Goran invested his savings in two investment funds. The amount he invested in Fund A was 7000 less than the amount he invested in Fund B. Fund A returned a 4% profit and Fund B returned a 2% profit. How much did he invest in Fund B, if the total profit from the two funds together was 500?

Answer and Step-by-step explanation:

The kite area formula:

A = [tex]\frac{pq}{2}[/tex]

P = Line RP

Q = Line QS

A = [tex]\frac{38 + 16}{2}[/tex] = [tex]\frac{54}{2}[/tex] = 27

27 is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

Step-by-step explanation:

There are various lines dividing this figure into shapes, such as rectangles and triangles; this makes it easier to find the area.

First, find the area of the triangles.

In this figure, there are two triangles with heights of 12 and bases of 18.

[tex]12 * 18 = 216[/tex]

Then, multiply the product by 1/2.

[tex]216 * 1/2 = 108[/tex]

There are two triangles, so multiply, the product, 108, by 2.

[tex]108*2 = 216[/tex]

The area of both combined triangles is 216 cm; the area of a single triangle is 108 cm.

Secondly, find the area of the rectangles.

There are two rectangles with widths of 25 and lengths of 15.

[tex]25*15 = 375[/tex]

There are two rectangles, so multiply the product, 375, by 2.

[tex]375*2 = 750[/tex]

The area of both rectangles combined is 750 cm; the area of a single rectangle is 375 cm.

Lastly, we find the area of the rectangle in the middle.

This rectangle has a length of 18 and a width of 25.

18[tex]18*25 = 450[/tex]

The area of this rectangle is 450 cm.

Lastly, add the areas of all the shapes.

[tex]108 + 108 + 375 + 375 + 450 = 1,416.[/tex]

Therefore, the area of this figure is 1,416 cm².

Answer:

d = √17, meaning that the number that goes beneath the radical symbol is 17.

Step-by-step explanation:

Refresh if you are unable to see below.

[tex]\text{Use the distance formula.}\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\text{Substitute the points.}\\d=\sqrt{(3-(-1))^2+((-1)-(-2))^2}\\\text{Subtract.}\\d=\sqrt{(4)^2+(1)^2}\\\text{Evaluate the powers of 2.}\\d=\sqrt{16+1}\\\text{Add.}\\d=\sqrt{17}[/tex]

Answer:

To determine which loan will have a higher balance at the time of repayment, we need to calculate the balance of each loan after the interest has been compounded over the repayment period.

The unsubsidized Stafford Loan has an annual interest rate of 3.85% and a grace period of six months from the time of graduation. This means that the loan will accrue interest for a total of 12 months - 6 months = 6 months.

The balance of the unsubsidized Stafford Loan at the time of repayment can be calculated using the following formula:

Balance = Principal * (1 + Interest rate / Number of compounding periods per year)^(Number of compounding periods)

Plugging in the given values, we have:

Balance = $10,958 * (1 + 0.0385 / 12)^(6) = $10,958 * (1.003125)^(6) = $11,283.16

The PLUS loan has an annual interest rate of 4.15% and a balance of $11,421.51 at the time of repayment.

The balance of the PLUS loan at the time of repayment can be calculated using the same formula:

Balance = $11,421.51 * (1 + 0.0415 / 12)^(6) = $11,421.51 * (1.003479)^(6) = $11,973.54

Therefore, the PLUS loan will have a higher balance at the time of repayment, by $11,973.54 - $11,283.16 = $690.38.

Step-by-step explanation:

The side lengths are;

tan x = e/f

cos x = e/d

sin x = f/d

We know that a right angled triangle is the kind of triangle that one of the sides of the triangle would be 90 degrees.

There are some ratios that are associated with the right angled triangle and we call them the trigonometric ratios. These include the sine the cosine and the tangent. All of these ratios does depend on the lengths of the sides of the right angled triangle.

The sides of the right angled triangle are the opposite, the adjacent and the hypotenuse and these can be obtained based on the relative position of the angle.

