Solve 7y-6=2y+8
Show that 7/8-5/6=1/24
Show that 5/8÷7/12=1 1/14
Simplify fully v4×v7÷vt

The area of region R, bounded above by the parabola y = 4x² and below by the line y = 1, is 2√3 units squared.

To find the area of region R, we need to determine the points of intersection between the parabola and the line. Setting the equations equal to each other, we have 4x² = 1. Solving for x, we find x = ±1/2. Since we are only interested in the region in the first quadrant, we consider the positive value, x = 1/2.

To calculate the area of R, we integrate the difference between the upper and lower functions with respect to x over the interval [0, 1/2]. Integrating y = 4x² - 1 from 0 to 1/2, we obtain the area as 2√3 units squared.

Therefore, the area of region R, bounded above by y = 4x² and below by y = 1, is 2√3 units squared.

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Copying a given segment is the process in which a given line segment is drawn following the required steps so that both object and image have the same length. Therefore,

i. PQ = 12 cm

ii. MN = 12 cm

Thus, PQ = MN

Construction is a process that requires the use of materials and instruments to produce a required image. This involves following stated or required steps.

A given line segment can be copied by following appropriate steps. Such that both lines would have the same length, and would be parallel to each other or as required.

The given question requires following the stated steps to produce the required construction. Such that line segment NM is the image of PQ, and both have equal length.

The required construction for the question is attached to this answer.

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The surface area of a rectangular prism is

Where w = 12, l = 4, and h = 4.

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer

\(y=\frac{3}{4} x+-5\)

Step-by-step explanation:

y= mx+b

mx is the slope (rise over run)

b is the y intercept

The partial fraction decomposition of (7x + 93)/(x² + 12x + 27) is: (7x + 93)/(x² + 12x + 27) = 12/(x + 3) - 5/(x + 9)

To rewrite the expression (7x + 93)/(x² + 12x + 27) using partial fractions, we need to decompose it into two fractions with denominators (x + 3) and (x + 9).

Let's start by expressing the given equation as the sum of two fractions:

(7x + 93)/(x² + 12x + 27) = A/(x + 3) + B/(x + 9)

To find the values of A and B, we can multiply both sides of the equation by the common denominator (x + 3)(x + 9):

(7x + 93) = A(x + 9) + B(x + 3)

Expanding the equation:

7x + 93 = Ax + 9A + Bx + 3B

Now, we can equate the coefficients of like terms on both sides of the equation:

7x + 93 = (A + B)x + (9A + 3B)

By equating the coefficients, we get the following system of equations:

A + B = 7 (coefficient of x)

9A + 3B = 93 (constant term)

Solving this system of equations will give us the values of A and B.

Multiplying the first equation by 3, we get:

3A + 3B = 21

Subtracting this equation from the second equation, we have:

9A + 3B - (3A + 3B) = 93 - 21

6A = 72

A = 12

Substituting the value of A back into the first equation, we can find B:

12 + B = 7

B = -5

Therefore, the partial fraction decomposition of (7x + 93)/(x² + 12x + 27) is:

(7x + 93)/(x² + 12x + 27) = 12/(x + 3) - 5/(x + 9)

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Therefore, the expression (7x + 93) / (x² + 12x + 27) can be rewritten as (43 - 5) / (x + 3)(x + 9), or simply 38 / (x + 3)(x + 9)  for the partial fraction.

To rewrite the given equations using partial fractions, we need to decompose the rational expression into simpler fractions. Let's work through it step by step.

OA + B = -7

A + B = -17

OA + B = 17

OA + B = 22

A + B = 7

OA + B = -22

To begin, we'll solve equations 2 and 5 simultaneously to find the values of A and B:

(2) A + B = -17

(5) A + B = 7

By subtracting equation (5) from equation (2), we get:

(-17) - 7 = -17 - 7

A + B - A - B = -24

0 = -24

This indicates that the system of equations is inconsistent, meaning there is no solution that satisfies all the given equations. Therefore, it's not possible to rewrite the equations using partial fractions in this case.

