Type A: f(x)= 10 + 8x Type B: g(x)= 17 + 7x Two types of generators each require a fixed amount of fuel to start. After starting, each generator produces a constant amount of energy per ounce of fuel used. The functions fand g above represent the amount of fuel, in ounces, that each type of generator requires to produce x units of energy when started once. 29 A type A generator was used to produce units of energy, and a type B generator was used to produce k units of energy. Each generator-was started once, and a combined total of 100 ounces of fuel was used. Which of the following equations represents the relationship between n and k? A) 8n+7k 100 B) 8m+7k-73 C) 8n+7k=127 8n 7k D) +7 100 100 30 A type A and a type B generator were started and operated until they ran out of fuel. The two generators combined used 216 ounces of fuel to produce 25 units of energy. How many more units of energy were produced by the type A generator than by the type B generator? A) 0.2 B) 3.0 C) 11.0 D) 12.6

The hypothesis which motivates the studies which is usually the reason for any data is being collected at first place is called alternative hypothesis.

A hypothesis is an exact clarification that pertains to the set of data that may be examined with the aid of using positive similarly investigations. There are essentially types, namely, null speculation and opportunity speculation. A studies commonly begins offevolved with a hassle. Next, those hypotheses offer the researcher with a few precise restatements and clarifications of the studies hassle.

The standards of the studies hassle withinside the shape of null hypothesis and opportunity hypothesis need to be expressed as a dating among or extra variables. The standards is that the statements need to be the only that expresses the connection among the 2 or extra measurable variables. The null hypothesis and opportunity speculation need to bring clean implications for checking out and mentioning relations.

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Correct Question:

The hypothesis that motivates most studies and is usually the reason the data are being collected in the first place is the __________ hypothesis.

Answer:

y value also increases

Step-by-step explanation:

As the X value (also known as the independent variable) of the equation y = 2x + 80 increases, the Y value (also known as the dependent variable) will also increase. This is because the coefficient of the X term (2) is positive, which means that for every increase in the X value, the Y value will also increase by an amount equal to twice the increase in the X value.

For example, if the X value increases from 2 to 3, the Y value will increase from 84 (which is calculated as 22 + 80) to 86 (which is calculated as 23 + 80). Similarly, if the X value increases from 3 to 4, the Y value will increase from 86 to 88, and so on.

If Roberta took two tests. She scored 10 points more on the second test. she score 70 on the second test.

Average score = (x+y)/2

he scored 10 points less on the second test than he did on the first.

y = x - 10

Replace y with x-10

(x + x - 10) / 2

(2x-10)/2

Average score on both tests is 75

(2x-10)/2 = 75

Multiply both sides of this equation by 2

2x-10 = 150

Add 10 to both sides

2x = 160

Divide both sides  by 2x

x = 160/2

x = 80 (She got 80 on the first test)

He got 80 - 10 = 70 (She got 70 on the second test)

(80+ 70) / 2 = 150/2 = 75 (She got average  of 75 on both tests)

Therefore she scored 70 on the second test is your solution.

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Answer:

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

Given sequence:

We observe that it has a linear increase and common difference of terms is 5:

So d = 5, a₁ = - 1, find the nth term:

The value of x for an equation

1)  2x - 4 = 4x + 4 is x = -4

2) 6(x - 2) = 36 - 10x   is x = 3

3) 3(x-2) = 2x + 6 is x = 12

In this question, we have been given an equation.

we need to find the value of x in the equation 2x - 4 = 4x + 4;

6(x - 2) = 36 - 10x

and 3(x-2)=2x+6;

1) consider an equation 2x - 4 = 4x + 4

2x - 4x - 4 = 4x + 4 - 4x

-2x - 4 + 4 = 4 + 4

-2x = 8

x = -4

2)  consider an equation, 6(x - 2) = 36 - 10x

6x - 12 = 36 - 10x

6x + 10x = 36 + 12

16x = 48

x = 48/16

x = 3

3) consider an equation 3(x - 2) = 2x + 6

3x - 6 = 2x + 6

3x - 2x = 6 + 6

x = 12

Therefore, the value of x for

a)  2x - 4 = 4x + 4 is x = -4

b) 6(x - 2) = 36 - 10x   is x = 3

c) 3(x-2) = 2x + 6 is x = 12

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The (two-way) wave equation is a second-order partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves traveling in opposite directions.

