A company invests $32000. after 4 years of growth at the same rate each year, the investment is worth $42692. find the annual growth rate as a percentage.

And

Answer:

x = 7.41 (nearest hundredth)

y = 9.53 (nearest hundredth)

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

From inspection of the triangle:

To find x, use the tan trigonometric ratio:

[tex]\implies \tan 39^{\circ}=\dfrac{6}{x}[/tex]

[tex]\implies x=\dfrac{6}{\tan 39^{\circ}}[/tex]

[tex]\implies x=7.409382939...[/tex]

Therefore, x = 7.41 (nearest hundredth)

To find y, use the sin trigonometric ratio:

[tex]\implies \sin 39^{\circ}=\dfrac{6}{y}[/tex]

[tex]\implies y=\dfrac{6}{\sin39^{\circ}}[/tex]

[tex]\implies y=9.534094374...[/tex]

Therefore, y = 9.53 (nearest hundredth)

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20+12+15= 32+15 = 47 minutes in total

300 meters per minute

300 * 47 = 14100 meters in total

with this we can see the first race was 4/9 that distance meaning the first race was 6266.6 meters long

14100 - 6266.6 = 7833.3

2/5 of 7833.3 is 3133.32

therefore 7833.3 - 3133.32 will give the distance of the third part of the race

meaning of course the answer is 4699.98 or rounding up 4700 meters for the third race

$14.90 spent with the amount left for an extra pencil or notebook being $0.30 or $1.50 short respectively indicates that a notebook costs $1.8 more than a pencil.

Let x represent the cost of a notebook and let y represent the cost of a pencil. The following equations can be obtained;

4•x + 3•y = 14.9...(1)

Let a represent the total money Tina has, which gives;

4•x + 4•y = a - 0.3...(2)

5•x + 3•y = a + 1.5...(3)

Subtracting equation (2) from equation (3) gives;

5•x - 4•x + 3•y - 4•y = a - a + 1.5 - (-0.3) = 1.8

Which gives;

Multiplying equation (4) by 4 and subtracting the result to equation (1) gives;

4 × (x - y) = 4 × 1.8 = 7.2

4•x - 4•y = 7.2

4•x - 4•x + 3•y - (-4•y) = 14.9 - 7.2 = 7.7

7•y = 7.7

x - y = 1.8

x = 1.8 + 1.1 = 2.9

The difference between the cost of a notebook and the cost of a pencil is therefore;

x - y = $2.9 - $1.1 = $1.8

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Answer:

a=70°

b=120°

we know,

a+b

=70+120

=190

Using the given information, the value of Σfd is 800

From the question, we are to determine the value of Σfd

The formula for mean, using the assumed mean method is given by

[tex]\bar x = A + \frac{\sum fd}{\sum f}[/tex]

Where [tex]\bar x[/tex] is the mean

A is the assumed mean

From the given information,

[tex]\bar x = 80[/tex]

[tex]A = 60[/tex]

[tex]\sum f = 40[/tex]

Putting the parameters into the equation, we get

[tex]80 = 60 + \frac{\sum fd}{40}[/tex]

[tex]80-60 = \frac{\sum fd}{40}[/tex]

[tex]20 = \frac{\sum fd}{40}[/tex]

[tex]\sum fd = 20 \times 40[/tex]

[tex]\sum fd = 800[/tex]

Hence, the value of Σfd is 800

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Answer:

55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

Step-by-step explanation:

To simplify this equation, follow these steps:

(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)

Multiply 7.5x² by all the terms in the right parenthesis.

7.5x² (7.4x² -2.1x +7.7)=55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²

Then multiply 5.4x by all the terms in the right parenthesis.

5.4x(7.4x²-2.1x+7.7)=39.96x³-11.34x²+41.58x

Now multiply 3.7 by all the terms in the right parenthesis.

3.7(7.4x²-2.1x+7.7)=27.38x²-7.77x+28.49

Add all of those answers together.

55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²+39.96x³-11.34x²+41.58x+27.38x²-7.77x+28.49=

=55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

The answer is 55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

Hope this helps!

If not, I am sorry.

The function that represents a geometric sequence is given by:

C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

Following this pattern, a function that is also a geometric sequence is:

C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.

For the function, we have that:

[tex]a_1 = P, q = 1 + i[/tex].

