Esther made the two-way table below showing the number of her schoolmates who have different pets. Students’ Pets Cats Dogs Total 7th Grade 8th Grade 26 35 61 Total 54 48 Which shows the correct values for Esther’s seventh-grade classmates who have pets? cats: 13; dogs: 28 cats: 28; dogs: 13 cats: 80; dogs: 83 cats: 83; dogs: 80.

The mean and standard deviation of the population is 19.8 and 0.004 respectively.

Mean:

The mean is the simple mathematical average of a set of two or more numbers. The mean of a given set of numbers can be calculated in several ways, including the arithmetic mean, which uses the sum of the numbers in the range, and the geometric mean, which takes the mean product of a set. However, all major methods of calculating simple averages produce the same approximate result most of the time.

Standard Deviation:

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values.  A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

Given that:

E(x) = μ = 19.8

var(x) = σ²/n = 0.2/50 = 0.004

from here can say that mean = 19.8 and

standard Deviation is 0.004.

Now,

295 -298 P(Bottle x < 295) =P(Z< ) =-1.00 =.15873

Thus, there is nearly a 16% probability that just 1 randomly selected

bottle contains < 295 ml.

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A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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The answer to this question is sigma < 13.08. The single-sided upper bounded 90% confidence interval for the population standard deviation (sigma) given that a sample of size n = 5 yields a sample standard deviation of 5.89 is sigma < 13.08.

Calculation of the single-sided upper bounded 90% confidence interval for the population standard deviation (sigma) given that a sample of size n=5 yields a sample standard deviation of 5.89 is shown below:

Upper Bounded Limit: (n-1)S²/χ²(df= n-1, α=0.10)

(Upper Bounded Limit)= (5-1) (5.89)²/χ²(4, 0.10)

(Upper Bounded Limit)= 80.22/8.438

(Upper Bounded Limit)= 9.51σ

√(Upper Bounded Limit) = √(9.51)

√(Upper Bounded Limit) = 3.08

Therefore, the upper limit is sigma < 3.08.

Now, adding the sample standard deviation (5.89) to this, we get the single-sided upper bounded 90% confidence interval for the population standard deviation: sigma < 3.08 + 5.89 = 8.97, which is not one of the options provided in the question.

However, if we take the nearest option which is sigma < 13.08, we can see that it is the correct answer because the range between 8.97 and 13.08 includes the actual value of sigma

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Answer:

kilometers she has walked his year is 1199.814 km

i hope it helps

have a nice day

Step-by-step explanation:

The Laplace equation is defined as Au=0. The aim is to solve analytically Laplace's equation in the square [0, 1]²2 with boundary conditions u(x,0) = 0 = u(0, y), u(x, 1) = u(1, y) = 1.

Let's consider the Laplace equation as followsAu = ∂²u/∂x² + ∂²u/∂y²= 0Given boundary conditions areu(x, 0) = 0u(0, y) = 0u(x, 1) = u(1, y) = 1The solution of the Laplace equation is as followsu(x,y) = X(x).Y(y)Let's find the boundary conditionsu(x, 0) = 0

Let's substitute the value of Y(0) in the solution to get X(x).Y(0) = 0, which implies Y(0) = 0Similarly, u(0, y) = 0 => X(0).Y(y) = 0 => X(0) = 0Now, let's find the remaining boundary conditionsu(x, 1) = 1X(x).Y(1) = 1 => Y(1) = 1/X(x)u(1, y) = 1 => X(1).Y(y) = 1 => X(1) = 1/Y(y)Now, let's put the values of X(0) and X(1) in the below equationX(0) = 0, X(1) = 1/Y(y)X(x) = x

Now, let's put the values of Y(0) and Y(1) in the below equationY(0) = 0, Y(1) = 1/X(x)Y(y) = sin(n.π.y) /sinh(n.π)Therefore, the solution of Laplace's equation u(x, y) is as follows;u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π)Answer:Therefore, the solution of Laplace's equation u(x, y) is u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π).

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Answer:

1.1(x+2) = 1.1x + 2.2

Step-by-step explanation:

I) Distribute the terms using the Distributive Property:

1.1(x+2)

= 1.1(x) + 1.1(2)

II) Simplify:

1.1(x) + 1.1(2)

= 1.1x + 2.2

The pooled mean standard error is a measure of the variability associated with the difference between two group means in a statistical hypothesis test with equal variances.

The pooled mean standard error is a measure of the variability or uncertainty associated with the difference between two group means in a statistical hypothesis test, where the two groups have equal variances. Specifically, it is the standard error of the difference between the means of two independent samples, calculated by combining the standard errors of the two sample means into a single estimate.

The formula for the pooled mean standard error is:

SEp = \(\sqrt{ [ (s1^2/n1) + (s2^2/n2) ]}\)

where SEp is the pooled mean standard error, s1 and s2 are the standard deviations of the two samples, n1 and n2 are the sample sizes, and sqrt represents the square root function.

