A sum of money in a savings account is represented by the following function:
A = 9, 000(1. 03)t where t is the number of years the money is invested.

What is the initial sum of money in the account?

Step-by-step explanation:

let's call the top of the pole T, and the ground point of the pole G.

so, the situation gives us 2 right-angled triangles:

PTG and QTB.

from both triangles we know one leg (TG, the pole = 9 m), the inner angles at G (90° in both cases), and actually the inner angles at T, because we know the angles of depression there.

the inner triangle angles at T are just the complementary angles of the angles of depression (that means they add up together to 90°).

the inner angle at PTG = 90 - 4 = 86°

the inner angle at QTG = 90 - 7 = 83°

and because the sum of all angles in a triangle is always 180°, we even know the third angles at P and Q :

angle P = 180 - 90 - 86 = 4°

angle Q = 180 - 90 - 83 = 7°

yes, they are the same as the angles of depression (must be the same).

so, we know from both triangles 1 side and all 3 angles.

with the law of sine we can get every missing side.

particularly we need the second legs (sides in the ground) to get the distance between both points.

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c being the sides always opposite of their related angles.

TG/sin(4) = PG/sin(86)

PG = 9×sin(86)/sin(4) = 128.7059963... m

TG/sin(7) = QG/sin(83)

QG = 9×sin(83)/sin(7) = 73.29911785... m

the distance between P and Q can have now 2 solutions :

if P and Q are on different sides of the pole, then

PQ = 128.7059963... + 73.29911785... = 202.0051142... m

but if they are on the same side of the pole, then their distance is

PQ = 128.7059963... - 73.29911785... = 55.40687846... m

due to the phrasing of the first sentence I suspect the first solution to be right.

but just in case, I gave you also the second possible solution.

Applying the centroid theorem, the length of TY is calculated as: 18 units.

According to the centroid theorem, given a triangle like TUV with Y as the centroid, the theorem states that:

TY = 2/3(TW)

YW = 9 units

TW = TY + 9

Plug the values into the equation

TY = 2/3(TY + 9)

3(TY) = 2(TY + 9)

3(TY) = 2(TY) + 18

3(TY) - 2(TY) = 18

TY = 18

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Answer:

see image

Step-by-step explanation:

Putting the data on the line plot is not too bad. Just put an x above the number on the numberline. If a number in the data set repeats, just stack those x's up over the numberline. It seems like the hardest part is labelling the number line. Each tick mark can be 1/8. On the image I wrote all the fractions in eighths at the bottom, then to label the numberline I used the simplified fractions. For example I started with 1 3/8 because it was the smallest number in the data set. Next is 1 4/8, but simplified that is 1 1/2. So 1 1/2 is how we label the numberline.

There were 12 pieces of data, but really only six numbers because some were repeated.

Stack x's above the numberline. Done! You have a line plot. See image.

Answer:

1. 1/⅜

2. 1/⅜

3 is 2/¼

4 is 2/¼

5 is 2/¼

6 is 2/⅞

7 is 2/⅞

8 is 2/⅞

9 is 3/⅛

10 is 3/⅛

11 is 3/⅛

Step-by-step explanation:

Mixed number to Improper Fraction

1.9/4

2.13/4

3.23/8

4.25/8

5.23/8

6.25/8

7. 5/2

8.9/4

9. 23/8

10. 5/2

11. 11/8

12. 25/8

then you make it into the same denominator

1. 18/8

2. 26/8

3. 23/8

4. 25/8

5. 23/8

6. 25/8

7. 20/8

8. 18/8

9. 23/8

10. 20/8

11. 11/8

12. 25/8

then what ever numerator is smallest you put at front and it goes onto the biggest one

e.g ASCENDING ORDER

However you'll need to put it back into the normal mixed number, so all you have to do is revert let's say 25/8 into 3/⅛, and put it onto the graph

