y? + y
y² - 2y ?
4y + 4
Find the simplified quotient.y? – 4y + 4
y(+ 1) (-2)(-2)
YO-2) 4(y + 1)
4(y + 1) y(+1)
(y-2)6-2) 0-2)
O
Y(+1) 419 + 1)
y0-2) (-2)(-2)

Answer:

x+5

Step-by-step explanation:

15+x-10=x+5

The input is x while the output is y = f(x). If we multiply both sides of y = f(x) by 2/3, then we'll get (2/3)y = (2/3)f(x) = (2/3)x^2

We see that the new outputs are 2/3 the size of the original. So the graph is shorter and has been vertically squished or compressed. If we multiplied both sides by some number larger than 1, then the graph will be vertically stretched.

No reflection has been done because that only happens if we multiplied both sides by a negative value. The negative flips things around (from positive to negative or vice versa).

Answer:

Step-by-step explanation:

m<1 = 50

m<2 = 22

m<3 = 108

m<4 = 50

m<5 = 65

m<6 = 50

m<7 = 43

m<8 = 65

m<9 = 75

m<10 = 18

m<11 = 25

m<12 = 40

m<13 = 115

m<14 = 65

m15 = 115

In any set of 700 English words, there must be at least two words that begin with the same pair of letters.

Consider a set of 700 English words. There are a total of 26 letters in the English alphabet. Since each word can have only two letters at the beginning, there are 26 * 26 = 676 possible pairs of letters.

If each word in the set starts with a unique pair of letters, the maximum number of distinct words we can have is 676. However, we have 700 words in the set, which is greater than the number of possible distinct pairs.

By the Pigeonhole Principle, when the number of objects (700 words) exceeds the number of possible distinct containers (676 pairs), at least two objects must be placed in the same container. Therefore, there must be at least two words that begin with the same pair of letters.

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What is the minimum number of cards that must be drawn from an ordinary deck of cards to guarantee that you have been dealt:

a) at least three aces?

b) at least three of at least one suit?

c) at least three clubs?

a) To guarantee getting at least three aces, we need to consider the worst-case scenario, which is that the first twelve cards drawn are not aces. In this case, the thirteenth card must be an ace. Therefore, the minimum number of cards that must be drawn is 13.

b) To guarantee getting at least three cards of at least one suit, we need to consider the worst-case scenario, which is that the first eight cards drawn are from different suits. In this case, the ninth card must be from a suit that already has at least two cards. Therefore, the minimum number of cards that must be drawn is 9.

c) To guarantee getting at least three clubs, we need to consider the worst-case scenario, which is that the first twelve cards drawn are not clubs. In this case, the thirteenth card must be a club. Therefore, the minimum number of cards that must be drawn is 13.

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In situation a, the predictor variable is age, as it is being tested to see if it affects the outcome variable, which is the number of risky behaviors. So, age is the independent variable and the number of risky behaviors is the dependent variable.

In situation b, the predictor variable is the number of family members, as it is being tested to see if it affects the outcome variable, which is the level of education of children. So, the number of family members is the independent variable and the level of education of children is the dependent variable.

It is important to identify the predictor variable and the outcome variable in any study as this helps in understanding the relationship between the two variables and in interpreting the results accurately.

For situation A, the predictor variable is "age," and the outcome variable is "number of risky behaviors." As age increases, the study aims to see if the number of risky behaviors changes.

For situation B, the predictor variable is "number of family members," and the outcome variable is "level of education of children." The study examines whether the children's level of education changes based on the number of family members.

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Answer:

false

Step-by-step explanation:

I took the test

Answer:

I think the answer is false

Answer:

1.47

Step-by-step explanation:

  2.15

-0.68

borrow from the one now you have 15 minus 8 or 7next borrow from the 2 now you have 11 minus 6 or 5 then drop the one and drop the decimal hope this helped

If P(A) = 7/13, P(B) = 5/13, and P(A and B) = 3/13, then the probability of P(AIB) = 3/5.

Probability is a measure of the likelihood of an event occurring. Many events cannot be predicted with absolute certainty. We can only predict the probability of an event by using it, i.e. the probability of it occurring.

The probability can range from 0 to 1, where 0 means the event is unlikely to happen and 1 means it will definitely happen. All events in the sample space have a probability of 1. For example, when we flip a coin, heads or tails, there are only two possible outcomes (H, T). But when you toss two coins, there are four possible outcomes, namely {(H, H), (H, T), (T, H), (T, T)}.

According to the Question:

Given that:

P(A) = 7/13

P(B) = 5/13

P(A∩B) = 3/13

We know that :

P(A|B) = P(A∩B) / P(B).

(By formula for conditional probability)

P(AIB) = (3/13)÷ (5/13)

          = 3/5

Hence, the value of P(A|B) = 3/5.

