the line in slope-intercept form is:

y = -1/2x -4

This is the equation of a line that is perpendicular to y = 2x - 5 and passes through the point (2, -5)

Lane Games

ChatGPT Jan 9 Version. Free Research Preview. Our goal is to ma

If the diameter of the output cylinder of a simple hydraulic system were greater, this would increase the output force.

In a simple hydraulic system, a small force applied to a small piston (input cylinder) is amplified and transferred to a larger piston (output cylinder) through a fluid. The output force is equal to the input force multiplied by the ratio of the areas of the two pistons. The area of a cylinder is equal to the radius squared times pi. So, if the diameter of the output cylinder is increased, the area of the output cylinder will increase and the output force will be greater.

It's important to note that increasing the diameter of the output cylinder will also increase the volume of the output cylinder, so more fluid will be required to fill the cylinder and the system may need a larger fluid pump or reservoir.

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Answer:

80 pennies

160 nickels

Step-by-step explanation:

.01p + .05n = 8.80   multiply through by 100

p + 5n = 880

2p = n

substitute 2p for n is the bold equation

p + 5(2p) = 880  

p + 10p = 880

11p = 880   Divide both sides by 11

p = 80

2p = n

2(80) = n

160 = n

Check:

(.01)(80) + (.05)(160) = 8.80

0.80 + 8 = 8.80

8.80 = 8.80  Checks

Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of the same size.

The frequency (or absolute frequency) of an event in statistics is the number of times the event occurred in an experiment or research. Histograms are frequently used to graphically show these frequencies.

The absolute frequency of an occurrence normalized by the total number of events is referred to as its relative frequency (or empirical probability). A frequency distribution can be created by plotting the values of all events.

A histogram is a graphical representation of tabulated frequencies that is displayed as consecutive rectangles erected at discrete intervals (bins) with an area equal to the frequency of the observations in the interval.

The frequency density of the interval, i.e. the frequency divided by the width of the interval, is also equal to the height of a rectangle.

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The horizontal distance that the jet has traveled in 10 seconds will be 3000feet and the jet’s altitude at this time is 6.44 minutes

Given: A plane flies off at a 15-degree angle and 350 feet per second.

Find The time needed to ascend to a height of 35,000 feet.

Imagine a right triangle with a 15-degree angle at the origin at Q1.

The plane's flight route is the hypotenuse.

speed = distance/time

speed * time = distance

distance = 300*10 = 3000feet

Sin(15) = opposite / hypotenuse

Sin(15) = 35000 / (350*t)

350*t  =  35000 / Sin(15)

t  =  35000 / (350 * Sin(15)

t  =  100 / Sin(15)

t   = 100 / .25882

t   =  386.37 seconds

t = (386.37 sec) * (1 min. / 60 sec)  = 6.44 minutes

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The slope is 1.33, the y-intercept is -1 and the equation is y = 1.333x -1.

The solution has been obtained using the slope intercept form.

What is slope intercept form?

The line with slope m and y-intercepts b is the graph of the linear equation y = mx + b. The values of m and c are real integers, and the form of the linear equation is known as the slope-intercept form.

A line's steepness is indicated by its slope, m. Sometimes, a line's slope is also referred to as its gradient. The y-coordinate of the place where the line's graph contacts the y-axis is represented by a line's y-intercept.

We are given graph with straight line.

The two points on the graph are (0,-1) and (3,3)

Let's find the slope(m)

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]m=\frac{3+1 }{3 -0 }[/tex]

m = 4/3

m = 1.333

We know that b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)

So,

⇒b = (-1) - 0(3 + 1)/(3 - 0)

⇒b = -1 + 0

⇒b = -1

The equation comes out to be

⇒y = mx + b

⇒y = 1.333x -1

Hence, the slope is 1.33, the y-intercept is -1 and the equation is

y = 1.333x -1.

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Since, there are multiple questions, so the question answered above is attached below

Answer:

  D)  500(1 +.03/4)^(4(5))

Step-by-step explanation:

You want to know the expression you would input to a calculator to find the money Joe will have in his account from a $500 deposit earning 3% interest compounded quarterly for 5 years.

The value of the account is given by the formula ...

  A = P(1 +r/n)^(n·t)

where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

Filling in the given values, you would want your calculator to evaluate ...

  500(1 +.03/4)^(4(5)) . . . . . . . matches choice D

__

Additional comment

The attachment shows a couple of different calculator inputs that could be used to find the account value. Note that the product (4)(5) is the exponent of the base (1 +.03/4). This calculator uses the caret (^) key to open the exponent expression.

The calculator also has a "future value" function that will compute the same result.

The value in the account will be $580.59.

<95141404393>

Answer:

I think r^2= 4S/πh

Step-by-step explanation:

S=1/4πr^2h

Multiple 4 on both sides

4S=πr^2h

Divide π and h on both sides

r^2=4S/πh

Sorry if this wrong

Answer:

54

Step-by-step explanation:

This is legit just 8 x 7,

Answer:

yes

Step-by-step explanation:

they are perpendicular so you can use 52/2 =26

26² + 33² = LM²

As per the statement the data are qualitative because they don't measure or count anything.

The term measurement in math is known as the process of associating numbers with physical quantities and phenomena.

Here we have the statement the types of food served by restaurants Italian, Chinese, fast, etc.

As we looking into the statement we have identified that the statement is defines the characteristics of the restaurant which is also defines that there is no value for counting in it.

So, this refers the quality of the product instead of quantity.

Which also defined that there is no measurement value in it.

Therefore, the correct option is (c).

