A college entrance exam has a mean of 500 and a standard deviation of 100 in the population. A small liberal arts college has 100 applicants with a mean of 510. The college wants to determine whether its applicants have significantly higher scores than the general population of applicants. The data analyst obtains a t statistic of 1. 70 and a one-tailed probability of. 4. What would the probability be if the analyst performed a two-tailed test?

The tangent of <S is 8/15

Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).

Given:

ST = 68

UT = 60

so, SU = √ST² - UT²

           = √68² - 60²

           = √4624  - 3600

           = √1024

           = 32

So, Tangent of <S = P/ B

tan S = SU / UT

tan S = 32 / 60

tan S = 8/15

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Dalton flies the plane at a speed of 251 mph when there is no wind.

To solve this proble,m we can use the formula for distance, which is distance = speed × time. We can also use the fact that the speed of the plane with the wind is the sum of the speed of the plane without the wind and the wind speed, and the speed of the plane against the wind is the difference between the speed of the plane without the wind and the wind speed.

Let x be the speed of the plane without the wind, and t be the time it takes for the return trip with the wind. Then we can write the following equations:

4661 = (x - 10) × (t + 20)  (1) for the trip against the wind
4661 = (x + 10) × t  (2) for the return trip with the wind

Multiplying equation (2) by (t + 20) and subtracting equation (1) from it, we get:

4661t + 93220 = 4661t + 20x^2 + 200x - 200x - 200
20x^2 = 93220
x^2 = 4661
x = 251

Therefore, Dalton flies the plane at a speed of 251 mph when there is no wind.

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That the complex number 5-i is indeed a solution of the equation [tex]x^2-10x+26=0[/tex].

To determine whether the complex number 5-i is a solution of the equation [tex]x^2-10x+26=0[/tex], we can substitute the value of x with the complex number and see if the equation holds true.

Substituting [tex]x = 5-i[/tex] into the equation:

[tex](5-i)^2 - 10(5-i) + 26 = 0[/tex]

Expanding the squared term:

[tex]25 - 10i + i^2 - 50 + 10i + 26 = 0[/tex]

Simplifying the equation:

[tex]25 - 50 + 26 + i^2 = 0[/tex]

Since[tex]i^2 = -1[/tex], we can substitute that value into the equation:

[tex]25 - 50 + 26 - 1 = 0[/tex]

Simplifying further:

[tex]0 = 0[/tex]

Since the equation holds true, we can conclude that the complex number 5-i is indeed a solution of the equation [tex]x^2-10x+26=0[/tex].

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Using midpoints, The length of RY is (9x - 1)/2 cm.

A midpoint is a point that is exactly halfway between two other points. In geometry, the midpoint of a line segment is the point on that line segment that is equidistant from both endpoints.

For example, in a line segment AB, the midpoint M is the point on AB that is equidistant from A and B. In other words, the distance from A to M is the same as the distance from M to B. The midpoint M is located at the exact center of line segment AB, and it divides the segment into two equal parts.

The midpoint can also be thought of as the average of the x-coordinates and y-coordinates of the endpoints. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint has coordinates:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Since R is the midpoint of XY, we know that RX = RY.

We are given that XR = 5x+2 cm and XY = 14x+1 cm.

Thus, RX + RY = XY

Substituting RX = RY, we get:

RY + RY = 14x + 1 - (5x + 2)

Simplifying the right side, we get:

RY + RY = 9x - 1

2RY = 9x - 1

RY = (9x - 1)/2

Therefore, the length of RY in cm is (9x - 1)/2.

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As per the concept of compound interest, the balance after 7 years will be $2,200.24.

In your case, you have a savings account balance that is compounded annually. The interest rate is 2% per year, which means that at the end of each year, the balance will increase by 2% of the previous year's balance. So, if your current balance is $1,932.00, the balance after one year will be:

Balance after one year = $1,932.00 + 2% of $1,932.00

= $1,932.00 + $38.64

= $1,970.64

After two years, the balance will be:

Balance after two years = $1,970.64 + 2% of $1,970.64

= $1,970.64 + $39.41

= $2,010.05

The formula for compound interest is:

A = P(1 + r/n)ⁿˣ

where:

A = the final amount

P = the principal amount (initial balance)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

ˣ = the number of years

In your case, the interest is compounded annually, so n = 1. The annual interest rate is 2%, which is equivalent to 0.02 as a decimal. The initial balance is $1,932.00, and you want to know the balance after 7 years, so t = 7. Using these values in the formula, we get:

A = $1,932.00(1 + 0.02/1)¹ˣ⁷

= $1,932.00(1.02)⁷

= $2,200.24

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Large corporations often offer better benefits and opportunities for career advancement.

Large corporations often have more resources available for employee training and development.

