A family club keeps a small amount of money on hand for members to borrow for short periods of time. The simple interest charged is 7.5%. Stephen borrowed $5,000 for 3 months. How much, to the nearest dollar, was he required to pay back at the end of 3 months?

Answer:

x=-3

y=3

(-3-3i)(3+5i)

Step-by-step explanation:

[tex](x-yi)(3+5i)\\=3x+5xi-3yi+5y\\=(3x+5y)+(5x-3y)i\\[/tex]

and we have that must equal

6-24i

3x+5y=6

5x-3y=-24 and if we work it we found out that the solutions are

x=-3 and

y=3

Answer:

see explanation

Step-by-step explanation:

Since (k, 3) lies on each of the lines, the point satisfies the equations.

Substitute x = k, y = 3 into each and solve for k

y = 3x + 1

3 = 3k + 1 ( subtract 1 from both sides )

2 = 3k ( divide both sides by 3 )

k = [tex]\frac{2}{3}[/tex]

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

y = 4x - 2

3 = 4k - 2 ( add 2 to both sides )

5 = 4k ( divide both sides by 4 )

k = [tex]\frac{5}{4}[/tex]

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

y = [tex]\frac{1}{2}[/tex] x

3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )

k = 6

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

2x + 3y = 4

2k + 3(3) = 4

2k + 9 = 4 ( subtract 9 from both sides )

2k = - 5 ( divide both sides by 2 )

k = - [tex]\frac{5}{2}[/tex]

Answer:

A

Step-by-step explanation:

A dotted line means its either greater than or less than. A undotted line means its also equal to the number aswell.

To find the right answer all you need is the first part because y has to be greater than or equal to 2 as shown from the graph. So the answer has to be A. As it is the only one that shows this.

Answer:

1. You can divide both sides of an equation by any number except zero. If dividing both sides simplifies the equation, then it's better to do than than to distribute.

2. A fraction can be thought of as a ratio. To keep the value of the fraction the same, you must multiply or divide the numerator and denominator by the same number. If you multiply only the denominator by a number, the value of the fraction changes.

Step-by-step explanation:

1.

6(3x + 4) = 12

Since the goal in solving this equation is to isolate x, meaning you want x alone on the left side, you need to do whatever legal operations that will accomplish that. Since 6 is a factor and (3x + 4) is a factor in a multiplication, you can divide both sides by 6 simplifying the left side. It is also correct to distribute on the left side, but it will make the solution longer.

Method 1: start by dividing both sides by 6

6(3x + 4) = 12

Step 1: Divide both sides by 6

3x + 4 = 2

Step 2: Subtract 4 from both sides

3x = -2

Step 3: Divide both sides by 3

x = -2/3

Method 2: start by distributing on the left side

6(3x + 4) = 12

Step 1: distribute the 6 on the left side

18x + 24 = 12

Step 2: subtract 24 from both sides

18x = -12

Step 3: divide both sides by 18

x = -12/18

Step 4: reduce the fraction

x = -2/3

As you can see, the solution is the same. The only difference is one extra step with the reduction  of the fraction in the case of distributing the 6.

2.

This has to do with the meaning of fractions.

For example, take the fraction 1/2.

This fraction means that you divided the unit into 2 equal parts, shown by the denominator of 2. Then you are taking 1 of those parts, shown by the numerator of 1. 1/2 means 1 out of 2. You can also think of 1/2 as the ratio of 1 to 2.

To add and subtract two factions, we need a common denominator. That means we must rewrite one or both fractions being added or subtracted in a way that they both have the same denominator. We need the fractions to represent the same amounts they did originally. If you changed only the denominator, you'd be changing the actual value of the fraction.

You need to add 1/2 and 3/10.

The least common denominator of 2 and 10 is 10, so we need to have both fractions with a denominator of 10. 3/10 already has a denominator of 10, so we just need to change 1/2 to a fraction with 10 in the denominator. By multiplying 2 by 5 we get 10, so we need to multiply the denominator of 1/2 by 5 to end up with a denominator of 10.

1/2 + 3/10

If you only changed the denominator of 1/2 to 10 by multiplying 2 * 5 = 10, you'd end up with

1/10 + 3/10,

but now think of the fraction 1/10 and compare it to 1/2.

1/2 means divide the unit into 2 equal parts and take 1 part.

1/10 means divide the unit into 10 equal arts and take 1 part.

1/2 is not the same as 1/10, so rewriting the addition

1/2 + 3/10 as 1/10 + 3/10 is actually changing the problem.

Now see what happens when we multiply both the numerator and denominator by the same number, in this case 5.

