The balance in Susan's checking account was $245.35. After the bank deposited interest into the account, her balance went to $248.02. How much interest did the bank pay Susan

Answer: 60

Step-by-step explanation: Plug in 8 for x and either use the linear supplements theorem to solve or the vertical angles congruence theorem.

Answer:

2.5cm

Step-by-step explanation:

area of trapezium = 4 * area of parallelogram

1/2(a+b)*h=4* bh

1/2(5+11)*4= 4* 3.2x

8*4=4*3.2x

8/3.2=x

2.5cm=x

Answer:

x = -85/3

Step-by-step explanation:

The solution is, the value of x is - 33.33 in 3(6x-5)-7(3x+10)=0.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given expression is:

3(6x-5)-7(3x+10)=0

now, we have to simplify the expression to solve for x

we get,

3(6x-5)-7(3x+10)=0

or, 18x - 30 - 21x - 70 = 0

or, 18x - 21x -30 - 70 = 0

or, - 3x - 100 = 0

or, 3x = -100

or, x = -100/3

or, x = - 33.33

Hence, The solution is, the value of x is - 33.33 in 3(6x-5)-7(3x+10)=0.

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Answer:

[tex](a)\ g(x) = \frac{2}{3}(x+1)[/tex]

[tex](b)\ h(y) = \frac{1}{3}[1 + 4y][/tex]

[tex](c)[/tex] [tex]P(x>0.5) =\frac{5}{12}[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \left \{ {{\frac{2}{3}(x+2y)\ \ 0\le x \le 1,\ 0\le y\le 1} \right.[/tex]

Solving (a): The marginal density of X

This is calculated as:

[tex]g(x) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dy[/tex]

[tex]g(x) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dy[/tex]

[tex]g(x) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dy[/tex]

Integrate

[tex]g(x) = \frac{2}{3}(xy+y^2)|\limits^{1}_{0}[/tex]

Substitute 1 and 0 for y

[tex]g(x) = \frac{2}{3}[(x*1+1^2) - (x*0 + 0^2)}[/tex]

[tex]g(x) = \frac{2}{3}[(x+1)}[/tex]

Solving (b): The marginal density of Y

This is calculated as:

[tex]h(y) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dx[/tex]

[tex]h(y) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dx[/tex]

[tex]h(y) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dx[/tex]

Integrate

[tex]h(y) = \frac{2}{3}(\frac{x^2}{2} + 2xy)|\limits^{1}_{0}[/tex]

Substitute 1 and 0 for x

[tex]h(y) = \frac{2}{3}[(\frac{1^2}{2} + 2y*1) - (\frac{0^2}{2} + 2y*0) ][/tex]

[tex]h(y) = \frac{2}{3}[(\frac{1}{2} + 2y)][/tex]

[tex]h(y) = \frac{1}{3}[1 + 4y][/tex]

Solving (c): The probability that the drive-through facility is busy less than one-half of the time.

This is represented as:

[tex]P(x>0.5)[/tex]

The solution is as follows:

[tex]P(x>0.5) = P(0\le x\le 0.5,0\le y\le 1)[/tex]

Represent as an integral

[tex]P(x>0.5) =\int\limits^1_0 \int\limits^{0.5}_0 {\frac{2}{3}(x + 2y)} \, dx dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 \int\limits^{0.5}_0 {(x + 2y)} \, dx dy[/tex]

Integrate w.r.t. x

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (\frac{x^2}{2} + 2xy) |^{0.5}_0\, dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 [(\frac{0.5^2}{2} + 2*0.5y) -(\frac{0^2}{2} + 2*0y)], dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (0.125 + y), dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}(0.125y + \frac{y^2}{2})|^{1}_{0}[/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125*1 + \frac{1^2}{2}) - (0.125*0 + \frac{0^2}{2})][/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125 + \frac{1}{2})][/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125 + 0.5][/tex]

[tex]P(x>0.5) =\frac{2}{3} * 0.625[/tex]

[tex]P(x>0.5) =\frac{2 * 0.625}{3}[/tex]

[tex]P(x>0.5) =\frac{1.25}{3}[/tex]

