Theorems and Proofs problemIll send a picture of the question

Answer:

  53

Step-by-step explanation:

You want the value of a^2 +b^2, given that 'a' and 'b' are roots of the polynomial x^2 +7x -2.

If the roots are 'a' and 'b', then the factored form is ...

  (x -a)(x -b) = x^2 -(a+b)x +ab

Comparing this to the given polynomial, we see that ...

  -(a+b) = 7

  ab = -2

The expression a^2 +b^2 can be written as the sum ...

  a^2 +b^2 = a^2 +2ab +b^2 -2ab = (a+b)^2 -2ab

Using the values of (a+b) and ab from above, we see that ...

  a^2 +b^2 = (-7)^2 -2(-2) = 49 +4 = 53

The given expression has a value of 53.

The number of pages that Kamala needs to reach each day is p ≥ 30.

Here are inequality signs and what they mean:

The inequality sign that would be used is ≥. This is because the pages Kamala needs to read each day  can be equal to 235 or greater than 235

25 + 7p ≥ 235

Combine similar terms: 7p ≥ 235 - 25

Add similar terms:  7p ≥ 210

Divide both sides of the equation by 7: p ≥ 210 / 7

p ≥ 30

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In terms of π, the area of the circle is 2.25π yd².

So, the radius of circle(r) = 1.5 yd

The area of the circle is given by:

Therefore, in terms of π, the area of the circle is 2.25π yd².

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The exponential function has the following form:

The function goes through the points ( 0, 19) and ( 2, 171 )

We will use the points to find the values of a and b

Substitute with the point ( 2, 171 ) and the value of a to find b

So, the answer will be:

The probability that the score of a randomly selected examinee is less than 370 is 0.113

Mean of the gmat score = 410

Standard deviation of the deviation = 33

The randomly selected examinee be X ,

Thus X = 370

So , we need to find the probability that the score of a randomly selected examinee is less than 370 i.e.

   P(X < 370)

Now , let us the z-score with normal distribution formula

        Z = (X - μ) / σ

        Z = (370 - 410) / 33

        Z = -40 / 33

       Z = -1.21

Thus P(X < 370) = P(Z < -1.21)

From the z - table , we can get that

         P(Z < -1.21) = 0.11314

By rounding off to three decimals ,

          P(Z < -1.21) = 0.113

Therefore , the probability of Z< -1.21 is 0.113

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Based on the amount of the loan, and the number of periods as well as the APR, the total amount of the monthly payment would be $6,423.

The monthly payments for the loan would be constant so they can be considered to be annuities.

The value of these annuities would be:

Present value of annuity = Annuity x ( 1 - (1 + rate)^-number of periods) / rate

6,100 = Annuity x (1 - (1 + 5%/12)⁻⁽²ˣ¹²⁾ / 0.05/12)

Annuity = 6,100 / 22.793898393955992921598741250451

= $267.62

The total monthly payment is:

= 267.62 x 12 x 2 years

= $6,423

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Organizations in College Edward Waters University include

College Edward waters university was the first independent higher institution and  black college located in Florida state of the United States of America.

The institution was found in 1866 in Jacksonville, Florida. It is owned by African Methodist Episcopal Church which is a Christian denomination.

Organizations refers to arrangement where people come together for a defined purpose. Organizations so exist in this high institution of learning

Delta Sigma Pi, Theta Omega Chapter is one of the organizations in this institution. The purpose of this organization is aid students in studying business in several ways and financial aids is one of them.

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As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile

We can calculate the total distance traveled by a body with position function s (t) if it moves along a coordinate line without changing direction from t = a to t = b. If the body changes direction during the journey, we must integrate the body's speed |v (t)| to find the total distance traveled.

Therefore,

We know Mary spent only a third of the time coming from school as she did going because she traveled three times as fast coming from school as she did going to school (6 miles per hour versus 2 miles per hour). If x represents the time it took her to get to school, then x/3 represents the time it took her to return.

Knowing that the total trip took 1 hour, we have:

x + x/3 = 1

3x/3 + 1x/3 = 1

4x/3 = 1

x  = 3/4

So we know it took Mary 3/4 of an hour to get to school (and 1/4 of an hour to get home).

Remembering that distance = rate × time, Mary's commute to school was (2 miles per hour) × (3/4 of an hour) = 3/2 mile. Furthermore, because she returned via the same route, she must have traveled 3/2 of a mile.

As a result, the total distance traveled by Mary in her round trip is 3/2 mile + 3/2 mile = 6/2 mile = 3 mile.

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Answer:

To stay within budget, she must use 3.9 gigabytes.

Caroline can use approximately 3.9 gigabytes of data while staying within her budget of $74 per month.

Let's assume the number of gigabytes of data Caroline can use while staying within her budget is represented by the variable "x."

The flat cost per month is $54.50, and Caroline pays an additional $5 per gigabyte.

