find the HCF of a²b²-2a+1​

Answer:

x = 5 , y = 15

Step-by-step explanation:

Since the figures are congruent then corresponding sides and angles are congruent , that is

WG = DG ( substitute values )

3x - 5 = 10 ( add 5 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

and

∠ WGF = ∠ DGF , that is

15x + y = 90 ( substitute x = 5 )

15(5) + y = 90

75 + y = 90 ( subtract 75 from both sides )

y = 15

The area of the shaded region is 9 square units.

To find the area of the shaded region between \(x=y^2-4y and x=2y-y^2\), follow these steps:
1. Set \(y^2-4y\) equal to \(2y-y^2\) to find the points of intersection.
2. Solve for y: \(2y^2-6y=0\), which simplifies to y(2y-6)=0.

3. Determine the two y-values: y=0 and y=3.
4. Set up the integral from y=0 to y=3, using the formula ∫(right curve - left curve) dy:\(∫(2y-y^2)-(y^2-4y) dy\).
5. Simplify the integrand: \(∫(6y-2y^2) dy\).

6. Evaluate the integral: \([3y^2 - (2/3)y^3]\)from 0 to 3.
7. Calculate the area by substituting the limits of integration and finding the difference: [27 - (2/3)(27)] - [0] = 27 - 18 = 9.

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Answer:

x = -522 19/30

Step-by-step explanation:

To solve for x, distribute the 3/5. This gives us 3/5x - 21/50 = -314. Add over 21/50 to the other side, allowing for 3/5x to equal -313 29/50. Divide by 3/5 on both sides and we get x equal to -522 19/30. This is the final answer as a mixed number and is also in simplest form.

The correct option id D. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time

A study was conducted to determine if more than 30% of Cal State East Bay students work full-time.

The sample of Cal State East Bay students selected was random.

Out of 100 students, 36 were found to be working full-time.

The p-value was calculated to be 0.0952.

The probability of having more than 36 Cal State East Bay students working full-time out of a random sample of 100 students is 9.52% if exactly 30% of Cal State East Bay students work full-time.

Therefore, it is concluded that the null hypothesis cannot be rejected.

The p-value is greater than 0.05 which shows the significance level.

Hence, we accept the null hypothesis.

The null hypothesis states that the proportion of Cal State East Bay students who work full-time is not greater than 30%.

The alternate hypothesis states that the proportion of Cal State East Bay students who work full-time is greater than 30%.

The test is a right-tailed test.

The sample proportion is p = 0.36. The test statistic is given as Z = (p - P0) / √ [P0 (1 - P0) / n]Z = (0.36 - 0.30) / √ [(0.30) (0.70) / 100] = 1.76The p-value is given as 0.0392.

Since the p-value is less than 0.05, we can reject the null hypothesis.

Thus, we can conclude that more than 30% of Cal State East Bay students work full-time.

Hence, option D is the correct answer.

There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.

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Answer:

slope is 3

Step-by-step explanation:

10,17

7,8

8-17=-9

7-10=-3

-9/-3=3

Step-by-step explanation:

4(2x-7)+4>-88

4(2x-7)>-92    Subtract 4 from both sides

8x-27>-92     Distributive property

8x>-65      Add 4 to both sides

-8x<65    I call this the negative switch, but it is called something else

x<-8.125

Answer:

3f5 Changes made to your input should not affect the solution:

(1): "f5"   was replaced by   "f^5". final result

3f5

Step-by-step explanation:

Answer:

2x² - xy - 15y²

Step-by-step explanation:

(2x + 5y)(x - 3y)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x - 3y) + 5y(x - 3y) ← distribute parenthesis

= 2x² - 6xy + 5xy - 15y² ← collect like terms

= 2x² - xy - 15y²

(b)To solve the differential equation, we have to find the roots of the characteristic equation. So, the characteristic equation of the given differential equation is: r² + r = 0. Therefore, we have the roots r1 = 0 and r2 = -1. Now, we can write the general solution of the differential equation using these roots as: y(t) = c₁ + c₂e⁻ᵗ, where c₁ and c₂ are constants. To find these constants, we need to use the initial conditions given in the question. y(0) = 1, so we have: y(0) = c₁ + c₂e⁰ = c₁ + c₂ = 1. This is the first equation we have. Similarly, y'(t) = -c₂e⁻ᵗ, so y'(0) = -c₂ = 0, as given in the question. This is the second equation we have.

