Simplify quantity x squared plus 3 x plus 2 end quantity over quantity x plus 1. x + 2 x − 2 x2 + 1 x2 − 1

Answer:

The lesser integer is 9.

Step-by-step explanation:

Let the lesser integer be x then the greater is x+2

So, we have:

3x = 2(x+2) + 5

3x = 2x + 9

x = 9

So the numbers are 9 and 11.

Answer:

-5.4 degrees

Step-by-step explanation:

First get the time passed by subtracting 2:00 pm from 8:00 pm, which will give you 6 hrs, you can then multiuply 6 hrs by -3.4 (temp changed per hr) and you will get -20.4. You then add together -20.4 and 15 to get -5.4 degrees.

The function f is increasing on the interval (6, ∞).

The function f will be increasing in the intervals where f'(x) > 0.

To find these intervals, we can examine the sign of each factor of f'(x), which is (x + 1)²(x - 3)⁵(x - 6)⁴.

We can analyze the sign of f(x) by considering the factors individually:

(x+1)²: This factor is always positive since it is the square of a real number.

(x - 3)⁵: This factor is positive when x>3 and negative when x< 3.

(x - 6)⁴: This factor is positive when x>6 and  negative when x< 6.

We need to consider the overlapping regions of positivity for each factor.

When x>6, all three factors are positive, so  f ′ (x) is positive.

When 3<x<6: In this interval, the factor  (x+1)² is positive, but both (x−3)⁵ and (x−6)⁴ are negative.

Thus, f ′ (x) is negative.

When x<−1: In this interval,  (x+1)² is negative, while (x−3)⁵ and (x−6)⁴ are positive.

Hence, f ′ (x) is negative.

Therefore,  the function f(x) is increasing on the interval x>6.

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Answer:

Side 3 = a - 2

Step-by-step explanation:

Perimeter of a ∆ = sum of all the sides of a triangle

Perimeter of the given ∆ = 6a + 3 units

Side 1 = 2(a + 3)

Side 2 = 3a - 1

Side 3 = ?

Therefore:

Side 3 = Perimeter - sum of side 1 and 2

Thus:

Side 3 = 6a + 3 - [2(a + 3) + (3a - 1)]

Side 3 = 6a + 3 - [2a + 6 + 3a - 1]

Side 3 = 6a + 3 - [5a + 5]

Side 3 = 6a + 3 - 5a - 5

Side 3 = a - 2

Step-by-step explanation:

Answer:

$40 in euros!

Step-by-step explanation:

Congruency is a type of equivalence relation that states that two geometric figures are the same size and shape. In other words, if two figures are congruent, then all of their corresponding parts are the same size and shape. Therefore, if ⊙a ≅ ⊙v, then it can be concluded that a is congruent to v, and the congruency statements that can be made are a ≅ v, a ≅ ⊙v, and ⊙a ≅ v.

A. a ≅ v

D. a ≅ ⊙v

E. ⊙a ≅ v

Since the symbol ⊙ represents congruency, ⊙a ≅ ⊙v implies that a is congruent to v. Therefore, the congruency statements that can be made are a ≅ v, a ≅ ⊙v, and ⊙a ≅ v.

Congruency is a type of equivalence relation that states that two geometric figures are the same size and shape. In other words, if two figures are congruent, then all of their corresponding parts are the same size and shape. Therefore, if ⊙a ≅ ⊙v, then it can be concluded that a is congruent to v, and the congruency statements that can be made are a ≅ v, a ≅ ⊙v, and ⊙a ≅ v.

The complete question is :

Given , ⊙a ≅ ⊙v, what congruency statements can you make? Check all that apply.

A. a ≅ v

B. a ~ v

C. ⊙a ~ ⊙v

D. a ≅ ⊙v

E. ⊙a ≅ v

The correct answers are: A. a ≅ v, D. a ≅ ⊙v, and E. ⊙a ≅ v.

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The hypothesis test suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the  t-value (-1.732) is less than the critical value (-2.429).

Null hypothesis, The true mean number of people who log onto the app daily is equal to or less than 1 million.

Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.