The pooled mean standard error is used in the calculation of the t-statistic in a two-sample t-test, which is used to test the hypothesis that there is a significant difference between the means of the two groups. By accounting for the variability of both groups, the pooled mean standard error provides a more accurate estimate of the standard error of the difference between the means, which in turn allows for more precise hypothesis testing.

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Answer:

476

Step-by-step explanation:

because if you do the reverse way its 68 x 7 which is 476 and if your not sure if your answer is right check it by doing 476/68 and see if it equals 7

hope it helps

Answer:

9.174 you can check it by dividing 68 and 9.174 which gives u 7

Step-by-step explanation:

hope this helps

The equation based on the information is:

34 = x - 18

In mathematics, an equation is an expression that states that two expressions are equal by joining them with the equal sign =. Equations and their cousins ​​in other languages ​​may have subtly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English any well-formed expression consisting of two expressions joined by an equal sign is an equation. To solve an equation involving variables, it is necessary to determine which values ​​of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values ​​of the unknowns that satisfy the equation are called the solution of the equation. There are two types of equations: identities and constraints. The ID applies to all values ​​of the variable. A constraint expression applies only to specific values ​​of a variable.

Given that :

Bella is baking 34 cookie for the holiday party tonight. She baked 18 before leaving for school and will bake the ret when he return home.

Therefore, the equation is:

34 = x - 18

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Answer:

x = 18/5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define equation

5x + 2 = 20

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 20 does indeed equal 20.

∴ x = 18/5 is a solution to the equation.

The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

It will take approximately 18.4 years for the sum of money to triple itself at the same rate.

If a sum of money doubles itself in 8 years, this means that its annual growth rate is given by:

r = 1/8 = 0.125 or 12.5%

Let P be the initial sum of money. After t years, the sum of money will have grown to:

P × (1 + r)^t

If this sum triples itself, we can write:

3P = P × (1 + r)^t

Dividing both sides by P, we get:

3 = (1 + r)^t

Taking the natural logarithm of both sides, we get:

ln(3) = t × ln(1 + r)

Solving for t, we get:

t = ln(3) / ln(1 + r)

Substituting r = 0.125, we get:

t = ln(3) / ln(1 + 0.125) ≈ 18.4 years

Therefore, it will take 18.4 years to triple the money

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The function f has a range of [0, 2] if the domain of the function is limited to [0, 2]

From the question, the definition of the functions are given as

f(x) = x³ - 6x² + 9x

g(x) = 4

The domain of the function f(x) is limited to the interval

Domain = [0, 2]

This means that we calculate the function values at ends of the intervals

i.e. at x = 0 and x = 2

Substitute x = 0 and x = 2 in the equation f(x) = x³ - 6x² + 9x

So, we have

f(0) = 0³ - 6(0)² + 9(0)

f(0) = 0

Also, we have

f(2) = 2³ - 6(2)² + 9(2)

f(2) = 2

So, we have

Range = [f(0), f(2)]

This gives

Range = [0, 2]

Hence, the range of the function f is [0, 2]

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Answer:

d

Step-by-step explanation:

hope this helps

Answer: The answer would be D) x²-12

explanation: Values mentioned in the form of table b are not a function. Option D is correct. Given that, Four functions in the tabulated options are given we have to find the one that is not a function. What are functions? Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable. Here, From observation Function mentioned in Tables A, C and D are proper functions because each of them has a relative and corresponding value of ordinate with respect to the abscissa. While in option B one of the abscissae gives two values of the ordinates but another abscissa relates to a single value. That is why Table in B does not represent the functions. Thus, values mentioned in the form of table b is not a function. Option D is correct.

Answer:

400 cubic yards

Step-by-step explanation:

There are three cubic feet in each cubic yard

Answer:

I think the answer is Criminology.

Step-by-step explanation:

Since a forensic linguist performs language analysis on written or recorded documents to help solve crimes.

Hope that helps. x

The formula for a line segment is:

segment = √((x2 - x1)^2 + (y2 - y1)^2)

1. Calculate the difference between the x-coordinates: x2 - x1

2. Square the result of step 1: (x2 - x1)^2

3. Calculate the difference between the y-coordinates: y2 - y1

4. Square the result of step 3: (y2 - y1)^2

5. Add the results of step 2 and step 4: (x2 - x1)^2 + (y2 - y1)^2

6. Calculate the square root of the result of step 5: √((x2 - x1)^2 + (y2 - y1)^2)

This final result is the length of the line segment.

The formula for a line segment is relatively straightforward. Begin by calculating the difference between the x-coordinates (x2 - x1) and square the result. Then find the difference between the y-coordinates (y2 - y1) and square the result. Add the two results together and take the square root of the sum. This final result is the length of the line segment. This formula can be used to calculate the length of any line segment, regardless of its size or shape.

