A carpenter's square is placed over a board as shown in the figure to the right. If 1 measures 77° what is the size of 2?

Given statement solution is :- None of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

To determine the meaning of the slope of the linear model for the given data, let's analyze the information provided. The table represents the distance traveled by a car at different time intervals.

Minutes | Distance Traveled (in miles)

50 | 20

20 | f

40 | 60

100 | a

125 | 80

100 | 100

To find the slope of the linear model, we need to calculate the change in distance divided by the change in time. Let's consider the intervals where the time changes by a fixed amount:

Between 50 minutes and 20 minutes: The distance changes from 20 miles to 'f' miles. We don't have the exact value of 'f', so we can't calculate the slope for this interval.

Between 20 minutes and 40 minutes: The distance changes from 'f' miles to 60 miles. Again, without knowing the value of 'f', we can't calculate the slope for this interval.

Between 40 minutes and 100 minutes: The distance changes from 60 miles to 'a' miles. We don't have the exact value of 'a', so we can't calculate the slope for this interval.

Between 100 minutes and 125 minutes: The distance changes from 'a' miles to 80 miles. Since we still don't have the exact value of 'a', we can't calculate the slope for this interval.

Between 125 minutes and 100 minutes: The distance changes from 80 miles to 100 miles. The time interval is 25 minutes, and the distance change is 100 - 80 = 20 miles.

Therefore, based on the given data, we can conclude that the car travels 20 miles in 25 minutes. To determine the meaning of the slope, we divide the distance change by the time change:

Slope = Distance Change / Time Change

= 20 miles / 25 minutes

= 0.8 miles per minute

So, none of the given options (a, b, c, or d) match the meaning of the slope. The correct interpretation is that the car travels approximately 0.8 miles every minute.

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Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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Answer:

1. 4

2. 20

3. 80

Step-by-step explanation:

The area of the painting, frame and painting, frame are 84 square inches, 174 square inches and 90 square inches. respectively.

Length = 10.5 in

Width = 8 in

Area of the painting = Length × Width

= 10.5 in × 8 in

= 84 square inches

Length = 14.5 in

Width = 12 in

Area of the frame and painting = Length × width

= 14.5 in × 12 in

= 174 square inches

Area of the frame = Area of the frame and painting - Area of the painting

= 174 square inches - 84 square inches

= 90 square inches

In conclusion, the areas are 84 square inches, 174 square inches and 90 square inches. respectively.

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(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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Answer: 106

Step-by-step explanation: 12x10=120 7x2=14 120-14=106

Answer:

\(A_{shaded} = 106\ m^2\)

Step-by-step explanation:

Step 1:  Get the area of the inside box

\(A=l*w\)

\(A_{inside\ box} = 7\ m* 2\ m\)

\(A_{inside\ box} = 14\ m^2\)

Step 2:  Get the area of the outside box

\(A = l * w\)

\(A_{outside\ box} = 12\ m * 10\ m\)

\(A_{outside\ box} = 120\ m^2\)

Step 3:  Subtract the inside box from the outside box

\(A_{shaded} = A_{outside\ box} - A_{inside\ box}\)

\(A_{shaded} = 120\ m^2 - 14\ m^2\)

\(A_{shaded} = 106\ m^2\)

Answer:  \(A_{shaded} = 106\ m^2\)

We know that

• 1/4 of the cookies are chocolate chips.

• 1/2 of the rest are peanut butter.

It is important to know that the rest of the cookies is represented by 3/4, so 1/2 of 3/4 is

The simplified form of the expression \(\frac{(s^{2}+1 )^{2} (-2)-(-2s)(2)(s^{2}+1)(2s)}{(s^{2}+1 )^{4} }\) is \(\frac{6s^{2}-2 }{(s^{2}+1 )^{3} }\)

To simplify simply means to reduce.

Therefore,

\(\frac{(s^{2}+1 )^{2} (-2)-(-2s)(2)(s^{2}+1)(2s)}{(s^{2}+1 )^{4} }\)

\(\frac{(s^{2}+1 )^{2} (-2)-(-2s)(2)(s^{2}+1)(2s)}{(s^{2}+1 )^{4} } = \frac{(s^{2} +1 )((s^{2}+1 )(-2)-(-2s)(2)(2s))}{(s^{2} +1)^{4} }\)

Therefore,

\(\frac{(s^{2} +1 )((s^{2}+1 )(-2)-(-2s)(2)(2s))}{(s^{2} +1)^{4} } = \frac{-2s^{2}-2+8s^{2} }{(s^{2} +1)^{3} }\)

