What is the value of x?

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X =

Answer:

$21,616.26.

Step-by-step explanation:

24000 =P(1 + 0.03/4)^14

P = 24000 / (1 + 0.03/4)^14)

21,616.26.

=

The present value that will grow to ​$24000 if interest is 3​% compounded quarterly for 14 quarters is $21,482.40

To find the present value that will grow to $24,000 at 3% interest compounded quarterly for 14 quarters, we use the formula for compound interest:

[tex]PV = FV / (1 + r/n)^{(n*t)}[/tex]

Where:

PV = Present Value

FV = Future Value ($24,000)

r = Annual interest rate (3% or 0.03 as a decimal)

n = Number of compounding periods per year (quarterly, so n = 4)

t = Number of years (14 quarters = 14/4 = 3.5 years)

Substitute the values into the formula:

PV = [tex]$24,000 / (1 + 0.03/4)^{(4*3.5)}[/tex]

PV = [tex]$24,000 / (1 + 0.0075)^{(14)}[/tex]

PV = [tex]$24,000 / (1.0075)^{14}[/tex]

PV ≈ $21,482.40 (rounded to the nearest cent)

Therefore, the present value required for it to grow to $24,000 in 14 quarters at 3% interest compounded quarterly is approximately $21,482.40.

In this explanation, we used the formula for compound interest to calculate the present value (PV). The formula accounts for the future value (FV), the annual interest rate (r), the number of compounding periods per year (n), and the time in years (t). By plugging in the given values and performing the calculations, we arrived at the present value of approximately $21,482.40.

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Answer:

The inequality is -3<x<3

Step-by-step explanation:

(-3,3)

Answer:

9x-10y+60=0

Step-by-step explanation:

slope is,

m = (6-(-3))/(0-(-10))

= 9/10

b = -3-(9/10)×(-10)

= 6

So, the equation of the line is,

y = 9x/10+6

or, 9x-10y+60=0

Answered by GAUTHMATH

Answer:

"97" is the appropriate answer.

Step-by-step explanation:

Given:

Number of trees,

= 485

Orchards of trees,

= 5

The number of trees in each orchard will be:

= [tex]\frac{Number \ of \ trees}{Orchards \ of \ trees}[/tex]

= [tex]\frac{485}{5}[/tex]

= [tex]97[/tex]

Answer:

11

Step-by-step explanation:

To calculate the mean you add all the numbers and divide by the number of numbers. There are 4 numbers in this set so we will divide by 4.

Let x be the unknown number,

(10+4+7+x)/4=8(mean)

To solve for x, we first mutliply both sides by 4.

To simplify the left side we can add 10+4+7 and get 21 where now our equation is 21+x=32. Subtract 21 on both sides and you will get 11 which is our answer.

Plug-in 11 and solve for the mean to verify where we do indeed get 8 as the mean.

Answer:

I say the fourth one just because

Answer:

25%

Step-by-step explanation:

profit percentage = (profit/cost price) * 100

selling price = 600

profit = 600 * 20/100 = 120

cost price = 600-120 =480

profit percentage = (120/480) * 100 = 25

Answer:

6

Step-by-step explanation:

how often is that question posted here ?

this means that we need to find the value of x, so that the functional (result) value is 7.

7 = (3x - 4)/2

14 = 3x - 4

18 = 3x

x = 6

Answer:

B. SAS

[tex] \frac{sm}{dl} = \frac{27}{9} = 3 \\ \frac{am}{el} = \frac{15}{5} = 3 \\ angle \: m= angle \: l[/tex]

Brainliest please~

By SAS similarity, ΔASM is similar to ΔDLE. Thus, option C is correct.

The SAS theorem is also known as the side-angle-side theorem, also known as a statement in Euclidean geometry that states two triangles are congruent if their corresponding sides are both the same length and their included angles are both of the same measures.

According to the given figure,

SM=27

DL=9

MA=15

LE=5,

∠M=∠L=31°

It is required to determine the similarity postulate that applies. Therefore,

From the ΔASM and ΔDLE, we have

[tex]\frac{SM}{DL}=\frac{27}{9} \\=3\\\frac{ML}{LE}=\frac{15}{5}\\ =3\\ Hence, \frac{SM}{DL}= \frac{ML}{LE}[/tex]

∠M=∠L=31°

Hence, by SAS similarity, ΔASM is similar to ΔDLE.

Therefore, it can be concluded that option C is correct.

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Answer:

3.88

Step-by-step explanation:

1. Subtract 5.74 from both sides of the equation

9.62-5.74=3.88

Answer:

320 minutes (5 hours and 20 minutes).

Step-by-step explanation:

2 hours and 17 minutes = 137 minutes

137 + 84 + 99 = 320

Therefore, they will spend 320 minutes (5 hours and 20 minutes) watching movies.

Answer:

i. 12cm

ii. 16.5cm

Step-by-step explanation:

The side lengths on an equilateral triangle are all equal to each other. So if one side is given we can find the perimeter of the triangle by multiplying one of the sides by 3.

4*3=12

5.5*3=16.5

Answer:

x is 28°

Step-by-step explanation:

Alternate angles of parallel lines:

[tex]{ \sf{x = \frac{1}{2} \times 56 \degree }} \\ { \sf{x = 28 \degree}}[/tex]

Answer:

Hello,

28°

Step-by-step explanation:

Calculate the complementary angle of x =y

In the triangle on the right :

y+y+56°=180°

y=62°

So x=90°-62°=28°

Answer:

a. linear pair 5 & 6

b. pair of vertical angles 5 & 2

c. pair of angles that are congruent 3 & 8

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect.

