Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
How much interest will Rich accrue during the 4.5-year non-payment period?

Answer:

Step-by-step explanation:

radius, r = 2√2

let the center be A(a, b):

The distance from the center to any of the 2 points is r.

So for (7, 2):

it satisfies the equation:

(x-a)²+(y-b)² = r²

Substituting x and y:

(7-a)²+(2-b)² = (2√2)²

squaring both sides:

(7-a)² + (2-b)² = 8

a² +b² - 14a -4b + 49+ 4= 8

a² +b² - 14a -4b + 45= 0        (Eqn 1)

For (3, 2):

it also satisfies the equation:

(x-a)²+(y-b)² = r²

Substituting x and y:

(3-a)²+(2-b)² = (2√2)²

squaring both sides:

(3-a)² + (2-b)² = 8

a² +b² - 6a -4b + 9+ 4= 8

a² +b² - 6a -4b + 5= 0        (Eqn 2)

We can now proceed by elimination:

(Eqn 2) - (Eqn 1):

(a² +b² - 6a -4b + 5) - (a² +b² - 14a -4b + 45) = 0

- 6a - -14a+ 5  - 45 = 0

8a - 40 = 0

8a = 40

a = 40/8

Putting a back into (Eqn 2):

a² +b² - 6a -4b + 5= 0

5² +b² - 6(5) -4b + 5= 0

25 +b² - 30 -4b + 5= 0

b² -4b = 0

b(b -4) = 0

Values of b:

POSSIBLE EQUATIONS OF CIRCLE:

Since we have 2 values of b, we have 2 possible centers:

(5, 0) and (5, 4)

Putting the centers into the standard equation of the circle above, we obtain:

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Answer:

801.66

Step-by-step explanation:

calculator

Answer:

801.6632653061

Step-by-step explanation:

.......

Answer:

the middle one

Step-by-step explanation:

y/x

and so 6/8 = y/16

Answer:

15.08 m

Step-by-step explanation:

The angle XZW :

XZW + 108° = 180°

XZW = 180° - 108°

XZW = 72°

Length of an arc = θ / 360 * πd

d = diameter = XV = 24

Length of arc XW = (72/360) * π * 24

Length of arc XW = 15.0796

Length of XW = 15.08 m

Answer:

15.08

Step-by-step explanation:

Answer:

Eka served about 1,047 pints of punch at the party

Step-by-step explanation:

Total pints of grape and cranberry juices mixed = 767 + 315 = 1052 pints

Number of pints left over = 5 pints

Number of pints served = (Number of pints mixed) - (Number left over)

Number of pints served = 1052 - 5 = 1,047 pints

Eka served about 1,047 pints of punch at the party

Answer:

April took out a loan of $600 and paid it back with simple interest of $60 after 5 years. The formula to calculate interest is  given the principal  and the time   and the interest rate  is . For this problem we have to find the interest rate   given  . To archive that , we can just solve the equation making the interest rate the subject of the formula as shown below,

The interest rate is  or 0.02 as a decimal. The interest rate is 2% as a percentage.

Step-by-step explanation:

Answer:

2%

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

In mathematics rational means "ratio like." so a rational number is one that can be written as the ratio of two integers. 1 3/23 can be converted into 26/23, which is a ratio, therefore, 1 3/23 is a rational number.

Hope this helps!

The value of the test​ statistic is - 0.462.

A standard deviation (or) would be a way of measuring of how widely distributed the data has been in relation towards the mean. A low standard deviation indicates that data is grouped around the mean, whereas a high standard deviation indicates that data is more spread out.

The null hypothesis is:

H0 = 0.25

The alternate hypothesis is:

H1 does not equal to 0.25,

the general formula for standard deviation is :-

σ=√1N∑Ni=1(Xi−μ)2 σ = 1 N ∑ i = 1 N ( X i − μ ) 2.

Our test statistic is:

t = (x- u) /s

In which X is the sample mean,  u is the population mean(the null hypothesis),   s is the standard deviation of the sample.

According to question,

x = 23/100

x = 0.23

u = 25/100

u= 0.25

s= √(0.25 * 0.75)/100

s = 0.0433

so for the value of t,

standard deviation = (x - u)/t

so , t=  (x- u) /s

t = (0.23 - 0.25)/0.0433

t = - 0.462

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Answer:

4.5

Step-by-step explanation:

one decameter is equal to 1000 centimeters 4500/100= 4.5

The subway car passes through 48 stations in 2hours

It is given that a subway car passes 4 stations every 10 mins.