Solving these two equations, we get: c₁ = 1 and c₂ = 0. Hence, the general solution of the differential equation is: y(t) = 1. (c)Now, we can use the result obtained in part (b) to solve the initial value problem y" + y' = 2t with y(0) = 1 and y'(0) = 0. We can rewrite the given differential equation as: y" = 2t - y'. Substituting the general solution of y(t) in this equation, we get: y"(t) = -e⁻ᵗ, y'(t) = -e⁻ᵗ, and y(t) = 1. Therefore, we have: -e⁻ᵗ = 2t - (-e⁻ᵗ), or 2e⁻ᵗ = 2t, or e⁻ᵗ = t. Hence, y(t) = 1 + c³, where c³ = -e⁰ = -1. Therefore, the solution of the initial value problem is: y(t) = 1 - t.

Part (b) of the given question has been solved in the first paragraph. We have found the roots of the characteristic equation r² + r = 0 as r₁ = 0 and r₂ = -1. Then we have written the general solution of the differential equation using these roots as y(t) = c₁ + c₂e⁻ᵗ, where c₁ and c₂ are constants. We have then used the initial conditions given in the question to find these constants.

Solving two equations, we got c₁ = 1 and c₂ = 0. Hence, the general solution of the differential equation is y(t) = 1.In part (c) of the question, we have used the result obtained from part (b) to solve the initial value problem y" + y' = 2t with y(0) = 1 and y'(0) = 0. We have rewritten the given differential equation as y" = 2t - y' and then substituted the general solution of y(t) in this equation. Then we have found that e⁻ᵗ = t, which implies that y(t) = 1 - t. Therefore, the solution of the initial value problem is y(t) = 1 - t.

So, in conclusion, we have solved the differential equation y" + y' = 2t and the initial value problem y" + y' = 2t with y(0) = 1 and y'(0) = 0.

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Answer:

The answer is B.

Step-by-step explanation:

The value of a cell phone is something that people are dependent on.

An amusement park allows 50 people to enter every 30 minutes. This statement can be modeled by a linear function.

A linear function is a function where the variable has the highest degree of 1.

Given, A. The population of bacteria triples everyday. Therefore, it is an exponential growth function. Here, the growth is three times than the previous day.

B. The value of a cell phone depreciates at a rate of 3.5% each year. Here, it is an exponential decay function. The decay factor is 0.035 than the previous day.

C.  An amusement park allows 50 people to enter every 30 minutes. Therefore, it is a linear function. Here, the number of people increases by 50 after every 30 minutes.

D. A baseball tournament eliminates half of the teams after each round. Here, it is an exponential decay function. The decay factor is 0.5 than the previous round.

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Answer:

  -2 and 1

Step-by-step explanation:

The two "mystery numbers" are described by two relations. We can assign variables to those numbers, and write a system of equations that express the given relations.

__

Let x and y represent the first and second mystery numbers, respectively. The first relation tells us ...

  10x +5y = -15

The second relation tells us ...

  6x +2y = -10

We can reduce both of these equations to lowest terms by factoring out the common factor of 5 from the first one and 2 from the second one:

__

We are told to solve this using elimination. We can eliminate the y-variable by subtracting the first equation from the second:

  (3x +y) -(2x +y) = (-5) -(-3)

  x = -2 . . . . . . . . . . simplify

  2(-2) +y = -3 . . . . substitute for y

  y = 1 . . . . . . . . . . add 4

The two numbers are -2 and 1.

The y coordinate of the solution to this system of equations is -2

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

3x+y=-2 x-2y=4

Express properly

So, we have

3x + y = -2

x - 2y = 4

Multiply the second equation by -3

so, we have the following representation

3x + y = -2

-3x + 6y = -12

Add the equations to eliminate x

7y = -14

Divide both sides by 7

y = -2

Hence, the value of y is -2

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Margaret is incorrect because the given information does not include enough details to determine if the quadrilateral WXYZ is a parallelogram.