1. 1/⅜

1. 1/⅜2. 1/⅜

. 1/⅜3 is 2/¼

. 1/⅜3 is 2/¼ 4 is 2/¼

. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼

. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞

. 1/⅜3 is 2/¼ 4 is 2/¼5 is 2/¼6 is 2/⅞7 is 2/⅞

8 is 2/⅞

9 is 3/⅛

9 is 3/⅛10 is 3/⅛

11 is 3/⅛

and number 12 which is the biggest and the last one the you should put(on the end of graph) is

3/¼

I did rush this so I hope this is the correct answers

A number line is a line that shows the locations of all directed numbers. The answers required to the question are:

i. The location of G is 2.18.

ii. The length of FG is 0.98.

A number system is a system that can be used to locate the position of directed numbers on a number line. A number line has two ends: positive and negative ends. This starts from negative infinity to positive infinity. Thus all numbers can be located on a number line.

Directed numbers are numbers that have either a positive sign or a negative sign. Thus all numbers are directed numbers.

From the given question, let the distance between FG and GH be represented by x (since Point H is the length of FG from point G).

Thus,

Point FH = 3.15 - 1.20

              = 1.95

x = [tex]\frac{FH}{2}[/tex]

   = [tex]\frac{1.95}{2}[/tex]

x = 0.975

So that,

Location of point G = 1.200 + 0.975

                                = 2.175

Therefore, the location of G is 2.175 (2.18). And the length of FG is 0.975 (0.98).

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Answer:

Location of G: 6.4

Length of FG: 5.2

Step-by-step explanation:

correct on Edementum/Plato

A percentage is a way to describe a part of a whole. The approximate percent decrease in the price is 21.87%, thus, the correct option is B.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given the reduction in the price is $7, while the original cost is $32. Therefore, the approximate percent decrease in the price is,

Percentage decrease = 7/32  × 100%

                                     = 21.87%

Hence, the approximate percent decrease in the price is 21.87%, thus, the correct option is B.

The correct question is:

Helen got a $7 reduction in the price of a pair of jeans that are normally $32. What is the approximate percent decrease in the price?

The percent decrease is approximately 15%.

The percent decrease is approximately 21%.

The percent decrease is approximately 43%.

The percent decrease is approximately 78%

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Answer:

£216.60

Step-by-step explanation:

If 5 calculators cost £31.25, then each calculator costs £6.25

If 3 pens cost £2.91, then each pen cost £0.97

30(6.25) + 30(0.97) = £216.60

Answer:

Complementary: Angle SRP and Angle PRQ

Supplementary: Angle SRO and Angle SRQ

Step-by-step explanation:

Complementary: 90 degrees

Angle SRP and Angle PRQ

Supplementary: 180 degrees

Angle SRO and Angle SRQ

Using Sarai's measurements, Line 3 must be parallel to Line 5 by option (A) Converse of Alternate Exterior Angles Theorem.

The alternate Exterior Angles theorem states, "If two lines are parallel and they are intersected by the same straight line then the alternative exterior angles formed by the figure are equal to each other."

The converse of this theorem states that "If two lines intersected by one transverse and formed alternate exterior angles, and if they are equal to each other then that two lines are parallel to each other."

Here in Sarai's measurement, we can conclude that Line 3 and Line 5 are intersected by one straight line, and the formed alternate exterior angles both are 65, which shows they are equal to each other.

Hence by Converse of the Alternate Exterior Theorem, we can say that both lines are parallel to each other.

So, Line 3 must be parallel to Line 5 according to the Converse of Alternate Exterior Angles Theorem.

Hence Option (A) is correct.

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Factorial design is the correct choice for the answer as an experimental design that permits statistical conclusions about two or more factors is a factorial design.

A factorial experiment is a type of research methodology that allows the study of main and interaction effects between two or more independent variables and on one or more outcome variables.

This is called a mixed factor experiment. For example, a researcher may choose to treat mobile phone use as a factor within a subject by testing the same participant with and without mobile phone use (the order of these two conditions). Balance).