If she wants to keep her bill at $74 per month, the equation can be set up as follows:

54.50 + 5x = 74

To solve for "x," we can isolate the variable on one side of the equation. First, subtract 54.50 from both sides:

5x = 74 - 54.50

5x = 19.50

Finally, divide both sides by 5:

x = 19.50 / 5

Simplifying the division gives us:

x = 3.9

Therefore, Caroline can use approximately 3.9 gigabytes of data while staying within her budget of $74 per month.

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Answer:

W=x/7+ 8z/7 + 4/7

Step-by-step explanation:

The cost of the jam Elmo uses to make the sandwiches =$1.65

What is the cost of the jam Elmo uses to make the sandwiches?

B globs of Peanut butter at 4 cents = 4B

J blobs of Jam at 5 cents = 5J

The number of sandwiches is given by the linear equation,

N(4B + 5J ) =$ 2.53

N(4B + 5J ) = 253 cents    ---(1)

The factors of 253 = 1, 11, 23, 253.

Since N > 1 , N is 11 or 23

Considering N = 11

11(4B + 5J ) = 253

4B + 5J  = 23   ---(2)

The possible values of B and J to satisfy the linear equation:

B = 2 and J = 3

Substituting B and J in (2)

4B + 5J  = 23

4 (2) + 5(3) = 23

8 + 15 = 23

23 = 23

The linear equation is verified.

The cost of jam Elmo uses to make the sandwiches =N( 5J)

                                                                                       =11 (5*3)

                                                                                       = 11 *15

                                                                                        = 165 cents or $1.65

The complete question is:

elmo makes N sandwiches for a fundraiser. for each sandwich he uses B globs of peanut butter at 4 cents per glob and J blobs of jam at 5 cents per blob. the cost of the peanut butter and jam to make all the sandwiches is $2.53. assume that B, J, and N are positive integers with N>1. what is the cost of the jam elmo uses to make the sandwiches?

What is a linear equation?

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Answer:

Step-by-step explanation:

I believe the answer is D!

DE will be equal to AB, then DE=8

Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. The required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.

The triangle exists a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

Angles 1 and 2 are remote interior angles while angle 3 exists as a remote exterior angle. So there exists a property of a triangle in that the sum of the remote interior angles exists equivalent to the remote exterior angle.

∠1 +∠2 = ∠3.

Therefore, the required relationship between the angles 1, 2, and 3 is ∠1 +∠2 = ∠3.

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The next place value on the right should be used to round a number to the closest tenth (the hundredths). Simply take away all the digits to the right if it's 4 or fewer. Remove all the digits to the right after adding 1 to the digit in the tenths position if the number is five or above.

To what decimal place do you round?

Examine the hundredth number to determine the decimal number's nearest tenth. Add one to the tenth value if the number is more than 5. Remove all the numbers that are present after the tenth place if the value is less than 5, but keep the tenth place value in place otherwise. As an illustration, if you want to round up to the nearest.

Triangle Area Solver

A=hbb

2

b Base

Enter value

hb Height

Enter value

γ

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Answer: 11

Step-by-step explanation:

5 + 7(6-4) - 2(5 - 1)

P E M/D A/S

5 + 7(2) - 2(4)

P E M/D A/S

5 + 14 - 8

P E M/D A/S

11

Answer: B

Step-by-step explanation:

The range of values for F(x) would be on the y - axis, so go up on the y - axis to find the points, and since it is not a line it has no inequality symbols, and how sideways it is doesn't matter, it is only how tall it is that matters because it is on the y - axis.

Exact number of steps taken by Anne to cross the road either by striding 80cm or by striding 70cm , then the least width of the road is equal to 5.6meters.

As given in the question,

Anne takes exact number of steps to cross the road either by striding 80cm or by striding 70cm.

Conversion of the units

1 meter = 100 centimeters

1 centimeter = 1/100 meter

80 cm = 80 /100

          = 0.8 meters

70 cm = 70 /100

          =0.7 meters

Least width of the road is calculated by finding least common multiple of 0.8 meters and 0.7 meters

0.8 = 8 × (1/10)

0.7 = 7 × (1/10)

least common multiple = 7 × 8 × (1/10)

                                    = 5.6 meters

Therefore, exact number of steps taken by Anne to cross the road either by striding 80cm or by striding 70cm , then the least width of the road is equal to 5.6meters.

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The probability that the mean of a sample of 78 computers would be less than 97.94 months exists 0.883.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

Let the given values be

[tex]\mu[/tex] = 99, [tex]$\sigma[/tex] = 8

Let x be the random variable that represents the life of a computer.

