2 numbers that can be true for the following equations. x+y=17 & x-y=7

Answer:

\(f(x) = 144\)

Step-by-step explanation:

This problem deals with a function. All this question is asking is to plug in -4 every time an x appears.

So, let's do that:

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

\(f(-4) = 10(16) - 12 - 4\)

\(f(-4) = 160 - 16\)

\(f(-4) = 144\)

The trigonometric equation that could be used to find x, the distance in feet from the base of the conveyor belt to the building, is x = 15 cos(30°).

To understand why this equation is used, we need to consider the properties of right triangles and the trigonometric functions. In this case, the conveyor belt, the ground, and the building form a right triangle. The angle between the ground and the conveyor belt is 30°, which means the angle between the conveyor belt and the building is 90° - 30° = 60°.

The side of the triangle opposite the 30° angle is the height of the conveyor belt, which is 15 feet. The side of the triangle adjacent to the 30° angle is the distance we want to find, x. The trigonometric function that relates the adjacent and hypotenuse sides of a right triangle is cosine. Therefore, we can use the equation x = 15 cos(30°) to find the value of x, which is approximately 13.0 feet.

In summary, the trigonometric equation used to find x, the distance in feet from the base of the conveyor belt to the building, is x = 15 cos(30°). This equation relates the adjacent and hypotenuse sides of a right triangle using the cosine function. By plugging in the given angle of 30° and the length of the conveyor belt of 15 feet, we can solve for x, which is approximately 13.0 feet.

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The minimum sample size needed to guarantee a given margin of error increases , the correct option is (b) .

What is Margin Of Error ?

The term margin of error is defined as an estimate of a small sample that is drawn from a relatively large population data.

the margin of error is usually governed by the parameters such as the standard deviation , sample size and desired confidence level.

to find missing term in the given statement , let us consider the values ,

where σ ⇒ Standard deviation for population

and m as "Margin of error"  and Z as "Empirical value of Z-score" at a given confidence level .

So , minimum sample size for given confidence level is given by

⇒ (Z×σ)²/m²

from above formula we can conclude that minimum sample size is directly related to population's standard deviation.

Therefore, the minimum sample size required would "increase" with the increase in population "standard deviation" .

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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The probability of getting exactly one face card is 0.72.

According to the questions two cards are drawn from a deck.

Since, we know that

Total number of cards in a deck = 52

Total number of face cards =  3 × 4 = 12

So, the number of ways of selecting 2 cards from a deck = \(^{52} C_{2}\)

And, the total number of ways of  getting exactly one face cards

= \(^{12} C_{1} \times ^{40} C_{1}\)  + \(^{40} C_{1} \times ^{12} C_{1}\)

= 2\(^{40} C_{1} \times ^{12} C_{1}\)

Therefore, the probability of getting exactly one face card

= \(\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }\)

\(= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }\)

\(= \frac{2(40\times 12)}{26\times 51}\)

\(=\frac{2\times 480}{1326}\)

= 0.72

Hence, the probability of getting exactly one face card is 0.72.

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A differential equation is a mathematical equation that relates a function to its derivatives. It involves the unknown function and one or more of its derivative. The solution to the differential equation -

xy' − 2y = x^2, x > 0

is y = (1/4)x^3 + C/x.

To solve the differential equation, we will use the method of integrating factors.

The differential equation is: xy' - 2y = x^2

We can rearrange it in the standard form: y' - (2/x)y = x

The integrating factor (IF) is defined as e^∫(2/x) dx. Integrating 2/x with respect to x gives us 2ln|x|.

Therefore, the integrating factor is IF = e^(2ln|x|) = e^(ln(x^2)) = x^2.

Now, multiply the entire equation by the integrating factor x^2:

x^2(y' - (2/x)y) = x^2(x)

x^2y' - 2xy = x^3

Next, we recognize that the left-hand side is the derivative of (xy) with respect to x. Applying this, we get:

d/dx(xy) = x^3

Integrating both sides with respect to x:

∫d(xy) = ∫x^3 dx

xy = (1/4)x^4 + C

Finally, divide both sides by x:

y = (1/4)x^3 + C/x

where C is the constant of integration.