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Answer:

x=18

Step-by-step explanation:

the sum of all the angles in a triangle is 180 degrees.

we can use this to get an equation:

5x-6 + 3x+13 + 2x-7 = 180

combine the x's to get:

10x-6-7+13=180

combine the numbers to get:

10x=180

divide both sides by 10 to get your answer:

x=18

Answer:

answer is 8

Step-by-step explanation:

√8*8=√64= 8!

The answer is D.

square root of 8 x square root of 8 = square root of 64 = just 8

Answer:

2x + 3

Step-by-step explanation:

(10x² + 19x + 6) ÷ (5x + 2)​ =

= (10x² + 15x + 4x + 6) ÷ (5x + 2)​

= [5x(2x + 3) + 2(2x + 3)] ÷ (5x + 2)​

= [(5x + 2)(2x + 3)] ÷ (5x + 2)​

= 2x + 3

Answer:

2x+3 is your answer

Trinomials are the polynomials with triplets. Ok, now let's solve the given question.

For The Better Preference, Plz have a look of the handwritten answer which i had solved in the above attachment.

So, the answer of the product of the following polynomials are:‐ 4m² – 3n² – 2p² + mn – 2mp + 5 np.

If my answer is helpful to you, So do give a thanks and A Brainliest. !❤!

Answer:

The answer is |-21.5|

D

-21.5

Step-by-step explanation:

number look at it

The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)

From the question, we have the following expression that can be used in our computation:

–3(2x – 5) < 5(2 – x)

Divide bot sides of the inequality by -1

So, we have the following representation

3(2x – 5) > -5(2 – x)

Next, we open the brackets

This gives

6x – 15 > -10 + 5x

Hence, the representation is 6x – 15 > -10 + 5x

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Complete question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

(a) 6x – 15 > -10 + 5x

(b) 6x – 15 < -10 + 5x

(c) 3(2x – 5) > -5(2 – x)

(d) 3(2x – 5) < -5(2 – x)

The best inequality that represents the relationship between the amount of hydrochloric acid (x) and the amount of distilled water (y) in the given graph is 3y - 2x > 0, option D is correct.

The graph shows a straight line with a negative slope passing through the origin. As the amount of hydrochloric acid, x, increases, the amount of distilled water, y, decreases

To see why, let's use a point on the line, such as (2, 3), and plug it into the inequality. We get:

3(3) - 2(2) > 0

9 - 4 > 0

This is true, so the point (2, 3) is a solution to the inequality. Any point on the line will also satisfy this inequality since it represents all possible combinations of x and y that Corrine can use in her experiment.

Alternatively, we can rewrite the inequality in slope-intercept form:

y < (2/3)x

This means that the y-values on the line are less than the corresponding values of (2/3)x. So as x increases, y must decrease to stay below the line. This confirms that 3y - 2x > 0 is the correct inequality.

Hence, option D is correct.

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The correct question is:

For a science experiment, Corrine is adding hydrochloric acid to distilled water. The relationship between the amount of hydrochloric acid, x, and the amount of distilled water, y, is graphed below. Which inequality best represents this graph?

A. 2y - 3x < 0

B. 3y - 2x < 0

C. 2y - 3x > 0

D. 3y - 2x > 0

The functions that do not involve fractional, radical, or exponential expressions are classified as polynomial functions. These functions, which include linear, quadratic, and cubic functions, are written in the form

    f(x) = \(a_nx^n+a_n_-_1x^n^-^1+....+a_1x+a_0\)

Now, According to the question:

Finding the Zeros and Multiplicities of a Function:

Most functions that do not involve fractional, radical, or exponential expressions are classified as polynomial functions. These functions, which include linear, quadratic, and cubic functions, are written in the form

    f(x) = \(a_nx^n+a_n_-_1x^n^-^1+....+a_1x+a_0\)

While it's relatively easier graphing linear and quadratic functions, graphing a polynomial function with a highest exponent more than 2 is sometimes challenging. However, several techniques such as determining the zeros and multiplicities of the function may help in estimating or describing the behavior of its graph.

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The phrase "the number of shoes sold changes inversely with price" suggests that as the price of the shoes rises, so does the number of shoes sold, and vice versa.

We know that 2000 shoes can be sold for $250 in this circumstance. Using the inverse variation formula, we can write: k/Price = number of shoes sold where k is a proportionality constant. We may use the following information to calculate the value of k: 2000 = k/250 When we multiply both sides by 250, we get: k = 500000 In this case, the equation for the inverse variation is: Price/number of shoes sold = 500000 We may use this equation to compute the number of shoes sold at various prices. For instance, if the price is If the price is $300, the number of shoes sold is: The number of shoes sold is 500000/300, which is 1666.67. As a result, at a price of $300, about 1666.67 pairs of shoes would be sold.