Moving on to the next part of your question, you provided an expression:

(7x + 93) / (x² + 12x + 27)

We want to express this in the form of (43 - B) / (x + 3)(x + 9).

To find the values of A and B, we'll perform partial fraction decomposition. We start by factoring the denominator:

x² + 12x + 27 = (x + 3)(x + 9)

Next, we express the given expression as the sum of two fractions with the common denominator:

(7x + 93) / (x + 3)(x + 9) = A / (x + 3) + B / (x + 9)

To determine the values of A and B, we multiply through by the common denominator:

7x + 93 = A(x + 9) + B(x + 3)

Expanding and collecting like terms:

7x + 93 = (A + B)x + 9A + 3B

Since the equation must hold for all values of x, the coefficients of corresponding powers of x on both sides must be equal. Therefore, we have the following system of equations:

A + B = 7 (coefficient of x)

9A + 3B = 93 (constant term)

We can solve this system of equations to find the values of A and B. By multiplying the first equation by 3, we get:

3A + 3B = 21

Subtracting this equation from the second equation, we have:

9A + 3B - (3A + 3B) = 93 - 21

6A = 72

A = 12

Substituting the value of A back into the first equation:

12 + B = 7

B = -5

Therefore, the expression (7x + 93) / (x² + 12x + 27) can be rewritten as (43 - 5) / (x + 3)(x + 9), or simply 38 / (x + 3)(x + 9).

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The equation of the altitude from vertex A of the triangle is y = (3/2)x + 3/2.

To write an equation for the altitude from vertex A of the triangle where point A is (-1,0), point B is (8,-5), and point C is (2,-3), we need to use the slope-intercept form of an equation for the line that contains the side opposite vertex A. Here are the steps:

1. Find the slope of the line containing side BC using the slope formula: m = (yb - yc)/(xb - xc) = (-5 - (-3))/(8 - 2) = -2/3.

2. Find the equation of the line containing side BC using point-slope form: y - yb = m(x - xb). Using point B, we get: y + 5 = (-2/3)(x - 8). Simplifying, we get y = (-2/3)x + 19/3.

3. The altitude from vertex A of the triangle is perpendicular to side BC. Therefore, its slope is the negative reciprocal of the slope of side BC, which is 3/2.

4. We can find the equation of the altitude by using point-slope form again, this time using point A: y - ya = m(x - xa). Using point A and the slope 3/2, we get: y - 0 = (3/2)(x + 1). Simplifying, we get: y = (3/2)x + 3/2.

Summary: To find the equation of the altitude from vertex A of the given triangle, we first found the slope of the line containing the side opposite vertex A, which is BC. Then, we found the equation of this line using point-slope form. Next, we used the fact that the altitude is perpendicular to side BC and found its slope, which is the negative reciprocal of the slope of side BC. Finally, we used the point-slope form again to find the equation of the altitude using point A and its slope. The equation we obtained is y = (3/2)x + 3/2.

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Answer:

Step-by-step explanation:

$66.67/month for three months

The monthly payment is calulated by dividing the total cost of the mountain bike by 3.  For example, if the total cost is $200, the three monthly payments will be $66.67 each:

   $200

---------------- = $66.67/month for three months

  3 months

A key feature of function g is that it takes the value of the function f, and adds 4 to it before evaluating it. This means that the output of g is always 4 units greater than the output of f.

Evaluating is the process of making judgments about something based on criteria and evidence. It involves analyzing and assessing the quality or value of something, based on a set of predetermined criteria. Evaluating can be used to assess the quality of a product, a performance, an argument, or any other object or entity. Evaluating requires the use of critical thinking skills and involves asking questions,

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Answer:

2.1 hr

Step-by-step explanation:

[0.8 m × (100 cm)/(1 m)]/(38.2 cm/hr) = 2.1 hr

Answer:

21245 rounded to the nearest thousand is 21000.