So, the solution to the given differential equation is y = (1/4)x^3 + C/x.

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Answer:

18

Step-by-step explanation:

Bisecting a line means to cut it at the middle.

Meaning we can set 3x = 27.

x=9

2x=18

Brainliest Please

The mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season or p = 52-43.

According to the question,

We have the following information:

A football team had 52 players at the start of the season, but then some players left the team. After that, the team had 43 players.

Now, let's take the number of players who left the team to be p.

So, we have the following expression:

p = 52-43

p = 9

Hence, the mathematical sentence that expresses the given information is the number of players who left the team, denoted by p, are 43 less than the number of players at the start of the season.

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(a). The estimation results may not be reliable.

(b). The correct regression model is: Y = Bo + B₁X + u where X is randomized based on covariate W₁ and u is the error term.

(c). The measurement errors are not random, but systematic, they can lead to biased parameter estimates and erroneous statistical inference.

(d).  The variance of the error term is low, the t-statistics will be large, and the hypothesis tests will be more powerful.

(1). The term that contains the information of W in the above regression is B₁X₁. If X, and W, are negatively correlated, then the OLS estimator of B₁ becomes less precise. In other words, the standard errors of the coefficient estimates increase because the covariance between the explanatory variables is negative, and the variance of the OLS estimator increases as a result.

Hence, the estimation results may not be reliable.

(2). A randomized regression model is a regression model in which a treatment is randomly assigned to the subjects in the sample. The model is used to test whether the treatment affects the outcome variable.

The correct regression model is: Y = Bo + B₁X + u where X is randomized based on covariate W₁ and u is the error term.

(3). Yes, measurement errors in the dependent variable can cause problems in the ordinary least square estimation. In this case, the errors are called measurement errors, which are due to inaccuracies in the measurement of the dependent variable.

If the measurement errors are not random, but systematic, they can lead to biased parameter estimates and erroneous statistical inference.

(4). The variance of the error term affects hypothesis testing of the regression in the following way: If the variance of the error term is high, it means that the noise in the data is large, and hence the accuracy of the parameter estimates is low.

As a result, the t-statistics will be small, and the hypothesis tests will be less powerful.

Conversely, if the variance of the error term is low, the t-statistics will be large, and the hypothesis tests will be more powerful.

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(1). The estimation results may not be reliable.

(2). The correct regression model is: Y = Bo + B₁X + u.

(3). The measurement errors are not random, but systematic, they can lead to biased parameter estimates and erroneous statistical inference.

(4).  The variance of the error term is low, the t-statistics will be large, and the hypothesis tests will be more powerful.

(1). The term that contains the information of W in the above regression is B₁X₁. If X, and W, are negatively correlated, then the OLS estimator of B₁ becomes less precise. Hence, the estimation results may not be reliable.

(2). The model is used to test whether the treatment affects the outcome variable. The correct regression model is: Y = Bo + B₁X + u where X is randomized based on covariate W₁ and u is the error term.

(3). Yes, measurement errors in the dependent variable can cause problems in the ordinary least square estimation.

(4). The variance of the error term affects hypothesis testing of the regression in the following way: If the variance of the error term is high, it means that the noise in the data is large, and hence the accuracy of the parameter estimates is low.

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Answer:

C. StartRoot x Endroot + 3 = 13

Step-by-step explanation:

the x variable under the root is what makes it a radical. all of the others dont have an x variable under the root. hope this helps !

The evaluation of the expression is -18.

In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.

Given, the algebraic expression 4x+2y–3z.

Given,

algebraic expression in mathematics is an expression which is made up of variables x, y and z and constants, along with algebraic operations (addition, subtraction, etc.).

Coefficients of x, y and z are 4, 2 and -3 respectively.

To find the value of expression  4x+2y–3z at x=–5, y=10, and z=6.

Substitute all the values in the expression,

4x+2y–3z

= 4(-5)+2(10)–3(6)

= -20 + 20 -18

= -18

That means, when x=–5, y=10, and z=6 the expression 4x+2y–3z yields -18.

Therefore, the value of the expression is 4x+2y–3z = -18.

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Answer:C

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2N - 3 = 5

2N = 5 +3 = 8

N = 8/2 = 4

The value of m in the proportion is given as follows m = 3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The proportion is defined as follows:

3/4 = (1/4)m.