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The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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Answer:

Question 3 - true

Step-by-step explanation:

It is onto function.

9514 1404 393

Answer:

  a.  4x^2 +16x -48 = 4x^2 +16x -48

  b.  -3x^2 +12x +36 = -3x^2 +12x +36

  c.  x^2 +12x +35 = x^2 +12x +35

Step-by-step explanation:

In general, you would prove this by transforming one of the expressions into the other. The easiest would be to transform the factored form into the vertex form, perhaps, as this would spare you trying to explain the magic of factoring.

Alternatively, you can transform both expressions into the same (standard) form. I believe that will be the easiest of all.

The product of two binomials is ...

  (x +a)(x +b) = x(x +b) +a(x +b) = x^2 +bx +ax +ab

  (x +a)(x +b) = x^2 +(a+b)x +ab . . . . after collecting terms

The square of a binomial is the same thing, but with b=a, so ...

  (x +a)^2 = x^2 +2a +a^2

Using these forms, we can avoid showing all of the intermediate "work" of making the desired transformations.

__

a.  4(x -2)(x +6) = 4(x +2)^2 -64

  4(x^2 +4x -12) = 4(x^2 +4x +4) -64 . . . . . expanding the products

  4x^2 +16x -48 = 4x^2 +16x +16 -64 . . . . using the distributive property

  4x^2 +16x -48 = 4x^2 +16x -48 . . . . . collect terms; expressions are equal

__

b.  -3(x +2)(x -6) = -3(x -2)^2 +48

  -3(x^2 -4x -12) = -3(x^2 -4x +4) +48

  -3x^2 +12x +36 = -3x^2 +12x -12 +48

  -3x^2 +12x +36 = -3x^2 +12x +36

__

c.  (x +5)(x +7) = (x +6)^2 -1

  x^2 +12x +35 = x^2 +12x +36 -1

  x^2 +12x +35 = x^2 +12x +35

Answer:

A. 3 and 1/3 (Fraction),  B. Has infinite answer (I think. I may have this wrong),  and C. 0.

Step-by-step explanation:

A. We have the equation 4(x-2)(4+6)= 4(x+2)^2 - 64.

1. (4x-8)(10)=(4x+8)^2 - 64  (We have to use PEMDAS, so the P goes first).

2.(4x-8)(10)= 16x +64 - 64 (Then we use E next.)

3. 40x-80 = 16x (Again with the P)

4. 40x = 16x +80 (Add 80 to both sides. And you might have drop the PEMDAS Here I think).

5. 24x = 80      (We subtract 16x from both sides)

6. x = 3 and 1/3  (Divide both sides by 24.

B. We have the equation: -3(x+2)(x-6)=-3(x-2)^2+48

1. Times the -3.

(-3x-6)(x-6)=(-3x-6)^2 +48

2. Times the exponent

(-3x-6)(x-6)=9x+36+48

3. Times the the ones that are in the braces the first using FOIL and add the other on the other side of the equation.

-3x^2 + 12x +36= 9x+84

4. Subtract 9x and 36 from both sides

-3x^2 +3x= 48

This may have an infinite answer to this, and I don't know if I'm wrong on this.

C. (x+5)(x+7)= (x +6)^2 -1

1. Times the exponent

(x+5)(x+7) = x^2 + 36 -1

2. Times the ones in the braces using FOIL.

x^2+7x+5x+35=X^2+36-1

3. Add all of the like Terms.

x^2+12x+35=x^2+35

4. Subtract x^2 from both sides  (I may did this wrong)

12x + 35 = 35

5. Subtract 35 from both sides.

12x = 0

6. Divide both sides by 12 (I may have this wrong too)

x=0

And that's it. I may have some things wrong, but it's worth a shot.

The antiderivative of f(x) = ³√x² + x√x is \(1/3 x^3/2 (2x^1/3 + 3x^1/2)\) + C.

The antiderivative of a capability is the converse of the subsidiary. As such, assuming that we have a capability f(x) and we take its subordinate, we get another capability that lets us know how the first capability is changing regarding x. The antiderivative of f(x) is a capability that lets us know how the first capability changes as for x the other way. It is additionally called the endless vital of f(x).

Presently, we should view as the antiderivative of the given capability f(x) = ³√x² + x√x. We can separate it into two sections:

f(x) = ³√x² + x√x

=\(x^(2/3) + x^(3/2)\)

To see as the antiderivative of \(x^(2/3)\), we want to add 1 to the example and separation by the new type:

∫\(x^(2/3)\) dx = (3/5)\(x^(5/3)\) + C

where C is the steady of incorporation. Also, to view as the antiderivative of\(x^(3/2)\), we add 1 to the example and separation by the new type:

∫\(x^(3/2)\) dx = (2/5)\(x^(5/2)\) + C

where C is the steady of incorporation.