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The solution to the inequality is x ≤ 15

The inequality is given as:

12 + x ≥ 3(x-6)

Open the bracket

12 + x ≥ 3x - 18

Evaluate the like terms

-2x ≥ -30

Divide by -2

x ≤ 15

Hence, the solution to the inequality is x ≤ 15

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The missing information in the proof is a which is option A.

Given d is the mid point of ab and e is the mid point of ac. Coordinates are point a (2b,2c), point e (ab, c), point c (2a, 0),point b (0,0), point d (b, c).

We have to find the missing proof in the solution.

To find the missing figure we have to just find the distance between point d and point e.

Distance formula for determining the distance between two points on a coordinate plane is given as :

d=[tex]\sqrt{(y_{2} -y_{1} )^{2} +(x_{2} -x_{1} )^{2} }[/tex]

where ([tex]x_{1} ,y_{1} ) (x_{2} ,y_{2} )[/tex] are the coordinates at the end of line.

DE=[tex]\sqrt{(a+b-b)^{2} +(c-c)^{2} }[/tex]

Simplifying this we get:

DE=[tex]\sqrt{(a^{2} +0^{2} }[/tex]

=[tex]\sqrt{a^{2} }[/tex]

=a

Hence the missing proof is a which is the distance or length of DE..

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It took 1.9 years to pay back the loan.

Interest is the amount of money given or received when a certain sum of amount is received as a loan or given or deposited for investment.

It is given that

Principal amount of loan = $ 8000

Interest paid = $ 600

Rate = 4%

Time Period = ?

Assuming Simple Interest has been applied

I = ( P* R* T) /100

600 = ( 8000 * 4 * T ) / 100

60000 = 8000 * 4 * T

T = 1.875 years

T = 1.9 years rounded to 1 decimal

T = 22.5 months

Therefore it took 1.9 years to pay back the loan.

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The value of the given expression is 136

From the question, we are to evaluate the give expression

The given expression is

−8×(−10+(−7))

The expression can be simplified as follows

−8×(−10+(−7))

−8×(−10−7)

−8×(−17)

= 136

Hence, the value of the given expression is 136

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The maximum amount of supplies that the storage unit can hold is 28 ft³

For us to calculate the volume or amount of space in Evan's prism, we will first of all calculate the volume of rectangular prisms. Formula is;

V = Length × width × height.

We are given;

length = 4 feet

width =  3.5 feet

height of the prism = 2 feet.

Thus;

V = 4 * 3.5 * 2

V = 28 ft³

Thus, the maximum amount of supplies that the storage unit can hold is 28 ft³

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[tex]doctors = 55\% \\ woman = 49\% \\ both = 29\%[/tex]

[tex]p(a) =0.55 + 0.49 - 0.29 \\ p(a) = 0.75[/tex]

Answer:

Put the equations in the form y=mx+c and after that, take any two values for x, fill in the equation of y=mx+c to get the corresponding y coordinate and take any value for y, to get the corresponding x coordinate. For this example i took x=0 and y=0, feel free to try it again with any other value. If you get a fraction and don't what to work with fractions, just do a trial and error till you get a whole number (as i did for Question 21 for the x and y coordinates)

Answer:

C

Step-by-step explanation:

12 /13   is definitely less than 36/30   because 36/30 =  1  1/5

Answer:

8

Step-by-step explanation:

Midpoint means half point of a certain shape. This means that if all the points of OPQ are midopoints of the bigger triangle, then OPQ has to be half the size of the big triangle. There are two ways to figure this out. The first way is to add all the numbers up to find the perimeter of the big triangle (6+6+4) which is 16. Then, you can do 16/2 to get the perimeter of the smaller triangle which is 8. The other method is to take each value of the bigger triangle and divide them by 2 (6/2, 6/2, 4/2). When you do that, you get (3, 3, 2). Now, you just add those values (3+3+2) which gets you 8 gor the smaller triangle. I hope this helps!

Answer:

a reflection in the line y=x

Step-by-step explanation:

The inverse relation of an equation is when the x and y are swapped. For this reason it's going to be reflected over the y=x line. You can also use an online graphing tool to show this as well:

Answer:graph a  

Step-by-step explanation:

bc if you subtract 3

from 2 you find the one you line your numbers up with

The coordinate of point R is 11/40, so the correct option is C.