I would prefer to work for a large corporation for two reasons. First, large corporations often offer better benefits and opportunities for career advancement. Second, large corporations often have more resources available for employee training and development. While working for a small business whose owners I know may provide a more personal and intimate work environment, I believe that the benefits of working for a large corporation outweigh the potential drawbacks.

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So, the experimental probability that the next student Meg talks will pick football is 0.2 or 20%.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. It is used to quantify the uncertainty or risk associated with a particular event or situation.

Given by the question.

The experimental probability of an event is the ratio of the number of times the event occurs to the total number of trials or observations. In this case, the event is selecting football as the favorite sport, and the trials are the number of students Meg talks to.

Based on the information given in the problem, Meg surveyed a total of 10 students (2 who selected football and 8 who selected other sports). Therefore, the probability of the next student she talks to selecting football as their favorite sport is:

P (selecting football) = number of students who selected football / total number of students surveyed

P (selecting football) = 2 / 10

P (selecting football) = 0.2

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Answer:

jimmy has 12 candy bars left

Step-by-step explanation:

28-7-9=12

Answer:

Jimmy has 12 candy bars.

Step-by-step explanation:

Subtract 28 from 7.
=21

21-9=12.
Jimmy has 12 candy bars left if he eats 7 and his mom takes 9.

The number that must be added to both sides of the equation x2 + 12x = 13 so that the method of completing the square can be used to solve the roots is 36. The correct answer is C. 36.

To complete the square, we need to add the square of half the coefficient of the x term to both sides of the equation. In this case, the coefficient of the x term is 12, so half of it is 6. The square of 6 is 36, so we need to add 36 to both sides of the equation. Hence the correct option is C) 36.

The equation then becomes:
x2 + 12x + 36 = 13 + 36

Simplifying the right side of the equation gives us:
x2 + 12x + 36 = 49

Now we can factor the left side of the equation into a perfect square:
(x + 6)2 = 49

From here, we can use the square root property to solve for x:
x + 6 = ±√49

Solving for x gives us:
x = -6 ± 7

So the roots of the equation are x = 1 and x = -13.

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Therefore , the solution of the given problem of fraction comes out to be  214 kilowatt hours of electricity for the month.

Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction. because the values, numerators, and numerators of real fractions vary

Here,

We must divide the total amount of electricity used by the number of businesses in order to calculate how many kilowatt hours each business is responsible for paying for:

=> 14, 14 businesses x 2,996 kilowatt hours = 214 kilowatt hours per company

As a result, each company is required to pay for roughly 214 kilowatt hours of energy per month.

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Answer:

A

Step-by-step explanation:

6x° and 54° form the angle of 90° , that is

6x + 54 = 90 ( subtract 54 from both sides )

6x = 36 ( divide both sides by 6 )

x = 6

then

6x = 6 × 6 = 36°

The value of d when t=3 is 45 miles. This means that Jake has covered a distance of 45 miles in 3 hours riding his bike at a rate of 15 miles per hour.

Distance is a measure of the length between two points. To calculate distance, we need to know the coordinates of the two points. We can use the Pythagorean theorem to calculate the distance.

The formula d=rt is used to calculate the distance traveled when a rate, r, and time, t, are given. In this case, Jake is riding his bike at a rate of 15 miles per hour for 3 hours. To calculate the distance, d, traveled, we can substitute the given values into the formula.

d = 15 * 3

d = 45

Therefore, the value of d when t=3 is 45 miles. This means that Jake has traveled 45 miles in 3 hours riding his bike at a rate of 15 miles per hour. This formula can also be used to calculate the time, t, when the rate, r, and distance, d, are known. To find the time, t, simply divide the distance, d, by the rate, r.

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The measures of the other three angles are: ∠2 = ∠3 = 67.5° and ∠4 = 0°.

An angle is a geometric figure formed by two rays that share the same endpoint called vertex. It is measured in degrees, radians or gradians and is usually denoted by the vertex letter in its center, with the endpoints labeled by two other letters or points.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can use this information to find the measures of the other three angles.

If ∠1 has a measure of 45°, then we know that the sum of the measures of ∠2 and ∠3 is 135° (180° - 45°).

If the triangle is isosceles, then ∠2 and ∠3 have the same measure. Therefore, we can divide 135° by 2 to get:

∠2 = ∠3 = 67.5°

Finally, we can use the fact that the angles of a triangle add up to 180° to find the measure of ∠4:

∠4 = 180° - 45° - 67.5° - 67.5° = 0°

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Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.

The function f(x) = [[x − 2]] is discontinuous at any value of x that is two units away from an integer. That means it is discontinuous at x = k - 2 and x = k + 2, where k is any arbitrary integer.

The discontinuities at x = k - 2 and x = k + 2 are both removable. That is because the discontinuities occur when the left- and right-hand limits of the function are not equal, and the limits can be made equal by redefining the value of the function at the point of discontinuity.