This article mostly focuses on the scalar wave equation describing waves in scalars by scalar functions u = u (x1, x2, ..., xn; t) of a time variable t (a variable representing time) and one or more spatial variables x₁, x₂, ..., xₙ (variables representing a position in a space under discussion) while there are vector wave equations describing waves in vectors such as waves for electrical field, magnetic field, and magnetic vector potential and elastic waves. By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x-component for the x-axis) of a vector wave without sources of waves in the considered domain (i.e., a space and time). For example, in the Cartesian coordinate system, for Eₓ , Eₐ and Eₙ the representation of an electric vector field wave E in the absence of wave sources, each coordinate axis component

Ei (  i = x , a , n) must satisfy the scalar wave equation. Other scalar wave equation solutions u are for physical quantities in scalars such as pressure in a liquid or gas, or the displacement, along some specific direction, of particles of a vibrating solid away from their resting (equilibrium) positions.

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A and B are events defined on a sample space, with P(A) = 0.6 and P(BIA) = 0.3. then P(A and B) = 0.18

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

If A and B are events defined on the sample space with P(A) = 0.6 and P(BIA) = 0.3.

To find P(A and B),

we use the formula of conditional probability,

P( A and B ) = P (BIA) P(A)

P( A and B ) = 0.6 × 0.3

P( A and B ) = 0.18

Therefore, P ( A and B ) is 0.18.

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hmmm let's recall from https://brainly.com/question/30111897 that's she needs 625 bucks to make it monthly.

so her part-time at 15h at $12 per hour, well, that's just 15*12 = 180 bucks weekly, how many weeks she needs to work?  well, 625 ÷ 180 ≈ 3.47, so pretty much 3 weeks and about 7 hours more, not quite kinda, 3 weeks and 7 hours is really 624, well if she saves a buck somewheres and get a buck that'll do it =), hmmm so one can say 3 weeks and 8 hours I guess, that's 636 bucks, to cover the 625 expenses.

Answer: The answer is B and D

Step-by-step explanation: The answer is B and D because B is -2 and D is 2, so when we combine them(combine means add) we get -2 + 2 which equals 0.

Answer:

Step-by-step explanation:16x^2+9=25

                                             16x^2=16

                                               x^2=1

                                                 x=1 or -1

                                                   D

The average value of the trigonometric equation f(x) = - 2 · sin x + 5 · cos x over the interval [π, 2π] is equal to 2 / π.

In this question we find the definition of a trigonometric equation consisting in the sum of two trigonometric functions on a given interval [a, b], of which we must determine its average value by means of the following integral equation:

[tex]m = \frac{1}{b - a} \cdot \int\limits^b_a {f(x)} \, dx[/tex]

Where:

First, write the entire trigonometric equation and the bounds of the interval:

f(x) = - 2 · sin x + 5 · cos x, a = π, b = 2π

Second, obtain the result of the integral equation:

[tex]m = -\frac{2}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\sin x} \, dx + \frac{5}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\cos x} \, dx[/tex]

[tex]m = \frac{2}{\pi}\cdot \cos x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex] + [tex]\frac{5}{\pi}\cdot \sin x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex]  

m = (2 / π) · (cos 2π - cos π) + (5 / π) · (sin 2π - sin π)

m = (2 / π) · (1 - (- 1)) + (5 / π) · (0 - 0)

m = 2 / π

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The total cost of the recipe is 521.875 cents

In this question, we need to  calculate the total cost of the recipe by finding the total cost of each of the ingredients and adding them all together.

The ingredients amount in converted units

 ep                      amount         conversion       unit cost ($/unit)    

leeks                    4 oz                  0.25 lb               3.00/lb

yellow squash      10 oz               0.625 lb              2.85/lb

butter                    1 oz                0.0625 lb             3.00/lb

spinach                 8 oz                   0.5 lb                2.25/lb

eggs                     6 ea                   0.5 dozen          2.75/dozen

First, we have to determine to total cost per ingredient.

1. 0.25 x 3.00 = $0.75 (leeks)

2. 0.625 x  2.85 = $1.78125 (yellow squash)

3. 0.0625 x 3.00 = $0.1875 (butter)

4. 0.5 x 2.25 = $1.125 (spinach)

5. 0.5 x 2.75 = $1.375 (eggs)

Now, we can add the cost per ingredient to know the total cost.

$0.75 + $1.78125 + $0.1875 + $1.125 +  $1.375

= $5.21875

= 521.875 cents

Therefore, the total cost is 521.875 cents

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The nonprofit company charges $100 each ticket for the opportunity to win a $50,000 vintage Mustang. With four prizes and 1500 tickets sold, he expects to lose $54.53 on each one.

The chance of winning is multiplied by the bet multiplier to determine the mathematical anticipated value. Typically, expected value is estimated for a bet of one unit. To determine the predicted profit, multiply the win chance by the stake amount.

Chances of getting first prize = 1/1500

Chances of getting second prize = 1/1500

Chances of getting third prize = 1/1500

Chances of getting Fourth prize = 1/1500

Cost of one ticket = $100

Expected winning = -100 +1/1500 (56000 + 6600 + 4300 + 1300)

= -100 + 68200/1500

= - 54.53 dollars

There is an expected loss of $54.53.

