You want to buy a $135,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at
6.1% interest for the rest.

How much is the loan amount going to be?

What will your monthly payments be?

How much total interest do you pay?

Suppose you want to pay off the loan in 15 years rather than 30. What will your monthly payment be?

The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long  The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

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Alright I got it.

So first what I did was I made an equation that match did the word problem.

The equation was 15x=250+10x

When I solved it the answer was 50.

so they would need to sell 50 Tshirts (x=50)

Amount of pounds that Ben get back is £75.

Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.

Ben changes £800 to Euros before he goes on holiday.

Before holiday, exchange rate is, £1 = 1.25 Euro

£800 = 800 × 1.25 Euros = 1000 Euros

He spends 895 Euros.

Euros left = 1000 - 895 = 105 Euros

Now, the exchange rate is £1 = 1.40 Euro.

or 1.40 Euro = £1

⇒ 1 Euro = £ 1/1.40

⇒ 105 Euros = £ (1/1.40) × 105 = £75

Hence Ben got £75 of pounds back.

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Answer:

point A

Step-by-step explanation:

Answer: 12x^3 y^3 (x − 4y)

(GCF is: 12x^3 y^3)

Step-by-step explanation:

This is the best I can do, sorry that I don't have an explanation.

If you are dealt one card from a​ 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.

Since there are 4 aces in a deck of card 52 first step is to find the number of cards  not aces in a deck of 52

Number of cards  not aces in a deck = 52 -4

Number of cards  not aces in a deck = 48

Now let find the probability that you won't draw an ace.

Probability = 48/52

Probability = 24/26

Probability = 12/13

Therefore we can conclude that the probability is 12/13.

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The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:

0.49x + 7.65 <= 10.00

This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."

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The value of the car will be £2,621 after 5 years.

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.

This is a situation of exponential decay.

Hence, using the exponential decay formula =

A = P(1-r)ⁿ

Where A is final value, P is principal value, r is rate of decrease and n is the number of years.

Here, we will find A, and we have,

P = £8,000.

r = 20% = 0.20

t = 5

Therefore,

A = 8000(1-0.20)⁵

A = 8000(0.80)⁵

A = 8000(0.32768)

A ≈ 2,621

Hence, the value of the car will be £2,621 after 5 years.

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The solution to the given quadratic equation is x = -1 + 3i OR x = -1 - 3i

From the question, we are to solve the given quadratic equation

From the given information,

The quadratic equation is

x² + 2x + 10 = 0

Using the Quadratic formula,

x = [-b ± √(b² - 4ac)] / 2a

From the equation,

a = 1, b = 2, and c = 10

Then,

x = [-b ± √(b² - 4ac)] / 2a

x = [-(2) ± √((2)² - 4(1)(10))] / 2(1)

x = [-2 ± √(4 - 40)] / 2

x = [-2 ± √(-36)] / 2

x = [-2 ± -6i] / 2

x = -1 ± 3i

x = -1 + 3i OR x = -1 - 3i

Hence, the solution is x = -1 + 3i OR x = -1 - 3i

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The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches

Perimeter of a triangle refers to the surface dimensions, this is calculated by the formula

Perimeter, P = a + b + c

where

a, b, c are sides of the triangle

The third side of the triangle will be calculated using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches

plugging the values as in the problem

let x be the required distance

x² = 30² + 5²

x² = 900 + 25

x² =  925

x = √925

x = 30.41 inches

Perimeter of the isosceles triangle

= 30.41 + 30.41 + 10

= 70.82 inches

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Answer:

-------------------------------

The height h of the tree is opposite to 49° angle of a right triangle with the other leg:

Use tangent to find the value of h:

The height of the tree is 40 feet to the nearest foot.

How can the height of the tree be found?

It can be found using similar triangles.

Let's call the height of the tree "x".

Since the angle of elevation to the sun is 49°, we have two similar triangles:

Triangle 1: Sun - Naomi - Ground (illustration attached)

Triangle 2: Sun - Tree - Ground

The height of Naomi, 5 feet, is one of the corresponding sides in the two triangles, and the height of the tree, x feet, is the other. We know the ratio of their heights is 8:1, so:

x ÷ 5 = 8

Solving for x, we find that:

x = 40

So the height of the tree is 40 feet to the nearest foot.