Hence,

\(\frac{-2s^{2}-2+8s^{2} }{(s^{2} +1)^{3} } = \frac{6s^{2}-2 }{(s^{2}+1 )^{3} }\)

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Answer:

Step-by-step explanation:

Hello,

\((1+1/3)^2-\dfrac{2}{9}=\left( \dfrac{3+1}{3}\right)^2-\dfrac{2}{9}\\\\=\dfrac{16}{9}-\dfrac{2}{9}\\\\=\dfrac{16-2}{9}\\\\=\boxed{\dfrac{14}{9}\\\\}\)

Thanks

Answer:

-4

Step-by-step explanation:

47-51 = -4

Answer: 3/8

Step-by-step explanation:1/2 divided by 4/3 is equal to 1/2 x 3/4 (you cannot divide by a fraction, you must multiply by it’s reciprocal- flip it, or cross multiply. Here we are flipping it)

Now multiply across the top ( numerators)

And then across the bottom (denominators)

1x3=3

2x4=8

Answer is 3/8

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

Answer:

11 - not enough information

12 - yes, Angle-Angle-Side (AAS)

13 - yes, Side-Angle-Side (SAS)

14 - yes, Angle-Side-Angle (ASA)

15 - yes, ASA

16 - yes, Side-Side-Side (SSS)

17 - yes, ASA

18 - yes, SSS

19 - no (different from "not enough information")

20 - yes, AAS

Step-by-step explanation:

11 - 1 pair of congruent sides is given; can conclude 1 pair of angles is ≅ by vertical angles; need 3 parts to prove congruence

12 - 1 pair of sides and a pair of angles given ≅; can show vertical angles ≅

13 - the side that's shared by the two triangles is the second ≅ side

14 - in addition to what's given, can show vertical angles ≅

15 - in addition to what's given, can show vertical angles ≅

16 - all given

17 - in addition to what's given, can show shared side ≅

18 - ..., shared side

19 - the congruent parts are not in the same order on each triangle

20 - all given

Answer:

9/25

Step-by-step explanation:

3 novels , 1 bio , 1 poetry = 5 books

P( novel) = novels / books

               = 3/5

Book is returned

3 novels , 1 bio , 1 poetry = 5 books

P( novel) = novels / books

               = 3/5

P(novel, return, novel) = 3/5 * 3/5 = 9/25

Answer:

its 16

Step-by-step explanation:

If a, b, c, and d are four different numbers and the proportion. The given statement is true.

We take one example,

When you split them, they will all equal the same thing.

A = 5 ,B = 20 20 divided by 5 equals 4

C = 28 ,D = 7 28 divided by 7 equals 4

The ratio is used to compare two amounts of the same type. For two numbers, a and b, the ratio formula is written as a: b or a/b. The ratio and proportion concepts are based on fractions. Ratio and proportion are the fundamental building blocks for many other notions in mathematics. Ratio and proportion are useful in addressing many everyday difficulties, such as comparing heights, weights, distance, or time, or when combining ingredients in cookery, and so on.

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Without knowing the total number of coins or the ratio between one dollar and two dollar coins in the jar, we cannot accurately determine the number of two dollar coins.

Amadi has a jar with both one dollar and two dollar coins. The question is asking how many of the coins in the jar are two dollar coins.
To determine the number of two dollar coins, we need more information. The question does not provide any details about the total number of coins or the ratio between one dollar and two dollar coins in the jar. Without this information, it is not possible to give an accurate answer.
If we assume that the jar contains a total of 100 coins, we can use algebra to solve for the number of two dollar coins.

Let's say the number of two dollar coins is x. Then, the number of one dollar coins would be 100 - x.
Since the value of the two dollar coins is double the value of the one dollar coins, we can set up the equation 2x + 1(100 - x) = total value of coins.
Simplifying the equation, we get 2x + 100 - x = total value of coins.
Combining like terms, we have x + 100 = total value of coins.
Since we don't know the total value of coins, we cannot solve for x. Therefore, we cannot determine the number of two dollar coins without additional information.

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Answer:

Sue rode 1885 miles total

Step-by-step explanation:

There are 31 days in March, 30 in April, and 30 in May.

31 * 12 + 30 * 12 + 30 * 12 = 1092

There are 30 days in June and 31 in august.

30 * 13 + 31 * 13 = 793

Now we find the total:

1092 + 793 = 1885

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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We reject the null hypothesis at a significance level of =0.01.