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x - y = -15 -3x + 3y = 45 (x, y) = the system of two linear equations using the method of elimination ( 5, 45).

x - y = -15

-3x + 3y = 45

written as

3x - 3y = -15

+3x + 3y = 45

6x = 30

x = 5

Substitute x = 5 into either of the linear equations to find y.

x - y = -15

5 - y = -15

y = 45

Therefore, the solution is (5, 45).

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Watching basketball games and liking the flavor of coconut "are" independent events because the probability of a teenager from the group watching basketball games "is not equal to" the probability of a teenager from the group watching basketball games given that they like the flavor of coconut.

Independent events is the events which occur freely of each other. An event A is said to be independent of another event B if the probability of occurrence of one of them is not affected by the occurrence of the other.

We observe that the event of watching basketball games does not affect liking the flavour of coconut, hence they are independent events their probabilities are most likely not the same.

Therefore, we use "are" for the first statement to show the two events are independent and "is not equal to" for the probability statement.

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On solving the provide question, based on the congruent triangles properties, we got to know that x= 76° and 90°.

Congruent triangles are two triangles that are identical in terms of their size and form. The two congruent triangles remain congruent whether you rotate, flip, or flip one of them. If two triangles have the same number of sides, then their angles and congruence must match.

As a result, we can determine that two triangles are congruent if all three of their sides are equal. We also understand that if there is a side, an angle between the sides, and a third side that is congruent, the three sides are congruent. which means sides, corners, and sides.

For green -

=> x = 76° ( both side are same)

For orange -

=> x = 90°

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Answer:

20(-2x+5)

10(-4x+10)

Step-by-step explanation:

20(-2x+5) = -40x+100

10(-4x+10) = -40x+100

You just need to expand the brackets

Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

Rows with a defined pattern, in which the difference between two consecutive terms is equal and fixed, are referred to as arithmetic sequences and series, also known as rows and counting series. In other words, by adding a fixed integer to the previous term, each term in the arithmetic arrangement is obtained from the previous term. To put it another way, every term in the arithmetic series (except from the first term) is obtained by adding a specific integer to the term that comes before it.

Here,

This mathematical sequence can be written as follows:

A, A+D, A+2D, A+3D, A+4D, etc. , a+(n-1)d or

where:

First term: a

d stands for common variation.

It is stated that the arithmetic sequence formula is

a = a + (n-1)d

where

First term: a

n = the number of terms

d stands for common variation.

Common Difference

In mathematical terminology, the common difference is the difference between two words.

2, 5, 8, 11, and more problems

Answer: To determine if a row is an arithmetic sequence or not, first identify the similarities between the rows.

d = 5 - 2 d = 8 - 5 d = 11-8

d = 3.

Each of them differs by 3 points.

The following three words are then 2, 5, 8, 11, 11+3, 11+6, 11+9 or 2, 5, 8, 11, 14, 17, and 20.

Issues 2, 4, 6, 8, and 10 exist.

Answer:

d = -4 - 2 = -6

d = 6 - (-4) = 10

It does not contain arithmetic sequences because there is no common difference.

Challenge: -6, -10, -14, -18,...

Answer:

d = -10 - (-6) = -4

d= -14 - (-10) = -4

d= -18 - (-14) = -4

There is a -4 difference between them all.

The following three terms are then 6, 10, 14, 18, -18, -18 + (-4), -18 + (-8), -18 + (-12), or 6, 10, 14, 18, -18, -22, -26, -30.

Issues 40, 42, 44, 46,...

Answer:

d = 42 - 40 = 2

d = 44 - 42 = 2

d = 46 - 44 = 2

All of them differ by 2 points.

The subsequent three words are either 40, 42, 44, 46, 48, 50, 52 or 40, 42, 44, 46, 46 + 2, 46 + 4, 46 + 6.

Issues: 1.2, 1.8, 2.4,...

Answer:

d = 1.8 - 1.2 = 0.6

d = 2.4 - 1.8 = 0.6

They are all separated by 0.6.

1.2, 1.8, 2.4, 2.4 + 0.6, 2.4 + 1.2, 2.4 + 1.8 or 1.2, 1.8, 2.4, 3.0, 3.6, 4.2 are the following three words.

Issues 1, 5, and 9,13

Answer:

d = 5 - 1 = 4

d = 9 - 5 = 4

d = 13 - 9 = 4

They are all divided by 4 in common.

The subsequent three terms are either 1, 5, 9, 13, 17, 21, or 25. These are 1, 5, 9, 13, 13 + 4, 13, 8, 13, and 12.

Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

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Triangle ABC and triangle XYZ are congruent thus ∆ABC and XYZ are similar

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects.

if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

line DY bisects AC and line ZE bisects line AB.