To solve the problem, set the left- and right-hand limits equal to each other and solve for x.

Left-hand limit: lim x→k-2  f(x) = lim x→k-2 [[x − 2]] = [[k - 2 - 2]] = [[k - 4]]
Right-hand limit: lim x→k+2  f(x) = lim x→k+2 [[x − 2]] = [[k + 2 - 2]] = [[k]]

Equating the two limits, we have [[k - 4]] = [[k]]. Solving for x, we get x = k - 2 and x = k + 2.

Therefore, f(x) = [[x − 2]] is discontinuous at x = k - 2 and x = k + 2. The discontinuities at these points are removable.
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The expression when factored by the GCF is 6x(x - 2y + 3y^2)

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

6x^2 - 12xy + 18xy^2

The greatest common factor (GCF) of 6x^2, -12xy, and 18xy^2 is 6x, which is the largest number that divides each term evenly.

To factor the polynomial by factoring out the GCF, we can divide each term by 6x to get:

6x^2/6x = x

-12xy/6x = -2y

18xy^2/6x = 3y^2

So the polynomial can be factored as:

6x^2 - 12xy + 18xy^2 = 6x(x - 2y + 3y^2)

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The answer is 49

To evaluate the given expression, we will use the special product formula for the square of a binomial:

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

In this case, we have:

52^(2)=(5+2)^(2)=5^(2)+2(5)(2)+2^(2)=25+20+4=49

Therefore, the answer is:

52^(2)=49

So, using the special products of algebraic expressions, we can evaluate the given expression to be 49.

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Answer:

-5 - 2sqrt6

Step-by-step explanation:

To simplify (sqrt2+sqrt3)/(sqrt2-sqrt3), we can rationalize the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of sqrt2-sqrt3 is sqrt2+sqrt3, so we can multiply both the numerator and denominator by sqrt2+sqrt3:

(sqrt2+sqrt3)/(sqrt2-sqrt3) * (sqrt2+sqrt3)/(sqrt2+sqrt3) = ((sqrt2+sqrt3)(sqrt2+sqrt3))/((sqrt2-sqrt3)(sqrt2+sqrt3))

Expanding the numerator and simplifying, we get:

(sqrt2+sqrt3)^2 / (sqrt2^2 - sqrt3^2)

= (2 + 2sqrt2sqrt3 + 3) / (2 - 3)

= (5 + 2sqrt6) / (-1)

= -5 - 2sqrt6

Therefore, (sqrt2+sqrt3)/(sqrt2-sqrt3) simplifies to -5 - 2sqrt6.

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

We have,

To simplify the expression (√2 + √3) / (√2 - √3), we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.

The conjugate of (√2 - √3) is (√2 + √3).

Multiplying the numerator and denominator by (√2 + √3), we get:

[(√2 + √3) x (√2 + √3)] / [(√2 - √3) x (√2 + √3)]

Expanding both the numerator and denominator:

[(√2 + √3)(√2 + √3)] / [√2 x √2 - √2 x √3 + √3 x √2 - √3 x √3]

Simplifying:

[2 + 2√2√3 + 3] / [2 - 3]

Combining like terms:

[5 + 2√6] / [-1]

Since the denominator is -1, we can multiply both the numerator and denominator by -1 to simplify further:

[5 + 2√6] / 1

Finally, we have:

(5 + 2√6)

Therefore,

The simplest form of the expression (√2 + √3) / (√2 - √3) is - (5 + 2√6).

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We have saved approximately 15% of the total cost.

What is the process to calculate the percentage saved in a sale?

When items are on sale, they are usually offered at a discounted price. The percentage saved is a measure of the amount that a buyer has saved on the original price of the item. The process to calculate the percentage saved in a sale involves determining the original price, the discounted price, and then using a formula to find the percentage saved.

The formula for the percentage saved is:

Percentage saved = (Amount saved / Original price) x 100%

Calculation of  the total amount saved and the percentage saved :

For the paperbacks, the original price is $9 each and we bought four of them, so the total original price is:

$9/book × 4 books = $36

With a 10% discount, the discounted price of each paperback is:

$9/book × 0.10 = $0.90 discount

$9/book - $0.90 discount = $8.10 discounted price

So, the total discounted price for the four paperbacks is:

$8.10/book × 4 books = $32.40

Therefore, we saved:

$36 - $32.40 = $3.60

For the hardbacks, the original price is $20 each and we bought two of them, so the total original price is:

$20/book × 2 books = $40

With a 20% discount, the discounted price of each hardback is:

$20/book × 0.20 = $4 discount

$20/book - $4 discount = $16 discounted price

So, the total discounted price for the two hardbacks is:

$16/book × 2 books = $32

Therefore, we saved:

$40 - $32 = $8

The total original price of all the books is:

$36 + $40 = $76

The total discounted price of all the books is:

$32.40 + $32 = $64.40

Therefore, we saved:

$76 - $64.40 = $11.60

Plugging in the values , we get:

percentage saved = ($11.60 / $76) × 100%

percentage saved ≈ 15%

Therefore, we have saved approximately 15% of the total cost.