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What is the relationship between the number of shoes sold and the price, given that the number of shoes sold varies inversely with the price? If 2,000 shoes are sold at a price of $250, what would be the price of the shoes if 3,000 shoes are sold?

Answer:

Refer to the step-by-step explanation. If you need any clarification on a part just add a comment under this answer :)

Step-by-step explanation:

Given a system of equations, there are a few methods to calculate solutions of that system. Two ways to do so are by using elimination or substitution.

To solve a set of equations by elimination you will take two equations and either add or subtract them to eliminate one of the variables. Here is a quick example...

\(\left \{ {{3x+y=5} \atop {2x-y=0}} \right.\)

If we were to add these equations together, we could eliminate the variable \(y\\\) to get an equation to solve for \(x\).

After adding these equations we get: \(5x=5\)

We then can solve the equation for \(x\\\), to find the value of \(x\), and use that value to plug back (a.k.a substitute) into the other equations to solve for \(y\)

To solve a set of equations by substitution you will take a system of equations, pick one of the equations and solve one of them for one variable. Here is a quick example...

\(\left \{ {{3x+2y=16} \atop {7x+y=19}} \right.\)

If we take the second equation and solve for the variable, \(y\), we will get an equation in terms of \(x\). We can then take that equation and plug it into the top, substituting \(y\), for the equation in terms of \(x\). Like so....

Solving bottom equation for \(y\), we get:  \(y=19-7x\), now substitute this equation for \(y\) into the top equation.

We get: \(3x+2(19-7x)=16\), you now have an equation only in terms of \(x\), so you can solve for \(x\). I won't complete the whole problem but hopefully you get the idea :)

Equation is true for one x and that x = 23/2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Find x.

9(x - 2) = 7x + 5

Distribute x

9x - 18 = 7x + 5

9x - 7x = 5 + 18

2x = 23

x = 23/2

Equation is true for one x and that x = 23/2

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Answer:

\(\textsf{A.} \quad -2x + y = -2\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}\)

Given equation:

\(y + 4 = 2(x + 1)\)

Distribute the right side of the equation:

\(\implies y+4=2x+2\)

Subtract 2 from both sides:

\(\implies y+4-2=2x+2-2\)

\(\implies y+2=2x\)

Subtract y from both sides:

\(\implies y+2-y=2x-y\)

\(\implies 2=2x-y\)

Switch sides:

\(\implies 2x-y=2\)

Therefore, the equation of the line written in standard form is:

\(\boxed{2x-y=2}\)

Since this is not one of the answer options, switch the signs:

\(\implies -2x+y=-2\)

Please note that this is not in standard form, since the coefficient of the term in x is negative.  However, as the equation in strict standard form is not a given answer option, the only answer can be -2 + y = -2.

The correct transformations:

1) 3 x Equation [A2] + Equation [A1] → Equation [B1]

2). 1/11 x Equation [B1} → Equation [C1]

The correct options are D and A respectively.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

We have three systems of linear equations.

To transform system A into system B:

Multiply 3 to the equation A2 and then add to equation A1,

we get,

-7x +18x -6y + 6y = 10- 54

11x = -44

equation B1.

To transform system B into system C:

Multiply 1/11 to equation B1,

we get,

x = -4

equation C1.

Therefore, the transformations are given above.

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After the logarithmic expression, "log(2x - 4) - log(x + 2) = 1", the value of x is -3.

In order to find the simplify the logarithmic expression, and find the value of "x", we use the "logarithmic-property", that : "log(a) - log(b) = log(a/b)",

The equation can be written as :

⇒ log[(2x - 4)/(x + 2)] = 1,

By using definition of logarithm, we can rewrite this equation as:

⇒ (2x - 4)/(x + 2) = 10

Simplifying this equation,

We get;

⇒ 2x - 4 = 10x + 20;

⇒ -24 = 8x

⇒ x = -3

Therefore, the required value of x is -3.

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We are 90% confident that the true difference in proportions between France and the United States falls between -0.1783 and 0.1383.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

The point estimate for the difference in proportions between France and the United States is:

p₁ - p₂ = (60/120) - (26/50) = 0.5 - 0.52 = -0.02

We can use the following formula to calculate the standard error of the difference in proportions:

SE = √(p₁ * (1 - p₁) / n₁ + p₂ * (1 - p₂) / n₂)

where n₁ and n₂ are the sample sizes.

SE = √((0.5 * 0.5 / 120) + (0.52 * 0.48 / 50))

SE = 0.0936

To construct a 90% confidence interval, we can use the formula:

(point estimate) ± (critical value) * (standard error)

The critical value for a two-sided 90% confidence interval with 169 degrees of freedom (calculated as df = (p₁ * n₁ + p₂ * n₂) / (p₁ + p₂)) can be found using a t-distribution table or calculator.

