A radio station is giving away free t-shirts to students in local schools. It plans to give away 40 shirts at Big Sky Middle School and 75 shirts at High Peaks High School. Big Sky Middle School has 350 students, and 800 students attend High Peaks High School.

a. What is the probability of getting a t-shirt if you are a student at the middle school?

b. What is the probability of getting a t-shirt if you are a student at the high school?

c. Are you more likely to get a t-shirt if you are a student at the high school, or at the middle school?​

The savings plan balance after 18 months will be 15,028.63 dollars.

So the answer is a) $15,028.63

What is the annuity problem?

An annuity is a series of equal payments made at regular intervals.

APR (Annual Percentage Rate) = 6%

Monthly payments = $800

Number of months = 18

We can use the formula for the future value of an annuity (FV) to find the savings plan balance after 18 months. The formula for the future value of an ordinary annuity is:

FV = PMT x (((1 + r)^n - 1) / r)

Where:

FV = future value of the annuity

PMT = the regular payment made

r = the interest rate per period (in this case, the monthly interest rate)

n = the number of payments or periods

The interest rate is given as an annual percentage rate (APR), so we need to divide it by the number of periods per year to find the interest rate per period. In this case, 6% / 12 months/year = 0.5% per month.

FV = 800 x (((1 + 0.005)^18 - 1) / 0.005)

FV = $15,028.63

Hence, the savings plan balance after 18 months will be 15,028.63 dollars.

So the answer is a) $15,028.63

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Answer:

A

Step-by-step explanation:

For the line segment MO, the ratio of the length of MN to length of NO is 3 : 7. The ratio of the length of MN to length of MO is 3 : 10.

Ratio or proportion is the relation describing the size, quantity, or the amount of two or more variables.

For example, the ratio of sugar and flour in a cake dough is 1 : 2. It means, if there is 200 grams of sugar in the dough, the amount of flour is 2 x 200 = 400 grams.

In the given problem, the ratio of length MN to the length NO is 3 : 7.

Notice that:

MO = MN + NO

Hence, the ratio of the length of MN to the length of MO is:

MN : MO = MN : (MN + NO)

MN : MO = 3 : (3 + 7)

MN : MO = 3 : 10

The picture in your question is missing. Most likely it was like the one in the attached picture.

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The columns of the matrix A span R2.

In order to determine if the columns of the matrix A span R2, we need to check if the columns of A can be used to generate all possible linear combinations of the form a1v1 + a2v2, where a1 and a2 are scalars and v1 and v2 are the columns of A.

A = [2 1]

[0 1]

[-3 -1]

The columns of A are [2, 0, -3] and [1, 1, -1]. To check if these columns span R2, we need to see if we can create any vector in R2 by taking linear combinations of the columns. We can see that by taking linear combinations of the columns, we can create any vector of the form (a, b) in R2.

For example, by taking a = 2, b = 1, we can generate the vector (2, 1) by taking

a[2, 0, -3] + b[1, 1]

And by taking a = 3, b = -1, we can generate the vector (3, -1) by taking

a[2,0,-3] + b[1,1,-1].

So the answer would be: The columns of the matrix A span R2.

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The cost of painting the room walls with two coats of paint would be $84.38

To determine the cost of painting the room walls with two coats of paint, you would need to know the total square footage of the walls you are planning to paint. Once you have that information, you can calculate the total cost by multiplying the number of gallons of paint required by the cost per gallon. For example, if the room has 800 square feet of walls, you would need 2.28 gallons of paint (800/350 = 2.28) and the total cost would be $84.38 (2.28 x $36.50). If you want to know the cost of one coat, you will need to divide that number by 2.

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Answer:

108 degrees

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon is given by the formula:

(n-2) x 180 degrees

Where n is the number of sides of the polygon. In the case of a pentagon, the number of sides is 5, so we can use the formula to find the sum of the measures of the interior angles of a pentagon:

(5-2) x 180 = 3 x 180 = 540

If we know that the pentagon is regular, meaning that all its angles have the same measure, we can use this information and the formula above to find the measure of each interior angle.

If we divide the sum of the measures of the interior angles by the number of sides, we get the measure of each interior angle of the regular pentagon.

540/5 = 108 degrees

So, the measure of each interior angle of a regular pentagon is 108 degrees

Answer:

Step-by-step explanation:

true true false

Answer:

15

Step-by-step explanation:

x + 2y

Putting x = 7, y = 4, we have

7 + 2(4)

= 7 + 8

= 15

Hope it helps.

If you have any query, feel free to ask.

Step-by-step explanation:

It's saying x = 7 and y = 4, which means everywhere there is an x, you'll place a 7 and everywhere there is a y, you'll place a 4

x + 2y turns into (7) + 2(4)

Now we can answer the bottom question

2(4) = 8

7 + 8 = 15

so...