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Answer:

Step-by-step explanation:

20c is the answer

Answer:

ans is 14

Step-by-step explanation:

i do not think is this by i know is 14

put y = 5x in equation 1 :

2x + 3 (5x) = 34

2x + 15x = 34

17x = 34

x = 2

Now put x = 2 in any of the two equation to get

y :

y = 5x

y = 5 × 2

y = 10

The answer is value of x when y=25 are 8.33.

The missing variable y varies directly with x, which means that y = kx, where k is a constant.

We can use this equation to find the value of k and then use it to find the value of x when y=25.

First, let's find the value of k:
y = kx
75 = k*25
k = 75/25
k = 3

Now that we know the value of k, we can use it to find the value of x when y=25:
y = kx
25 = 3x
x = 25/3
x = 8.33

Therefore, the value of x when y=25 is 8.33.

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The cοrrect statement is the segment GC is transversal tο segments KG and QC.

A line that crοsses twο οr mοre lines in the same plane at different lοcatiοns is said tο be transversal. Accοrding tο the fundamental prοpοrtiοnality theοrem (alsο knοwn as Thales' theοrem), if three οr mοre parallel lines crοss acrοss twο transversals, they prοpοrtiοnally cut οff the transversals.

We have given the statements are:

A). KG QC.

B) KG and QC intersect at a right angle.

C) KQ || GC.

D) GC is transversal tο KG and QC.

Therefοre, here in the figure, segment GC intersects segments KG and QC in the same plane at different lοcatiοns.

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The statement, a number divided by 6 equals 3, is written as an equation is x/6 = 3

Algebraic expressions are simply defined as expressions that are made up of terms, coefficients, variables, constants and factors.

These expressions are also identified with arithmetic operations, such as;

From the information given, we have that;

A number divided by 6 equals 3

Now, let's say the number be x

This is represented as an equation thus;

x/6 = 3

Hence, the equation is x/6 = 3

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Answer:

342.02

Step-by-step explanation:

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

A - B is 5.

To find A - B, subtract each corresponding element in B from the corresponding element in A.

For the element in row 3, column 2, it is 2 - (-3) = 5.

Therefore,

the element in row 3, column 2 of A - B is 5.

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Yes, the given trinomial is a perfect square trinomial.

To determine whether a trinomial is a perfect square trinomial, we can use the formula:
(a-b)^(2) = a^(2) - 2ab + b^(2)

In this case, we can compare the given trinomial with the formula and see if it matches.

16a^(2)-40ab+25b^(2) = (4a)^(2) - 2(4a)(5b) + (5b)^(2)

This matches the formula, so we can conclude that the given trinomial is a perfect square trinomial.

Another way to determine whether a trinomial is a perfect square trinomial is to factor it and see if it can be written as a binomial squared.

In this case, we can factor the given trinomial as follows:

16a^(2)-40ab+25b^(2) = (4a-5b)(4a-5b) = (4a-5b)^(2)

Since the trinomial can be written as a binomial squared, we can conclude that it is a perfect square trinomial.

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Riya applying mulch in m³/ m² at the rate of 0.25 m³

To calculate the rate of mulch application in m³/m², we need to convert the given rate of 250,000 cm³/m² into m³/m². We can do this by using the conversion factor: 1 m³ = 1,000,000 cm³.

So, 250,000 cm³/m² can be converted to m³/m² as follows:

250,000 cm³/m² × (1 m³/1,000,000 cm³) = 0.25 m³/m²

This means that for every square meter of garden space, Riya is applying 0.25 m³ of mulch.

It's important to note that rate refers to the amount of mulch applied per unit of garden space. In this case, the unit is m². By expressing the rate in m³/m², we're specifying the volume of mulch applied per unit of area.

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Complete Question:

Riya is applying mulch to her garden. She applies it at a rate of 250,000 cm³ of mulch for every m² of garden space. At what rate is Riya applying mulch in m³/ m²?

Answer:

Since the diagonals of a rectangle bisect each other, we know that angle AEB is congruent to angle CED. Therefore, we can set the expressions for these angles equal to each other and solve for x:

13x = 3x - 5

Subtracting 3x from both sides gives:

10x = -5

Dividing both sides by 10 gives:

x = -0.5

Therefore, the value of x that satisfies the equation is x = -0.5. Note that this means that angle measures are negative, which doesn't make sense in this context. It's possible that there is an error in the problem statement or that some additional information is needed to determine a valid value of x.

Answer: bob

Step-by-step explanation:

92199+20923+29290+83292+2819+99279+38471+378141

= 744414