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Answer:

3 feet

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:

x^2 + 12^2 = 15^2

Solving for x, we get:

x = sqrt(15^2 - 12^2)

x = sqrt(9)

x = 3

Therefore, the distance from the tent pole to the rope is 3 feet.

The equation of the line passing through the points (-2,9) and (1,3) is

y = -2x + 11 where the slope is -2 and the y-intercept is +11

The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

m = (y2 - y1) / (x2 - x1)

y1 = 9

y2 = 3

x1 = -2

x2 = 1

m = (3 - 9) / (1 - (-2))

m = - 6 / 3

m = - 2

The equation of the line;

m = (y - y1) / (x - x1)

-2 = y - 9 / x - 1

y - 9 = -2(x - 1)

y - 9 = -2x + 2

y = -2x + 11

Therefore the y-intercept is +11.

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A number between 47 and 53 such that the prime factors are not repeated is:

3*17 = 51

Remember that any number can be written as a product of prime factors.

If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.

For example:

2*3*5*7 = 210

There are no repeated factors, but the number is not in the desired range.

2*5*7 = 70

Still not in the range.

You can try some times until you get for example:

3*17 = 51

This a number in the desired range, such that their prime factors are not repeated.

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Answer:

x = 32

Step-by-step explanation:

• any lower base angle is supplementary to any upper base angle.

here base angle = 2(x - 10) and upper base angle = 4x + 8

supplementary angles sum to 180°

sum the base and upper base angles and equate to 180

2(x - 10) + 4x + 8 = 180

2x - 20 + 4x + 8 = 180

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

4.8

Divide 250 by 2 which is 125 then do 600 divided by 125. Then your answer should be 4.8.

Hello there!

Answer:

14

Step-by-step explanation:

Let the smaller side is x. Then the largest side is x * 7/5.

Perimeter is equal to 2 * (x + 7/5 * x) or 48.

2 * (x + 7/5 * x) = 48

5/5 * x + 7/5 * x = 24

12/5 * x = 24

12/5 * 5/12 * x = 24 * 5/12

x = 10.

Tha larger side is 10 * 7/5 = 14.

Step-by-step explanation:

Given ,

To Find : Which side is longer

We know the formula to find the perimeter of a parallelogram is,

[tex]P = 2(a+b)[/tex]

We take 'x' to find out which side is longer

[tex]48 = 2(7x+5x)\\48 = 2(12x)\\48 = 24x\\\frac{48}{24} = x[/tex]

[tex]2 = x[/tex]

Side a = 7x = 7 x 2 = 14

Side b = 5x = 5 x 2 = 10

Side a [tex]\geq[/tex] Side b

Hence,  side a is longer

Answer: There is no picture

Step-by-step explanation:

The  value of the given polynomial equation would be: [tex]6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

In contrast to the vertex form of a quadratic equation, which is y = a (x h) 2 + k, the normal quadratic form is written as an x 2 + b x + c = y. The constant that indicates whether the parabola is facing up (+ a) or down ( a) is called a. It is represented in both forms by the letters y, x, and a.

In the equation we are given the value of y as: 1

[tex]6y2 + 3y - 1 4 \\\\6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

Therefore, we can say that the value of the given polynomial is: 8

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Complete question is: Find 6y2 + 3y - 1 4 for y = 1

Sales Tax = $3.00

The total amount paid by the group was $48.15

The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:

Sales tax = $37.50 * 8% = $3.00

The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:

Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15

So the total amount paid by the group was $48.15.

The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.

Truth value is defined as whether the given proposition is either true or false, not both.

Here the proposition is of the form if p, then q.

Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.

Here, both of the propositions are false.

The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.

Here, since both of the statements are false, the truth value is true.

Hence the truth value of the given proposition is true.

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The value of y is 16 when x = 32 for equation y = (1/4)x divided by 2.

Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It displays how the expressions on the left and right sides are equally related. We have LHS = RHS in any mathematical equation. Equations can be solved to get the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation.

The given equation is

y = 1/4 x divided by 2

So,

y = ((1/4)x)/ 2

y = (2/4) × x

Put x = 32

y = 2/4 ×32

y = 2 × 8

y = 16

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Answer: The conditions for inference are met in this scenario.