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the value of functions f(-2)=-15, g(3) =12.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

f(x) = 4x - 7

g(x) = 4*x

f(-2) = 4(-2)-7 = -8-7 = 15

g(3) = 4*3 = 12

Hence the value of functions f(-2)=-15, g(3) =12.

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The average of three consecutive numbers 17, 18, 19 is 18 and the average of three consecutive numbers -100, -99, -98 is -99

Consider the three consecutive numbers 17, 18, 19.

We find the average number would be found by adding all the terms and dividing by 3:

(17 + 18 + 19)/3

= (54)/3

= 18

consider another example: three consecutive numbers are -100, -99, -98.

Their average would be,

[-100 + (-99) +  (-98) ] ÷ 3

= -297  ÷ 3

= -99

We can observe that the average of three consecutive numbers is the second term given in that set.

Let m, m + 1,  m + 2 be set of any three consecutive numbers.

The average of these three consecutive numbers would be,

A = [m + (m + 1) + (m + 2)] ÷ 3

A = (3m + 3) ÷ 3

A = 3(m + 1) ÷ 3

A = m + 1

Thus, the rule will always work, as we know that average is the central value of a set of numbers.

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The complete question is:

Consecutive numbers follow one right after the other. An example of three consecutive numbers is 17, 18, and 19. Another example is -100, -99, -98. Choose any set of three consecutive numbers. Find their average. What do you notice? Find the average of another set of three consecutive numbers. What do you notice? Explain why the thing you noticed must always work, or find a counterexample.​

The value of g in 27+g=44 is 17 and the value of g in 30+g=44 is 14.

Multiplication, division, addition, and subtraction. A mathematical equation's two sides will remain equal if we add the same integer to each of them.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the equal sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

= 27 + g = 44

= 27 - 44 = g

g =  17

= 30 + g = 44

= 30 - 44 = g

g = 14

Therefore, the value of g in 27+g=44 is 17 and the value of g in 30+g=44 is 14.

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17)

The situation models a function, the independent variable is the number of plans and the dependent variable is the cost.

b) The domain of the function is {x:x≤4} while the range is {y:y≤120}

18) The independent variable is the miles travelled and the dependent variable is the cost.

b) The domain of the function is  {x:x≤20} and the range is  {y:y≤72.8}

We know that the domain of the function represents all of the values can be assigned to the independent variable in the function while the range has to do with all the values that the functions can be able to return.

In this case, we have real life models and we are told to convert them into functions;

a) y = 30 x

b) y = 2.80 + 3.50x

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Alternative Hypothesis is sufficient evidence at the 0.05 level that the bags are underfilled.

In the given question, we have to explain that there is sufficient evidence at the 0.05 level that the bags are underfilled or not assuming that the population is normally distributed.

We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). Or else, we are not able to rule out the null hypothesis.

The claim in the alternative hypothesis that you anticipate or hope to be accurate.

The complement of the null hypothesis is the alternative hypothesis. The extensive nature of null and alternative hypotheses ensures that they account for all potential outcomes.

Since, bag filling machine works correctly at the 436 gram setting. Test the alternative hypothesis in place of the claim that the true mean is less than 436. This test has a left tail.

The null and alternative hypothesis are

H(0): μ = 436

H(a): μ < 436

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The method used to assign probabilities when the results of experimentation or historical data are used to assign probability values is referred to as the relative frequency method.

The relative frequency method is a way to assign probability values to events based on how often they have occurred in the past.

The probability of an event is determined by counting the number of times the event has occurred in a given set of observations, and dividing that number by the total number of observations. For example, if a certain event has occurred 20 times out of 100 total observations, the probability of that event would be 0.2 (20/100). This method is based on the idea that the probability of an event is related to its frequency of occurrence in a large number of trials.

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The set of ordered pairs represents a function would be; {(-4, 9), (-1,0), (0,9), (-4, 8), (0, 5)}.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We need to know that to be a function each x value (first component) has to have one only y value (second component).

In the option 1 the first component 1 has two different y values (-1 and 0),

In option 3 the x value 5 has two different y values (-5 and 9) and in option four the x value -3 has three different y values (1, 2 and -3).

Then, the correct option is the second one.

{(-4, 9), (-1,0), (0,9), (-4, 8), (0, 5)}.

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The area of a circle with a radius of 3.5cm rounded to the nearest tenth is 38.5 cm².

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

Area = πr²

Where r is radius and π is constant pi ( π = 3.14 )

From the diagram;

Plug the given value into the above equation and solve for A.

Area = πr²

Area = 3.14 × ( 3.5cm )²

Area = 3.14 × 12.25 cm²

Area = 38.5 cm²

Therefore, the area of the circle is 38.5 cm².

Option B) 38.5 cm² is the correct answer.

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30 different combinations can be made among six people.

The total number of arrangements is called Permutations.

According to the question,

There are 6 members to choose from.

And there are 2 posts to be filled. i.e, President, Vice-President.

Let's assume each position is a blank. Here each blank represents a placeholder.

The first position can be filled in 6 ways (because any one of the students can get that position)

The second position can be filled in 5 ways (as one person already got the first position, he can't get the second position).

The total number of ways all three positions can be filled in

= 6 * 5 = 30

So, the total number of ways in the combination = 30.

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Answer:2.5cm

Step-by-step explanation:1cm =0.01 m

Answer:

48×14 in.

Step-by-step explanation:

[tex]50^{2} =48^{2} +14^{2}[/tex]

[tex]2500=2304+196[/tex]

[tex]2500=2500[/tex]

The TV screen is 48 inches long and 14 inches high.

Hope this helps.