Level of significance = 1%

We can use a one-sample t-test to test the hypothesis.

t = (X - μ) / (s / √n)

where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the values, we get

t = (998,946 - 1,000,000) / (23,876 / √65)

t = -1.732

Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the critical value is 2.429.

Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.

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The sensitivity of the portfolio to a 1% rise in inflation is approximately 0.8.

To determine the sensitivity of the portfolio to a 1% rise in inflation, we need to calculate the portfolio's sensitivity or beta with respect to inflation. Here are the steps in two parts:

Part 1: Calculate the Sensitivity of Stock A to Inflation

The sensitivity of Stock A to inflation (FINF) is the coefficient multiplying the inflation variable in the equation for Stock A's returns.

Sensitivity of Stock A to Inflation (βA) = -1

Part 2: Calculate the Sensitivity of Stock B to Inflation

The sensitivity of Stock B to inflation (FINF) is the coefficient multiplying the inflation variable in the equation for Stock B's returns.

Sensitivity of Stock B to Inflation (βB) = 2

The sensitivity or beta of a stock measures its responsiveness to changes in a specific variable, in this case, inflation. The beta indicates how much the stock's returns are expected to move in response to a 1% change in inflation.

In this scenario, Stock A has a sensitivity (beta) of -1 to inflation. This means that for every 1% increase in inflation, Stock A's returns are expected to decrease by 1%.

On the other hand, Stock B has a sensitivity (beta) of 2 to inflation. This indicates that for every 1% rise in inflation, Stock B's returns are expected to increase by 2%.

Since the portfolio consists of 40% in Stock A and 60% in Stock B, we can calculate the overall sensitivity of the portfolio to a 1% rise in inflation by using the weighted average of the individual sensitivities:

Portfolio Sensitivity to Inflation = (Weight of Stock A * Sensitivity of Stock A) + (Weight of Stock B * Sensitivity of Stock B)

= (0.4 * -1) + (0.6 * 2)

= -0.4 + 1.2

= 0.8

Therefore, the portfolio's sensitivity to a 1% rise in inflation is 0.8. This indicates that for every 1% increase in inflation, the portfolio's returns are expected to increase by 0.8%.

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Rounding to the nearest thousandth, the margin of error for this survey, expressed as a proportion, is approximately 0.020.

To calculate the margin of error for a survey, we can use the formula:

Margin of Error = Z × √((p × (1-p)) / n)

Where:

Z represents the z-score corresponding to the desired confidence level,

p represents the proportion of respondents who preferred candidate A,

n represents the sample size.

The sample size (n) is 1900, and the proportion of respondents who preferred candidate A is 1520/1900.

p = 1520/1900

≈ 0.8

We need to find the z-score corresponding to a 95% confidence level. For a 95% confidence level, the z-score is approximately 1.96.

Substituting the values into the formula:

Margin of Error = 1.96 × √((0.8 × (1-0.8)) / 1900)

Calculating the expression inside the square root:

(0.8 × (1-0.8)) ≈ 0.16

Margin of Error = 1.96 × √(0.16 / 1900)

Calculating the square root:

√(0.16 / 1900) ≈ 0.01016

Margin of Error = 1.96 × 0.01016

≈ 0.0199

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The probability that three of out nine cars need new brakes is 0.294  

Combination:

The combination is the process of selecting items from a group of objects where the order of objects does not matter. In simple words, we can say that it is a combination of n things in r times without repetition.

The formula for the combination of 'a' things from the set of n things without replacement is given

Here from the given problem,

Number of automobiles = 25

Number of automobiles that need new tune-ups = 15  

Number of automobiles that need new brakes = 10

Number of automobiles chosen at time = 9  

From above formula

The number of ways of selecting 9 cars from 25 cars

²⁵C₉ = 25!/9!(25 - 9)!

= 25!/9!(16)!  

= 2,042,975

The number of ways that can be chosen as 3 out of 9 cars that need breaks

Choosing 3 cars that need breaks from 10 cars = ¹⁰C₃

= 10!/3!(10 - 3)!  

= 10!/3!(7)!

