Use the formula a=p(1 rn)nt to find the amount in a compound interest account after t years, compounded n times a year. mary deposited $5,600 in an account, which compounded 1.9 percent quarterly, and left it there for 10 years. what was the amount in the account at the end of 10 years? round to the nearest dollar. $7,120 $6,769 $6,026 $5,872

A fraction is a way to describe a part of a whole. The quotient of the fraction is 1/(t+4)².

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The quotient of  [tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}[/tex] can be found by factorizing the denominator of the fraction. Therefore, the factors of the denominator are,

t² + 7t + 12

= t² + 4t + 3t + 12

= t(t+4) +3(t+4)

= (t+4)(t+3)

Now, quotient will be,

[tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\\\\\\=\dfrac{\dfrac{t+3}{t+4}}{(t+4)(t+3)}\\\\\\=\dfrac{(t+3)}{(t+4)(t+3)(t+4)}\\\\\\= \dfrac1{(t+4)^2}[/tex]

Hence, the quotient of the fraction is 1/(t+4)².

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Answer: 10

Step-by-step explanation:

By definition, the point at which a median intersects the side of the triangle opposite from the vertex from which it is drawn is the midpoint of that side.

The number of ways that Grant can arrange 3 of the 10 plants is 120 ways and the number of ways that 4 floats out of 8 can be arranged is 70 ways.

Grant can arrange 3 out of 10 plants in the following number of ways:

= 10!/ ((10! - 3!)3!)

= ( 10 x 9 x 8) / (3 x 2)

= 120 ways

The parade organizer can arrange 4 floats out of 8 as:

= 8!/((8! - 4!)4!)

= (8 x 7 x 6 x 5) / (4 x 3 x 2)

= 70 ways

When 4! is written in expanded form, it comes out as:

= (4 x 3 x 2)

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Answer:

80 oz

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

the length is how many units greater than twice the width ?

you skipped that information from us.

so, all we can say

length = 2×width + x

the perimeter is

2×length + 2×width

with width = w we get by using the first equating in the second :

2×(2×w + x) + 2×w = 4w +2x + 2w = 6w + 2x

so the right answer must be d.

it is the only option with "6w".

it means that 2x = 5 and x = 2.5.

so it was that the length is 2.5 units greater than twice the width

Answer:

step1:add 3y to both sides

step2:add 4 to both sides

step3:multiply both sides by(1/5)

14/15

Step-by-step explanation:

The weighted average cost of capital for the firm will be 11.25%.

The weighted average cost of capital is the calculation of the cost of capital for a firm where each category of capital is weighted.

Here, the weighted average cost of capital will be:

= 0.5(10%)(1 - 15%) + 0.5(14%)

= 0.5(0.1)(0.85) + 0.5(0.14)

= 11.25%

The corporate value at 70% debt when WACC is 11.94% will be:

= (EBIT)(1 - T)/WACC

= (13.24)(1 - 0.15)/0.1194

= $94.26 million

The corporate value at 30% debt when WACC is 11.14% will be:

= (EBIT)(1 - T)/WACC

= (13.24)(1 - 0.15)/0.1114

= $101.02 million

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Answer: rectangle

Step-by-step explanation:

The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.

To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.

[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]

So, the most specific classification is a rectangle

AND means multiply, so if probability is dependent on two things happening, then we will multiply the individual probabilities together.

1. P(A and 1) = 1/4 x 1/6 = 1/24

2. P(C and 2) = 1/4 x 2/6 = 2/24 = 1/12

3. P(B and 3) = 2/4 x 1/6 = 2/24 = 1/12

4. P(A and 4) = 1/4 x 2/6 = 2/24 = 1/12

5. P(C and 3) = 1/4 x 1/6 = 1/24

6. P(B and 2) = 2/4 x 2/6 = 4/24 = 1/6

7. P(a consonant and an odd #) = 3/4 x 2/6 = 6/24 = 1/4

8. P(a consonant and a prime #) = 3/4 x 3/6 = 9/24 = 3/8

9. P(a vowel and a 5) = 1/4 x 0/6 = 0

10. P(a vowel and a number less than 3) = 1/4 x 3/6 = 3/24 = 1/8

11. P(B and 1) = 2/4 x 1/6 = 2/24 = 1/12

Experimental probability is based on something that has already happened, or data that has already been collected.