We change 1/2 to (1 * 5)/(2 * 5) = 5/10. 1/2 equals 5/10. If you divide a unit into 10 equal parts and you take 5 parts, you have taken the same number of parts as if you had divided the unit into 2 parts and taken 1 part.

In other words, 1/2 is exactly the same amount as 5/10. The only difference between 1/2 and 5/10 is the way they are written.

Now we can correctly continue with the addition:

1/2 + 3/10 = 5/10 + 3/10 = 8/10

Finally we reduce 8/10 to 4/5 by dividing both the numerator and denominator by 4.

Answer:

P(NOT printed page) = 3/38

Step-by-step explanation:

Total pages = 27+8+3=38

Types of pages that satisfy requirement(s)= 3

Therfore, P(NOT printed page) = 3/38

Surface area of sphere is what referred to as Total surface area or lateral surface area because here the surface is curved everywhere.

[tex] \large{ \boxed{ \rm{ \orange{Surface \: area \: of \: sphere = 4\pi {r}^{2} }}}}[/tex]

Total surface area of other 3-D shapes:

Lateral surface area of these shapes:

━━━━━━━━━━━━━━━━━━━━

Answer:

2/5

Step-by-step explanation:

There are 2 white and 4 yellow  = 6

P(yellow) = yellow /total = 4/6 = 2/3

We keep the ball

Now there are 2 white and 3 yellow  = 5

P(yellow) = yellow /total = 3/5

P ( yellow, keep, yellow) = 2/3 * 3/5 = 2/5

We are given 4 yellow balls and 2 white balls. In total, this adds up to 6.

Divide the number of yellow balls to the total number of balls:

4/6 -> 2/3

We are also given 3 yellow and 2 white.

Divide the number of yellow balls to the total number of balls:

3/5

Divide both fractions together:

3/5 * 2/3 = 6/15 = 2/5

Best of Luck!

Answer:

Step 1: Isolate the absolute value expression.

Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.

Step 3: Solve for the unknown in both equations.

Step 4: Check your answer analytically or graphically.

Step-by-step explanation:

Answer:

Rewrite the absolute value equation as two separate equations, one positive and the other negative

Solve each equation separately

After solving, substitute your answers back into original equation to verify that you solutions are valid

Write out the final solution or graph it as needed

Step-by-step explanation:

Let's first denote:

F - a favorable response

F' - an unfavorable response

S - successful

We know that:

[tex]P(F) = 0.6\\\\P(F')=0.4\\\\P(F\cap S)=0.5\\\\P(F'\cap S)=0.3[/tex]

So, from the conditional probability, we can calculate:

[tex]P(S|F) = \dfrac{P(S\cap F)}{P(F)} = \dfrac{0.5}{0.6}=\dfrac{5}{6}\approx\boxed{0.83}[/tex]

Answer E.

Answer:

E IS CORRECT

Step-by-step explanation:

Answer:

the value of x = 9  and y =11.

Given the system of equation:

12x + 4y =152                  .......[1]

32x + 12y = 420              ......[2]

Multiply equation [1] by 3 we get;

Using distributive property:  

            ......[3]

On solving equation [2] and [3] simultaneously we get;

x = 9

Substitute the value of x= 9 in [1] to solve for y;

108 + 4y = 152

Subtract 108 from both sides we have;

108 + 4y -108 = 152- 108

Simplify:

4y = 44

Divide both sides by 4 we get;

Simplify:

y= 11

therefore, the value of x = 9  and y =11.

Answer:

it will take her 79.76 minutes to rise to the surface

Step-by-step explanation:

Total distance to the surface = 40 yards

speed of rising = 1 foot per seconds

1 foot = 1 second

since the total distance is in yards, let's convert from foot to yards:

1 yard = 3 feet

1 foot = 1/3 yards = 0.333 yards

0.33 yards = 1 second

Next, let's convert from seconds to minutes

60 seconds = 1 minute

∴ 1 second = 1/60 minute

1 second = 0.0167 minute

Therefore the speed at which she rose:

speed

0.333 yards = 0.0167 minutes

Now for a distance of 40 yards:

[tex]1\ yard = \frac{0.0333}{0.0167} minutes\\\therefore\ 40\ yards = \frac{0.0333}{0.0167} \ \times\ \frac{40}{1} \\= \frac{1.332}{0.0167} \\= 79.76\ minutes[/tex]

Answer:

4 minutes

Step-by-step explanation:

Answer:

The options are not visible enough (See Explanation)

Step-by-step explanation:

Given

x:-  1   || 2   || 3   || 4   || 5

y:-  13 || 22 || 37 || 58 || 85

Required

Determine if the function is quadratic

Calculate the difference between the values of y

[tex]Difference = 22 - 13 = 9[/tex]

[tex]Difference = 37 - 22 = 15[/tex]

[tex]Difference = 58 - 37 = 21[/tex]

[tex]Difference = 85 - 58 = 27[/tex]

The resulting difference are: 9 || 15 || 21 ||  27

Next; Calculate the difference between the difference of values of y

[tex]Difference = 15 - 9 = 6[/tex]

[tex]Difference = 21 - 15 = 6[/tex]

[tex]Difference = 27 - 21 = 6[/tex]

The resulting difference are: 6 || 6 || 6

For the function to be quadratic, the above difference must be the same and since they are the same (6), then the function represents a quadratic function.

