Your credit card has a limit of $4,925. To maintain an acceptable debt ratio (50%), what is the maximum balance you can have on the card?

Answer:

12500

Step-by-step explanation:

11830 - 10464 = 1366 (difference 1995 to 96)

10464 - 8958 = 1506 (94 to 95)

8958 - 8135 = 823

8135 - 7537 = 598

7537 - 6642 = 895

6642 - 5942 = 700

5942 - 3579 = 2363 (5 years)

so, we have the annual differences over 11 years.

the expectation for the following year would be based on the mean value of growth rate and not on the mean value of the absolute numbers, as we know the number of transactions for 1997 will be higher than for 1996.

so, the mean value of growth over these 11 years is 750.

so, based on this we would estimate for 1997

11830 + 750 = 12580 (12500 being the closest answer option).

but if the business environment has changed over the most recent years, we should not bring in earlier years into that calculation (or at least not with the same weight).

we could argue that the last 2 years had a totally different behavior than the years before.

so, just creating a mean value of the last 2 years' changes would be

(1366 + 1506) / 2 = 2872 / 2 = 1436.

now, or prediction would be

11830 + 1436 = 13266, which would be closer to the 13500 answer option.

Answer:

s4 = 270

18+36+72+144 = 270

-- convergent sums to a single value

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Choice A

Step-by-step explanation:

An arithmetic sequence is one which has an incremental change.

for our answer, our change is +5

Answer:

The answer is 3x=50-10y

Answer:

Actually the answer is "A"

this is a very strange way to present a problem...

this issue her is that [tex](x^{a}) ^{b} = x^{a*b}[/tex]

so you need 1/3 * 3 in the answer... none of them have 1/3 * 3

BUT !!!!! 1/3 + 1/3 + 1/3  is the same as  1/3 * 3 So "A" is the solution

Step-by-step explanation:

Answer:

0.75 → 0.5 → 1/3(0.33) → 1/4(0.25)

Answer:

I think this is the ans

Step-by-step explanation:

ab+c=0

(p+q)(p-q)=0

p Square-q Square =0

0=p Square-q Square

Answer:

14

Step-by-step explanation:

7*4*1/2=14

Answers:

t is the number of seconds after the rocket is released

V(r) is the volume of the ball with radius r.

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

Explanation:

There isn't much to say in terms of explanation. These variables are simply definitions.

Answer:

100

Step-by-step explanation:

0.2*500=100

Answer:

Step-by-step explanation:

The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:

                          original                 new

length

width

And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:

                           original                  new

length                       L

width                       2L

Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.

The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:

                            original                        new

length                      L                       100%L + 50%L

width                       2L

The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:

                             original                       new

length                        L                     100%L + 50%L

width                        2L                  100%(2L) - 20%(2L)

And now we'll simplify that "new" column:

                              original                         new

length                        L                         150%L = 1.5L

width                         2L               80%(2L) = 160%L = 1.6L

Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:

248 = 2(1.5L) + 2(1.6L) and

248 = 3L + 3.2L and

248 = 6.2L so

L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)

Answer:

x = 25

Step-by-step explanation:

When you combine both angles, you can get a supplementary angle which means that when they are both added, it should add up to be 180 degrees. With that being said, we can create an equation and solve for x.

5x - 5 + 2x + 10 = 180

~Combine like terms

7x + 5 = 180

~Subtract 5 to both sides

7x = 175

~Divide 7 to both sides

x = 25

Best of Luck!

Answer: x = 25

Step-by-Step Explanation:

We are given a line, hence it is a straight angle being 180°

Therefore,

=> 5x - 5 + 2x + 10 = 180

= 5x - 5 + 2x = 180 - 10 = 170

= 5x + 2x = 170 + 5 = 175

= 7x = 175

=> x = 175/7 = 25

Therefore, x = 25

Additionally, finding the values of each angle :-

=> 5x - 5

= 5(25) - 5

= 125 - 5

=> 120°

=> 2x + 10

= 2(25) + 10

= 50 + 10

=> 60°

Therefore, one angle is 120° and the other is 60°

Answer:

Step-by-step explanation:

That 3 sitting outside there in that little "box" thing is a root/solution/zero of the polynomial. The numbers underneath the line are the coefficients of the depressed polynomial, which means that the polynomial is 1 degree lower than the degree with which we started. If we started with an x-squared, this degree is a single x, better known as linear (a line). Anyway, (x - 3) is a zero of the polynomial, which also means that it's a factor. So A applies. x = 3 is a root, so C applies. And F also because the depressed polynomial, the remainder, is 2x + 4.

Answer:welcome

Step-by-step explanation: sorry I jsit really needed the points

Answer:

Choice D. [tex]F(x)=x^2-4[/tex]

Step-by-step explanation:

Answer:

B: 63

Step-by-step explanation:

Answer:

1.5×10^17

Step-by-step explanation:

it would be better to first multiply the two then divide the answer by 9.4×10^-3

I hope this helps

Answer:

(C) 2x^3 - 3x^2 - 35x + 36

Step-by-step explanation:

First multiply 2x by x^2 + 3x - 4:

(2x)(x^2 + 3x - 4)

2x^3 + 6x^2 - 8x

Next multiply -9 by x^2 + 3x - 4:

(-9)(x^2 + 3x - 4)

-9x^2 - 27x +36

Now add the two polynomials by adding like terms:

(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)

2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36

2x^3 - 3x^2 - 35x + 36

Hope this helps (●'◡'●)

Answer:

y = 1/2x - 3 (option - d)

Step-by-step explanation:

The lines are parallel if they have the same slope/gradient. So by comparing with y = mx + c (where 'm' is the slope and 'c' is the y-intercept).

