Simplify the expression x - 2/3 - 1/2x .

(A) 1/2x - 2/3
(B) -1/3x - 3/4
(C) 1/4x - 1/2

Answer:

There is no picture or graph to go with the question so I am afraid I will not be able to give you a specific answer.

To find out if a point (x, y) is on the graph of a line, we plug in the values into that equation and see if we get a true statement, such as 10 = 10. If we get something different, like 6 = 4, we know that the point is not on the line because it does not satisfy the equation. Plug in (-301, 601) into the equation of the line to see whether that point lies on it or not.

Step-by-step explanation:

Suppose the equation of the straight line that passes through E and F is this:

y = 7x + 2

We are to figure out whether or not the point (1, 10) lies on that line. In order to do this we would plug in (1, 10) into the equation, with 1 being x and 10 being y.

10 = 7(1) + 2 = 7 + 2 = 9

10 = 9 is a false statement. Therefore, the point (1, 10) does NOT lie on the line y = 7x + 2.

If you were to provide an image or graph that shows the equation of line AB then perhaps I would be able to answer your question with a specific answer.

Answer:

NP=8 cm and MN = 16 cm

Step-by-step explanation:

lets suppose NP = x and MN = 2x - because it is twice of NP.

we know that the distance of MP = 24 cm

so MP = MN+NP

24=x+2x

3x=24 and

x=24/3

x=8

x means NP = 8 cm

AND 2x means MP = 2(8) = 16 cm

your answer is C 2/3 referring to over to the right 2 times and up 3 times

The probability that the sample proportion will be at least k is 0.7580.

Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:

Z = (X - μ) / σ

Here, X = number of people who cooperate and respond to the questions in the sample

μ = E(X) = np,  σ = sqrt(npq)

q = 1 - P

Now, to calculate the probability, first calculate μ = np =

σ = sqrt(npq)

Then, find the z-score using z = (k - μ) / σ.

Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.

The probability that the sample proportion will be at least k is 0.7580.

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The triangle ABC would be an isosceles triangle.

An isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and Skelos are the sources of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

Given, Two angles of triangle ABC are 72 and 36 (in degrees). Since the sum of all the angles in a triangle is 180 degrees. Hence,

72 + 36 + third angle = 180

third angle = 72

Since if a triangle has two equal angles in it. Then it is known as an isosceles triangle.

Therefore, The given ABC triangle would be an isosceles triangle.

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\(\displaystyle \large \boldsymbol{} (7 \sqrt[5]{6x-10}) ^2 +\backslash\!\!\!8=\frac{49}{x^{-\tfrac{2}{5} }} +\backslash\!\!\!8 \\\\\\ 49\!\!\!\! \diagup \sqrt[5]{(6x-10)^2} = 49\!\!\!\! \diagup \cdot \sqrt[5]{x^2} \ \ ; \\\\\\ (6x-10)^2=x^2 \\\\ (6x-x-10)(6x+x-10) =0 \Rightarrow x_1=2 \ ; \ x_2=\frac{10}{7 }\)

We can conclude that the special tutoring session seems to have had a positive impact on the students' performance, as their mean score increased from below 60% to 70%.

We can conclude that the special tutoring session has been effective since the students' mean score increased from 60 percent to 70 percent on the second test.

The students who scored less than 60 percent on the first test were given a special tutoring session, which resulted in their mean score increasing to 70 percent on the second test.

Therefore, we can conclude that the special tutoring session has been effective in improving the students' performance on the second test.

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The tolerable deviation rate decreases, it necessitates a larger sample size to maintain the desired level of confidence and accuracy in the Sampling size.

In attributes sampling, the tolerable deviation rate refers to the acceptable level of non-conforming items or errors in a population. It represents the maximum rate of deviation or non-conformance that is considered acceptable for a given attribute or characteristic being inspected.