As the values have a proportional relationship, the value of m can be obtained applying cross multiplication, as follows:

3/4 = (1/4)m

cross multiplication;

3/4 x 4 = m

m = 3

Hence m =3 is the value that satisfies the proportion in this problem.

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The accepting state will be state 0 since it represents even numbers in base-3. The NFA can transition to both states at the beginning, but it only needs to be in the accepting state at the end to accept an even number.

a) DFA for {strings in which the number of even digits is odd}:

The DFA will have two states: an even state and an odd state. The initial state will be the even state. When the DFA reads an odd digit (1 or 3), it will transition to the other state. When it reads an even digit (0 or 2), it will stay in the same state. The accepting state will be the odd state. This DFA will accept strings in which the number of even digits is odd.

b) DFA for {strings, when interpreted as a base-3 number, are even numbers}:

The DFA will have three states: state 0, state 1, and state 2. The initial state will be state 0. When the DFA reads a digit, it will transition to the state corresponding to that digit. For example, if it reads a 0, it will transition to state 0; if it reads a 1, it will transition to state 1, and if it reads a 2, it will transition to state 2. The accepting state will be state 0 since it represents even numbers in base-3.

c) DFA for {strings, when interpreted as a base-3 number, are even numbers having an odd number of even digits}:

This DFA will have three states: state 0, state 1, and state 2. The initial state will be state 0. When the DFA reads a digit, it will transition to the state corresponding to that digit. Similar to the previous DFA, the accepting state will be state 0. However, we need to keep track of the number of even digits. To achieve this, we can introduce a counter. Every time the DFA transitions to state 2, representing an even digit, the counter will be incremented. If the counter becomes odd, the DFA will transition to state 1. In state 1, it will accept only odd numbers of even digits.

d) DFA for {strings, when interpreted as a base-3 number, are not an even number}:

This DFA will have three states: state 0, state 1, and state 2. The initial state will be state 0. When the DFA reads a digit, it will transition to the state corresponding to that digit. The accepting state will be state 1 and state 2 since these states represent odd numbers in base-3.

e) NFA for {strings, when interpreted as a base-3 number, is an even number}:

The NFA will have two states: state 0 and state 1. The initial state will be state 0. When the NFA reads an odd digit (1 or 2), it will transition to both state 0 and state 1. When it reads an even digit (0), it will stay in the same state. The accepting state will be state 0 since it represents even numbers in base-3. The NFA can transition to both states at the beginning, but it only needs to be in the accepting state at the end to accept an even number.

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Answer:

Be a Butthole back or ignore them

Step-by-step explanation:

Answer:

tell them tvgyfttttrfrt6

Your welcome!

x = 4

Please mark brainiest

The answer will be x = 4, the way to know that is practically move the 8 to the side where is the 3 and convert the positive 8 into a negative 8, then you move the 3 to the other side an change it into a negative 3 to then subtract the 3 with the x and have -2. After that you divide the -2 with the -8 and there is your answer

If Flyer Co. buys back 5102 shares of their $3 par value common stock for $17 per share. The amount debited to the treasury stock account to record the purchase would be $ 86,834.

To calculate the amount debited to the treasury stock account, we need to multiply the number of shares bought back by the price per share.

In this case, Flyer Co. buys back 5102 shares at $17 per share.

The amount debited to the treasury stock account is calculated as follows:

Amount = Number of shares bought back * Price per share

Amount = 5102 * $17

Amount = $86,834

Therefore, the amount debited to the treasury stock account to record the purchase would be $86,834.

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Answer:

$2,611.21

Step-by-step explanation:

A = P(1 + r/n)^nt

A = 1500(1 + 0.057/1)¹⁰

A = 1500(1.057)¹⁰

A = 1500(1.740803988528..)

A = 2611.205982792..

A ≈ $2,611.21

______________________

Where A is the total amount including interest, P is the initial amount or principle, r is the rate, n is how many times it is compounded per year, and t is the time in years.