Accordingly, the antiderivative of f(x) = ³√x² + x√x is:

∫f(x) dx = ∫\(x^(2/3)\) dx + ∫\(x^(3/2)\) dx

= (3/5)\(x^(5/3)\) + (2/5)\(x^(5/2)\) + C

where C is the steady of incorporation.

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The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Step-by-step explanation:

Given equation is 2t/(t-5) + 1/(t-3) = 3

=> [2t(t-3)+1(t-5)]/(t-5)(t-3) = 3

=> (2t²-6t+t-5)/(t²-5t-3t+15) = 3

=> (2t²-5t-5)/(t²-8t+15) = 3

=> 2t²-5t-5 = 3(t²-8t+15)

=> 2t²-5t-5 = 3t²-24t+45

=>3t²-24t+45-2t²+5t+5 = 0

=> t²-19t+50 = 0

The standard form is t²-19t+50 = 0

Let $C$ be the event that the camera gets a 10% discount, $G$ be the event that the game gets a 25% discount, and $N$ be the event that neither item gets a discount. Then the probability of each event is:

\begin{align*}

P(C) &= 0.35\cdot 0.1 = 0.035 \\

P(G) &= 0.05\cdot 0.25 = 0.0125 \\

P(N) &= 0.6\cdot 1 = 0.6

\end{align*}

The amount saved on the camera is $0.1\cdot 200=20$, and the amount saved on the game is $0.25\cdot 80=20$. So, we want to find the probability that either event $C$ or $G$ occurs. Since the events are mutually exclusive, we can use the addition rule:

$$

P(C\text{ or }G) = P(C) + P(G) = 0.035 + 0.0125 = 0.0475

$$

The amount saved in dollars at the cash register is $X = 20 + 20 = 40$. To find the probability that the total amount saved is $20$, we need to sum the probabilities of all the ways to get $X=20$. There are two ways to do this: either the camera gets a 10% discount while the game gets no discount, or the game gets a 25% discount while the camera gets no discount. Using the multiplication rule and the probabilities above, we have:

\begin{align*}

P(\text{camera gets 10% discount, game gets no discount}) &= P(C)\cdot P(N) = 0.035\cdot 0.6 = 0.021 \\

P(\text{game gets 25% discount, camera gets no discount}) &= P(G)\cdot P(N) = 0.0125\cdot 0.6 = 0.0075

\end{align*}

Therefore, the probability that the total amount saved is $20$ is:

$$

P(X=20) = P(\text{camera gets 10% discount, game gets no discount}) + P(\text{game gets 25% discount, camera gets no discount}) = 0.021 + 0.0075 = 0.0285

$$

So the chance you save a total of $20$ is $\boxed{0.0285}$.

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Metrics and data are intimately connected in the sense that metrics rely on data to function. Metrics are used to measure the performance of an organization Data is the source of information that is used to calculate metrics.

It is the raw numbers and facts that are collected, analyzed, and turned into metrics that can be used to measure performance. Data is the foundation of metrics because metrics are just a way of interpreting and organizing the data to gain insight into performance.

Without data, metrics would not exist. It is through data that metrics are able to provide an understanding of what is working and what is not. Metrics are the tool used to interpret data and make decisions that can help guide an organization or individual to success.

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We need to find the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45.

In order to find this probability, we need to find the number of doctors that are General Practitioner or under under the age of 45. Then, divide that number by he total of 17.

We know that 7 doctors are General Practitioners. And 2 of them are also under the age of 45.

Therefore, since ther are 4 doctors that are under the age of 45, there are 2 additional doctors, besided those 2 that follow in both categories, there are under the age of 45.

Summarizing, the number of doctors that are General Practitioner or a doctor under the age of 45 is:

Notice that this result can also be obtained by the formula:

where A is the set of General Practitioners, B is the set of doctors under the age of 45, and the symbol |...| represents the number of elements in that set:

Therefore, the required probability is:

Answer

Answer:

y = 25 degrees

Step-by-step explanation:

straight line has 180 degrees

so 180 - 115 = x which is 65 degrees

traingle has 180 also

65 + 90 = 155          180 - 155 = y which is 25 degrees

The triangle on the other side is the equivalent.

Answer:

y = 25°

Step-by-step explanation:

x = 180° - 115° (115° and x are supplementary angles)

x = 65°

In the triangle,

x + y + 90° = 180°

65° + 90° + y = 180°

155° + y = 180°

Subtract 155 from both sides,

y = 180° - 155° = 25°

Answer:

60n-30

Step-by-step explanation:

you would do 15 * 4n

that would give you 60. since 15 *4 is 60 and then you would just put the n

15*2 equals 30. You would make it a negative 30 since it is a negative 2.

then you would combine them and get the answer

60n-30

Hope this helps!