Express as a fraction, properly

[tex]P(x>0.5) =\frac{1.25*4}{3*4}[/tex]

[tex]P(x>0.5) =\frac{5}{12}[/tex]

Answer:

The graph shows the solution set of the equality √x < -1

(No Solutions)

Answer:

the answer is 72 inches

Step-by-step explanation:

a²+b²=c²

a²+900=6084

a²=5184

a=72

Answer:

54 cm²

Step-by-step explanation:

To find the area, use the formula, A = lw

Plug in the length and width, and solve:

A = lw

A = 9(6)

A = 54

So, the area of the rectangle is 54 cm²

Answer:

[tex] \bf \huge 54 \: cm \: {}^{2} [/tex]

Step-by-step explanation:

where,

⟼ l = 9 cm

⟼ W = 6 cm

⟼ Area = l × b

⟼ Area = 9 × 6 cm

⟼ Area = 54 cm².

∴ the area of rectangle is 54 cm².

Answer:

....

Step-by-step explanation:

mean: 16

median: 16

there is no mode

range: 8

The frequency data table is missing, so i have attached it.

Answer:

0.5

Step-by-step explanation:

We want to find conditional relative frequency and conditional relative frequency is used to compare the frequency count to the marginal total that represents the particular condition we are dealing with.

In this case, the condition is the popular vote of the state being won by the Democrat in 2012, given that the same popular vote was won by the Democrat in 1976.

In the frequency data table attached, we see that the joint frequency count for Democrat winning in 1976 and 2012 is given as 12.

While the corresponding marginal frequency total is given as 24.

Thus;

Conditional relative frequency = joint frequency count/marginal frequency total = 12/24 = 0.5

The conditional relative frequency of a state's popular vote being won by the Democrat in 2012, given that it was won by the Democrat in 1976:

Thus;

Conditional relative frequency = joint frequency count/marginal frequency total = 12/24 = 0.5

The conditional relative frequency of a state's popular vote being won by the Democrat in 2012, given that it was won by the Democrat in 1976 is 0.5.

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Answer:

5

Step-by-step explanation:

Common factor: 4. Divide 20 by 4 to get 5

Answer: X=5

Step-by-step explanation:

Since the triangles are similar shape-wise, then that means that the sides are going to be similar numerically.

12/4 got us 3, which is the side of that smaller triangle. Since we divided 12 by 4, then we need to divide 20 by 4 to get the unknown side. 20/4 is 5, therefore x is 5.

Answer:

second one

Step-by-step explanation:

Because when you try to remove the brackets then you should multiply coefficient of x and coefficient of y by 2

So it will be 2x+18y

2*9=18

Answer:

14

Step-by-step explanation:

area of sector = 153.9

or, (1/2) r²∅ = 153.9

or, r²∅ = 153.9 ×2

or, r²∅ = 307.8

or, r²× π/2 = 307.8

or, r² = 615.6/π

or, r² = 196

or, r=√196

r = 14

The best estimate is 11/24.

To solve, find a common denominator between both 8 and 12. They can both multiply into 24.

To turn 8 into 24, you multiply by 3, so you must do the same with its numerator. To turn 12 into 24, you multiply by 2, so again, you must do the same with its numerator:

3/8 ---> 9/24

1/12 ---> 2/24

Then, you can add the numerators together and keep the denominator 24:

9/24 + 2/24 = 11/24.

Answer:

ABC is translated right 5 units and down 5 units

Step-by-step explanation:

The vertices of the original and new triangles haven't moved. Only the triangle as a whole moved from one place to another. The other choices involved reflecting the triangle in which the vertices change locations that are different from their original locations. Hope this helps!

Answer:

A and E

Step-by-step explanation:

Answer:

1. 1/6 2. 80

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:-5,-2, 0, .7,1.5,7

Step-by-step explanation:

AS shown above

Answer:

1/6

Step-by-step explanation:

convert ti decimal then compare the two

Answer:

Hello There!!

Step-by-step explanation:

1/6 is less.You can check this by 2÷5=0.4 and 1÷6=0.1666666667 so 1/6 is less.

hope this helps,have a great day!!