12. P(1) = 3/30 = 1/10

13. P(2) = 8/30 = 4/15

14. P(3) = 7/30

15. P(4) = 5/30 = 1/6

16. P(5) = 3/30 = 1/10

17. P(6) = 4/30 = 2/15

Hope this helps!

Answer:

5.656854249 cm

Step-by-step explanation:

Use the Pythagorean theorem to solve this (assuming that the bottom of the cup is a right angle). [tex]a^{2} +b^{2} =c^{2}[/tex]. a and b are sides, and c is the hypotenuse.

The length of the pencil would be the hypotenuse (c), and how tall the cup is (7 cm) would be one of the sides (a).     The diameter of the cup, would be the other side (b).

Plug this into the Pythagorean theorem to get the equation: [tex]7^{2} +b^{2} =9^{2}[/tex]. From here, we can find the diameter of the cup by isolating b - remove everything from the left side, but remember, what you do to one side you must do to the other.

First, solve all of the exponents: [tex]49+b^{2}=81[/tex]

Second, subtract 49 from both sides: [tex]b^{2}=32[/tex] This cancels out the 49 on the left.

Lastly, square root both sides: [tex]x=5.656854249[/tex] This cancels out the exponent on the left.

In conclusion, the diameter of the cup is 5.656854249 centimeters.

Answer: 3ln4 + 3lna

Step-by-step explanation:

[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]

Answer:

The answer would be 5.

Step-by-step explanation:

To solve proportions, you multiply the denominator (6) by the numerator (15). 15 times 6 is equal to 90. You then divide 90 by the denominator (18) to get an answer of 5. I hope this helps you! Have a great day! :)

Answer:

AB=CD and BC=AD because both of them are visually paired with the same longitude.

Answer:

AB = CD, BC = AD

Step-by-step explanation:

According to parallelogram properties,

Angle A = 180-Angle B; False
AB!=BC; False

AC==BD is only true when AB = BC, False
AB ==CD, BC == AD; True

Circumference = diameter x PI

Circumference = 8 in x Pi

Circumference = 8PI in. (Exact)

Or as a decimal answer: 25.12 in.

Answer:

25.1 in (nearest tenth)

Step-by-step explanation:

Formula

Circumference = πd  (where d is the diameter)

From inspection of the diagram:

⇒ Circumference = 8π

                             = 25.1 in (nearest tenth)

An equation is formed of two equal expressions. The number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let c represent the cost of a phone plan, m represent the number of months, and g represent the number of gigabytes of data used each month.

Equation1: C = 40m + 3.5mg = (40+3.5g)m

Equation2: C = 75m + 0.5mg = (75+0.5g)m

Equating C,

(40+3.5g)m = (75+0.5g)m

40 + 3.5g = 75 + 0.5g

3g = 35

g = 11.6667 gigabyte of data per month

Hence, the number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.

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Answer:

49,64

Step-by-step explanation:

Every time the number changes there is an addition of two. for instance, from 4 to 9 the was an addition of 5 and from 9 to 16 there was an addition of 7. Thats how it works

The height of the scale model 1.304 scale units.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

Given:

The Bloomington Bank has a height of 163 meters.

Molly is making a scale model of this building using a scale of 125 meters.

125 meters = 1 scale unit

1 meter = 1/125 scale unit

So, for 163 meters = 1/125* 163

                              = 1.304 scale units.

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Answer:

take the dots and either put them together or rake them away

Step-by-step explanation:

Example: .....+..=....... five dots plus two dots equals seven dots.

......-...=... six dots minus three dots equals three since you are taking away three

i hope u found this helpful.