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The skew lines are CG, DH, AD, BC.

Two or more lines which have no intersections but are not parallel.

Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions.

As, by the definition

The lines skew to EF is CG, DH, AD, BC

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Answer: 16

Step-by-step explanation:

[tex](g \circ f)(-6)=g(f(-6))\\\\f(-6)=-(-6)-2=4\\\\\implies g(f(-6))=g(4)=4^2 = \boxed{16}[/tex]

The value of the function estimation; (g°f)(-6) is; 64.

It follows from the task content that; the fumcti given are; f(x) = -x-2 and g (x) =x².

Hence, the function (g°f) (x) can be evaluated as; (-x-2)² = x² +4x +4.

Ultimately, when x = 6; (g°f)(-6) = 6² +4(6) +4 = 64.

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Its the first one, because x wont be affected, and 1 and -3 is a constant.

The total lemonade the two friends bring to the cookout when one brings 2.7 liters and the other brings 3.54 liters of lemonade is 6.24 liters of lemonade, computed using decimal addition.

The methods we use to add or subtract decimals are as follows:

In the question, we are informed that two friends bring lemonade to the cookout. The first brings 2.7 liters and the second brings 3.54 liters.

We are asked to find the total lemonade brought by them to the cookout.

To find the total lemonade, we add both the decimal quantities following the steps discussed.

    2.7

+   3. 54

Step 1: Adding zeroes:

    2.70

+   3. 54

Step 2:  Treating them as numbers and adding:

    2.70

+   3. 54

________

    624

Step 3: Aligning decimal points:

    2.70

+   3. 54

________

    6.24

Thus, the total lemonade the two friends bring to the cookout when one brings 2.7 liters and the other brings 3.54 liters of lemonade is 6.24 liters of lemonade, computed using decimal addition.

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Answer:

[tex]a)\ y=-(x-5)^2;\\b)\ y=4x^2-5;\\c)\ (y-2)^2=4*(x+3).[/tex]

Good luck!

Answer:

x = -1

y = -2

Step-by-step explanation:

You can use the method of substitution to solve this equation. Since you know that y= 2x, you can substitute that value into x + y = -3:

x + (2x) = -3

Combine like terms:

3x = -3

x = -3/3

x = -1

Now that you know the value of x, you can substitute it into any of the two equations (I'll be choosing y = 2x)

y = 2x

y = 2 (-1)

y = -2

So your solution is x = -1, y = -2

Point form: (-1, -2)

The answers are as follows:

A trapezoid with its two nonparallel sides equal.

Given:

<BAD =65

As, MN is mid segment

So,

BC= 2CM

BC = 16

Now, ABCD is isosceles trapezoid

BC= AD

So, AD= 16

and, Using mid- point theorem

MN= 1/2 AB

MN = 1/2* 22

MN= x = 11

Also, co- interior angle sum is 180 in trapezium

<BAD + <BCD = 180

<BCD + 65 =180

<BCD = 115

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Since there are 10 values that have the zero digits, hence the zero digits appear 10 times in the sequence

Series are defined as sum of sequences. Given the following sequence

5, 10, 15, ..., 100

The common difference is 5 and the number that have digits zero in the sequence are 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100

Since there are 10 values that have the zero digits, hence the zero digits appear 10 times in the sequence

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Answer: C

Step-by-step explanation:

[tex]\sqrt10 10=10\sqrt{10}[/tex]

Answer: 14.79

Step-by-step explanation:

[tex]\frac{b}{\sin B}=\frac{a}{\sin A}\\\\a=\frac{b \sin A}{\sin B}\\\\a=\frac{23 \sin 40^{\circ}}{\sin 88^{\circ}}\\\\a \approx 14.79[/tex]

Answer:

600

Step-by-step explanation:

So I'm assuming an outfit is considered one shirt, and one pair of pants... But anyways, this can be expressed in a graph. So for each shirt, there are going to be 15 possible pants you can chose. And this goes for each shirt. So in other words you're simply adding up 15, 40 amount of times. Or 15 * 40, which is 600. I attached an image that illustrates this graph. You can also think of it in terms of choosing one of 15 pants and then for each pant, there are 40 possible shirts to choose from. This is essentially adding up 40, 15 times, or in other words 40 * 15, which is going to get you the same result. But in my diagram I used it in terms of choosing a shirt first.