To prove that a quadrilateral is a parallelogram, the four sides must be equal in length and the opposite angles must be congruent. The given information does not include any measurements or angles, so it is not possible to determine if the quadrilateral is a parallelogram.

No, 144 inches of tape is not enough to finish the job. The hazard sign has two identical parallelogram-shaped stripes, and each stripe will require more than 144 inches of tape to outline. The area of a parallelogram can be calculated using the formula A = bh, where b is the base and h is the height. In order to determine how much tape is needed to outline the stripes, the base and height of the parallelograms must be known.

There is not enough information to prove that a quadrilateral is a parallelogram, as all four sides must be equal in length and the opposite angles must be congruent. Additionally, 144 inches of tape is not enough to outline the hazard sign's two identical parallelogram-shaped stripes, as the base and height of the parallelograms must be known in order to calculate the area.

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Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.

Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.

A hypothesis in a study is a statement that is made to explain a given observation without prior testing to prove or disprove the statement.

The two types of hypothesis are:

The null hypothesis states that there is no significant difference between two variables while the alternative hypothesis states that there is a significant difference between the variables.

For the given observation:

Null hypothesis: the mean entry-level salary of an employee and is not significantly less than that of professionals in the company.

Alternative hypothesis: the mean entry-level salary of an employee is significantly less than that of professionals in the company.

In conclusion, the null hypothesis is the hypothesis of no significant difference.

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The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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Answer:

your answer............................

The solution of the double inequality is -11 <= a <= 1 and the  three solutions in the solutions are -11, -10 and -9

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

1 <= (4 - a)/3 <= 5

Multiply through the inequality expression by 3

So, we have the following inequality expression

3 * 1 <= 3 * (4 - a)/3 <= 5 * 3

Evaluate the products in the above inequality expressions

So, we have

3 <= 4 - a <= 15

Subtract 4 from all sides of the inequality expression

So, we have

-1 <= - a <= 11

Multiply all sides of the inequality expression by 1

So, we have

1 >= a >= -11

Rewrite as

-11 <= a <= 1

The numbers in the above solution are -11, -10 and -9

Hence, the solution of the double inequality is -11 <= a <= 1 and the  three solutions in the solutions are -11, -10 and -9

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Answer:

  -1/11, +1/11

Step-by-step explanation:

You want the two square roots of 1/121.

A square root can be either positive or negative.

  \(\pm\sqrt{\dfrac{1}{121}}=\pm\dfrac{1}{\sqrt{121}}=\boxed{\pm\dfrac{1}{11}}\)

__

Additional comment

The √ symbol generally means the principal square root, the positive root. To get the negative root, we precede the symbol with a minus sign. So, both square roots are identified as ±√( ).

Answer:

What is the elimination method?

The elimination method is a technique for solving systems of linear equations. Let's walk through a couple of examples.

Example 1

We're asked to solve this system of equations:

\begin{aligned} 2y+7x &= -5\\\\ 5y-7x &= 12 \end{aligned}2y+7x5y−7x=−5=12

We notice that the first equation has a 7x7x7, x term and the second equation has a -7x−7xminus, 7, x term. These terms will cancel if we add the equations together—that is, we'll eliminate the xxx terms:

\begin{aligned} 2y+\redD{7x} &= -5 \\ +~5y\redD{-7x}&=12\\ \hline\\ 7y+0 &=7 \end{aligned}2y+7x+ 5y−7x7y+0=−5=12=7

Solving for yyy, we get:

\begin{aligned} 7y+0 &=7\\\\ 7y &=7\\\\ y &=\goldD{1} \end{aligned}7y+07yy=7=7=1

Plugging this value back into our first equation, we solve for the other variable:

\begin{aligned} 2y+7x &= -5\\\\ 2\cdot \goldD{1}+7x &= -5\\\\ 2+7x&=-5\\\\ 7x&=-7\\\\ x&=\blueD{-1} \end{aligned}2y+7x2⋅1+7x2+7x7xx=−5=−5=−5=−7=−1

The solution to the system is x=\blueD{-1}x=−1x, equals, start color #11accd, minus, 1, end color #11accd, y=\goldD{1}y=1y, equals, start color #e07d10, 1, end color #e07d10.

