Tricia needs to bring cookies and fruit to her class of 16 students. There will be a total of 48 items, including 1 piece of fruit for each student.

If a first time homebuyer is given the choice of two loans: loan a: 390,000, 15 year-fixed, 4 discount points. The amount the hole buyer save in total by choosing loan is:  b) 11,427.

To compare the total cost of each loan, we need to calculate the total payments made over the life of the loan.

For loan A, the monthly payment is $3,509.71 and the loan term is 15 years, so the total payments would be:

Total payments = monthly payment x number of months

Total payments = $3,509.71 x (15 x 12)

Total payments = $631 747.8

However, loan A also has a 4-point discount, which means the borrower paid 4% of the loan amount upfront to reduce the interest rate.

Discount points = loan amount x discount rate

Discount points = $390,000 x 0.04

Discount points = $15,600

To calculate the total cost of loan A, we need to add the discount points to the total payments:

Total cost of loan A = total payments + discount points

Total cost of loan A = $631 747.80 + $15,600

Total cost of loan A = $647,347.80

For loan B, the monthly payment is $3,659.86 and the loan term is 15 years, so the total payments would be:

Total payments = monthly payment x number of months

Total payments = $3,659.86 x (15 x 12)

Total payments = $658,774.5

To calculate the total cost of loan B, we simply add the total payments:

Total cost of loan B = total payments

Total cost of loan B =  $658,774.5

Therefore, the total amount saved by choosing loan A over loan B is:

Savings = total cost of loan B - total cost of loan A

Savings = $658,774.5 - $647,347.80

Savings = $11,427

Therefore, the answer is option b) $11,427.

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Answer:

14.728

Step-by-step explanation:

m³ + n if m = 1.2 and n = 13

= (1.2)³ + 13

= 1.728 + 13

= 14.728

The length of the missing side is, 5 unit.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Two sides of a triangle are, 3 and 4.

Now, We can use the Pythagoras theorem to find the missing side of a triangle as;

Let the missing side = x

⇒ x² = 3² + 4²

⇒ x² = 9 + 16

⇒ x² = 25

⇒ x = √25

⇒ x = 5

Thus, The missing side of triangle = 5 units

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Answer:

To show that 3 divided by 1/4 is equal to 3x4 on a number line:

1. Draw a number line starting from 0 and mark every 1/4 division.

2. Label 3 divisions with the corresponding value '3'.

3. Move 4 divisions in the same direction as that of 3 divisions.

4. Mark the point at 4 divisions and label it as ’12’.

5. From the starting point to the point labelled ‘12’, there are 7 divisions.

6. Since each division represents a quantity of 1/4, dividing 3 by 1/4 (or multiplying by 4) will result in a total of 12, or 3x4.

Answer:

Step-by-step explanation:

You need the area.

If this is a square - it is 54 × 54 = 2916 inches squared

Answer: x = 52 degrees

Step-by-step explanation:

90 degree - 38 degrees is 52

i hope this helped:)

Answer:

22.5%

Step-by-step explanation:

45×50/100 gives you the answer using BODMAS

Answer: 21.6

Step-by-step explanation:

length X height

4(5.4)=21.6

The answer is:

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There are 50 calories per cup of popcorn and 16 per ounce of soda.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

Let's represent x be the number of calories per cup of popcorn

And let's represent y be the number of calories per ounce of soda.

The two equations are based on the given details:

2x + 7y = 212 ....(i)

1x + 11y = 226 ....(ii)

From equation (ii), we have

x + 11y = 226

x = 226 - 11y

Substitute the value of x = 226 - 11y in equation (i), and solve for y:

y = 16

Substitute the value of y = 16 in equation (ii), and we get

x = 50

Thus, the number of calories per cup of popcorn is 50 and the number of calories per ounce of soda is 16.

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6 cmAnswer:

Step-by-step explanation:

The solution of the equation y = - 7x + 1 are,

⇒ (6, - 41) and (- 8, 57)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = - 7x + 1

Hence, Substitute the given points into equation and check the solution as;

Put (x, y) = (- 6, - 35)

⇒ y = - 7x + 1

⇒ - 35 = - 7 × - 6 + 1

⇒ - 35 ≠ 43

Thus, It is not the solution.

Put (x, y) = (4, 27)

⇒ y = - 7x + 1

⇒ 27 = - 7 × 4 + 1

⇒ 27 ≠ - 27

Thus, It is not the solution.

Put (x, y) = (6, - 41)

⇒ y = - 7x + 1

⇒ - 41 = - 7 × 6 + 1

⇒ - 41 = - 41

Thus, It is the solution.

Put (x, y) = (- 8, 57)

⇒ y = - 7x + 1

⇒ 57 = - 7 × - 8 + 1

⇒ 57 = 57

Thus, It is the solution.

