2. solve the equation p2 4p = 1 by completing the square. show your work.

Answer:

Step-by-step explanation:

the 2nd one

Answer:

m = -3

Step-by-step explanation:

4(4m - 3) - 1(m - 5) = -52

Distribute both expressions (don't forget that the 1 is -1, so distribute -1.)

16m - 12 - m + 5 = -52
Add like terms

15m - 7 = -52

Add 7 on both sides

15m = -45

Divide by 15 on both sides

m = -3

The correct expression that is equivalent to the algebraic expression -5x - 15 + 25x - 30 is -5(-4x + 9).

We shall simplify the given algebraic expression by carrying out basic mathematics operations as follows;

Given: -5x - 15 + 25x - 30

we group like terms together

25x - 5x - 15 - 30

20x - 45

the number 5 is a common factor of 20x and 45, so we have that;

5 × 4x - 5 × 9

by factoring out 5

5(4x - 9)

also;

5(4x - 9) = -5(-4x + 9)

Therefore, -5(-4x + 9) is an equivalent expression to the algebraic expression -5x - 15 + 25x - 30

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Answer:

i. X represents the difference between the mean entry-level mechanical engineering salary and the mean entry-level electrical engineering salary.

ii. t distribution with df = 96

iii. t = -2.38

iv. p-value = 0.0190

v. Alpha = 0.05

i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).

ii. We used the t-distribution for the test due to unknown population standard deviations and relatively small sample sizes.

iii. The calculated test statistic is -2.1095.

iv. The degrees of freedom for the t-distribution are approximately 113242.

v. The p-value associated with the test statistic and degrees of freedom is approximately 0.0001.

i. The random variable X - Xe represents the difference in mean salaries between mechanical engineering (X) and electrical engineering (Xe).

ii. We will use the t-distribution for the test since the population standard deviations are unknown, and the sample sizes are relatively small (less than 30).

iii. The test statistic for this hypothesis test is calculated as:

[tex]t = (X - Xe) / \sqrt(s_m^2 / n_m) + (s_e^2 / n_e))}[/tex]

Where:

X = sample mean for mechanical engineering

Xe = sample mean for electrical engineering

Sm = standard deviation for mechanical engineering

Se= standard deviation for electrical engineering

nm = sample size for mechanical engineering

ne = sample size for electrical engineering

t = (46100 - 46900) / √(3450² / 46) + (4230² / 52))

= -800 / √(3450² / 46) + (4230² / 52))

= -800 / 379.4303

= -2.1095

iv.

Calculating the degrees of freedom:

df = (3450² / 46 + 4230² / 52)² / ((3450² / 46)² / (46 - 1) + (4230² / 52)² / (52 - 1))

= (119023.913 + 180714.2308)² / ((119023.913)² / 45 + (180714.2308)² / 51)

= 113242.1436

The degrees of freedom are approximately 113242.

Now, we need to find the p-value associated with the test statistic and degrees of freedom.

We can use a t-distribution table to look up the p-value.

Since the test is one-tailed and the test statistic is negative, we will look up the p-value in the left tail of the t-distribution with the given degrees of freedom.

Assuming the p-value is less than 0.0001, we can state that the p-value is approximately 0.0001.

v. To conduct a hypothesis test at the 5% level to determine if you agree that the mean entry- level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.

So, the significance level (alpha) is given as 5%.

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The correct option is (a). basic statistical tests the technique is likely to discover a value that is 10x larger than the next highest value in a dataset of 500,000 records is basic statistical tests.

Statistical assessments are utilized in speculation trying out. They may be used to: decide whether a predictor variable has a statistically substantial relationship with an outcome variable. estimate the distinction between or more groups.

Two main statistical techniques are used in data analysis: descriptive facts, which summarize records of the usage of indexes along with suggestions and median and every other is inferential facts, which draw conclusions from records of the usage of statistical assessments including pupil's t-take look at.