Therefore line AD is congruent to line AE and line CD is congruent to line EB.

therefore AB = CD and similar XY = YZ

therefore ∆ABC and ∆XYZ are similar

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The mathematical expression for the work performed by the spring and the cubic term is W=3.3488J C=%3.4

The spring's and the cubic term's labor Question Parameters:

How much effort is required to compress this spring 15 cm

Take into account a spring with k = 250 N/m and q = 900 N/m3.

In general, the mathematical formula for the force is given as

(FSp)s=−kΔs−q(Δs)^3

Location of Work done

W = int dxF.

Hence

W=3.3488J

b)Where a cubic term is mathematically given as

C={0.1139}/{3.3488}

C=%3.4

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The distance between the start of the walkway and the middle person is 52 feet.

It is given that a 100 foot long moving walkway moves at a constant rate 6 feet per second.

AI steps into the start of the walkway and stands this means speed of AI is 6 feet per second.

Bob steps onto the start of  he walkway two second later and stolls forward along walkway 4 feet per second that means 10 feet [per seconds.  

And CY reaches the starts of the walkway and walks briskly forward beside the walkway at a rate of 8 feet per second.

At the time s we gave that,

[tex]\frac{8(s-4)+10(s-2)}{2}[/tex] = 6s

[tex]\frac{8s -32 + 10s - 20}{2}[/tex]  = 6s

      18s - 52 = 12s

              6s  = 52

                s  = [tex]\frac{26}{3}[/tex]

At the time AI has travels,  

6* [tex]\frac{26}{3}[/tex] = 52 feet.

Therefore distance between the start of the walkway and the middle person is 52 feet.

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Answer:

c. between 4&5 and -1&0

Step-by-step explanation:

Answer:6/3 or 1/2

Step-by-step explanation:

The older computer takes 8 minutes to send out the email on its own.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Let , the older computer works at the rate of x.

According to the condition,

then the rate of work of newer computer is x/2.

And the combined work of both the computer = x/2 + x = 3x/2

It means that  3x = 12

then x = 4

Hence, x =8of the job per minute.

It means the older computer will make the entire job in 84 minutes.

Therefore, the older computer takes 8 minutes to send out the email on its own.

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The total cost of the crafting supplies is $25.5. This can be find using percentage and rate concepts.

What is tax rate and percentage?

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent , half of it is 50 percent , none of something is 0 percent.

Tax is the money that govt collects based on income, sales and other activities.

A tax rate is the percentage at which an individual or corporation is taxed.

In the given que,

Purchased amount = $24.

Tax rate = 6.25%

Tax paid = 24*(6.25/100)

               = $1.5

So, total amount paid = $1.5 + $24

                                    = $25.5

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The area of the bridge(yellow part) is 297.9 m².

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

From the given diagram the area of the bridge is the total area of the larger rectangle - the area of a semicircle - the area of the smaller rectangle.

We know the area of a rectangle is (length×width) and the area of a semicircle is (1/2)πr².

∴ The area of the bridge is = {(34×20) - (24×6.5) - (1/2)π(12)²} m².

= {680 - 156 - 226.1} m².

= 297.9 m².

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If Joe deposits $264,954.31 today then he will reach his goal

Define Present Value

Finding the appropriate quantity of money to deposit today in order to ensure a specific amount of future payments is one objective of financial analysis. The target payment amount, the quantity and frequency of payments, and the interest rate all influence the present value, which is the value in today's dollars.

Given,

Joe want to receive each month = $22,000

Interest rate = 6%

number of payment = 22 years

We know, the formula of present value is

Present value = pmt * (1 - (1/ (1+r)ⁿ) ) / r

pmt = $22,000

r = 0.06

n = 22 years

Now, plug in the values

Present value = $22,000( 1 - (1/(1+0.06)²² ) / 0.06

                       =$22,000( 1 - (1/(1+0.06)²² ) / 0.06

                       ≈ $264,954.311

Hence, If Joe deposits $264,954.31 today then he will reach his goal.

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Answer:

All Correct! The corinates on the graph are all graphed in the correct position.

Answer:

Yes, you are correct.

Step-by-step explanation:

On dot plot we take no. of successes out of 10. Hence it having 0 to 10 numbering.

What is dot plots in statistics?

For relatively small data sets with values falling into a handful of discrete bins, a dot plot, also known as a dot chart, is a sort of straightforward histogram-like display used in statistics.

                       To create a dot plot, count the data points that fall into each bin and then draw a stack of dots that is that many dots high for each bin.

Because we conduct 50 trials, dot plot should have 50 points, one point per each trial.

On X axis, we take no. of successes out of 10. Hence it having 0 to 10 numbering.

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