Answer:

40[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

V = L × W × H

V = 1.5 × 6 × 4.5

V = 40.5 or 40[tex]\frac{1}{2}[/tex]

Answer:

40 1/2ft

Step-by-step explanation:

H(4 1/2 )x W(1 1/2) = 6.75

HW(6.75)x L(6) = 40.5

Answer:

see below

Step-by-step explanation:

You didn't include the choices but here is a solution

tan 68 = opp/adj = height / 13

13 Tan 68  = height of pole

Answer:

3 minutes per table

Step-by-step explanation:

15 minutes = 5 tables

to get how much it will be per table, divided both sides by 5

since 5 / x = 1 and x would be 5

15 / 5 minutes = 5 / 5 tables

3 minutes = 1 table

Answer:

x = 10/3

x = -3

Step-by-step explanation:

3x² - x = 30

3x² - x - 30 = 0

multiply 3 and -30 which =

-90

what are 2 numbers that when multiplied make

-90

and that when added make

-1

(-1 is the number in -x in the equation)

they are the numbers 9 and 10

namely -10 and +9

3(x-10/3)(x+9/3)=0

divide both sides by 3

(x-10/3)(x+9/3)=0

then split factors being multiplied

(x-10/3)=0

(x+9/3)=0

x = 10/3

x = - 9/3 = -3

There are 750 many outcome pairs you can have

The given parameters are:

Website 1 = 25

Website 2 = 30

The number of outcome pairs is calculated as:

Outcome = Website 1 * Website 2

So, we have:

Outcome = 25  * 30

Evaluate the product

Outcome = 750

Hence, there are 750 many outcome pairs you can have

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[tex]-4(4x-6)=3(-7x-1)[/tex]

[tex]-16x+24=3\left(-7x-1\right) [/tex]

[tex]-16x+24=-21x-3 [/tex]

[tex]-16x+24+21x=-3 [/tex]

[tex]5x+24=-3 [/tex]

[tex]5x=-3-24 [/tex]

[tex]5x=-27 [/tex]

[tex]x=\frac{-27}{5} [/tex]

[tex]x=-\frac{27}{5} [/tex]

Explanation:

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Answer:

below

Step-by-step explanation:

f. =. m²

------

3e

hope makes sense dive both sides by 3e to get f alone

There are [tex]\binom{52}4[/tex] ways of drawing a 4-card hand, where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient.

There are 13 different card values, of which we want the hand to represent 4 values, so there are [tex]\binom{13}4[/tex] ways of meeting this requirement.

For each card value, there are 4 choices of suit, of which we only pick 1, so there are [tex]\binom41[/tex] ways of picking a card of any given value. We draw 4 cards from the deck, so there are [tex]\binom41^4[/tex] possible hands in which each card has a different value.

Then there are [tex]\binom{13}4 \binom41^4[/tex] total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is

[tex]\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761[/tex]

The partial products of 5 * 1234 are 5 * 1000, 5 *200, 5 * 30 and 5 * 4

The product expression is given as:

5 * 1234

Express 1234 as the sum of numbers

5 * (1000 + 200 + 30 + 4)

Expand

5 * 1000 + 5 *200 + 5 * 30 + 5 * 4

Hence, the partial products of 5 * 1234 are 5 * 1000, 5 *200, 5 * 30 and 5 * 4

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Answer:

sometimes

Step-by-step explanation:

a supplementary angle is "either of two angles whose sum is 180°".

So, x or y could be any degree, (less than 180 of course) and either one could be obtuse (>90) or acute (<90).

A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)

A) This is a parabolic graph and from the graph, we see that, the y-values remain the same from x-values of 0 to 15. Thereafter the x-values increases with a corresponding decrease in y-values until the vertex point before increase in x-values with corresponding increase in y-values.

A relationship could be: Battery percentage remains at the mark of 40 for the first 15 minutes of use. Thereafter, it begins to decrease parabolically until 45 minutes when it it is almost at 0 level and is charged before it starts to increase in a parabolic manner again for another 20 minutes when it increases linearly.

B) A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)

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