In fact, there are foremost kinds of assessments: parametric and non-parametric. each sort of assessment is used to make inferences about a populace based on a sample. The difference between the 2 styles of tests lies within the assumptions that they make about the records.

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6.908 is greater than 6.098 as the second digit from the left is greater.

We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, are two numbers 6.098 and 6.908.

Now, starting from left both the numbers have the same digit so we can't

differentiate.

The digit after the decimal place to the first number is 0 and on the second it is 9 so definitely, the second number is greater.

∴ 6.098 < 6.908.

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The square root √(7 · x - 4) = 2 has a solution for the variable x is 8 / 7.

In this problem, we find a square root whose solution for the variable x has to be found solely by algebra properties. First, write the radical equation:

√(7 · x - 4) = 2

Second, elevate to the square of the expression:

7 · x - 4 = 4

Third, clear the variable x by algebra properties:

7 · x = 8

x = 8 / 7

The solution to the square root is equal to 8 / 7.

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Answer:

You can make up to "9" different 5-digit codes

Answer:

-1/3

Step-by-step explanation:

3-6/5-(-4) = -3/9

simplify -3/9

-1/3

Answer:

x = 10

y = 15

Step-by-step explanation:

Start with y.

The smaller triangle has a right angle and two congruent legs.

Since the legs are congruent, then the opposite angles are also congruent.

The measures of the 3 angles of the right triangle are:

3y, 3y, 90

The sum of the measures of the angles of a triangle is 180°.

3y + 3y + 90 = 180

6y + 90 = 180

6y = 90

y = 15

The larger triangle has 2 congruent sides. The opposite angles are congruent. Each of the congruent angles measures 2x + 3y. The angle above measures 50°.

2x + 3y + 2x + 3y + 50 = 180

4x + 6y + 50 = 180

4x + 6y = 130

We know from above that y = 15.

4x + 6(15) = 130

4x + 90 = 130

4x = 40

x = 10

Answer:

y-3= -11/6(x+1)

Step-by-step explanation:

y-3 = -11/6(x-(-1)

y-3 = -11/6(x+1)

Extrapolation is the process of making predictions outside the range of numbers by using the regression line.

Extrapolation refers to using the regression line to produce predictions outside of the data's range.

Thus,despite the correlation maybe having a linear shape within the range being observed, this method can be risky because it's possible that it wouldn't hold true over a wider range.

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Answer:

Yes you are right

Step-by-step explanation:

It equals 5.45

The predicted income for a 43-year- old who left school after the 10th grade is in option (A) i.e.  $35,700.

Given that:

Educational status is a dummy variable with 0 = high school or less and 1 = some education beyond high school

Regression equation = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e

X1 => Age; X3→ (0 if high school or less and 1 if some education beyond high school)

X2 => (X2 * X3)→ (0 if high school or less and X1 if some education beyond high school)

Given: X1 = 43, X2 and X3 = 0

Putting these values in the below equation.

y = 14.2 + 0.5 X1 + 1.7X2 + 0.1X3 + e

y = 14.2 + (0.5 x 43) + 1.7 x 0 + .1 x 0 + e

y = 14.2 + (0.5 x 43) + 0 + 0 + e

y = 14.2 + 21.5 + e

y = 35.7 + e

The value of e can be neglected as it is a constant value.

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In multiple linear regression analysis, the correlation among independent variables is termed multicollinearity i.e. option C.

Definition:

a) Homoscedasticity: Homoscedasticity, also known as homogeneity of variances, is the presumption that variations in various groups being compared are equivalent or comparable.

b) Linearity: A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear. Proportionality and linearity are closely linked concepts.

c) Multicollinearity: Multiple independent variables in a model that are correlating from a statistical concept known as multicollinearity.

d) Adjusted Coefficient of Determination: The number of variables in a data collection is taken into account when calculating the adjusted coefficient of determination (also known as adjusted R-squared). Additionally, it penalizes you for any points that deviate from the model.

Hence, the required choice is Option C.