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

28 : 14

Step-by-step explanation:

4 : 2

4 + 2 = 6

42 ÷ 6 = 7

7 × 4 = 28

7 × 2 = 14

Answer:

x = -5/6

Step-by-step explanation:

First, set the equation (6x + 5) * 86 equal to 0. The equation is now (6x + 5) * 86 = 0. Next, simplify (6x + 5) * 86 by multplying 86 to 6x and 5. This will turn the equation into 516x + 430 = 0. Next, subtract 430 from both sides, cancelling out the 430 on the left side. After that, get the x value by itself by dividing 516 on both sides, cancelling out the 516 on the left side. Now, x = -430/516. From here, find the common factor of both the numerator and denominator; this turns out to be 86. Since 86 is the common factor, divide the numerator and denominator by 86 and you get x = -5/6.

The value of a and b are respectively 15 and 17 respectively.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Given that csc θ = 17/8 and cos θ = a/b.

The reciprocal of sin θ is csc θ.

Therefore,

1/sinθ = 17/8

or, sin θ = 8 /17

Applying the trigonometry identity cos²θ = 1- sin²θ

cos²θ = 1- (8/17)²

cos²θ = 1- 64/289

cos²θ = 225/289

cos θ = 15/17

The value of a is 15 and the value of b is 17.

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While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no relationship between variables.

What is alternative hypothesis?

The alternative to your research topic is represented by the alternative hypothesis (Ha). It asserts that there is a population-wide impact.  

                                     Frequently, your study hypothesis and alternate hypothesis are the same. Alternatively said, it's the assertion that you anticipate or hope will be accurate.

What is meant by a null hypothesis?

A common statistical theory called the null hypothesis asserts that there is no statistical relationship or significance between two sets of observed data and measured events for a given single observed variable.

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The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.

The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set.

In mathematics, a function's domain is the collection of possible inputs it will accept.

Given equation is 2y = 6x - 10 and domain is {-1, 3, 8}

We can also write the given equation is

y =(6x-10)/2      ------------equation 1

As we know, domain is considered as the value of x,

Consequently, if we enter x = -1 in equation 1, we will receive

y = (-16)/2

y = -8

Similarly put x = 3 in equation 1, we will get

y = 8/2

y = 4

Similarly put x = 8 in equation 1, we will get

y = 38/2

y = 19

By combining the values of x and y, we get

The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.

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Answer:

Seven days

Step-by-step explanation:

From the information given, you know that you drink in a day 1.25 cups of the tea in the morning morning and 1.5 cups of the tea in the evening which is equal to:

1.25+1.5=2.75 cups a day

Now that you know the amount of cups that you drink in a day, you can divide  the amount of cups in the pitcher by the amount of cups you drink in a day:

19.25/2.75= 7

According to this, the answer is that you will run out of iced tea after seven days.

If a logical vector z has at least one entry TRUE, the function all(!z) will always be false.

If a logical vector contains only TRUE items, the all() method returns FALSE; otherwise, it returns TRUE.

The any() function, on the other hand, gives a result of TRUE if a logical vector has at least one element that is TRUE and FALSE otherwise.

any(z) will always be TRUE if z contains at least one TRUE element since there is at least one TRUE element. On the other hand, depending on whether all of the components of z are TRUE, all(z) may or may not be TRUE.

any(!z) will always return FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

Additionally, all(!z) will always return FALSE if any element is FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

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Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation is

\(y = - \frac{5}{4} x + 2\)

Comparing with the general equation above the slope is the line is

Hope this helps you

The solution to the given system of equations is as follows:

(-1,-39) and (1,-1).

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

From the graph of the system given at the end of the answer, it is found that the solution to the system of equations is given as follows:

(-1,-39) and (1,-1).

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The amount of the material left after 11 years is approximately 147.8 grams, and it will take approximately 45.2 years to have only a 100g sample left.

To find the amount of material left after 11 years, we can use the formula A = P(1 - r)^t, where A is the amount after t years, P is the initial amount, r is the decay rate, and t is the time in years. Plugging in the given values, we get A = 260(1 - 0.019)^11 ≈ 147.8 grams.

To find how long it will take for the sample to decay to 100g, we can solve for t in the same formula. We get t = log(100/260)/log(1 - 0.019) ≈ 45.2 years. So it will take approximately 45.2 years for the sample to decay to 100g.

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