Scott takes a student loan to go to college after high school. If he pays $750 in interest at a rate of 3%, how much must the loan have been for originally?

Answer:

[tex]\large\boxed{(x-5)^2+(y+7)^2=36}[/tex]

Step-by-step explanation:

The equation of a circle in standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We hace the center at (5, -7) → h = 5 and k = -7.

The radius is equal to the distance petween the center and other point on the circumference of a circle.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Substitute the coordinates of the points (5, -7) and (5, -1):

[tex]d=\sqrt{(5-5)^2+(-1-(-7))^2}=\sqrt{0^2+6^2}=\sqrt{36}=6[/tex]

Therefore the equation of a circle is:

[tex](x-5)^2+(y-(-7))^2=6^2\\\\(x-5)^2+(y+7)^2=36[/tex]

let's recall that in an isosceles triangle, the twin sides make twin angles at the bottom/base, so on the triangle on the left-side, if the "vertex" atop has an angle of 116°, then the twin sides below are simply 180° - 116 = 64, split that in half and that's 32° each.

The same is true for the isosceles triangle on the right side.  Also recall that a flat-line is always 180°, 32 + 72 + 76 = 180.

Check the picture below.

Answer: b) rolled three times, number of 2s rolled

              d) rolled twice, number of odds rolled

Step-by-step explanation:

A binomial experiment must meet the following criteria:

a) rolled twice --> satisfies #1 & #2 (n = 2)

   X is the sum --> fails #3 (more than two outcomes)

b) rolled three times --> satisfies #1 & #2 (n = 3)

   X is the number of 2s rolled --> satisfies #3 & #4 (P success = 1/6)

c) rolled an unknown number of times - fails #1

d) rolled twice --> satisfies #1 & #2 (n = 2)

   X is the number of odds rolled --> satisfies #3 & #4 (P success = 1/2)

14.(22) = 14.(20 + 2)

We still have 14 multiplying 22 but now it will multiply it by 20 and sum it after multiply by 2

So we have the distributive proppertie.

Answer:

distributive property.

Step-by-step explanation:

If you rewrite the problem 14(22) as 14(20+2) so that you can use mental math

22 is written as 20+2

so we got 14(20+2)

to multiply this we distribute 14 inside the parenthesis

we multiply 14 with 20 and then multiply 14 with 2

we are distributing 14 inside the parenthesis so its distributive property.

Choice D, because you would have to divide 3 1/2 by 2 to find the answer

the rest are either subtraction or multiplication

Answer:

Option D  is best modeled with a division expression

Step-by-step explanation:

A)  How much does it cost to buy 3 and 1/2 pounds of apples at $2 per pound?

Cost of 1 pound = $2

Cost of 3 and 1/2 pounds  = [tex]2 \times 3.5[/tex]

B) B. How many apples are needed for 2 pies if the recipe uses 3 and 1/2 apples per pie?

1 pie requires 3.5 apples

So, 2 pies requires apples = [tex]3.5 \times 2[/tex]

C)  How many more apples are needed if a recipe uses 3 and 1/2 apples and you only have 2 apples?

Recipe requires 3.5 apples

You have 2 apples

More apples required = 3.5 - 2

D) . How many apples are in each pie if a total of 3 and 1/2 apples were used to bake 2 pies?

Apples required in 2 pies = 3.5

Apples required in 1 pie = [tex]\frac{3.5}{2}[/tex]

Hence Option D  is best modeled with a division expression

Answer:

0.56

Step-by-step explanation:

125 in total.

Let x be the number of those who passed both tests.

Thus,

x+(85-x)+(95-x)+15=125,

195-x=125,

x=70.

Thus, the probability that they passed both tests is

[tex]Pr=\dfrac{70}{125}=\dfrac{14}{25}=0.56.[/tex]

Answer:

30

Step-by-step explanation:

At the northside store there are 12 females with college degrees

At the southside store there are 18 females with college degrees

The total number of females at the two stores with college degrees is

12+18 = 30

Answer:

2:15

Step-by-step explanation: First you - 15 by 3:15 which = 3:00 then - 45 by 3:00 or 60 - 45 = 15. so therefore 2:15 is the answer. Have a good day, hope I helped

Answer:

Your answer should be 56

Marlena can choose 3 out of 8 essay questions in 56 different ways.