~Pinky~

Answer:

90 Degrees.

The angle which is equal to its supplement is 90 degrees.

Answer:

90

Step-by-step explanation:

Let the required angle be x°

Therefore, it's supplement = (180-x)°

Now, x = 180-x

= x+x = 180

= 2x = 180°

Therefore x\ =\ \frac{180°}{2}\ =\ 90°x = 2180° = 90°

Answer:

-9

Step-by-step explanation:

Hello! So, we need to find log_6 1/6. The definition of log is the power that you need to multiply that number by to get the next number. 1/6=6^-1, so our equation would be:

-1=x/9, so x is clearly -9.

Have a nice day.

~cloud

Answer:

You are correct

Step-by-step explanation:

[tex]log_{6} \frac{1}{6} =\frac{x}{9}[/tex]

[tex]log_{6} 6^{-1} =\frac{x}{9}[/tex]

[tex](-1)log_{6}6=\frac{x}{9}[/tex]

[tex]-1=x/9[/tex]

[tex]-9=x[/tex]

Hope that helps :)

Answer:

Write in Slope-Intercept Form

Graph

Find the x and y Intercepts

Find the Slope

Find the Slope and y-intercept

Write in y=mx+b Form

Write in Standard Form

Answer:

-6

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

This explanation mostly depends on what you're learning right now. The first way would be to convert this matrix to a system of equations like this.

g + t + k = 90

g + 2t - k = 55

-g - t + 3k = 30

Then you solve using normal methods of substitution or elimination. It seems to me that elimination is the quickest method.

g + t + k = 90

-g - t + 3k = 30

____________

0 + 0 + 4k = 120

4k = 120

k = 30

No you can plug this into the first two equations

g + t + (30) = 90

g + t = 60

and

g + 2t - (30) = 55

g + 2t = 85

now use elimination again by multiplying the first equation by -1

g + 2t = 85

-g - t = -60

_________

0 + t = 25

t = 25

Now plug those both back into one of the equations. I'll just do the first one.

g + (25) + (30) = 90

g = 35

Therefore, we know that Ted spent the least amount of time on the computer.

The second method is using matrix reduction and getting the matrix in the row echelon form, therefore solving using the gauss jordan method. If you would like me to go through this instead, please leave a comment.

Answer:

According to me it should be -6 [tex]\leq[/tex] y [tex]\leq[/tex] 2.

Step-by-step explanation:

Answer:60$

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number of clips in box A = 40

Number of clips in box B = 23

If Sally took out 6 clips from each box

Remaining clips in box A = 40 - 6 = 34 which is twice of 17

Remaining clips in box B = 23 - 6 = 17

Answer:

Sally took 6 paperclips from each box

Step-by-step explanation:

Paper clips in Box A = 40

Paper clips in Box B  = 23

Let the equal number paperclips removed from each box = x

Number of clips in box A after taking 'x' clips = 40 -x

Number of clips in box B after taking 'x' clips = 23 -x

40 - x = 2*(23 -x)

40 - x = 2*23 - 2*x

40 -x = 46 - 2x  {Add 2x to both sides}

40 - x + 2x = 46          {Combine like terms}

40 + x = 46         {Subtract 40 form both sides }

x = 46 - 40

x = 6

Sally took 6 paperclips from each box

Answer:0.66666666666667

Step-by-step explanation:

Answer:

D. 3 points purchased

Step-by-step explanation:

Took the bullet

Option D is correct, based on the information Gordon purchased 3 point

A fraction represents a part of a whole.

Given that Gordon decided on purchasing a $141,000 home.

At closing he brought a check for $7570.

One point is equal to 3% of the total loan amount, so the cost of one point would be:

Cost of one point = 3% of $130,090

Cost of one point = $3,902.70

To find out how many points Gordon purchased

we need to divide the total cost of points by the cost of one point:

Number of points = Total cost of points / Cost of one point

Number of points = $10,910 / $3,902.70

Number of points = 2.8

=3

Therefore, based on the information Gordon purchased 3 points, Option D is correct.

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Answer:

This is possible and the answer is (-1,0,1)

Step-by-step explanation:

It’s difficult to write out matrices here.

I apologize!