Line y = 1/2 x - 6 has the slope m = 1/2

and the line in option 'd'

y = 1/2 x -3 has the slope m = 1/2

Slopes are equal and lines are parallel.

Thank-you.

#Muhib

Answer:

27

Step-by-step explanation:

Hi there!

We are given this set of data:

22, 15, 31, 40, 27

And we want to find the average (or the mean) of the set

To find the mean, we add up all of the values of the data set and then divide it by how many pieces of data we have

So first, add 22, 15, 31, 40 and 27 together

22+15+31+40+27=135

We have 5 pieces of data, so divide 135 by 5

135/5=27

The mean is 27

Hope this helps!

[tex]\boxed{\large{\mathbf{\blue{ANSWER~:) }}}}[/tex]

we know that,

[tex]\boxed{\sf{mean=\dfrac{sum ~of~ data}{no~ of~ data } }}[/tex]

According to the question,

Therefore,

the average (mean) of the given set of data.(22,15,31,40,27) is 27.

Answer:

 y = 2x²-11x +5    

Step-by-step explanation:

We know that a polynomial of degree n with roots (x-intercepts) {x₁, x₂, ..., xₙ} and a leading coefficient A can be written as:

p(x) = A×(x - x₁)×...×(x - x₂)

Here we will find:

P(x) = (x - 1/2)×(x - 5)

Let's see how we found that:

Here we know that is a parabola, so n = 2, and the x-intercepts are:

x₁ = 1/2

x₂ = 5

And we do not know the leading coefficient, so we can assume  A = 1.

Then the polynomial is just:

P(x) = (x - 1/2)×(x - 5)

The graph of this polynomial can be seen below.

If you want to learn more, you can read:

https://brainly.com/question/24371640

Answer:

1 kg

Step-by-step explanation:

Number of chickadees = 100

Quantity of seed eaten = 100 kg

Number of days = 100

Quantity of seeds each chickadee eats per day =Number of chickadees ÷ Quantity of seed eaten ÷ Number of days

= 100 ÷ 100 ÷ 100

= 1 ÷ 100

= 0.01 kg of seed

How many kg of seeds can 10 chickadees eat in 10 days?

= Quantity of seeds each chickadee eats per day × number of chickadee × number of days

= 0.01 kg × 10 × 10

= 1 kg

10 chickadees eat 1 kg of seeds in 10 days

Answer:

x = -6

Step-by-step explanation:

cube each side :

3x + 7 = 2x + 1

solve for x:

x = -6

Answer:

B

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{5}{13}[/tex]

sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]

tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{12}{5}[/tex]

Then

cosA = sinC → B

Answer:

C

Step-by-step explanation:

Note that x is opposite to the given angle and we are also given the hypotenuse.

Since we have an angle and the side opposite to it and the hypotenuse, we can use the sine ratio. Recall that:

[tex]\displaystyle \sin \theta =\frac{\text{opposite}}{\text{hypotenuse}}[/tex]

The opposite side is x, the hypotenuse is 15, and the angle is 53. Substitute:

[tex]\displaystyle \sin 53^\circ = \frac{x}{15}[/tex]

Solve for x:

[tex]x=15\sin 53^\circ[/tex]

Use a calculator (make sure you're in Degrees Mode!). Hence:

[tex]x=11.9795...\approx 12[/tex]

Our answer is C.

Answer:

C. 12

Step-by-step explanation:

Pythagoras Theorem

Answer:

see explanation

Step-by-step explanation:

Using the identities

cotA = [tex]\frac{1}{tanA}[/tex]

cot²A = cosec²A - 1

tan²A = sec²A - 1

Consider the left side

(cotA + tanA)² ← expand using FOIL

= cot²A + 2cotAtanA + tan²A

= cosec²A - 1 + 2 .[tex]\frac{1}{tanA}[/tex] . tanA + sec²A - 1

= cosec²A - 1 + 2 + sec²A - 1

= sec²A + cosec²A - 2 + 2

= sec²A + cosec²A

= right side, thus proven

Answer:

Remember that a triangle rectangle of length L and width W has an area:

A = W*L

In our rectangle, we have two sides along the x and y axes.

So one of the vertices of our triangle rectangle is the point (0, 0)

And the other vertex, is along the line:

y = -4x + 20

So, if the opposite vertex is at the point:

(x₁, y₁)

We can define the length as the difference between the x-values of each vertex.

L = (x₁ - 0) = x₁

And the width, similarly, as:

W = (y₁ - 0) = y₁

Such that the point (x₁, y₁) is a solution for the equation y = -4x + 20, then we have:

y₁ = -4x₁ + 20

Then we can rewrite the width as:

W = -4x₁ + 20

Now, we can write the area of our rectangle as:

A = (x₁)*(-4x₁ + 20)

A = -4*x₁^2 + 20*x₁

Now we want to maximize the area, notice that the area is given by a quadratic equation with a negative leading coefficient.

Thus, the maximum will be at the vertex of that quadratic equation.

Remember that for a general quadratic equation:

y = a*x^2 + b*x + c

The x-value of the vertex is:

x = -b/(2*a)

so, in our case, the x-value of the vertex will be:

x₁ = -20/(-4*2) = 20/8 = 5/2

Now we can evaluate this in our area equation:

A = -4*(5/2)^2 + 20*(5/2)  = 49.36

This is the maximum area of the rectangle.