The question asked by the student is related to combinations in mathematics. Marlena must choose 3 out of 8 essay questions on her writing test. To determine how many ways Marlena can choose 3 questions, we use the formula for combinations:

C(n, k) = n! / [k! * (n - k)!]

Where n is the total number of items to choose from (in this case, 8 questions), and k is the number of items to choose (3 questions). The symbol '!' represents a factorial, which is the product of all positive integers up to that number. So we calculate as follows:

This simplifies to:

C(8, 3) = (8*7*6) / (3*2*1) = 56

Therefore, Marlena has 56 different ways to choose 3 out of the 8 essay questions.

Answer:

A

Step-by-step explanation:

We can use a simple formula to solve for SST. The formula is:

[tex]SST=\frac{SSE}{1-R^2}[/tex]

Where

the coefficient of determination is  [tex]R^2[/tex]

Now, we are given  [tex]R^2[/tex]  is 0.25 and SSE is 12 (not SEA, it's SSE). we simply put it into the formula and solve for SST:

[tex]\\SST=\frac{12}{1-0.25}\\SST =16[/tex]

correct answer choice is A

Answer:

The answer is B

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

area of a rectangle is determined by length times width so 5 units lies between -7 and -2; and 4 units lie between -5 and -1

The area of the rectangle with given vertices is calculated as the product of the lengths of two adjacent sides, resulting in 20 square units.

To find the area of the rectangle with vertices at A(-7,-5), B(-2,-5), C(-2,-1), and D(-7,-1), you can calculate the lengths of adjacent sides and multiply them together. The length of side AB is the difference in the x-coordinates of A and B, which is |-2 - (-7)| = 5. Similarly, the length of side AD is the difference in the y-coordinates of A and D, which is |-1 - (-5)| = 4.

Therefore, the area of the rectangle is 5 units times 4 units, which equals 20 square units.

By dividing the total amount of £1890 by 1.125, we find that the original price the Jones family thought they would be paying for their holiday was £1680, before the 12.5% surcharge was added.

The Jones family encountered a last-minute surcharge on their holiday package with Shark Tours, which affected the total cost they paid. Given a 12.5% surcharge applied to their original cost, we can calculate the initial price by considering the final amount (£1890) to be 112.5% (100% + 12.5%) of the original price. To find the original price, we divide the total amount by 112.5% (or 1.125 as a decimal).

Original price = Total amount paid / Surcharge rate

We then have:

Original price = £1890 / 1.125

Original price = £1680

Therefore, the Jones family originally thought they would be paying £1680 for their holiday before the surcharge was added.

Answer:

B

Step-by-step explanation:

Answer:

$14.00

Step-by-step explanation:

30% less than 100% of the regular price is 70% of the regular price.

Erica paid ...

0.70 · $20.00 = $14.00

Answer:

Step-by-step explanation:

First, i would add 15 until you get to 60, or divide.

15 / 60 = 4

Then multiply 30 by 4:  30 X 4 =120.

120 is the awnser.

Answer:

30 times

Step-by-step explanation:

subtract 250 from 400, then divide the number (150) by 5 to get your answer 30.

Answer:

C:  (4, 8)

Step-by-step explanation:

Rewrite the given equation x² - 8x = -y² + 16y - 44 in std. form:

                                              x² - 8x + 16 - 16 + y² - 16y + 64 =  64 - 44,  or

                                                 (x - 4)²  + (y - 8)² = 64 - 44 + 16

         Comparing this to            (x - h)² + (y - k)² = 6²

we see that h = 4 and k = 8.  The radius is 6.  The center is at (4, 8) (Answer C).