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines.

If two angles are complements of the same angle (or congruent angles), then the two angles are congruent. All right angles are congruent.

Answer:

x = 94, y = 76

Step-by-step explanation:

The opposite angles of a cyclic quadrilateral sum to 180° , then

x + 86 = 180 ( subtract 86 from both sides )

x = 94

and

y + 104 = 180 ( subtract 104 from both sides )

y = 76

Answer:

(-4,17)

Step-by-step explanation:

y = f(x)

f(-4) = (-4)^2+1 = 17

y-coordinate = 17

Answer:

D). (-4, 17)

Step-by-step explanation:

Plug in -4 for x.

[tex]f(-4)=(-4)^2}+1[/tex]

Solve.

[tex]f(-4)=16+1[/tex]

[tex]f(-4)=17[/tex]

We already know that the x-coordinate is -4. (-4, y)

f(x) stands for y, so y=17.

(-4, 17)

I hope this helps!

Answer:

x^3 + y^3 + z^3

Step-by-step explanation:

x^3+(y+z)^3

Remove brackets

x^3 + y^3 + z^3

Answer:

Call option and put option ( D )

Step-by-step explanation:

During hedging in stock/financial markets both the Call and put option can be used to hedge the trading position of the trader against the change in exchange. This is because the call or put option is used depending on the initial position of the trader.

Call option is used when the trader is currently holding a short position

Put option is used when the trader is currently holding a long position

Answer:

c ≥ 600

p ≥ 5000

Step-by-step explanation:

Let :

credit score = c

Cost of car, p

To qualify :

Credit score must be atleast 600 ;

c ≥ 600

Cost of car must be atleast 5000

p ≥ 5000

Answer:

I think that there might be some complex differential equation

stuff going on here if this were in the real world, but for the sake of this problem... may I suggest that the tank is filling up  at a rate of

1/8 of a tank per hour...

it is evaporating at a rate of 1/12 tank per hour

you can subtract the rates

1/8 - 1/12 = 12/96- 8/96 = 3/96 = 1/32 tank/hr

so to fill the tank it should take 32 hours...

I think the logic and math work... lets see if someone else will verify this analysis?

Step-by-step explanation:

Answer:

AOB

Step-by-step explanation:

An obtuse angle is larger than 90 and less than 180

COB = 90

AOB is larger than COB and less than 180

Answer: (a): Good course, (b): Bad course

Step-by-step explanation:

Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.

Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.

Answer:

101

10+6+16+6*5

I hope it's correct

Answer:

13/9

Step-by-step explanation:

Given

5/9 + 8/9

Both fractions have the same denominator.

Therefore, pick one of the denominator and add the numerators

5/9 + 8/9

= (5+8) / 9

= 13/9

5/9 + 8/9 = 13/9

y = -2x-3

Lines that are perpendicular have slopes that are negative reciprocals of each other. Meaning, if a line has slope  , then a line perpendicular to this has slope . That means the slope of our perpendicular line is

The equation of the line that is perpendicular to 8x - 2y = 4 and passes through the point (4, 3) is y = (-1/4)x + 4.

To find the equation of a line that is perpendicular to the line 8x - 2y = 4 and passes through the point (4, 3), we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

First, let's rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope:

8x - 2y = 4

-2y = -8x + 4

Divide both sides by -2:

y = 4x - 2

The slope of the given line is 4.

The slope of a line perpendicular to this line would be the negative reciprocal of 4, which is -1/4.

Now, we have the slope (-1/4) and a point (4, 3). We can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Substituting the values, we have:

y - 3 = (-1/4)(x - 4)

Expanding and simplifying, we get:

y - 3 = (-1/4)x + 1

Adding 3 to both sides, we have:

y = (-1/4)x + 4

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Answer:

Step-by-step explanation:

Answer:

[tex]-\frac{3p^8}{4q^3}[/tex]

Step-by-step explanation:

One is given the following expression,

[tex]\frac{15p^-^4q^-^6}{-20p^-^1^2q^-^3}[/tex]

Since (15) and (-20) are both divisible by (5), one can divide both terms by (5) to simplify it.

[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]

Now bring all of the terms with a negative exponent to the numerator. Multiply the exponents by (-1), then add them to the exponents of the like term in the numerator. Simplify the resulting exponents

[tex]\frac{3p^-^4q^-^6}{-4p^-^1^2q^-^3}[/tex]

[tex]\frac{3p^-^4^+^(^-^1^)^(^-^1^2^)q^-^6^+^(^-^1^)^(^-^3^)}{-4}[/tex]

[tex]\frac{3p^-^4^+^1^2q^-^6^+^3}{-4}[/tex]

[tex]\frac{3p^8q^-^3}{-4}[/tex]

Rewrite the fraction such that there are no negative exponents. Remember the rule, when bringing a number from the numerator to the denominator and back, multiply the exponent of the number by (-1). One can only switch numbers between the numerator and the denominator when all operations are multiplication or division.

[tex]\frac{3p^8q^-^3}{-4}[/tex]

[tex]-\frac{3p^8}{4q^3}[/tex]

Answer:

27/20

Step-by-step explanation:

[tex]\frac{13.5}{10} = \frac{13.5 * 2}{10 * 2} = \frac{27}{20}[/tex]