In order to use inference to determine if the true proportion of American adults who work more than one job differs from 12%, the following conditions must be met:

The sample must be randomly selected from the population.

The sample size must be large enough (usually at least 30).

The sample must be representative of the population.

In this case, it is stated that a random sample of 100 American adults was selected, which meets the first condition.

The sample size of 100 is also large enough, which meets the second condition.

There is no information given about whether the sample is representative of the population, but this is not necessary for the conditions for inference to be met.

Therefore, the conditions for inference are met in this scenario.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given L is the line through A(1, 2, -1) and B(5, -3, 4), you want its direction vector, a parameterization of L, 2 points on L that are 2 units from A, and a unit speed parametrization of L.

A direction vector for L will be the vector AB.

  [tex]\overrightarrow{AB}=B-A=(5,-3,4)-(1,2,-1)\\\\\boxed{\overrightarrow{AB}=(4, -5,5)}[/tex]

The parameterized equation will be ...

  [tex]L=A+t\cdot\overrightarrow{AB}\\\\\boxed{L=(1+4t,2-5t,-1+5t)}[/tex]

The direction vector has length √66, so we can find two points on L that are 2 units from A by using t = ±2/√66 in the parameterized equation.

Here, they are:

  P1 = L(2/√66) = (1 +8/√66, 2 -10/√66, -1 +10/√66)

  P2 = L(-2/√66) = (1 -8/√66, 2 +10/√66, -1 -10/√66)

In the Answer section above, these are written with rationalized denominators.

The unit speed parametrization uses the unit direction vector instead of the unnormalized direction vector in the parameterized equation. Effectively, t is scaled by a factor of 1/√66.

  L = (1 +4t/√66, 2 -5t/√66, -1 +5t/√66)

In the Answer section above, this is written with rationalized denominators.

You might notice here that it is easier to answer part 3 if you have this equation. You need only substitute t=±2 to get the points 2 units from A.

Answer:

= 18√2

decimal =25.45584412

6% of the salary is $366

The total amount that would in the retirement account in the account each month is $732.

The amount that would be in the retirement account when you retire is $345,418.50.

The amount of money that you put in the account is $162,504.

The amount of money that the employer put in the account is $162,504.

The interest that was gained over the years is $20,410.50.

3% of the salary is $183.

The total amount that would in the retirement account in the account each month is $366.

The amount that would be in the retirement account when you retire is $172,709.25.

The amount of money that you put in the account is $81,252

The amount of money that the employer put in the account is $81,252

The interest that was gained over the years is $10,205.25.

6% of the salary = salary x percentage

6% of the salary = 6% x $6,100

6% of the salary = 0.06 x $6,100 = $366

The amount in your account at the end of the month = amount the company puts + amount you deposit

= $366 + $366 = $732

Amount that would be in your retirement account = (1 + interest rate) x amount in the account

Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year

Amount in the account at retirement = $732 x 12 x (62 -25)

$732 x 12 x 37 = $325,008

Amount in the account at retirement = (1 + 0.0628) x $325,008 = $345,418.50

Amount the employer put in the account =  $325,008 \ 2 = $162,504

Interest earned = $345,418.50 - $325,008 = $20,410.50

3% of the salary = salary x percentage

3% of the salary = 3% x $6,100

3% of the salary = 0.03 x $6,100 = $183

The amount in your account at the end of the month = amount the company puts + amount you deposit

= $183 + $183 = $366

Amount that would be in your retirement account = (1 + interest rate) x amount in the account

Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year

Amount in the account at retirement = $366 x 12 x (62 -25)

$366 x 12 x 37 = $162,504

Amount in the account at retirement = (1 + 0.0628) x $325,008 = $172,709.25

Amount the employer put in the account =  $162,504 \ 2 = $81,252

Interest earned = $172,709.25 - $162,504 = $10,205.25

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For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.

An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.

Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.

Let, n = 0.

Therefore,

7⁴ - 7⁰.

= 2401 - 1.

= 2400.

= 30×80, Divisible by 30.

Similarly for n = 1 we have,

7⁵ - 7¹.

= 16807 - 7.

= 16800.

= 30×560.

Hence by induction, the cycle will continue.

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