Answer:

43.96 ft, or about 44 ft

Step-by-step explanation:

C = 2πr.  Here, π is approx. 3.14 and r is 7 ft.  Thus, the circumference of the yard is

C = 2(3.14)(7 ft) = 43.96 ft

Answer:

it is A

Step-by-step explanation:

Answer:

B, E, F

Step-by-step explanation:

Equivalent expressions are expressions which are equal. To show expressions are equal, reduce to lowest terms by simplifying using exponent rules.

A. 8^2*8^x  = 8^2+x

B. (8*8)^x  = 64^x

C. 8*8^2x  = 8^(2x +1)

D. 8*8^x  = 8 ^ (x+1)

E. 8^2x  = 64^x

F. 8^x*8^x = 8^(x+x) = 8^(2x) = 64^x

Answer:

8^2x 8^x (8•8)^x

Step-by-step explanation:

Answer:

41.8%

Step-by-step explanation:

From the table, the total number of female patients is given as 335. On the other hand, the total number of female patients with type-O blood is given as 140. The probability that a randomly selected female patient will have type-O blood can be calculated as;

the total number of female patients with type-O blood/the total number of female patients

140/335 = 0.4179

As a percentage this becomes;

0.4179 * 100 = 41.8%

Therefore, the percentage of female patients with type-O blood is 41.8%

Answer:

[tex]\$10,665.64[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-r)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$19,900\\r=7.5\%=0.075\\x=8\ years[/tex]

substitute the values in the formula

[tex]V=\$19,900(1-0.075)^{8}=\$10,665.64[/tex]  

Answer: The answer is 10665.64

Step-by-step explanation:

Exponential Functions:

y=ab^x

A= starting value = 19900

r=rate = 7.5%=0.075

Exponential Decay:

b=1-r=1-0.075=0.925  

Write Exponential Function:

y=19900(0.925)^x

Plug in time for x:

y=19900(0.925)^8

y= 10665.6404317  

Evaluate

y≈10665.64

Final answer:

To calculate h(-3) for the function h(x) = x² - 2x - 5, we plug in -3 for x and simplify to get a result of 10.

Explanation:

To find h(-3) when given h(x) = x² - 2x - 5, we need to substitute x with -3 into the function and simplify:

h(-3) = (-3)² - 2(-3) - 5

= 9 + 6 - 5

= 15 - 5

= 10.

Therefore, h(-3) equals 10.

Answer: 64 daisies

Step-by-step explanation:

8 x 4 = 32                                                                                                                            8 x 8 = 64 daisies

Answer:

C

Step-by-step explanation:

Answer: C) 110

Step-by-step explanation:

ANSWER

[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]

EXPLANATION

We want to find the coordinates of the point W(x,y) which divides V(-3,3) and X(9,13) in the ratio m:n=3:4.

The x-coordinate of this point is given by:

[tex]x= \frac{mx_2+nx_1}{m + n} [/tex]

[tex]x= \frac{3(9)+4( - 3)}{4 + 3} [/tex]

[tex]x= \frac{21 - 12}{4 + 3} [/tex]

[tex]x= \frac{9}{7} [/tex]

The y-coordinates is given by;

[tex]y= \frac{my_2+ny_1}{m + n} [/tex]

[tex]y= \frac{3(13)+4( 3)}{4 + 3}[/tex]

[tex]y= \frac{39+12}{4 + 3}[/tex]

[tex]y= \frac{51}{7}[/tex]

Hence

[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]

Final answer:

The number of different subcommittees possible from a board of 10 members when forming a subcommittee of 3 members is 120, calculated using the combination formula C(10, 3).

Explanation:

To calculate the number of different subcommittees possible from a board of directors consisting of 10 members when forming a subcommittee of 3 members, we must use the concept of combinations because the order of selection does not matter. This is a problem of counting without regard to the order and is solved by using the combination formula:

C(n, k) = n! / (k! * (n-k)!) where 'n' is the total number of items to choose from, 'k' is the number of items to choose, 'n!' represents the factorial of n, and 'k!' is the factorial of k.