We can check our solution by plugging these values back into the original equations. Let's try the second equation:

\begin{aligned} 5y-7x &= 12\\\\ 5\cdot\goldD{1}-7(\blueD{-1}) &\stackrel ?= 12\\\\ 5+7 &= 12 \end{aligned}5y−7x5⋅1−7(−1)5+7=12=?12=12

Yes, the solution checks out.

If you feel uncertain why this process works, check out this intro video for an in-depth walkthrough.

Example 2

We're asked to solve this system of equations:

\begin{aligned} -9y+4x - 20&=0\\\\ -7y+16x-80&=0 \end{aligned}−9y+4x−20−7y+

Emilio can make 6 servings of soup.

As Emilio needs 13 3/4 ounces of chicken broth to make one serving of soup, To find the number of servings of soup he can make using 82.5 ounces of chicken broth, we need to divide the total amount of chicken broth by the amount required to make one serving.

So, the number of servings of soup Emilio can make is; Number of servings of soup = Total amount of chicken broth ÷ Amount of chicken broth required for one serving.

Putting the values we get, Number of servings of soup = 82.5 oz ÷ 13 3/4 oz.

We know that, 3/4 oz = 0.75 oz.

Therefore, Number of servings of soup = 82.5 oz ÷ (13 + 0.75) oz.

Number of servings of soup = 82.5 ÷ 13.75.

Number of servings of soup = 6.

Therefore, Emilio can make 6 servings of soup.

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Answer:

5 ( y + 3 ) = 4

a. The appropriate amount of safety stock is 92 kg. b. The item should be reordered when the inventory level reaches approximately 692 kg.

To determine the amount of safety stock and the reorder point (ROP), we need to consider the expected demand during the lead time, the standard deviation of demand during the lead time, and the acceptable stockout risk.

a. Amount of safety stock:

Safety stock is the additional inventory kept to mitigate the risk of stockouts. It acts as a buffer to account for unexpected fluctuations in demand. The formula to calculate safety stock is:

Safety stock = (Z * Standard deviation of demand during lead time)

Where Z is the z-score corresponding to the acceptable stockout risk. Since the acceptable stockout risk is 5 percent, we need to find the corresponding z-score.

Looking up the z-values table for a 5 percent risk (two-tailed test), the z-score is approximately 1.645.

Substituting the values into the formula:

Safety stock = (1.645 * 56)

≈ 92.12 kg

b. Reorder point (ROP):

The reorder point is the level of inventory at which an item should be reordered to ensure that it arrives before the stock runs out during the lead time. It can be calculated using the formula:

ROP = Expected demand during lead time + Safety stock

Substituting the given values:

ROP = 600 + 92

≈ 692 kg

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The expression that can be factored by grouping is pr + ps + qr + qs. We can group the terms into two groups, factor out the common factors from each group, and simplify the expression to get (p+q)(r+s). So, the correct answer is D).

The expression that could be factored by grouping is

pr + ps + qr + qs

To factor this expression by grouping, we can first group the first two terms and the last two terms

(pr + ps) + (qr + qs)

We can then factor out the common factors from each group

pr + ps = p(r+s)

qr + qs = q(r+s)

We can see that both groups have a common factor of (r+s), so we can further simplify the expression

(p+q)(r+s)

Therefore, the final factored form of the expression pr + ps + qr + qs is (p+q)(r+s).

None of the other expressions given can be factored by grouping.

For pq + ps - pr + pt, we cannot group any two terms that have a common factor. For pq + rs - pq + rs, we can simplify it as 2rs, but it cannot be factored by grouping. For pr + ps - qr - qs, we cannot group any two terms that have a common factor. So, the correct option is D).

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Answer:

  69 miles

Step-by-step explanation:

Put the number in place of the variable representing it and do the arithmetic.

  L = 41 +28 = 69

After 28 days, the length of the road is 69 miles.

Answer:

12 is to the right of -15 on a number line.

Step-by-step explanation:

Hope this helps! - CJ

Answer:

49.0?

Step-by-step explanation:

its probably wrong lol

I would say 50 meters

Answer:

7

Step-by-step explanation:

16-9=7

parralel lines

I kNoW I SPelLed dat WrOnG