On the number line we can see that:

M = -1/4

T = 5/8

There are 5 segments between T and M, and the difference between T and M is:

5/8 - (-1/4) = 5/8 + 2/8 = 7/8

The measure of each segment will be equal to:

m = (7/8)/5 = 7/(8*5) = 7/40

Now, coordinate R is 2 segments to the left of T, so the coordinate of point R is given by:

R = 5/8 - 2*(7/40)

R = 25/40 - 14/40 = 11/40

The correct option is C.

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Answer: 7) Step 1 8) Step

Step-by-step explanation:

The answer to 7 is 11. The error starts in step 1, as you can see youre supposed to do 8 divided by 2 plus 3 times 3 minus 2, instead it seems like 3+3 were added instead of becoming 9 thus the answer becomes 7.

The answer to 8 is also 11. 18-14/2 is 11.

The expression that represents the total amount earned last week $100 + $19t.

The expression is a function of the amount her friend paid for the photoshoot, the hours worked and the wages per hour.

Total pay = (amount earned per hour x total hours worked) + amount paid for photoshoot

($19 x t) + $100

$19t + $100

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The graph that best describes the new function is shown in the image attached below.

The equation for a linear function with a slope of m and y-intercept of b is represented as y = mx + b.

Given a linear function graph passes the points (-0.5, 0) and (0, 1):

Y-intercept (b) = 1 (value of y when x = 0)

Slope (m) = change in y/change in x = (1 - 0)/(0 - (-0.5)) = 2

If the slope (1) is multiplied by 2, the new slope would be: 2

If the y-intercept (2) is increased by 3 units, the new y-intercept would be: 5

The equation of the new function would be: y = 2x + 5

The graph that best represents the function is shown in the image attached below.

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Answer:

[tex]\frac{x-3}{2x-3}[/tex]. hole or removable discontinuity at x=2

Step-by-step explanation:

Well generally if you want the simplest form, you factor each the denominator and numerator and then see if you can cancel any of the factors out (because they're in the denominator and numerator)

So let's start by factoring the first equation:

[tex]x^2-5x+6[/tex]

Now let's find what ac is (it's just c since a=1...)

[tex]AC= 6[/tex]

List factors of -6

[tex]\pm1, \pm2, \pm3, \pm6[/tex].

Now we have to look for two numbers that add up to -5. It's a bit obvious here since there isn't many factors, but it's -2 and -3, and they're both negative since 6 is positive, and -5 is negative...

So using these two factors we get

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

Ok now let's factor the second equation:

[tex]2x^2-7x+6[/tex]

Multiply a and c

[tex]AC = 12[/tex]

List factors of 12:

[tex]\pm1, \pm2, \pm3, \pm4, \pm6, \pm12[/tex].

Factors that add up to -7 and multiply to 12:

[tex]-3\ and\ -4[/tex]

Rewrite equation:

[tex]2x^2-4x-3x+6[/tex]

Group terms:

[tex](2x^2-4x)+(-3x+6)[/tex]

Factor out GCF:

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

Rewrite:

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

Now let's write out the equation using these factors:

[tex]\frac{(x-2)(x-3)}{(2x-3)(x-2)}[/tex].

Here we can factor out the x-2 and the simplified form is:

[tex]\frac{x-3}{2x-3}[/tex]

So we can "technically" define f(2) using the most simplified form, but it's removable discontinuity, so it has a hole as x=2. since it makes (x-2) equal to 0 (2-2) = 0.

Triangle XYZ = UYW

We know that the 2 triangles are similar using angles Theorem

Let us find XZ to determine UY (for confirmation):

To determine XZ, use the Pythagorean Theorem:

[tex]a^{2} + b^{2} = c^{2} \\ OR\\leg^{2} +leg^{2} = Hypotenuse^{2} \\24^{2} + b^{2} = 26^{2} \\576+b^{2} =676\\b^{2} =100\\b=10[/tex]

You can see that XZ = WU

Now find UY= 26

Corresponding angles

Hope it helps!