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Answer of the following questions for given mean and standard deviation along with sample size are:

a. Null hypothesis , H₀: μ = 4.00

   Alternative hypothesis, H₁ : μ > 4.00

b. Value of test statistic is 1.647

c. Conclusion is no evidence to conclude mean wait time for customer is longer than 4.00 minutes.

As given in the question,

Wait time for customer is at most 4.00 minutes

a. Null hypothesis is given by

H₀: μ = 4.00

Mean time is not exceeding the requirement

Alternative hypothesis is given by:

H₁ : μ > 4.00

b. Value of test statistic is given by :

([tex]\bar{x}[/tex] - μ₀) ÷ ( s/√n )

Sample mean [tex]\bar{x}[/tex] = 4.14

Population mean μ₀ = 4.00

Standard deviation 's' = 0.55 minutes

Sample size 'n' = 42

Substitute the value in the formula we get,

(4.14 - 4.00) ÷ (0.55/ √42)

= 0.14 / (0.55/ 6.5)

=0.14/ 0.085

= 1.647

c. α = 1 - 98%

   = 1 - 0.98

   = 0.02

Decision value limit :

Reject H₀ ; if P value < α

Using table ,

P value = P(Z < 1.647)

              = 0.04997

⇒P value = 0.04997

0.04997 > 0.02

Here P value > α

Fail to reject Null hypothesis .

Therefore, from the given standard deviation and mean conclusion is that there is no sufficient evidence to prove that mean wait time for customers is longer than 4.00.

The complete question is:

The board of a major credit card company requires that the mean wait time for customers when they call customer service is at most 4.00 minutes. to make sure that the mean wait time is not exceeding the requirement, an assistant manager tracks the wait times of 42 randomly selected calls. the mean wait time was calculated to be 4.14 minutes. assuming the population standard deviation is 0.55 minutes, is there sufficient evidence to say that the mean wait time for customers is longer than 4.00 minutes with a 98% level of confidence?

1. State the null and alternative hypotheses for the test.

2. Compute the value of the test statistic.

3. Draw a conclusion and interpret the decision.

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Answer:

n = 15

Step-by-step explanation:

the triangles are similar so the correspondent sides are proportional

2: 5 = 6 : n

n = 6 x 5 /2

n = 3 x 5

n = 15

Answer:

$400

Step-by-step explanation:

y= 320×(1+0.25)=400

The college sophomores analysed by Parker represent demographics.

Demographics is defined as the statistics concerned with characteristics and population of any particular group. Inspecting the question, we see the Parker travels multiple countries focussing on sophomores.

Hence, sophomores are specific population being studied thus representing demographics. They will be represented as statistical data. There are multiple examples of demographics characteristics such as age, religion, gender, ethnicity, disability status, home ownership, income, education, psychiatric diagnosis and many others.

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Answer: 4:1

Step-by-step explanation:

We know that there are 16 squares in 4 circles, so the ratio is 16:4 and we can simplify this ratio by dividing by 4 which equal 4:1

If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!

Answer:  The correct answer is b = √13 or b = −√13

Step-by-step explanation:

When factoring squared variables or numbers, use the square root

b^2 = 13

Take the square root of both sides

√b^2 = √13

b = √13 or b = −√13

The equation for the parabola is  y = (5/3)(x + 2)(x - 1.2)

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about mathematical equations.

Remove parentheses from each side of the equation and combine similar terms to make it simpler.

To separate the variable term on one side of the equation, use addition or subtraction.

To find the variable, use division or multiplication.

y = A [x - (-2)] (x - 1.2)

y = A(x + 2)(x - 1.2)

At the y-intercept,

-4 = A(0 + 2)(0 - 1.2)

-4 = -2.4A

A = 4/2.4 = 5/3

y = (5/3)(x + 2)(x - 1.2)

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The steps that are used to solve the above equation by substitution include the following:

1.) X = 11 + 2y

2.) -7 ( 2y + 11) -2y = -13

3.) -14y -77- 2y = -13

4.) -16y - 77 = -13

5.) -16y = 64

6.) y= -4

7.) X = 2(-4) + 11 --> X = 3

8.) (3, -4)

A substitution equation is defined as the type of equation that involves solving the equation for one variable, and substituting the value of the variable in the other equation.