If x =7 and y=4, then x+2y= 15

According to the given statement the area of shaded region is is 20 units squared.

As an outcome, an isosceles triangle has two equal sides as well as two equal angles. As from Greek words iso (same) and skelos, the phrase is formed (leg). Except for a right triangle, which has quadrilateral on all sides, a scalene triangle lacks equal sides on each side.

The slope of the line connecting the bottom right vertex of something like the triangle to the top left vertex of both the square is equal to -1/2.

This line's equation is y = (-1/2)x + 10. (1)

The point at the triangle's top vertex is (15, 10)

The slope of the segment between (10, 0) and (15, 10) is 10/5, which equals two.

The line connecting these two locations has the equation y = 2(x - 10) y = 2x - 20. (2)

You may get the x coordinate of the point where these lines cross by putting (1) = (2) 

(-1/2)x + 10 = 2x - 20 

30 = [5/2]. x x equals 12 and y equals 2(12) - 20 = 4.

Therefore, the triangle's shaded area's height is 4 and its base is 10.

Its area is therefore (1/2)(4)(10) = 20 units squared.

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Answer:

Step-by-step explanation:

To calculate how many boxes of cookies Marcel needs to make to earn a profit of $245.00, we need to use the following formula:

Profit = (Revenue - Expenses) / Number of boxes

We know that the revenue is $15.00 per box and the expenses are $50.00. We also know that the profit should be at least $245.00.

So we can substitute these values into the formula and solve for the number of boxes:

$245.00 = ($15.00 - $50.00) / x

Where x is the number of boxes.

To solve for x, we'll need to multiply both sides of the equation by x:

$245.00*x = ($15.00 - $50.00)

$245.00*x = -$35.00

x = -$35.00/$245.00 = -0.142857143

The number of boxes is a negative value which is not possible, so Marcel will not earn a profit of $245.00. She will need to increase her revenue or decrease her expenses to reach a profit of $245.00.

So on solving the provided question we cans say that  sides of a square are given as 18 units, area = 324 cm sq.

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

here,

sides of a square are given as 18 units

so area will be s^2 18*18 = 324 cm sq.

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The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

The equation of a curve in the xy-plane is given by F(x,y) = 0. To find such a curve that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2, we can use the method of implicit differentiation.

First, we can find the equation of the tangent line at a point (x,y) on the curve by computing the derivative of F(x,y) with respect to x and setting it equal to 2x/y^2. This gives us:

F_x(x,y) = 2x/y^2

Next, we can use the fact that the curve passes through the point (0,3) to set up the following equation:

F(0,3) = 0

Solving for F(x,y) in terms of x and y and substituting in the equation for F_x(x,y) gives the implicit equation of the curve is

y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant

This is the equation of a curve in the XY-plane that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2.

Therefore, The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

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Answer:

2023

Step-by-step explanation:

3 + 4x = y

y = 3 + 4(505)

y = 3 + 2020

y = 2023

11423 be the number of dogs are at the rescue center.

An expression is combination of variables, numbers and operators.

A pet rescue center is creating a monthly food budget.

The center currently has two-thirds as many dogs as cats.

Each animal is fed 2 cans of food a day.

Dog food costs $0.08 per can, cat food costs $0.05  per can

The rescue center has budgeted a total  2581.8 of  for food for this .

2(0.08)x+2(0.05)y= 2581.8

Let x be the number of dogs.

cats be y.

2/3x =y

2(0.08)x+2(0.05)2/3x= 2581.8

0.16x+0.066x=2581.8

0.226x=2581.8

x=11423

Hence, 11423 be the number of dogs are at the rescue center.

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Answer:

a) 4 cosx^4 - cos²2x=0

We can start by splitting the equation into two parts:

4 cosx^4 = cos²2x

cosx^4 = (1/4)cos²2x

From here, we can use the identity:

cos²2x = (cos 2x)² = (2cos²x -1)²

So, we have:

cosx^4 = (1/4)(2cos²x -1)²

Now we can square root both sides:

cosx^2 = (1/2) (2cos²x -1)

Now we square both sides again:

cos²x = (1/4) (2cos²x -1)

We can now subtract (1/4) from both sides and add cos²x to both sides:

(3/4)cos²x = (1/4)

We can now divide both sides by (3/4) to find the value of cosx:

cosx = sqrt(1/3)

So the solutions of the equation are x = (2n+1)π/3, where n is an integer.

b) sec x tan x =sqrt(2)

We know that sec x = 1/cosx and tan x = sinx/cosx.

So we can substitute these values into the equation:

1/cosx * sinx/cosx = sqrt(2)

This simplifies to:

sinx = sqrt(2)cosx

We can now divide both sides by cosx:

tan x = sqrt(2)

So the solutions of the equation are x = pi/4 + nπ, where n is an integer.