At a significance level of α=0.01, we reject the null hypothesis if the p-value is less than 0.01. In this case, the p-value of 0.0291 is greater than 0.01, so we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion of students in Yvonne's school who rarely or never argue with their friends is significantly different from the national average of 0.72 at a significance level of α=0.01.

In other words, we do not have enough evidence to say that Yvonne's school is significantly different from the national trend of 72% of teens who say they seldom or never argue with their friends.

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Answer:

Given that the vertices of quadrilateral PQRS are P(6,3), Q(4,2), R(2,4) and S(4,5) and the quadrilateral is dilated with a scale factor of 2, about the origin.

Now, let's find the new vertices of the dilated image:

Vertex P is dilated by a scale factor of 2, its new coordinates will be (2 × 6, 2 × 3) = (12, 6). Therefore, the new vertex P' is at (12, 6).

Vertex Q is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 2) = (8, 4). Therefore, the new vertex Q' is at (8, 4).

Vertex R is dilated by a scale factor of 2, its new coordinates will be (2 × 2, 2 × 4) = (4, 8). Therefore, the new vertex R' is at (4, 8).

Vertex S is dilated by a scale factor of 2, its new coordinates will be (2 × 4, 2 × 5) = (8, 10). Therefore, the new vertex S' is at (8, 10).

Therefore, the coordinates of the vertices of the final image are P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).So, the correct option is D. P’(12, 6), Q’(8, 4), R’(4, 8), and S’(8, 10).

Step-by-step explanation:

Hope this helps you!! Have a good day/night!!

Answer:

Ratio of cost of a pen to cost of a ball pen is 15:7

Step-by-step explanation:

Given that:

Cost of dozen pens = ₹180

Unit rate = \(\frac{180}{12}\)

Unit rate = ₹ 15 per pen

Cost of 8 ball pens = ₹ 56

Unit rate = \(\frac{56}{8}\)

Unit rate = ₹7 per ball pen

Ratio of cost of a pen to cost of a ball pen,

15 : 7

Hence,

Ratio of cost of a pen to cost of a ball pen is 15:7

Answer: you need to add

Step-by-step explanation: I would ask your teacher to help you understand the lesson.  

Option III "E(y) = B₀ + B₁x₁ + B₂x₂ + B₃x₃, where x₁ = 1 if treatment B, x₁ = 0, otherwise; x₂ = 1 if treatment C, x₂ = 0, otherwise; x₃ = 1 if treatment D, x₃ = 0, otherwise." is a correct multiple regression equation that can be used to analyze these data. So the option III is correct.

Randomized design involving four treatments: A, B, C, and D.

So total number of treatments = 4(A, B, C, D)

So the number of dummy variable is required = 4 - 1

The number of dummy variable is required = 3

The three variables would be x₁ x₂ and x₃ and the fourth treatment scenario would be represented if all three were zero.

So the option III is correct because this is a correct multiple regression equation because it contains all the necessary components to define a linear regression model.

Specifically, it contains a dependent variable (y), a constant (B₀), and three independent variables (x₁, x₂, x₃). Additionally, each of the independent variables is either assigned a value of 1 or 0 depending on the treatment, which is how a linear regression model is typically constructed.

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The complete question is:

Consider a completely randomized design involving four treatments: A, B, C, and D. Select a correct multiple regression equation that can be used to analyze these data. Define all variables.

I. E(y) = B₀ + B₁ x₁ x₂ x₃ x₄, where x₁ = 1 if treatment A, x₁ = 0, otherwise; x₂ = 1 if treatment B, x₂ = 0, otherwise; x₃ = 1 if treatment C, x₃ = 0, otherwise; x₄ = 1 if treatment D, x₄ = 0, otherwise.

II. E(y) = B₀ + B₁x₁ + B₂x₂ + B₃x₃ + B₄x₄, where x₁ = 1 if treatment A, x₁ = 0, otherwise; x₂ = 1 if treatment B, x₂ = 0, otherwise; x₃ = 1 if treatment C, x₃ = 0, otherwise; x₄ = 1 if treatment D, x₄ = 0, otherwise.

III. E(y) = B₀ + B₁x₁ + B₂x₂ + B₃x₃, where x₁ = 1 if treatment B, x₁ = 0, otherwise; x₂ = 1 if treatment C, x₂ = 0, otherwise; x₃ = 1 if treatment D, x₃ = 0, otherwise.

Answer:

32 inches

Step-by-step explanation:

Because height times width equals area,

we can divide 112 by 3.5 to get the width

So it is 32 inches

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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