Answer:

$12,750,000

Step-by-step explanation:

15,000,000 x 0.15 = 2,250,000

15,000,000 - 2,250,000 = 12,750,000

Answer:

Step-by-step explanation:

[tex]15\% \: discount \:on \: 15,000,000\\\\= \frac{15}{100} \times 15,000,000\\\\\\= \frac{225000000}{100}\\ \\= 2250000\\\\15 000 000 - 225 0000= 12750000[/tex]

Answer:

Step-by-step explanation:

In order to find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

x is the hypotenuse

the opposite is 19

So we have

sin 20 = 19/x

x = 19/sin 20

x = 55.55

We have the final answer as

Hope this helps you

Answer:

x = 55.6

Step-by-step explanation:

Answer:

Step-by-step explanation:

A. m∠4 = 180° - m∠3

   m∠1 = 180° - (m∠3 + m∠2)

  m∠3 < m∠3 + m∠2  ⇒  m∠4 >m∠1

B. m∠4 = 180° - m∠3

   m∠2 = 180° - (m∠3 + m∠1)

  m∠3 < m∠3 + m∠1  ⇒  m∠4 >m∠2

C. Not necessarily {could be but not always}

D.   m∠4 = 180° - m∠3

m∠1 + m∠2 + m∠3 = 180°  ⇒  m∠1 + m∠2 = 180° - m∠3 = m∠4

E.  m∠3 = m∠1 + m∠2  only if m∠3 = 90°

F.  Not necessarily. {Could be but also could not be. In the picture is, but we don't know if the diagram is accurate or just approximate.}

Answer:

Domain = x - values

Range = y - values

Step-by-step explanation:

main points I'll use as examples for the rest on graph are: (-3,4) (1,2) and (1,6)

Domain: simple numbers here are {-3,1} dont repeat the same x value twice!

Range: {2,4,6}

Make sure values are in numerical order.

Find the rest by these three points! (Which are on graph)

Hope this helps, have a good day :)

Answer:

try 2

Step-by-step explanation:

because it an X-value and it on the graph

Answer:

-8.58

Step-by-step explanation:

p = 9.7

=> -3.28 - (-4.4) + (-p)

=> -3.28 - (-4.4) + (- (9.7))

=> -3.28 - (-4.4) + (-9.7)

=> -3.28 - (-4.4) -9.7

=> -3.28 +4.4 -9.7

=> -12.98 +4.4

=> -8.58

Answer:

The evaluated answer for this equation is -8.58

Step-by-step explanation:

We are given a value of p so we will use this value for the equation.

-3.28 - (-4.4) + (-p)

Replace p with 9.7

-3.28 - (-4.4) + (-9.7)

Since there is a double negative in front of 4.4, then that means that we are going to be adding -3.28 to 4.4

1.12 + (-9.7)

Subtract 1.42 from 9.7 because there is negative sign in front of 9.7

-8.58

Answer and Step-by-step explanation:

For the first part

Tara is incorrect as she practices the softball in 4 days in a week and she do each practice of minimum one hour

So we can conclude that she practices minimum hours in a week  

For the second part

Also in 4 days, she does practice [tex]1 \frac{1}{3}[/tex] hours per day i.e [tex]5 \frac{1}{3}[/tex]

Now convert [tex]1 \frac{1}{3}[/tex] this into a fraction which comes [tex]\frac{4}{3}[/tex]

For four days, it is

= [tex]4 \times \frac{4}{3} \\\\ \frac{16}{3} \\\\ 5 \frac{1}{3}[/tex]

Step-by-step explanation:

Without multiplying, explain how you know Tara is incorrect.

How long will Tara have softball practice this week? Write your answer as a mixed number.  

Each practice is [tex]1\frac{1}{3}[/tex] hours

Each practice is more than 1 hour. so 4 days of practice is more than 4 hours.

So Tara is incorrect

Practice for 4 days

[tex]1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}+1\frac{1}{3}=4\frac{4}{3}=5\frac{1}{3}[/tex]

More than 5 hours .