Note that the solutions are restricted to the domain where cos(x) is not equal to 0.

It is important to note that this solution is only a small part of the full solution set and that there might be more solutions in specific intervals.

Answer:

D. 60

Step-by-step explanation:

Not yellow marbles are 15/25 = 60/100

i)The amount of petrol sold by the petrol station on a particular day is 21,600 L

II) Number of customers who would expect to buy 44 L of petrol is 2.28

i)The amount of petrol sold by the petrol station on a particular day can be estimated using the following equation:

Total petrol sold = Mean amount of petrol per customer x Number of customers

= 36 L x 600 customers

= 21,600 L

ii) To find the number of customers who would expect to buy 44 L of petrol, we need to find the probability of a customer buying that amount. We can use the standard normal table and the z-score formula (z = (x - mean) / std dev) to calculate the probability of a customer buying 44 liters of petrol.

z = (44 - 36) / 7 = 2.57

Using the standard normal table, we can find that the probability of a customer buying 44 liters of petrol is about 0.0038 or 0.38%.

Therefore, we can estimate that about 2.28 customers would expect to buy 44 liters of petrol on that day by multiplying the probability of buying 44 liters of petrol by the total number of customers.

Number of customers who would expect to buy 44 L of petrol = 0.38% * 600 = 2.28

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The complete question is:

The amount of petrol bought by a customer at a petrol station is normally distributed with mean 36 L and standard deviation 7 L.                                                                                                              on a particular day, the petrol station has 600 customers. i) how much petrol would you expect the petrol station to sell on this day? ii) how many customers would you expect to buy 44 l of petrol?          

The probability that the sample contains two white balls and two red ones is 0.264. There are multiple draws without replacement.

Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

An urn contains 6 white balls and 15 red balls. A sample of four balls is selected at random from the urn. Find the probability that the sample contains two white balls and two red ones!

It means that there will be multiple draws without replacement.

The total balls are 6 + 15 = 21 balls.

The probability of drawing two white balls and two red ones is

= P(1st is white ∩ 2nd is white ∩ 3rd is red ∩ 4th is red)

= P(1st is white)*P(2nd is white)*P(3rd is red)*P(4th is red)

= (6/21)*(5/20)*(15/19)*(14/18)

= 0.044

There are 6 possible orders (WWRR, WRWR, WRRW, RWWR, RWRW, RRWW). So, the probability in any order would be

= 0.044 × 6

= 0.264

Hence, the probability of drawing two white balls and two red ones in any order is 0.264.

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Answer:

y=10

Step-by-step explanation:

18/9=1/2

so

x/5=1/2

Answer: The value of y will be 10 when the value of x is 5.

x and y are directly proportional to each other so,we can write  the given relation in mathematical form as:

y=kx

k is any constant

We are given: The value of y is 18 when value of x is 9:

x=9 and y=18

Putting the value of x and y in the above equation , we get:

18=9k

 k=18/9=2

 k=2

So now we have the proportional relation(k) between x and y.

Again,

we have been given the value of x=5 and we are asked the value of y using same proportional relation.

y=k(5)

y=2(5)=10

Hence the value of y the value of x is 10.

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Answer:

NOLO

Step-by-step explanation:

Assuming that the company’s claims are true, there is a probability of 0.9824 that the first person to have a college degree is the third person selected at random.

The company claims that 74% of its employees hold college degrees.

Taking the total number of employees as 1,

The probability of employees who do hold a college degree P(3) is 0.74

Therefore, the probability of employees who do not have a college degree is (1-0.74) = 0.26

The probability that the first 2 employees do not have a college degree P(1&2) is 0.26^2

The equation thus turns out to be;

Probability that the 3rd person is the first to hold a college degree = P(1&2)*P(3)= (0.26^2)*0.74= 0.9824

Therefore, the probability that the first person to hold a college degree in the company is the third person chosen at random is 0.9824.

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A = P(1+r/n)(nt), where P is the original principal, r is the annual interest rate, n is the number of times the interest is compounded annually, and t is the number of years the money has been held, is the formula for compound interest.

To calculate the final amount of money in the account:

 First, divide the 8% annual interest rate by 100 to get a decimal value: 0.08.

Find the number of times the interest is compounded annually. Since it is done quarterly, the answer is n = 4.

Put these values into the formula now, along with the $1200 principle sum and the number of years, 5, to complete it:

A = $1200(1+(0.08/4))^(4*5) = $2490.07

  to determine how long it will take for the initial sum to double to $2400.

 Divide the final sum by the starting sum: 2400/1200 = 2

 Take the natural logarithm of 2: ln(2) = 0.693

Decimalize the result and divide it by the interest rate: 0.693 / 0.08 = 8.66 years

 Therefore, the time it will take for the initial sum of money to double to $2400 is 8.66 years.