When the tolerable deviation rate is decreased, it means that a lower level of deviation or non-conformance is deemed acceptable. This has an effect on the sample size required for the attributes sampling.

Generally, a decrease in the tolerable deviation rate will lead to an increase in the required sample size. The reason for this is that when the acceptable level of deviation is reduced, it becomes more stringent, and a larger sample is needed to ensure that the observed deviation rate is statistically representative of the population.

By increasing the sample size, there is a higher likelihood of capturing a sufficient number of defective or non-conforming items to make reliable conclusions about the population's quality level. This helps to reduce the risk of accepting a batch or population that actually has a higher defect rate than what is considered tolerable.

the tolerable deviation rate decreases, it necessitates a larger sample size to maintain the desired level of confidence and accuracy in the sampling results. The increased sample size allows for a more precise estimation of the population's quality level, providing greater assurance in decision-making regarding acceptance or rejection of the population based on the observed deviation rate.

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To prove the given trigonometric identity: \(cot(x+y) = )\frac{(cot(x)cot(y) - 1) }{(cot(x) + cot(y)}\), we can use the definition of cotangent and some trigonometric identities.

Recall that \(cot(x) = \frac{1}{tanx}\) and \(tan(x) = \frac{sin(x)}{cos(x)}\).
First, let's find the\(tan(x+y)\)using the angle sum formula for tangent:
\(tan(x+y)=\frac{(tan(x) + tan(y))}{ (1 - tan(x)tan(y))}\)
Now, substitute cot(x) and cot(y) using the definition of cotangent:
\(tan(x+y) =\frac{ (1/cot(x) + (1/cot(y)}{(1 - (1/cot(x))(1/cot(y))}\)
To simplify the expression, find the common denominator for the numerators:
\(tan(x+y) = \frac{ (cot(x)cot(y) + cot(x) + cot(y)) }{cot(x)cot(y) - 1}\)
Now, take the reciprocal of both sides to get \(cot(x+y)\)
\(cot(x+y) =\frac{ (cot(x)cot(y) - 1)}{ (cot(x) + cot(y))}\)
So, we have proven that \(cot(x+y) = \frac{ (cot(x)cot(y) - 1)}{ (cot(x)cot(y) - 1)}\)

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To solve this problem, we can use the Chinese Remainder Theorem. We need to find the remainder when 2202 202 is divided by both 2101 and 251.

First, note that 2101 and 251 are relatively prime. Therefore, by the Chinese Remainder Theorem, there exists a unique remainder between 0 and 2101 * 251 - 1 (inclusive) that satisfies the two conditions.

To find this remainder, we can use the remainders when 2202 202 is divided by 2101 and 251.

Note that 2202 is congruent to 101 (mod 2101) and 0 (mod 251). Therefore, we can use the Chinese Remainder Theorem to find that the remainder when 2202 202 is divided by 2101 * 251 is congruent to:

101 * (251^2) * (251^(-1)) + 0 * (2101^2) * (2101^(-1)) (mod 2101 * 251)

Using the fact that 251^(-1) is congruent to 201 (mod 2101) and 2101^(-1) is congruent to 1922 (mod 251), we can simplify this expression to:

101 * (251^2) * (201) + 0 * (2101^2) * (1922) (mod 2101 * 251)

Simplifying further, we get:

101 * 251 * 201 (mod 2101 * 251)

This is congruent to 101 * 201 (mod 251), which is congruent to 101 (mod 251).

Therefore, the remainder when 2202 202 is divided by 2101 251 1 is 101, which is option (b).

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Answer:

Sure thing! Volume is length times width times height. It does not matter what order you put the numbers in, though

Step-by-step explanation:

1 is 0.6666666666666666666666666666 infinity

2 is 0.421875

4 is 0.3

5 is 1.3125.

please mark brainliest!!

Answer:

Step-by-step explanation:

1. 1/6 feet

2. 27/64 yards

4. 3/10 inches

5. 21/16 cm

hope this helped you!!