Answer:

600

Step-by-step explanation:

Pair 1 of pants goes with 40 shirts

Pair 2 of pants goes with 40 shirts

Pair 3 of pants goes with 40 shirts

Pair 4 of pants goes with 40 shirts

Pair 5 of pants goes with 40 shirts

Pair 6 of pants goes with 40 shirts

Pair 7 of pants goes with 40 shirts

Pair 8 of pants goes with 40 shirts

Pair 9 of pants goes with 40 shirts

Pair 10 of pants goes with 40 shirts

Pair 11 of pants goes with 40 shirts

Pair 12 of pants goes with 40 shirts

Pair 13 of pants goes with 40 shirts

Pair 14 of pants goes with 40 shirts

Pair 15 of pants goes with 40 shirts

Add up everything (not including the 1,2,3,4,5,...14,15 pairs of pants because each pair of pants goes with 40 different shirts so u just add up all the 40's)  and you would get 600 outfits.

Another simple way of doing this would just be multiplying 40x15

Answer:

C

Step-by-step explanation:

x²-10x+(-10×0.5)²=4+(-10×0.5)²

x²-10x+25=29

Answer: 0

Step-by-step explanation:

When x=0, y=4.

When x=4, y=4.

So, the rate of change is 0.

Answer:

Step-by-step explanation:

[tex]\bf \cfrac{AB}{BC} = \tan(60) [/tex]

Length of tower:-

Therefore, the tower is 93.6ft tall.

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

Answer:

4

Step-by-step explanation:

LCM of 2 and 4 (denominators of fraction)

= 4

Using the law of cosines, it is found that the approximate measure of angle G is of 41.4º.

The law of cosines states that we can find the angle C of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

In this problem, we want to find angle G, hence c = 8, then:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

[tex]8^2 = 10^2 + 12^2 - 2(10)(12)\cos{G}[/tex]

[tex]240\cos{G} = 180[/tex]

[tex]\cos{G} = \frac{3}{4}[/tex]

[tex]G = \arccos{\left(\frac{3}{4}\right)}[/tex]

G = 41.4º.

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Answer: DE NADA

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

Answer:

i don't know sorry :(

Step-by-step explanation:

Answer:

See attached image.  

250 shirts at $50/shirt is the equilibrium.

Step-by-step explanation:

The graph of f(x) is shifted up by 5 units to get g(x)

The functions are given as:

g(x) = x + 5

f(x) = x

Substitute f(x) = x in g(x) = x + 5

So, we have:

g(x) = f(x) + 5

The above means that the graph of f(x) is shifted up by 5 units to get g(x)

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The values gotten for the  coordinate plane are;

The Reason for the obtained value is that since thee rule for the dilation of ΔRST is:

Then, the distance that exist between the x-coordinate of R and T will be:

3 - 0

= 3

Then the distance between the y-coordinate of R and T will be:

4 - (-2)

= 6

Note that the location of the point R' is said to be relative to point T and as such:

The location of point R'

= (-1 + 3, 2 - 2)

= R'(2, 0)

Hence R' is (-1, 2) from T, and the coordinates of R' is (2, 0)

Therefore, The values gotten for the  coordinate plane are;

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Answer:

C.) ✔ 3

D.) ✔ 6

B.) ✔ 1 unit left, 2 units up

D.) ✔ (2, 0)

Step-by-step explanation: i hope this helps :)