Aiden invested $98,000 in an account paying an interest rate of 2 3/8% compounded
continuously. Autumn invested $98,000 in an account paying an interest rate of 2 3/4%
compounded quarterly. After 11 years, how much more money would Autumn have in
her account than Aiden, to the nearest dollar?

Answer:

x = 6 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

6^2+ x^2 = 12^2

36 + x^2 = 144

Subtract 36 from each side

x^2 = 144-36

x^2 =108

Take the square root of each side

sqrt(x^2) = sqrt(108)

x = sqrt(36*3)

x = 6 sqrt(3)

Answer:

1 and 8,  4 and 5

Step-by-step explanation:

There are two pairs, 1 and 8,  4 and 5

The angles in each pair must be on opposite sides of the transversal k, and on the outsides of the parallel lines l and m.

Answer:

The answer is -1

Step-by-step explanation:

-[(5-8)+12] ÷ 9

-[-3+12] ÷ 9

[3-12] ÷ 9 {becoz (- × + = -) (- × - = +)}

-9 ÷ 9

-1

Hope this may help you to solve these problems ☺

Answer:

30 squares would be next in sequence

Step-by-step explanation:

each block of squares are adding as many as it takes to make an L around the previous square

Answer:

Step-by-step explanation:

sin 32 degree = x/48

0.529*48 = x

25.392 = x

x = 25.4 (after converting to the nearest tenth)

tan 62 degree = 25/x

1.88 = 25/x

x = 25/1.88

x = 13.29

x = 13.3 (after converting to the nearest tenth)

Answer:

The correct answer is - 6 hours 24 minutes.

Step-by-step explanation:

Given:

Clock A - The short hand points just after 2 and the long hand points to the third tick mark after 2 = 2'O clock and thirteen minutes.

Clock B - The short hand points about halfway between 8 and 9 and the long hand points to the second tick mark after 7 = 8'O clock and 37 minutes.

Solution:

The time difference between two clocks can be calculated by subtracting the time of clock A from the time of clock B.

time passed = 8'O clock and 37 minutes - 2'O clock and thirteen minuts

= 6 hours and 24 minutes.

Answer:

1,200 one decimeter pieces can be cut

Step-by-step explanation:

Find how many 1 decimeter pieces can be cut by converting the 120 meters to decimeters.

In 1 meter, there are 10 decimeters.

So, convert 120 meters to decimeters by multiplying it by 10:

120(10)

= 1,200

So, there are 1,200 decimeters in the strip. This means that 1,200 one decimeter pieces can be cut, since 1,200 divided by 1 is 1,200.

So, 1,200 one decimeter pieces can be cut

Answer:

y - 22 = 14(x - 1)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 14x - 3 ← is in slope- intercept form

with slope m = 14

Parallel lines have equal slopes

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 14 and (a, b) = (1, 22) , then

y - 22 = 14(x - 1)

Answer:

5

Step-by-step explanation:

If you multiply each side by 5 to get 42:30 then subtract 42 by 30, 12 is leftover.

Answer:

The numbers should be 42 and 30

Step-by-step explanation:

Okay, so the equation should be:

7x - 5x = 12

2x = 12

x = 6

and find the numbers:

7 x 6 = 42

5 x 6 = 30

Answer:

Perimeter= 20 cm

Area = 25 cm^2

Difference between 28cm^2 and 8cm^2= 20cm^2

Step-by-step explanation:

The formula to calculate the perimeter of a square is P= 4 * (the length of any side or "s").

Therefore:

P = 4 * 5cm

P = 20 cm

The formula for calculating the area of a square is A= (length of any side or "s")^2

So:

A= 5cm^2

A= 25cm^2

Remember the units in your answer!

The difference between indicates subtraction, and 28cm^2 and 8 cm^2 are like terms so:

28cm^2 - 8 cm^2 = 20 cm^2

===========================================================

Explanation:

Let's go through the answer choices

Going back to choice C, again we don't have enough info to determine if the system is independent or dependent, but we at least know it's consistent. Consistent systems have one or more solutions. So part of choice C can be confirmed. It being the only thing left means that it has to be the final answer.

If it were me as the teacher, I'd cross out the "independent" part of choice C and simply say the system is consistent.