Tara will have [tex]5\frac{1}{3}[/tex] softball practice this week

Answer:

Tara will have [tex]5\frac{1}{3}[/tex]  hours softball practice this week

Answer:

12) 1/8 inch =  0.125 inch

    = 0.003175 m

    = 3.175 x 10-3 m

    = 0.3175 cm

13) 2 is rational and  π  is  irrattional.  π   is approximately   3.14 and is the bigger of two

14) C= 40,005,306.33 m

  = 4.0005 x 107 m

15)  12,615,800,000

= 1.26158 x 1010

=126158 x 105

16) Let's take speed of ant as 1Km/h=1000m/h. Then time 1666.875 days

Step-by-step explanation:

Answer:

131 1/4 in.²

Step-by-step explanation:

To find the area of the figure, you would have to divide the figure into two parts.  The figure can be divided into two rectangles.

Rectangle 1

The length is 11 3/4 in.  The width is 6 in.

A = lw

A = (11 3/4 in.)(6 in.)

A = 70 1/2 in.²

Rectangle 2

The length is 9 in.  The width is 6 3/4 in.

A = lw

A = (9 in.)(6 3/4 in.)

A = 60 3/4 in.²

Add the two areas together.

70 1/2 in.²  +  60 3/4 in.²  =  131 1/4 in.²

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  Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Factor [tex]x^3 - 6x^2 + 11x - 6[/tex]

[tex]x^3 - 6x^2 + 11x - 6[/tex]

= [tex]( x - 1) ( x - 2) ( x - 3)[/tex]

So you would be : [tex]( x - 1) ( x - 2) ( x - 3)[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

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If this helped you, could you maybe give brainliest..?

Also Have a great day/night!

❀*May*❀

Answer:

x = -1.5

Step-by-step explanation:

16x - 5 = 18x -2

Subtract 16x from each side

16x-16x - 5 = 18x-16x -2

-5 = 2x-2

Add 2 to each side

-5+2 = 2x-2+2

-3 = 2x

Divide by 2

-3/2 = 2x/2

-3/2 =x

Answer:

-3/2

Step-by-step explanation:

To solve this problem, start by moving all of your x's on to one side, and all of your constants on to the other as such:

16x-5=18x-2

     +2       +2

16x-3=18x

-16x    -16x

-3=2x

-3/2 = x

P.S. please give me brainliest. Thank you! :)

P( A U B) = 37/50

Step-by-step explanation:

7/20+3/5+21/100

IF YOU NEED MORE HELP LMK

If you can please mark this as the brainliest

Answer:

2/3

Step-by-step explanation:

(3,2) and (0,0)

The slope of the line is given by

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

   = (2-0)/(3-0)

 2/3

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use tan

tan∅ = opposite/ adjacent

From the question

The opposite is 9

The adjacent is x

Substitute the values into the above formula

That's

[tex] \tan(30) = \frac{9}{x} [/tex]

[tex]x \tan(30) = 9[/tex]

Divide both sides by tan 30

[tex]x = \frac{9}{ \tan(30) } [/tex]

We have the final answer as

Hope this helps you

Answer:

a^2 × a^4

= a^2+4

= a^6

Remember:

a^n × a^m= a^n+m

Hope it helps

if u have any question let me know in comments ^_^

Answer:

[tex]a^2 * a^4 = \\a^{(2 + 4)} = \\a^6[/tex]

Step-by-step explanation:

Hope it helps!

Answer:

m∠A = 62°

m∠C = 28°

AC = 17 units

Step-by-step explanation:

In the given triangle ABC,

m∠B = 90°, Cos(C) = [tex]\frac{15}{17}[/tex] and AB = 16 units

Since, Cos(C) = [tex]\frac{\text{Corresponding side}}{\text{Hypotenuse}}[/tex]

Cos(C) = [tex]\frac{\text{Corresponding side}}{\text{Hypotenuse}}=\frac{15}{17}[/tex]

[tex]\text{C}=\text{Cos}^{-1}(\frac{15}{17})[/tex]

m∠C = 28.07°

m∠C ≈ 28°

Therefore, side BC = 15 units and AC = 17 units

Now we apply Sine rule in the given triangle.

Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

         = [tex]\frac{\text{BC}}{\text{AC}}[/tex]

         = [tex]\frac{15}{17}[/tex]

A = [tex]\text{Sin}^{-1}(\frac{15}{17} )[/tex]

A = 61.93°

m∠A = 62°

Answer:

80 cube units

Step-by-step explanation:

Answer:

dicontinuity at (-4.-2)zero at (-2.0)

Step-by-step explanation:

answer c

this shoud be correct