Rounding to the nearest thousand means finding the number that is closest to the original number, but ends in three zeroes. In this case 21000 is the nearest number ending in three zeroes to 21245.

Answer:

21000

Step-by-step explanation:

If the hundreds place is 500 or bigger, round to 22000, if the number is 499 or under it will be 21000.

Answer:

Step-by-step explanation:

\(2. \: a. \: \sqrt[3]{ - 1} \)

\( = \sqrt[3]{( - 1 )\times ( - 1 )\times( - 1)} \)

= -1 (Ans)

\(b. \: \sqrt[3]{ - \frac{8}{27} } \)

Since,

\( \sqrt[3]{ - x} = - \sqrt[3]{x} \)

Hence,

\( = - \sqrt[3]{ \frac{8}{27} } \)

\( = - \sqrt[3]{ \frac{2 \times 2 \times 2}{3 \times 3 \times 3} } \)

\( = - \frac{2}{3} (ans)\)

\(3. \: a. \: 10 - 2 \sqrt{9} \)

\( = 10 - 2 \sqrt{3 \times 3} \)

= 10 - 2 × 3

= 10 - 6

= 4 (Ans)

\(b. \: 70 - {( \sqrt[3]{64} )}^{3} \)

\( = 70 - \sqrt[3]{ {64}^{3} } \)

\( = 70 - \sqrt[3]{64 \times 64 \times 64} \)

= 70 - 64

= 6 (Ans)

Answer:

C. \(\frac{1}{45^{6}}\)

Step-by-step explanation:

Concepts Used:

Simplifying the given expression:

We are given the expression:

\(\frac{45^{-3}}{45^{3}}\)

According to the rule of negative exponents, 45⁻³ = 1/45³

\(\frac{1}{45^{3}}*\frac{1}{45^{3}}\)

\(\frac{1}{45^{3}*45^{3}}\)

According to the Power of a Product rule: aⁿ X aᵇ = aⁿ⁺ᵇ

Using the Power rule to further simplify our expression:

\(\frac{1}{45^{6}}\)

Hence, Option C is correct

Judging from the two results, increasing the temperature of the freezer to -4 °C reduces the power consumption by 1.25 kW, while decreasing the temperature inside the house to 26 °C reduces the power consumption by only 0.5 kW. Hence, the owner should consider increasing the temperature of the freezer to -4 °C to save more energy assuming that both the heat pump and the freezer are operating at their maximum possible thermodynamic efficiencies.

To determine which option would be more energetically efficient

With Increasing the temperature of the freezer to -4 °C:

Assuming that the freezer operates at maximum efficiency, the heat absorbed from the compartment is given by

Q = W/Qh = 2.5 kW

If the temperature of the freezer is increased to -4 °C, the heat absorbed from the compartment will decrease.

If the efficiency of the freezer remains constant, the heat absorbed will be

\(Q' = W/Qh = (Tc' - Tc)/(Th - Tc') * Qh\)

where

Tc is the original temperature of the freezer compartment (-7 °C),

Tc' is the new temperature of the freezer compartment (-4 °C),

Th is the temperature of the outside air (2 °C),

Qh is the heat absorbed by the freezer compartment (2.5 kW), and

W is the work done by the freezer (which we assume to be constant).

Substitute the given values, we get:

\(Q' = (Tc' - Tc)/(Th - Tc') * Qh\\Q' = (-4 - (-7))/(2 - (-4)) * 2.5 kW\)

Q' = 1.25 kW

Thus, if the temperature of the freezer is increased to -4 °C, the power consumption of the freezer will decrease by 1.25 kW.