Answer:

Above that (1, 0, 1) is a solution to a system of three linear equations, The system can only be independent and consistent. is true about the system.

Answer:

Question 12: Find the slope from these two points: (-3,-3) and (-4,-8)

The formula for finding the slope from two points is attached to this answer.

So if we plug in our values that correspond to the formula we get the following:

First pair: -3 is our x1, -3 is our y1,

Second pair: -4 is our x2, -8 is our y2

-8--3/-4--3

-8+3/-4+3

-5/-1=5, Our slope is 5 for question 12

Question 18: Find the area of a circle with a diameter of 31.

Area=[tex]\pi r^2[/tex]

So we have [tex]15.5^{2} \pi[/tex]

240.25 times 3.14 is 754.385, if we round to the nearest whole number we receive 754 as our answer for question 18

Question 21: Find the measurement of a missing leg in a right triangle when given the hypotenuse and another leg

We know that the hypotenuse is 8cm and one of the legs is 5cm

the formula would be [tex]a^{2} +b^{2}= c^{2}[/tex] for the hypotenuse but this can be used to find the missing legs as well.

[tex]5^{2} +b^{2} =8^{2}[/tex]

[tex]25+b^{2} =64[/tex]

Subtract 25

[tex]b^{2} =39[/tex]

b would equal 6.44 something but the question said to round to the nearest whole number which would be 6.

Question 23: Find the volume of a cone

Radius: 10, height: 7

Formula to find the volume of a cone: 1/3 times 3.14 times r^2 times the height

1/3 times 3.14 times 10^2 times 7

1/3 times 3.14 times 700

1.046 (the 46 is repeating) repeating times 700

732.06 repeating, the 6 is repeating.

The question also asks us to round to the nearest whole number so the answer to question 23 would be 733

Question 26: Find the volume of a sphere

Radius is 6 and pi is 3.14

Formula: [tex]4\pi \frac{r^3}{3}[/tex]

So we have 4 times 3.14 times 6^3 divided by 3

4 times 3.14 times 108/3

4 times 3.14 times 36

12.56 times 36

452.16, I didn't see this answer listed on your worksheet, so please correct me if I'm wrong

Question 47: Probability of a number cube rolled many times to see how many times an even number is rolled.

Since this is a standard number cube there must be 6 sides, therefore half the numbers are even so

65 * 2 = 32.5, which rounds up to 33

33 is our answer to question 47

Hope I helped, have a nice day :)

Answer:

The same as

Step-by-step explanation:

When writing coordinates₋₋also known as "points" on a coordinate plane₋₋you write it as (x point,y point) more simply written as (x,y).

So in both tables, you can see that there are several coordinates listed. Each with the same format (x,y).

If you compare the two tables, you can see that the numbers in the (x,y) position are the exact same for corresponding coordinates.

Now you can conclude what the answer is:

The x-coordinates in Table A are the same as the x-coordinates in Table B.

Answer:

A. y = 1/4x - 2

Step-by-step explanation:

The y- coordinate is placed at -2, on the y-axis

Then the line rises up 1 unit, and runs 4 units, landing on a point and forming the line.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

the mistake they made was the wrong offset from point (0,0) into the y direction. the incline of the line was correct.

the correct equation is y = 1/2×x - 2, because this line contains both points (4,0) and (0,-2)

Step-by-step explanation:

we are looking for a line equation

y = a×x + b

the 2 points give us 2 equations to solve for the 2 variables a and b :

0 = a×4 + b

-2 = a×0 + b

=> b = -2

=> -b = a×4, => a = -b/4 = 2/4 = 1/2

so, the right equation for the line going through both points is

y = 1/2×x - 2

the difference to the original equation is simply the offset from the x- axis in the y direction.

the original equation would be parallel to the correct equation but hit the y-axis at (0,4) instead of (0,-2), and it would hit the x-axis at (-8,0) instead of (4,0)

Answer:

20

Step-by-step explanation:

GF = 3

HF = 9

GE = 14

HG = 9 - 3 = 6

6 + 14 = 20

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Step-by-step explanation:

system of Linear Equations 2 variables

hamburger = x

fries = y

Stefan

3x + 4y = $26.5

Nancy

4x + 2y = $29.5

elimination

3x + 4y = $26.5 | ×1 |

4x + 2y = $29.5 | ×2 | -

3x + 4y = $26.5

8x + 4y = $59. -

-5x = $-32,5

x = $-32,5 ÷ -5

x = hamburger = $6.50

I hope this help

Answer:

[tex]\fbox{3\sqrt{2}}[/tex][tex]3\sqrt2[/tex]

Step-by-step explanation:

Step 1:

Let us figure out the measurements of all the angles first. We are given one angle of 45º, and another of 90º. The angles of a triangle must add up to 180º, hence we can use basic addition and subtraction to find the last angle.