Subway car is being referred to the metro system of New York city

It is known to us that an hour has 60 mins

We are given that subway car passes 4 stations every 10 mins

Therefore number of stations passed by subway car in 1 hour

= 60/10 x 4 = 24 stations

We are required to find the number of stations crossed by subway car in 2 hours

Therefore, number of stations crossed by subway car in 2 hours= 24 x 2

= 48  stations

Therefore, the subway car passes 48 stations in 2 hours

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Answer:

See below

Step-by-step explanation:

Need the choices.....

     essentially,  you can multiply this equation  by any constant to get an equivalent equation with the same solutions.

x^2 + 8x + 2 = 0      multiply both sides by '3' to get

3x^2 + 24 x + 6 = 0     <===== this will have the same solutions

    or this one:

x^2 + 8x + 2  = 0            Multiply both sides by   '6' to get

6x^2 + 48x + 12 = 0      <===== this will have the same solutions also

etc....

Answer:

27318 dollars

Step-by-step explanation:

add 24,789 to 2529 to get 27,318

The probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected is 65.53%.

This can be calculated using the normal distribution. The mean of the normal distribution is the population means, which in this case is 21,604 dollars per annum. The standard deviation is 727 dollars per annum. Using this information, we can calculate the z-score of 21635 dollars per annum by subtracting the population mean from it and dividing it by the standard deviation. This gives us a z-score of 0.42.

21635-21329/727=0.42

Using a z-table, we can calculate the probability of the sample means being less than 21635 dollars to be 0.6553.

This can also be written as 65.53%. This means that there is a 65.53% probability that the sample mean of 193 persons randomly selected would be less than 21635 dollars per annum.

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Answer:

x=70

Step-by-step explanation:

The value of x is 70 because this triangle is isosceles, meaning that there are two congruent sides and two congruent angles (which are the base angles). x is one of the base angles, 70º is the other base angle's measurement, so x=70.

Answer:

  2048

Step-by-step explanation:

You want the value of a10 = 4(2^(10 -1)).

If you don't have powers of 2 memorized, you can put this expression into your calculator or spreadsheet to get it evaluated. You will need parentheses around the exponent.

  4(2^(10-1)) = 4(2^9) = 4(512) = 2048

The value of the expression is 2048.

__

Additional comment

This looks like an instance of the equation for the n-th term of a geometric sequence:

  an = a1·r^(n -1)

where a1 = 4, r = 2, and n = 10.

This is why we have assumed that the "-1" is part of the exponent, and that you simply want the value of the right-side expression.

If this equation means something else, then it needs to be written differently. For example, if a10 means 'a' to the 10th power, it needs to be written as a^10, and we need to be told we're solving for 'a'.

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The numeric values of the graphed function are given as follows:

To obtain the numeric values of a function from its graph, you can use the following steps:

When x = 1, the point with a closed circle is at y = 4, hence the numeric value is given as follows:

g(1) = 4.

When x = -12, we have that y = -10, hence the numeric value is given as follows:

g(-12) = -10.

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Given:

Point A'(6,3) is a dilation of point A(18,9).

To find:

The scale factor.

Solution:

We know that, if a point P is dilated by factor k and origin is the center of dilation, then

\(P(x,y)\to P'(kx,ky)\)

Let the scale factor for the given problem be k. So,

\(A(18,9)\to A'(18k,9k)\)

On comparing A'(18k,9k) and A'(6,3), we get

\(18k=6\text{ and }9k=3\)

\(k=\dfrac{6}{18}\text{ and }k=\dfrac{3}{9}\)

\(k=\dfrac{1}{3}\text{ and }k=\dfrac{1}{3}\)

Therefore, the scale factor is \(\dfrac{1}{3}\).

Answer: x=6y−5 x = 6 y - 5.

Step-by-step explanation:

I answered this math question edge.

Step-by-step explanation:

g(x) = x² + 3

g(-5) = (-5)² + 3

g(-5) = 25 + 3

g(-5) = 28

In the final year of the truck's useful life, Basic Bass Company should record a depreciation expense of $5,000.