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A right skewed distribution means that the majority of the data falls to the left of the mean, with a long tail to the right. This can also be called a positive skew.

In this type of distribution, the median is typically less than the mean, and the mode is even smaller than the median. This type of distribution is common in data sets that have a lower bound but no upper bound, such as income or age.

The opposite of a right skewed distribution is a left skewed distribution, where the majority of the data falls to the right of the mean with a long tail to the left.

In a right-skewed distribution, the mean is typically greater than the median and the mode. This is because the mean is influenced by the values in the long tail on the right-hand side of the distribution, which pull the mean in that direction.

The median and mode, on the other hand, are less affected by the extreme values in the tail and are therefore more representative of the central tendency of the distribution.

Examples of right-skewed distributions include the distribution of income, where a few individuals have very high incomes that create a long tail on the right-hand side, and the distribution of test scores, where a few high-performing students may create a similar tail.

Right-skewed distributions are common in many natural and social phenomena, and understanding their properties is important for statistical analysis and modeling.

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The height of the cylindrical concrete pillar is approximately 153.2 centimeters.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

We are given that;

Length of prism=8.8cm

Height=4.4cm

Volume=271.04 cubic centimeters.

Now,

We can use the formula for the volume of a cylinder to find the height of the pillar. The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

First, we need to find the radius of the pillar. The diameter of the pillar is given as 10 centimeters, so the radius is half of that:

r = 10/2 = 5 centimeters

Now we can substitute the given volume and radius into the formula and solve for the height:

12,042 = π(5)^2h

Divide both sides by π(5)^2:

h = 12,042 / (π(5)^2)

h ≈ 153.2 centimeters (rounded to one decimal place)

Therefore, by the given volume the answer will be 153.2 centimeters.

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Answer:

Bx=8

Step-by-step explanation:

U always have to remember to put a “x” or “y” next to your letter it’s important.

There are 1000 cubic centimetres in a litre (cm3). This is so because one cubic centimetre (cc) equals one millilitre (ml), and one litre (l) equals 1000 ml.

1000 ml make up 1 litre (L).

ml (millilitres) = cm3

1000 ml = 1000 cm3

1 L = 1000 cm3

One litre is equal to one thousand cubic centimetres (cm3). This is because one cubic centimetre is equivalent to one millilitre (ml), and one litre is equal to 1000 millilitres (ml). The subsequent actions can be conducted in order to calculate this. Initially, one litre (L) equals one thousand millilitres (ml). Second, one cubic centimetre is equivalent to one millilitre (cm3). Thus, one millilitre is equivalent to one hundred cubic centimetres. Last but not least, one litre equals one thousand cubic centimetres, or 1 L = 1000 cm3. Anybody wishing to translate between the two different volume measures will find this information valuable. For instance, if a recipe calls for a certain amount of an ingredient in litres, it is simple to convert that amount to cubic centimetres if necessary.

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The specific steps for using a travel time are determining your starting point and destination, choose the mode of transportation, set any relevant parameters, review the results, adjust your plans if necessary.

Determine your starting point and destination: Enter the starting point and destination of your trip, typically using either the addresses or the names of the locations.

Choose the mode of transportation: Select the mode of transportation you plan to use for your trip, such as driving, walking, biking, or using public transit.

Set any relevant parameters: Depending on the travel time calculator you are using, there may be additional parameters you can set, such as the time of day you plan to travel or any stops you plan to make along the way.

Review the results: After entering the necessary information, the travel time calculator should provide you with an estimate of the travel time for your trip, as well as any additional information such as the distance traveled, estimated fuel cost, or suggested routes.

Adjust your plans if necessary: If the estimated travel time is longer than you expected or if there are any unexpected delays or road closures, you may need to adjust your plans accordingly.

Overall, a travel time calculator can be a useful tool for estimating travel times and planning your trip.

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The price of each ticket is given as follows:

The prices for each type of ticket are obtained via a system of equations, for which the variables are given as follows:

On the first day of ticket sales the school sold 12 senior citizen tickets and 6 student tickets for a total of $252, hence:

12x + 6y = 252

2x + y = 42 (simplifying by 6).

y = 42 - 2x.

The school took in $98 on the second day by selling 6 senior citizen tickets and 1 student ticket, hence:

6x + y = 98

y = 98 - 6x.

Equaling the two equations, the value of x is obtained as follows:

42 - 2x = 98 - 6x

4x = 56

x = 56/4

x = 14.

Then the value of y is of:

y = 98 - 6(14)

y = 14.

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Answer:

What is the distance between the two control stations on the earth's surface?

To find the distance between the two control stations, we can use the law of cosines. Let's call the distance between the control stations "d". Then, using the information that the angle of separation between the two stations is 10°:

d^2 = 2 * 3963^2 - 2 * 3963^2 * cos(10°)

d = sqrt(2 * 3963^2 - 2 * 3963^2 * cos(10°))

Using a calculator, we find that d = approximately 5657 miles. Rounding to the nearest whole number, the distance between the two control stations is 5657 miles.