Answer:

A = 20.25 sq units

Step-by-step explanation:

to find the area of a square you only need to know the measure of one side -- all other sides will be equal to it

it appears the segment is 4.5 units so you would square that to get the area

A = 4.5²

A = 20.25

Answer:

Applying the formulae, (a+b)2+(a−b)2=2(a2+b2)

and (a+b)2−(a−b)2=4ab where a=5x;b=2

4×(5x)×22((5x)2+22)=1213

20x25x2+4=1213

On cross multiplying and simplifying,

75x2−65x+12=0

75x2−20x−45x+12=0

5x(15x−4)−3(15x−4)=0

(5x−3)(15x−4)=

x={53,154}={0.6,0.27}

Hence, m=0.6

you please do like this method

\(~~~~~~(5x+2)(5x-2)+(5x-2)(x-1)-(5x-2)^2 = 0\\\\\implies (5x-2)(5x+2+x-1-5x+2)=0\\\\\implies (5x-2)(x+3)=0\\\\\implies x+3 = 0~~ \text{or}~~ 5x -2 = 0\\\\\implies x = -3,~ x =\dfrac 25\)

Answer:

1. 185.71% 2. 30.56%

Step-by-step explanation:

(1) Initial no of books = 14

Final no of books = 40

Increase in books = 40-14 = 26

\(\%\ \text{increase in books}=\dfrac{\text{increase in books}}{\text{initial no of books}}\times 100\\\\=\dfrac{26}{14}\times 100\\\\=185.71\%\)

(2) Initial points = 72

Final points = 50

Decrease in points = 72-50= 22

\(\%\ \text{decrease in points}=\dfrac{\text{decrease in points}}{\text{initial points}}\times 100\\\\=\dfrac{22}{72}\times 100\\\\=30.56\%\)

Hence, this is the required solution.

Let X be exponential with a rate of lambda and let Y = [X] + 1. Substituting it, we get

P(Y = k) = e ^ (-λ(k-1))(1 - p). Therefore, P(Y = k) = (1 - p)pk-1.

We need to show that Y is geometric with a parameter of p = 1 - e ^ (-lambda).

To solve the problem, we have to show that P(Y = k) = (1 - p)pk-1 for all k ≥ 1.P(Y = k) = P([X] + 1 = k)

We know that [X] ≤ X < [X] + 1.

Substituting Y = [X] + 1,

we get [Y - 1] ≤ X < Y - 1. ⇒ Y - 1 ≤ X < Y

It follows that

P(Y = k) = P([X] + 1 = k)

= P(Y - 1 ≤ X < Y)

= P(X ≥ k - 1, X < k)

= P(X < k) - P(X < k - 1)P(X < k)

= 1 - e ^ (-λk)P(X < k - 1)

= 1 - e ^ (-λ(k-1))

Therefore, P(Y = k) = (1 - e ^ (-λk)) - (1 - e ^ (-λ(k-1)))

= e ^ (-λ(k-1))(1 - e ^ (-λ))

We know that p = 1 - e ^ (-λ).

Substituting it, we get P(Y = k) = e ^ (-λ(k-1))(1 - p)

Therefore, P(Y = k) = (1 - p)pk-1.

Hence proved.

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(112)3 =336

(211)3 =633

sum of the numbers:

(112)3 +(211)3=

336+633=

969

product of the numbers:

(112)3 × (211)3=

336×633=

212688

The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:

Input the initial value of x, for example x=0.

Calculate f(x) and g(x):

If f(x) is less than g(x), then x should be increased and vice versa.

Increase or decrease x accordingly and calculate the new values of f(x) and g(x).

Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.

The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

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We are to find the percentage of births which occurred among women between the ages of 38 and 40 using the graph.

The percentage of births which occurred among women between the ages of 38 and 40 using the graph is 98.0

From the graph above, each bar represent 2 years.