Sample size: n = 69

Then, the z-score corresponds to x = 97.94 will be :-

[tex]$z=\frac{97.94-99}{\frac{8}{\sqrt{69}} \quad[\because} \quad z=\frac{x-\mu}{\left.\frac{\sigma}{\sqrt{n}}\right]}$[/tex]

z = -1.10062

Required probability ( using standard z-value table ) :-

P(x < 97.94) = P(z < -1.10) = 1 - P(z < 1.10)

= 1 - 0.1170 = 0.883

Therefore, the probability that the mean of a sample of 78 computers would be less than 97.94 months exists 0.883.

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The prices for jeans and shirts are $6 and $6

Given that:

3 pairs of jeans and 7 shirts for $60.

And 2 pairs of jeans and 3 shirts for $30.

Let jeans be x

Let shirts be y

3x + 7y = 60.... eq 1

2x + 3y = 30...... eq 2

Let us make x the subject formula from equation 2

2x = 30-3y

x= (30-3y)/2..... eq 3

Put the value of x into equation 1

3 * (30-3y)/2 + 7y = 60

(90- 9y)/2 + 7y = 60

45 - 4.5y + 7y = 60

2.5y =15

y = 6

Then, put the value of y into eq 3

x= (30-3(6))/2

x= 15 - 9

x= 6

Hence, we can see that the values of x and y are 6 apiece.

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Answer:

yeah it's correct , very much well

ANSWER

$24

EXPLANATION

You had $30 yesterday and you spent 20% of it today.

Since you spent 20% of it, the percentage you will have left is:

100 - 20 = 80%

So, you have 80% of $30.

That is:

You have $24 left.

Answer:

1.95 hours or 1 hour and 57 minutes.

Step-by-step explanation:

You can read the problem as 13% of the battery. "Of" is a keyword that means to multiply.

The battery lasts 15 hours, so multiply by 13%. You need to change 13% to a decimal first by dividing it by 100, or moving the decimal left two places.

13% = 0.13

Now solve.

0.13 × 15 = 1.95

If you need to convert the 0.95 to minutes, multiply it by 60 since there are 60 minutes in an hour.

0.95 x 60 = 57 minutes.

The box plot that matches the data is a box and whisker plot is shown above a number line that extends from 0 to 20 with 1-unit markings. The box extends from 4 to 8, with the median at 5. There is also a point marked at 7. The whisker on the left extends from 2 to 4. The whisker on the right extends from 8 to 12.

A box and whisker plot is a graph that is made up of two lines and a box. The two lines are known as whiskers. The end of the first whisker is the minimum value and the end of the second whisker is the maximum value.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

The data : 2, 3, 4, 4, 5, 5, 7, 8, 9, 12

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Answer:

9

Step-by-step explanation:

because in one hour it fills 18÷2 =9.

Answer: It's 10 because 20* Divided by 2 is 10

Step-by-step explanation:

2) w = 16.5 mis the equation represents the relationship shown in the table.

3) The number of minutes is proportional to the number of pages, with a unit rate of 2.25 minutes per page is the best statement describes the relationship in the table.

When determining if two ratios or fractions are equivalent, the proportion formula is utilized. We can calculate the missing value by dividing the given values. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, a:b::c: d = a/b = c/d.

2) Divide the number of  gallons of water with  number of minutes

66/4 = 16.5

So, the equation represents the relationship shown in the table is

w = 16.5 m

3) Divide number of minutes by number of pages, we get

9/4 = 2.25

13.5/6 = 2.25

So, option (B) best describes the relationship in the table.

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The total amount earned from mowing lawns by George is $50

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

Earnings percentage = 140%

Angel total earnings in mowing lawns = $70

The amount earned from mowing lawns by George is then calculated as

Angel total earnings in mowing lawns = Earnings percentage  x Total amount earned from mowing lawns by George

Substitute the known values in the above equation

So, we have

70 = 140% x Total amount earned from mowing lawns by George

Divide both sides by 140%

Total amount earned from mowing lawns by George = 50

Hence, the total amount is $50

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Step-by-step explanation:  Check the photo

Answer:

x = -2

Step-by-step explanation:

7/(2x) - 2/x + 1 = 1/4

7/(2x) - 4/(2x) + 1 = 1/4

(7-4)/(2x) = 1/4 - 1

3/(2x) = 1/4 - 4/4

3/(2x) = - 3/4

3 = (-3/4)(2x)

3 = -6x/4

3*4 = -6x

12 = -6x

12/-6 = x

-2 = x

Check:

7/(2*-2) - 2/-2 + 1 = 1/4

7/-4 + 1 + 1 = 1/4

-7/4 + 2 = 1/4

-7/4 + 8/4 = 1/4

The population mean, exists even comprehended as the average or mean of all values in a population, exist determined by summing all population values and dividing that total by the number of population values.

The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The sign μ stands for the population mean.

The population mean, also known as the average or mean of all values in a population, is determined by summing all population values (represented by the symbol X) and dividing that total by the number of population values (represented by the symbol N).

Therefore, the correct answer is option a. less than the population mean.

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