The given equation is as follows;

-7x -2y = -13

X - 2y = 11.

To solve for X the following is done;

X = 2y + 11

Substitute X = 2y + 11 into equation 1

-7 ( 2y + 11) -2y = -13

Multiple out to open the brackets;

= -14y -77- 2y = -13

= -16y - 77 = -13

= -16y = 64

= y= -4

Then substitute y = -4 into equation two as follows;

X = 2(-4) + 11

X = 3

Therefore, y = -4, while X = 3 that is ( 3,-4)

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If the surface area of the cylinder is 8cm , then the largest possible volume of such cylinder is (16/3)√(2/3π)  cubic units  .

In the question ,

it is given that ,

the cylinder is an open top ,

given that surface area = 8cm² ,

So , the surface area is = 2πrh + πr²,

8 = 2πrh + πr²

So , h = (8 - πr²)/2πr ,

the volume of the cylinder is (V) = πr²h ,

Substituting the value of h ,

we get ,

V = (8r - πr³)/2,

to find the largest volume , we differentiate it with respect to "r" and equate to 0 ,

we get ,

(8r - πr³)/2 = 0

On Simplifying we get ,

r = √(8/3π) ,

the volume is maximum when r = √(8/3π) ,

So , Volume is = ( 8(√8/3π) - π√(8/3π)³)/2

V = 4(√(8/3π)) - (4/3)(√(8/3π))

V = (8/3)√(8/3π)

V = (16/3)√(2/3π)  cubic units .

Therefore , the maximum volume is (16/3)√(2/3π)  cubic units  .

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Answer:

B. 21

Step-by-step explanation:

Composite numbers have more than two factors.

Answer: 21

Step-by-step explanation:

Juliet was charged $18 for driving 120 miles.

Given,

The rent of car per day = $80

The charge for per miles driven = $0.15

Juliet was charged a total of $98 for the rental and mileage.

We have to find the total miles of driving;

Here,

Charge for miles driven = Total charge - Rent of car for a day

Charge for miles driven = 98 - 80

Charge for miles driven = $18

Now,

Total miles driven = Charge for miles driven / Charge for one mile

Total miles driven = 18/0.15

Total miles driven = 120

That is,

Juliet was charged $18 for 120 miles of driving.

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Answer:

15 weeks.........

Step-by-step explanation:

3×15=45

Answer: The answers to the first page

Step-by-step explanation:

Question 1

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

6

−48

​ >x

Divide −48 by 6 to get −8.

−8>x

Swap sides so that all variable terms are on the left-hand side. This changes the sign direction.

x<−8

Question 2

−3x+8>11

Subtract 8 from both sides.

−3x>11−8

Subtract 8 from 11 to get 3.

−3x>3

Divide both sides by −3. Since −3 is negative, the inequality direction is changed.

x<

−3

3

​Divide 3 by −3 to get −1.

x<−1

Question 3

15x+60>240

Subtract 60 from both sides.

15x>240−60

Subtract 60 from 240 to get 180.

15x>180

Divide both sides by 15. Since 15 is positive, the inequality direction remains the same.

x>

15

180

​Divide 180 by 15 to get 12.

x>12

Question 4

3rd answer choice

Question 5

First, let's calculate how many miles he has left.

80 - 14 = 66

Now, to figure out how many miles a day in 6 days, divide.

66/6 = 11

Xavier should bike 11 miles on each of the 6 remaining days.

Answer: It's ten...please give me brainliest. I'm begging you.

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

a = 3; b = 5

3a + b − 4 =

= 3(3) + 5 - 4

= 9 + 5 - 4

= 14 - 4

= 10