To calculate the depreciation expense in the truck's final year, we need to determine the annual depreciation amount. The formula for straight-line depreciation is:

Annual Depreciation = (Initial Cost - Residual Value) / Useful Life

In this case, the initial cost of the truck is $28,000, the residual value is $3,000, and the useful life is 5 years. Therefore, the annual depreciation is:

Annual Depreciation = ($28,000 - $3,000) / 5 = $5,000

Since Basic Bass Company has already recorded 4 full years of straight-line depreciation, the remaining depreciation expense for the truck's final year is equal to the annual depreciation amount:

Depreciation Expense in Final Year = Annual Depreciation = $5,000

Therefore, Basic Bass Company should record $5,000 in depreciation expense in the truck's final year.

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Answer:

(-35) * (100 - 1)

Step-by-step explanation:

She was able to find the value of (-35) * 99 without using the missing 9 button on her calculator.

The easiest way to do this is to replace 99 with another set of numbers that has the same value as 99.

(100 - 1) has the same value as 99. So, Teena can replace 99 with (100 - 1):

(-35) * (100 - 1)

It will yield the desired result.

Answer:

4√2 or 5.66

Step-by-step explanation:

x² + x² = 8²

=> 2x² = 64

=> x² = 32

=> x = √32 = 4√2 or 5.66

Answer:

7.834 × 10^-8

Step-by-step explanation:

= 7.834 × 10^-8

(scientific notation)

= 7.834e-8

(scientific e notation)

= 78.34 × 10^-9

(engineering notation)

(billionth; prefix nano- (n))

= 0.00000007834

(real number)

^ means the number after is exponent.

Answer:

10.8 cm

Step-by-step explanation:

Using cosine law

g² = 7.1² + 6.7² - 2(7.1)(6.7)cos(103)

g² = 116.7018433

g = 10.80286274

Answer:

10.8

Step-by-step explanation:

deltamath

Answer:

<stv and <stq

Step-by-step explanation:

adjacent angles have the same vertex and are side by side.

Susan's cost of 35.2 ounces (that is, 2.2 pounds) pumpkin is   $3.96.

At a store, Susan selected a pumpkin that weighed 35.2 ounces.

We know that one pound consists of sixteen (16) ounces by methods of conversion.

That is, 16 ounces = 1 pound

⇒ 1 ounce = 1/16 pound

⇒ 35.2 ounces = (35.2)(1/16) pound = 2.2 pounds

Thus, Susan selected a pumpkin that weighed 2.2 pounds.

The cost of per pound of pumpkin is  $1. 80.

That is in simple words, one pound of pumpkin costs  $1. 80.

Therefore cost of 2.2 pounds of pumpkin is =  ${(1. 80)(2.2)} =  $3.96

Thus, the cost of 35.2 ounces of pumpkin Susan paid is  $3.96.

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To determine if a differential form is exact, we need to check if its partial derivatives satisfy the condition of equality. If the differential form is not exact, we can multiply it by an integrating factor to make it exact.

Given a differential form of the form M(x, y)dx + N(x, y)dy, we can determine if it is exact by checking if ∂M/∂y = ∂N/∂x. If this condition is not satisfied, the differential form is not exact. However, we can multiply the differential form by an integrating factor to make it exact.

By multiplying the original differential form by an integrating factor, which is usually a function of either x or y, the resulting form will have equal partial derivatives, satisfying the condition for exactness. The integrating factor effectively "corrects" the form and makes it exact.

By finding the appropriate integrating factor and multiplying it with the given differential form, we can transform it into an exact form. This process is a fundamental technique in solving certain types of differential equations and allows us to find solutions that would otherwise be challenging to obtain.

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Answer:

113.04

Step-by-step explanation:

Given:V = 324 cu

cmh = 9 cm

Since the formula for the volume of a cylinder is V = AreaBase*heightAreaBase = V/height = 324cu cm/ 9 cmAreaBase = 113.04 square centimetresTherefore, the area of the pillar in square centimeters is 113.04

The base area of the cylindrical pillar would be; 113.04 cm²

The volume of the cylinder is the product of the height, pie, and square of the radius.

v = πr²h

where, r = radius, h = height

Therefore,

v = 324π cm³

h = 9cm

Consider find the radius;

324π = 9πr²

r² = 324π  /9π

r² = 36

r = √36

r = 6 cm

Base area of the pillar = πr²

Base area of the pillar = 36π

Base area of the pillar = 36 × 3.14

Base area of the pillar is 113.04 cm²

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