[tex]y=78^{\circ}[/tex] (alternate interior angles theorem)

[tex]x=78^{\circ}[/tex] (alternate segment theorem)

[tex]z=24^{\circ}[/tex] (angles in a triangle add to 180 degrees)

T

Step 1 and 2: Draw an isosceles right triangle

See attachment (figure 1) for this triangle

The legs of this triangle have a length of 1 inch

Step 3: The hypotenuse

This is calculated using the following Pythagoras theorem

[tex]h^2 = 1^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 2[/tex]

Step 4: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 2) for this triangle

The legs of this triangle have lengths of 1 inch and 2 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 2^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 5[/tex]

Step 5: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 3) for this triangle

The legs of this triangle have lengths of 1 inch and 3 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 3^2 + 1^2[/tex]

This gives

[tex]h = \sqrt {10[/tex]

Step 6: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 4) for this triangle

The legs of this triangle have lengths of 1 inch and 4 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 4^2 + 1^2[/tex]

This gives

[tex]h = \sqrt{[17[/tex]

See that the hypotenuse is the square root of 17

Hence, the right triangle whose legs are 1 inch and 4 inches has an hypotenuse of √17

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Answer:

The required linear equation satisfying the given conditions f(-1)=4 and f(5)=1 is [tex]$y=\frac{-1}{2} x+\frac{7}{2}$[/tex]

Step-by-step explanation:

It is given that f(-1)=4 and f(5)=1.

It is required to find out a linear equation satisfying the conditions f(-1)=4

and f(5)=1. linear equation of the line in the form

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$[/tex]

Step 1 of 4

Observe, f(-1)=4 gives the point (-1,4)

And f(5)=1 gives the point (5,1).

This means that the function f(x) satisfies the points (-1,4) and (5,1).

Step 2 of 4

Now find out the slope of a line passing through the points (-1,4) and (5,1),

[tex]$$\begin{aligned}&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\&m=\frac{1-4}{5-(-1)} \\&m=\frac{-3}{5+1} \\&m=\frac{-3}{6} \\&m=\frac{-1}{2}\end{aligned}$$[/tex]

Step 3 of 4

Now use the slope [tex]$m=\frac{-1}{2}$[/tex] and use one of the two given points and write the equation in point-slope form:

[tex]$(y-1)=\frac{-1}{2}(x-5)$[/tex]

Distribute [tex]$\frac{-1}{2}$[/tex],

[tex]$y-1=\frac{-1}{2} x+\frac{5}{2}$[/tex]

Step 4 of 4

This linear function can be written in the slope-intercept form by adding 1 on both sides,

[tex]$$\begin{aligned}&y-1+1=\frac{-1}{2} x+\frac{5}{2}+1 \\&y=\frac{-1}{2} x+\frac{5}{2}+\frac{2}{2} \\&y=\frac{-1}{2} x+\frac{7}{2}\end{aligned}$$[/tex]

So, this is the required linear equation.

Step-by-step explanation:

45+45

90

I guess is the answer

Answer:

The product is the difference of squares is [tex]$$\left(9c+5\right)\left(9c-5\right)=81{{c}^2}-25$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(9 c+5)(9 c-5)=(9 c)^{2}-(5)^{2} \\&(9 c+5)(9 c-5)=81 c^{2}-25\end{aligned}$$[/tex]

1. x = a

2. y = b

3. The slope of a vertical line is undefined..

4. Change in y/change in x (m) or rise/run

5. Rewrite the equation in slope-intercept form to find the value of the y-intercept. The value of x will always be 0.

The equation, y = mx + b, in slope-intercept form, defines a line, where m is the slope and the y-intercept = b.

1. Slopes of vertical lines are always undefined, therefore, for a vertical line that contains (a, b), the equation would be: x = a.

2. Horizontal lines have a slope of 0, therefore, the equation of a horizontal line that contains the point, (a, b), will  be: y = b.

3. The slope of a vertical line is undefined.

4. Two ways of finding the slope if we are given two points on a line are:

Change in y/change in x (m) = y2 - y1 / x2 - x1

or

rise/run

5. If we have an equation in point-slope form, for example, y - 2 = 2(x - 4), rewrite the equation in slope-intercept form and find the value of the y-intercept:

y - 2 = 2x - 8

y = 2x - 8 + 2

y = 2x - 6

The y-intercept = -6, therefore, the coordinates of the y-intercept would be: (0, -6).

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