There are 5 bars each between 20 and 30, 30 and 40 respectively.

The percentage of births occurred among women between the ages of 38 and 40 is 98

To one decimal place

= 98.0

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This one is an interesting question.

Lets solve first the equation by isolation of the unknown x:

6x + 6 +2 = (3k / 5x )+3 +3

6x = (3k/5x) + 6 -6-2

6x = (3k/5x) -2

6x = (3k / 5x) - (10x / 5x)

6x = (3k-10x)/5x

6x*5x = 3k - 10x

30x² = 3k - 10x

30x² + 10x = 3k

30x² + 10x - 3k = 0

This is really interesting because this looks exactly like a polynomial function. So we know that there is no solution for a polynomial once the discriminant delta is strictly less than 0.

But delta = b² - 4ac where b = 10, a = 30 and c = -3k

So we need to solve delta < 0

100 - 4*30* (-3k) < 0

100 - 120*(-3)*k < 0

100 - (-360)k < 0

100 + 360k < 0

360k < -100

k < -100/360= -10/36

So there is no solution for all k strictly less than -10/36

Good luck

Answer:20

Step-by-step explanation:

because why not you know

The proof for the given proportion or two equivalent ratios given as (y+x):(y-x) = k:1 is shown below

What is a proportion?

On ratio and fractions, proportion is based. Two ratios are equal when they are represented as a fraction (a/b), a ratio (a:b), and then a proportion. A and B are two integers. Two sets of supplied numbers are said to be directly proportional if they increase or decrease in the same ratio for both sets. The symbols "::" or "=" are used to indicate proportions. If the ratio between the first and second is equal to the ratio between the second and third, then any three quantities are in continuing proportion.

Given that (y+x) : (y-x) = k : 1

We know that product of extremes = product of means

Extremes=(y+x) and 1

Means=(y-x) and k

(y+x) . 1   = (y-x) . k

y + x = ky - kx

y - ky = -kx - x

y - ky = - x(k + 1)

-(y - ky) = x(k + 1)

ky - y = x(k + 1)

y(k - 1) = x(k + 1)

y=\(\frac{x(k+1)}{(k-1)}\)

Hence proved.

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Answer:

x = 47

Step-by-step explanation:

180 = x + (180 - 107) + (x + 13)

Subtract in the parenthesis.

180 = x + 73 + x + 13

Combine terms.

180 = 2x + 86

Subtract 86 from both sides.

2x = 94

Divide both sides by 2.

x = 47.

Proof:

180 = x + (180 - 107) + (x + 13)

180 = 47 + (180 - 107) + (47 + 13)

180 = 47 + 73 + 60

180 = 120 + 60

180 = 180

Answer:

f(3) = 16

Step-by-step explanation:

f(3) = 3(3) +7

f(3) = 9 + 7

f(3) = 16

Answer:

\(\frac{5}{24}(11x+28)\)

Answer: -3,2

Step-by-step explanation:

The combination of entrees and desserts that the restaurant serve will be:

A. The restaurant could serve 40 entrees and 25 deserts.

E. The restaurant could serve 64 entrees and 40 deserts.

The word problem in mathematics refers to a question that is written as a sentence which requires an individual to use his or her mathematics knowledge.

In this case, the local restaurant serves 8 entrees for every 5 desserts.

In this case it should be noted that:

40 / 25 = 8 / 5

64 / 40 = 8 / 5

The correct options are A and E.

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Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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The confidence interval for estimating the mean sale price of homes in the neighborhood is made at a 95% level of reliability.

The confidence level for the given interval is 95%. This means that if the sampling and estimation process is repeated many times, the calculated interval will contain the true mean sale price of homes in the neighborhood 95% of the time.

The given printout already indicates a confidence level of 95%, which means that you can be 95% certain that the true mean sale price falls within the range of the lower limit (38,886.4) and the upper limit (54,113.6).

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