Here, 'n' is 10 (the total number of board members) and 'k' is 3 (the number of members to be chosen for the subcommittee). Thus, the formula for our calculation is:

C(10, 3) = 10! / (3! * (10-3)!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Therefore, there are 120 different subcommittees possible when selecting 3 members from a board of 10.

Final answer:

To find the number of different subcommittees possible from 10 members when selecting 3, the combination formula C(n, k) = n! / (k! * (n - k)!)is used, which results in 120 different subcommittees.

Explanation:

The student's question pertains to combinatorics, which is a field of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. Specifically, the student is asking about the number of ways to form a subcommittee of 3 members from a larger committee of 10 members. To solve this, one would use the combination formula, which is used for selecting items from a group without regard to the order in which they are selected.

The combination formula is given by:

C(n, k) = n! / (k! * (n - k)!)

Where:

n is the total number of items to choose from (in this case, 10 board members),

k is the number of items to choose (in this case, a subcommittee of 3 members),

n! (n factorial) is the product of all positive integers up to n,

k! (k factorial) is the product of all positive integers up to k,

(n - k)! is the factorial of the difference between n and k.

Applying the formula to the student's scenario:

C(10, 3) = 10! / (3! * (10 - 3)!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

So, there are 120 different subcommittees possible when choosing 3 members from a board of 10 members.

Answer:

294.5 m²

Step-by-step explanation:

shaded region = area of major sector + area of triangle

central angle of major sector = 360° - 130° = 230°

area of sector = area of circle × fraction of circle

A = π × 11.1² × [tex]\frac{230}{360}[/tex]

   = [tex]\frac{x11.1^2(230)\pi }{360}[/tex] ≈ 247.3 m²

area of triangle = 0.5 × 11.1 × 11.1 × sin130° ≈ 47.2 m²

shaded area = 247.3 + 47.2 ≈ 294.5 m²

Answer:

294.5 m^2 to the nearest tenth.

Step-by-step explanation:

First work out the area of the blue sector (not including the triangle):

The measure of the large arc =  360 - 130 = 230 degrees and the area of the Whole circle is π(11.1)^2 so, by proportion:

Area of the large sector = 230/360 * π(11.1)^2

= 247.30 m^2.

The area of the triangle = 1/2 * 11.1^2 sin 130 = 47.19 m^2.

So the area of the whole shaded region is 247.30 + 47.19

=  294.49 m^2 (answer)

The area of a circle with a diameter of 15 inches is 176.63 square inches and the circumference is 47.1 inches, using the formulas A = (pi)r² and C = (pi)d with (pi) approximated as 3.14.

The area and circumference of a circle can be calculated using the formulas A = (pi) r² for the area, and C = (pi) d for the circumference, where r is the radius, d is the diameter, and (pi) is approximately 3.14.

Given the diameter d = 15 inches, we first find the radius by dividing the diameter by 2, which gives us r = 7.5 inches. We then use the area formula to calculate:

Area = (pi) r² = 3.14 ×(7.5 inches)²

Area = 3.14 ×56.25 square inches

Area = 176.625 square inches

After rounding to the nearest hundredth, we get:

Area = 176.63 square inches

For the circumference, we use the formula:

Circumference = (pi) d = 3.14 ×15 inches

Circumference = 47.1 inches

Answer:

Option B. Area = 30 Perimeter = 22.31

Step-by-step explanation:

step 1

Find the measure of the sides of the pentagon

Observing the graph

AE= 5 units

ED ----> Applying Pythagoras theorem

ED²=2²+3²=13

ED=√13 units

DC=3 units

BC=4 units

AB ---->Applying Pythagoras theorem

AB²=3²+6²=13

AB=√45 units

step 2

Find the perimeter

P=AE+ED+DC+BC+AB

substitute

P=5+√13 +3+4+√45=22.31 units

step 3

Find the area

The area of the figure is equal to the area of two trapezoids

so

A=(1/2)(2+5)(6)+(1/2)(6+3)(2)=21+9=30 units²