What is the height of the satellite above the surface of the earth?

To find the height of the satellite, we can use the law of sines. Let's call the height of the satellite "h". Then, using the information that the distance between the two control stations is d:

h / sin(10°) = d / 2

h = d / 2 * sin(10°)

Using the value of d from the previous question, and a calculator, we find that h = approximately 22,795 miles. Rounding to the nearest whole number, the height of the satellite above the surface of the earth is 22,795 miles.

Step-by-step explanation:

The vertical asymptote is at x = -2

The horizontal asymptotes are at y =0.

First, the vertical asymptote, it happens when the denominator becomes zero, then we need to solve:

-x - 2 = 0

x = -2

The vertical asymptote is at x = -2

For the horyzontal asymptotes we need to check the limit as x tends to ±∞, in both cases because x is only in the denominator, the function will tend to zero.

So we have two horizontal asymptotes at y = 0.

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The probability of spinning a red, then green is 1/4.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1. Probability is applied in many areas, including finance, statistics, weather forecasting, and gambling.

The probability of spinning a red, then green is 1/4. This is because there are four equal parts on the spinner (red, blue, yellow, and green), and spinning red first and then green means that you have a 1 out of 4 chance of getting the desired result. Therefore, the numerator is 1 and the denominator is 4.

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Answer: It is 1/16

Step-by-step explanation: It said twice so you had to multiple 8 by 2 since there are 8 possible color panels.  

The number of games in the "72 or more" category is 1.

Counting of numbers is the fundamental block in mathematics usually being used is natural numbers.

So natural numbers are also called counting numbers.

Given that the categories of the scores scored by the team in each game are done into 4 categories as 51 - 57, 58 - 64, 65-71, and 72 or more.

And the scores are given as,

51, 70, 63, 59, 56, 75, 60, 55, 67, 64

Number of scores which are 72 or more = 1

Hence there is only 1 game which has the score in the category "72 or more".

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Answer:22.5

Step-by-step explanation:

Answer: 6x^2-x-1

Step-by-step explanation:

(3x+1)(2x-1) = 6x^2 - 3x + 2x -1

6x^2-x-1

The equivalent perimeter expression is 3 * 3

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

Side lengths = 3m, 3m and 3m

The perimeter of the triangle is the sum of the side lentths

So, we have

perimeter = 3 + 3 + 3

Using the distributive property, we have

Perimeter = 3 * 3

Hence, the perimeter expression is 3 * 3

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Complete question

The lengths of the sides of a triangle are represented by 3m, 3m and 3m.

The angles m∠1and m∠2 can be classified as vertical angles, while the angles m∠3 and m∠4 is not a linear pair, neither are they vertical or adjacent angles.

Angles are classified as a linear pair if they are formed by the intersection of two lines making them a pair of adjacent angles.

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

Two angles are said to be adjacent when they share a common vertex and one common side. Two adjacent angles sum up to 180°.

From observation, angles m∠1and m∠2 can be classified as vertical angles as they are vertically opposite each other.

But angles m∠3 and m∠4 cannot be classified as any of the three defined classes of angles.

In conclusion, angles m∠1and m∠2 are vertical angles, while the angles m∠3 and m∠4 is not a linear pair, neither are they vertical or adjacent angles.

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The solution of the given system of equations is (15, 1)

A system of equations is the set of equations in which we perform operations simultaneously to solve the equation.

Given that, is a system of equations is x+y = 16 and x-y = 14

Solving the system of equations,

Add both the equations,

(x+y = 16) + (x-y = 14)

2x = 30

x = 15

Put x = 15 in any equation to find y,

x-y = 14

y = 1

Hence, the solution of the given system of equations is (15, 1)

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The question is solved for consider the system x+y=16 x-y=14, find the solution of the system,

Answer:

a. Elena has fewer roses than Lin. Lin has 6 roses and Elena has x roses.

Step-by-step explanation:

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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25 mcg is equal to 0.025 mg. both are unit of measurement of weight.

The prefix "mcg" stands for microgram, which is a unit of measurement in the metric system that is one millionth of a gram (10⁻⁶ g). On the other hand, "mg" stands for milligram, which is one thousandth of a gram (10⁻³ g). Therefore, to convert from mcg to mg, you need to divide the value in mcg by 1000.

In this case, 25 mcg divided by 1000 equals 0.025 mg. It's important to be mindful of the units when dealing with measurements, as confusion between different units of measurement can lead to incorrect calculations and dosing errors.

Overall, when converting from mcg to mg, you can easily make the conversion by dividing the value in mcg by 1000, as the prefix "milli" represents a factor of 1000 in the metric system.

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