With decreasing the temperature of the inside of the house to 26 °C:

If the heat pump operates at maximum efficiency, the amount of heat it needs to pump from the outside to the inside is given by

Q = W/Qc = 4 kW

If the temperature inside the house is decreased to 26 °C, the amount of heat that needs to be pumped from the outside to the inside will decrease.

\(Q' = W/Qc = (Th' - Tc)/(Th - Tc) * Qc\)

Substitute the given values, we get:

\(Q' = (Th' - Tc)/(Th - Tc) * Qc\\Q' = (26 - 28)/(2 - 28) * 4 kW\)

Q' = -0.5 kW

Therefore, if the temperature inside the house is decreased to 26 °C, the power consumption of the heat pump will decrease by 0.5 kW.

Judging from the two results, increasing the temperature of the freezer to -4 °C reduces the power consumption by 1.25 kW, while decreasing the temperature inside the house to 26 °C reduce the power consumption by only 0.5 kW.

Therefore, the owner should consider increasing the temperature of the freezer to -4 °C to save more energy.

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The value of MN in the diagram is 38 units.

Base on the diagram MQP and MRP are right angles(90 degrees). And also JP is equals to PK. This is because PK and JP are the radius of the circle.

Hence,

JP  =  PK

∠MQP  = ∠MRP = 90 degree

Therefore,

QM = MR

6x - 11 = 2x + 9

6x - 2x = 9 + 11

4x = 20

x = 20 / 4

x = 5

Let's find MN as follows:

PK is perpendicular to MN. Therefore, PK bisect MN into two equal parts.

Hence,

MR = RN

2MR = MN

2(2x + 9) = MN

MN = 2(2(5) + 9)

MN= 38 units

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Answer: 47 your welcome :)

10 + 8 = 18

18 x 4 = 72

72 + 5 = 77

The answer is 77

To test the claim about the average weight of high school students in Riyadh city, we can use a one-sample t-test. Here are the steps to perform the test:

Define the null hypothesis (H0) and the alternative hypothesis (Ha):

Null hypothesis (H0): The average weight of high school students in Riyadh city is 230 pounds or less.

Alternative hypothesis (Ha): The average weight of high school students in Riyadh city is greater than 230 pounds.

Set the significance level (α): The significance level is given as α = 0.1, which means we are willing to accept a 10% chance of making a Type I error.

Calculate the test statistic:

Sample mean (): 232

Population standard deviation (σ): 10

Sample size (n): 52

The test statistic is calculated using the formula:

t = (- μ) / (σ / √n)

where μ is the hypothesized population mean.

Plugging in the values, we get:

t = (232 - 230) / (10 / √52)

Determine the critical value: Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value from the t-distribution table at the given significance level and degrees of freedom (n - 1 = 52 - 1 = 51).

Compare the test statistic with the critical value:

If the test statistic is greater than the critical value, we reject the null hypothesis.

If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis.

Calculate the p-value: If desired, you can calculate the p-value associated with the test statistic and compare it with the significance level. If the p-value is less than the significance level, we reject the null hypothesis.

Please provide the critical value associated with the given significance level (α) and the degrees of freedom (df = n - 1).

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Answer:

For example, the phrase "3 more than an unknown number" becomes the mathematical expression "x + 3." Because the unknown number has no explicitly stated value, we label it with a variable x. To get a value three more than x, simply add 3 to it.

hope it helps ya mate. ~^~

Answer:

3 + x

Step-by-step explanation:

"More than" means addition. 3 more than x is saying 3 plus x. In an algebraic expression, this would look like:

3 + x

Answer:

b

Step-by-step explanation:

Answer: b

Step-by-step explanation: fdfdfd

The first term (a) of the arithmetic sequence is 45, and the common difference (d) is 7.

To determine the first term (a) and the common difference (d) of an arithmetic sequence, we can use the following formulas:

a + (n-1)d = nth term

where a is the first term, d is the common difference, and n is the position of the term in the sequence.