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The number of different ways can a person choose eight cookies will be 1,680.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

At a cookie shop, four different kinds of cookies are sold: chocolate chip, macaroon, peanut butter, and white chocolate.

Then the number of different ways can a person choose eight cookies will be given as,

⁸P₄ = 8! / (8 - 4)!

⁸P₄ = 8 x 7 x 6 x 5 x 4! / 4!

⁸P₄ = 1,680

The number of different ways can a person choose eight cookies will be 1,680.

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The cost of a 3.4 mile ride when a taxi charges a base fee of $3.00 and $0.15 for every mile of the ride is $3.51.

Therefore the answer is $3.51

The cost of a 3.4 mile ride can be calculated by multiplying the distance of the ride by the cost per mile and adding the base fee. Here base fee is the fixed charge and $0.15 is the variable charge that depend on distance covered.

To calculate the cost of the ride:

= (3.4 miles * $0.15 per mile) + $3.00 base fee

= $0.51 + $3.00

= $3.51

So, a 3.4 mile ride would cost $3.51.

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Average annual tuition in 2020 is 14,286.70.

Value is the worth of something in terms of its usefulness, quality, or importance. It is the importance that an individual, group or organization places on something and is an important concept in economics, business and politics. Value can be seen as a measure of how much someone or something is worth, both in terms of money and in terms of intangible qualities, such as respect or admiration. Value is subjective, meaning that it is based on personal opinion and perspective.

Using a graphing calculator, the equation of the line of best fit is y = 96.98x + 11145.46. The slope of the line is 96.98 and the y-intercept is 11145.46.

By substituting x = 15 into the equation, the estimated average annual tuition in 2020 is 14,286.70. This can be rounded to the nearest hundred dollars, giving an estimate of 14,300 dollars.

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If the Gasoline costs $3.58 per gallon and Karl paid $30.43 , the number of gallons Karl purchased is  8.5 gallons .

The Per unit cost of Gasoline is = $3.58  ;

the amount paid by Karl for gasoline is = $30.43   ;

we have to calculate the number of gallons of gasoline purchased by Karl,

the number of gallons can be calculated by the formula :

Number Of Gallons purchased = [tex]\frac{Total \; Amount }{Cost \; per \; Gallon}[/tex] ;

Substituting the values of amount and cost per gallon in the formula ,

we get ;

Number of gallons = [tex]\frac{30.43}{3.58}[/tex] ;

we get ; ⇒ 8.5 .

Therefore , Karl purchased 8.5 gallons of gasoline .

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Bori will run 10.5 miles in 75 minutes, using the concepts of unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method. We typically utilise this technique for math calculations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

Let us use the unitary method to solve this sum as well.

Bori can run 7 miles in 50 minutes.

This implies that, in 50 mins, Bori will run 7 miles.

Therefore, in 1 minute, Bori will run [tex]\frac{7}{50}[/tex] miles.

We have to find the number of miles Bori will run in 75 minutes.

Thus, in 75 mins, Bori will run [tex]\frac{7}{50} * 75[/tex] miles.

= 10.5 miles

Therefore, Bori will run 10.5 miles in 75 minutes.

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Answer: The cosine of angle C is -0.0168.

Step-by-step explanation: To find the cosine of the angle opposite the side of length 2.92 meters, you can use the cosine law which states that:

c^2 = a^2 + b^2 - 2ab * cos(C)

where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides, and C is the angle opposite side c.

So in this case,

c = 8.82 m

a = 2.92 m

b = 7.67 m

then we can substitute the values into the equation and solve for cos(C):

(8.82)^2 = (2.92)^2 + (7.67)^2 - 2(2.92)(7.67) * cos(C)

cos(C) = (a^2 + b^2 - c^2) / (-2ab)

cos(C) = (2.92^2 + 7.67^2 - 8.82^2) / (-22.927.67)

cos(C) = -0.0168

(x^2  - 5x -  14 = 0) has the solution set as F: "x = 7 , -2" .

Solve the equation by factorization method.

x^2 - 5x - 14 = 0

x^2 -  7.x + 2.x - 14 = 0

taking x common from the frist two terms and +2 common from the last two terms.

[ x(x - 7 ) PLUS (+) 2 (x -7) ] = 0

[( x - 7) . (x + 2)] = 0

x - 7 = 0 , &   x + 2  =0

x = 7  , & x = -2

Thus the solution is x = 7 and x = -2.

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The  expression that shows how many minutes it will take to complete an order, assuming there are x parts in an order is 2x+10y = x

The statement states that  it takes 2 minutes to manufacture each part and 10 minutes to pack all the parts for an order.

Also, it is stated that there are  x parts in an order

This implies that  2(x) + 10(y) = x

Opening the brackets to have

2x + 10y = x

This is to say that 2 minutes of manufacture and 10 minutes of packing will give all the parts.

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