[tex]\angle=180-90-45\\\angle=45[/tex]

Great our angle is 45º! Notice something...?

Step 2:

We now have two 45º angles in our triangle. This means we have an isosceles triangle.

According to BATh (base angle theorem), in an isosceles triangle, the angles opposite the congruent sides are congruent. Thus, y is congruent to the given side of [tex]3\sqrt2[/tex].

y=[tex]\fbox{3\sqrt{2}}[/tex][tex]3\sqrt2[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

12x3+6x2+34x+17

Step-by-step explanation:

(2x+1)(6x2+8+9)

=(2x+1)(6x2+8+9)

=(2x)(6x2)+(2x)(8)+(2x)(9)+(1)(6x2)+(1)(8)+(1)(9)

=12x3+16x+18x+6x2+8+9

=12x3+6x2+34x+17

Answer:

1300

Step-by-step explanation:

4 times 5 = 20

260 times 5 = 1300

Answer:

1300 times

Step-by-step explanation:

195 is is 3 X 65 so dividing 195 by 3 gets you 65

65 X 20 = 1300

Answer:

The cylindrical one

Step-by-step explanation:

We know that the container does not have anything inside it, and we only want the surface, so we will figure out the surface area. The less surface area the package has, the less plastic is used.

The surface area for a cylinder is 2πrh +2πr². Plugging 5 in for r (the radius) and 19 in for the height, we get

2π(5)(19) + 2π(5)² = 753.98

The surface area for a rectangular prism is 2(wl + hl +hw), with 10 being the width, 12 being the length, and 19 being the height in this example, resulting in

2(10*12 + 19 * 12 + 10 * 19) = 1076

The surface area for the cylinder will clearly have less surface area/plastic

Answer:

$1251.59

Step-by-step explanation:

tax percent = 6.7%

cost price of watch = $113

tax amount = tax percent of total price

=6.7 % * 1173

=6.7/100 *1173

=78.591

Now find total cost of a watch with tax

total cost = tax amount + original cost price

=$78.591 + $1173

=$1251.59

Answer:

$15

Step-by-step explanation:

50% = .50

$10 × .50 = 5

10 + 5 = 15

Answer:

$20 - $1.75N

Step-by-step explanation:

the amount of change she receives is equal to the amount she paid less the total value of cards

total value of cards = price per card x total quantity of cards bought

$1.75 x N =  $1.75N

Amount of change = $20 - $1.75N

If she buys 10 cards, the amount of change she receives would be

$20 - $1.75(10) =

20 - 17.5 = 2.5

Answer:

A. It increased both her intensity and her workout time.

Step-by-step explanation:

A. It increased both her intensity and her workout time.

B. It decreased her intensity but increased her workout time.

C. It increased her intensity but decreased her workout time.

D. It decreased both her intensity and work out time

Last week = 4 miles per day

This week = 5 miles per day

Intensity refers to how hard one exercises.

Workout time refers to how long one exercises the body.

By adding a mile, she has increased how hard she exercises her body (intensity))

And also increased how long she exercises the body (workout time) because the time she spent on 5 miles per day is more than time spent on 4 miles per day

Answer:

68

Step-by-step explanation:

Let x=adult tickets and y=child tickets

1) 15x+11y=1889

2) x+y=147

multiply equation 1 by -1/11 on both sides to get:

-(15/11)x-y=-171.73

add new equation with equation 2 to get

-4/11x=-24.73

Isolate x to get:

x=67.99999

Round up to get 68 adult tickets

Answer:

D

Step-by-step explanation:

an undefined slope has the same x value no matter what y value it has, therefore, D

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