= 120

Choosing the remaining 6 cars from the 15 groups of cars that need new tune-ups =  ¹⁵C₆

=  15!/6!(15 - 6)!  

=  15!/6!(6)!    

= 5,005

From above calculations

The number of ways that can be chosen as 3 out of 9 cars that need new  breaks  = 120 × 5,005

= 600600

As we know that

Probability of event = No of favorable outcomes / total outcomes  

The probability that three of them need new brakes

= 600600/2042975

= 0.294  

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Answer:

30 miles per 3 hours

Step-by-step explanation:

10 miles = 1 hour

10 x 3 = 30

Answer:

30 miles, if you times .5 by 3 it tells you 6 and then you times 5 by 6.

By permutation, in 95040  ways we can choose a starting lineup consisting of a center, a power forward, a shooting forward, a point guard, and a shooting guard

A permutation is a set up of things in a certain sequence. Here, the members of sets or their constituent parts are sorted in a linear or sequential manner.

Take the number of possibilities for each event and multiply it by itself X times, where X is the total number of events in the sequence, to find the number of permutations. For instance, four-character PINs have a total of 10 possible combinations because each digit can vary from 0 to 9.

\(12^P_{5} = \frac{12!}{(12-5)!} =\frac{12!}{5!} = 12 X 11 X 10 X 9 X 8 = 95040\)

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Answer:

1.5^2 = 2.25

(it looks like 1.5 but if it's 15 then it would be 225)

Step-by-step explanation:

1.5^2 means (1.5*1.5) you multiply the number by itself by how many it says to do. So if it were 1.5^52 you would multiply 1.5 by 1.5, 52 times.

a) To factor the quadratic expression x^2 - x - 20, let's first check if there is a greatest common factor (GCF) that can be factored out. In this case, there is no common factor other than 1.

Next, we need to find two numbers whose product is -20 and whose sum is -1 (coefficient of the x-term). By inspecting the factors of 20, we can determine that -5 and 4 satisfy these conditions.

Therefore, we can rewrite the quadratic expression as follows: x^2 - x - 20 = (x - 5)(x + 4)

b) For the quadratic expression x^2 - 13x + 42, let's again check if there is a GCF that can be factored out. In this case, there is no common factor other than 1.

Next, we need to find two numbers whose product is 42 and whose sum is -13 (coefficient of the x-term). By inspecting the factors of 42, we can determine that -6 and -7 satisfy these conditions.

Therefore, we can rewrite the quadratic expression as follows: x^2 - 13x + 42 = (x - 6)(x - 7)

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Answer:

i don't know how to leave questions, but you're missing some information to complete the question

Step-by-step explanation:

Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

The given expression can be written in factor form as 4a(2ab)

Given:

2³a²b to be expressed in factor form

To express the above given expression in factor form follow the steps below;

Finally, the given expression can be written in factor form as 4a(2ab)

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The optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

To solve this linear programming problem using the Simplex method, we first need to convert it into standard form by introducing slack variables.

Our problem can be rewritten as follows:

Minimize w = 9x1 + 6x2

Subject to:

x1 + 2x2 + x3 = 5

2x1 + 2x2 + x4 = 8

x1 + 2x2 + 2x3 = 6

where x1, x2, x3, and x4 are all non-negative variables.

Next, we set up the initial simplex tableau:

Basic Variables x1 x2 x3 x4 RHS

x3 1 2 1 0 5

x4 2 2 0 1 8

x5 1 2 2 0 6

z -9 -6 0 0 0

The last row represents the coefficients of the objective function. The negative values in the z-row indicate that we are minimizing the objective function.

To find the pivot column, we look for the most negative coefficient in the z-row. In this case, the most negative coefficient is -9, which corresponds to x1. Therefore, x1 is our entering variable.

To find the pivot row, we calculate the ratios of the RHS values to the coefficients of the entering variable in each row. The smallest positive ratio corresponds to the pivot row. In this case, the ratios are:

Row 1: 5/1 = 5

Row 2: 8/2 = 4

Row 3: 6/1 = 6

The smallest positive ratio is 4, which corresponds to row 2. Therefore, x4 is our exiting variable.