We have that the 5th term is 73 and the 15th term is 143, we can set up the following equations:

a + 4d = 73   (1)

a + 14d = 143  (2)

To solve this system of equations, we can subtract equation (1) from equation (2):

(a + 14d) - (a + 4d) = 143 - 73

10d = 70

d = 7

Substituting the value of d into equation (1), we can solve for a:

a + 4(7) = 73

a + 28 = 73

a = 73 - 28

a = 45

Therefore, the first term (a) of the arithmetic sequence is 45 and the common difference (d) is 7.

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Answer:

Well, the answer is 0.

Step-by-step explanation:

Answer: 0

Step-by-step explanation: the answer will be zero because since -456 and 456 are both the opposite the answer will be zero I hope this helps :)

Answer:

square root of 8 is 2.82842712475

If you meant 8^2 then it would be 64

Step-by-step explanation:

For figure 1; the value of angle ELF is 50⁰.

For figure 2; the value of angle ELF is 35⁰.

The measure of angle ELF is calculated by applying intersecting chord theorem as follows;

For figure 1; the value of angle ELF is calculated as;

m∠ELF = arc angle EF (interior angles of intersecting secants)

arc angle EF = 2 x (m∠EKF)  (interior angles of intersecting secants)

arc angle EF = 2 x 25⁰

arc angle EF = 50⁰

For figure 2; the value of angle ELF is calculated as;

arc EF = 42⁰

arc SK = 112⁰

m∠ELF  = ¹/₂ (SK - EF) (exterior angles of intersecting secants)

m∠ELF  = ¹/₂ (112 - 42)

m∠ELF  = 35⁰

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Answer: The answer to this is 7.

H² = B² + P²

(25)² = (24)² + p²

625 = 576 + p²

p² = 49

p = 7

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

y=4x-2

Step-by-step explanation:

Simplified form of the expression 8 ( 3 + 4 ) using the Distributive Property of Multiplication over Addition is 56

To apply the Distributive Property of Multiplication over Addition, you need to multiply the number outside the parentheses by each term inside the parentheses and then add the products together.

In this case, the number outside the parentheses is 8, and the terms inside the parentheses are 3 and 4. So, you can apply the distributive property as follows:

8 ( 3 + 4 ) = 8 × 3 + 8 × 4

Multiply the numbers

= 24 + 32

Add the numbers

= 56

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Proposals for research studies include a methodology section.

This section is an important component of a research proposal as it outlines the procedures and techniques that will be used to conduct the study. It provides the reader with a detailed description of the research design, the data collection methods, and the data analysis methods that will be employed. The methodology section of a research proposal should be well-structured and clearly written to demonstrate the feasibility and validity of the proposed study.

Here are some key components of a methodology section in a research proposal:

Research design: This section describes the overall approach that will be taken to conduct the research, including the type of study (e.g. experimental, qualitative, quantitative), the sample size and selection method, and the data collection methods that will be used.

Data collection methods: This section outlines the methods that will be used to collect data, including the type of data that will be collected (e.g. surveys, interviews, observations), the instruments or tools that will be used, and the procedures for collecting and storing the data.

Sampling method: This section describes the method that will be used to select the participants for the study, including the criteria for inclusion and exclusion, and the process for obtaining informed consent from participants.

Data analysis methods: This section outlines the methods that will be used to analyze the data, including the statistical methods and software that will be used, and any assumptions or limitations associated with the analysis methods.

Ethics and safeguards: This section discusses any ethical considerations associated with the study, including informed consent, confidentiality, and protection of participants' rights. It should also describe any safeguards that will be put in place to ensure that the data is collected and analyzed in a valid and reliable manner.

By including a well-structured methodology section in a research proposal, researchers can demonstrate their understanding of the research process, and provide a clear and detailed plan for conducting the study. This helps to increase the credibility and feasibility of the proposed study, and can increase the chances of the proposal being approved and funded.

Therefore, Proposals for research studies include a methodology section.

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