For a 90% confidence level, the critical value is approximately 1.656.

Using these values, the 90% confidence interval for the difference in proportions is:

-0.02 ± 1.656 * 0.0936

which simplifies to:

-0.1783 to 0.1383

Therefore, we are 90% confident that the true difference in proportions between France and the United States falls between -0.1783 and 0.1383.

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expected value of defected lamps =1.5

Probability of 5 defected lamps= 0.166

probability less than five defected lamps=0.995

Given, the probability that a lamp is defective is 0.05. A random sample of 30 lamps is tested.

(a) The number of defective lamps expected in the sample is found by calculating the expected value of the number of defective lamps in a sample. The expected value of the number of defective lamps in a sample is E(X) = np = 30 × 0.05 = 1.5 defective lamps.    

(b) The probability that there are exactly five defective lamps in the sample is found using the probability mass function (PMF) of the binomial distribution. The PMF is P(X = k) = C(n, k) × p^k × (1 - p)^(n - k)

where C(n, k) is the number of ways to choose k items from a set of n items, p is the probability of success, and n is the number of trials.

P(X = 5) = C(30, 5) × 0.05^5 × (1 - 0.05)^(30 - 5) = 0.166.

(c) The probability that there are fewer than five defective lamps in the sample is found using the cumulative distribution function (CDF) of the binomial distribution. The CDF is

P(X ≤ k) = Σ P(X = i) where Σ is the sum from i = 0 to i = k.

P(X ≤ 4) = Σ P(X = i) = 0.995.

The expected value of the number of defective lamps in a sample is E(X) = np = 30 × 0.05 = 1.5 defective lamps.

The probability that there are exactly five defective lamps in the sample is P(X = 5) = C(30, 5) × 0.05^5 × (1 - 0.05)^(30 - 5) = 0.166.

The probability that there are fewer than five defective lamps in the sample is P(X ≤ 4) = 0.995.

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Answer: 10, 10sqrt(2)

Step-by-step explanation:

The value of each variables are,

x = 10

y = 10√2

We have to given that,

A right triangle is shown in image.

Now, For the value of each variables,

tan 45° = x / 10

1 = x/10

x = 10

By Pythagoras theorem we get;

⇒ y² = x² + 10²

⇒ y² = 10² + 10²

⇒ y² = 100 + 100

⇒ y² = 200

⇒ y = √200

⇒ y = 10√2

Therefore, the value is,

x = 10

y = 10√2

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Answer:

24/7

Step-by-step explanation:

16 = ½ (7x + 8)

Multiply both sides by 2.

32 = 7x + 8

Subtract 8 from both sides.

24 = 7x

Divide both sides by 7.

x = 24/7

Indifferent curves are convex to the origin, and no two can intersect. The slope of the curve is given by the marginal rate of substitution, which shows how much of Y an individual is willing to give up to obtain another unit of X.

The slope of an indifferent curve, therefore, reflects how much an individual is willing to substitute between two goods while still retaining the same level of satisfaction. Indifferent curves are a graphical representation of utility, indicating the amount of satisfaction a consumer obtains from a given combination of two commodities or goods.In contrast, Budget line is a graphical representation of the combination of two goods that a consumer can buy with a given amount of income and prices of goods. The budget line is downward sloping, indicating the number of goods that can be purchased for a given amount of money.The equation of the budget line is given by;

M = PxX + PyY, where M is the total money available for spending, Px is the price of good X, Py is the price of good Y, X is the amount of good X, and Y is the amount of good Y.The equation of the budget line is; 40X + 20Y = 200.On the vertical axis, put Y and on the horizontal axis, put X, the intercepts are X = 5 and Y = 10, the budget line will be at (5,0) and (0,10).The marginal utility of X is greater than the marginal utility of Y. Therefore, the consumer will increase the consumption of X and reduce the consumption of Y until the ratio of marginal utilities of both goods equals the ratio of their prices.The consumer will be in equilibrium when;MUx/Px = MUy/Py.

The indifferent curve and budget line concepts are critical in analyzing consumer behavior and their buying patterns. By understanding the principles of utility analysis, businesses can set prices for their goods and services that ensure consumers are willing to buy them. This, in turn, leads to increased sales, revenue, and profits for the business.

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The equation of linear function which relate y to x is,

⇒ y = - 4x - 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 2, 6) and (- 1, 2).

Now,

Since, The equation of line passes through the points (- 2, 6) and (- 1, 2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 6) / (- 1 - (-2))

m = - 4 / 1

m = - 4

Thus, The equation of line with slope - 4 is,

⇒ y - 6 = - 4 (x - (-2))

⇒ y - 6 = - 4 (x + 2)

⇒ y = - 4x - 8 + 6

⇒ y = - 4x - 2

Therefore, The equation of linear function which relate y to x is,

⇒ y = - 4x - 2

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