To perform the pivot operation, we divide row 2 by 2 to make the coefficient of x1 equal to 1:

Basic Variables x1 x2 x3 x4 RHS

x3 0 1 1 -1 1

x1 1 1 0 1/2 4

x5 0 1 2 -1 2

z 0 -3 9 9/2 -18

We repeat the process until all coefficients in the z-row are non-negative. In this case, we can stop here because all coefficients in the z-row are non-negative.

Therefore, the optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

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Explanatory variable: The type of pill the men took each day.

Response variable: Whether a subject had a heart attack.

We have been given that :

Participated candidates are 400

Men are divided randomly so we find out explanatory and response  variable.

The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.

Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.

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X is equal to 8 and Y is equal to 3.

A pair that has two values stated in a certain sequence between parenthesis is known as an ordered pair. It is made up of the x coordinate (abscissa) and the y coordinate (ordinate). For greater visual comprehension, it helps to locate a point on the Cartesian plane.

Each domain element should have exactly one picture for the function, therefore the newest element in the column of x shouldn't be 6,3,9,7. Thus, we have two options for x = 8 or 12

Taking 8 will allow us to add another to the column on y, making y equal to 3.

thus, x = 8 and y = 3.

When an ordered pair is used, the numbers do not repeat.

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Answer:

3b/2 + 3

Step-by-step explanation:

The formula to calculate perimeter of rectangle is 2l + 2w

The length is half the width so length is 1/2 (b/2 +1), which when simplified is b/4 + 1/2

Using the formula to calculate perimeter you can substitute and calculate

p= 2l + 2w

p= 2(b/4 + 1/2) + 2(b/2 + 1)

p= 2b/4 +2/2 + 2b/2 +2

p= 1/2b + 1 + b + 2

p= 3/2b + 3

Simplified it's 3b/2 +3

Solution:

Given that;

The students hold a carwash.

They charge $5 per car. And, if they wash 23 cars, te

Answer: y = 2x+8

Check out this graph I supplied you with!

Given:

Number of green peas = 475

Number of yellow peas = 193

Let's find the 94% confidence interval to estimate the percentage of yellow peas.

Where:

Total number of peas = 475 + 193 = 668

For the sample proportion, we have:

For a 94% confidence interval, the significance level will be:

1 - 0.94 = 0.06

For the critical value, using the z-table, we have:

Now, to find the 94% confidence interval, apply the formula::

Where:

To find the margin of error E, we have:

Thus, we have:

Hence the confidence interval will be:

Lower limit = 0.2559 ==> 25.59%

Upper limit = 0.3219 ==> 32.19 %

The confidence interval does not contain 0.25, hence we can say that the true results contradicts the expectations.

ANSWER:

The confidence interval does not contain the expectation of 25%, hence, the true results contradicts the expectation.

Answer:51 cm^2

Step-by-step explanation:

You can consider this as a circle.

To find the area of a given sector of a circle you have to use this formula  

Angle/360 x  π x r ^ 2

in this case you can find the angle of one side by substracting 180 from 120

180-120=60

then

60/260 x  π x 7^2 = 25.6563 rounded of to 26 , multiply this by 2 to get the total area .

total area = 51 cm^2

If a number cube is rolled 25 times and 6 appears only four times, then the experimental probability of getting 6 is 4/25.

The experimental probability of an event happening is the number of times the event occurred divided by the total number of trials. In this case, a number cube is rolled 25 times and lands on 6 four times. Here are the steps to determine the experimental probability of landing on 6:

So, the experimental probability of landing on 6 is 4/25, which means that if we roll the number cube many more times, we would expect to get a 6 approximately 4 out of every 25 rolls.

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The given system of equations is:

As y=y then we can equal both equations and solve for x as follows:

Now, we have an equation in the form:

Where a=2, b=-16 and c=-3, we can apply the quadratic formula:

Replace the a, b and c values and solve to find the x-values:

Then the x-values are: 8.18 and -0.18, and its multiplication is:

Answer: -1.5

Answer:

St rt ok is et cell pic ch se art on FB