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Answer:

D

Step-by-step explanation:

Frank is at point G: (-6,-1)

Jimmy is at point B: (4,1)

Answer:

189 sq mm

Step-by-step explanation:

area = (21×18)/2 = 189 sq mm

There were 8 roses on each bushes

Gemma has 3 rose bushes

Each bush has the same number of roses

She picks 4 of the roses

After picking the roses, there are 20 left in the bushes

Therefore the number of rose on each bush can be calculated as follows

20 + 4

= 24

24/3

= 8

Hence there are 8 roses in each bush

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3/4 > 1/5
6/9 > 2/5
6/7 > 3/10
2/11 < 4/9

Answer:

3/4 > 1/5

6/9 > 2/5

6/7 > 3/10

2/11 < 4/9

Step-by-step explanation:

Manera facil de comparar fracciones:.

3/4    1/5

Multiplica el denominador (numero abajo) de cada fraccion por el numerador de la otra fraccion y escribe el producto arriba del numerador.

El numero mas grande esta arriba de la fraccion mas grande.

5 x 3 = 15 arriba  de 3/5

4 x 1 = 4 arriba de 1/5

Como 15 > 4, 3/4 > 1/5

30      18

6/9    2/5

6/9 > 2/5

 60     21

6/7    3/10

6/7 > 3/10

18       44

2/11   4/9

2/11 < 4/9

Answer:

She ate 1/10 of the pizza.

Hope this helps!!

Answer:

3

Step-by-step explanation:

768 can be broken down to:

2×2×2×2×2×2×2×2×3

The part made up of twos is already a perfect square. The 3 needs a partner for it to be a perfect square also.

768 × 3 is 2304.

Sqrt2304 is 48.

Multiply 768 by 3 to make it a perfect square.

Refer To The Given Image

Answer:

78 ft x 1 in/ 13 in = 6 ft

1 inch represent 6 ft

The surface area of the composite figure is 416 square cm because the composite figure is made up of two figures.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

We have a composite figure shown in the picture.

As we can see in the picture the composite figure is made up of two figures.

The first one is a rectangular prism

Second one is a triangular prism.

The surface area of the composite figure:

= area of the two triangle shapes + area of the two rectangles in triangular prism + surface area of the rectangular prism - (12x5)

= 2(1/2)12x10 + 2(10x5) + 2(4x5 + 12x5 + 12x4) - 12x5

= 120 + 2(50) + 2(20 + 60 + 48) - 60

= 120 + 100 + 2(128) - 60

= 120 + 100 + 256 - 60

= 416 square cm

Thus, the surface area of the composite figure is 416 square cm because the composite figure is made up of two figures.

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Answer:

A. 4%

Step-by-step explanation:

remember that there are 52 weeks in a year, so multiply 1000 by each answer, then multiply what you get by 52 to see if it is either below 2000 or just above 2000, and you'll see how i got 4%.

Answer:

3 or 2

Step-by-step explanation: I don't know, but I am gonna say that is the interest rate for the invest for saving up $2000

(Please correct me if I am wrong)

Answer:

Height of the silo = 18 feet.

Step-by-step explanation:

From the figure attached BC is the length of the silo and the height of the farmer is 5 ft.

Farmer is standing at 8 ft distance from the silo.

From triangle AEC,

tan(∠CAE) = CE/AE=5/8

m(∠CAE) = tan-1 (5/8)

= 32°

m∠BAE = 90° - 32° = 58°

From the triangle ABE,

tan58° = BE/AE

BE = 8tan58°

BE = 12.8 ft

Total height of the silo = BE + EC

= 12.8 + 5

= 17.8

≈ 18 ft          

Therefore, the total height of the silo is 18 ft.

Answer:

a^4b^24

Step-by-step explanation:

We know, (xy)^n = x^ny^n. So,

(ab^6)^4 = a^4b^(6×4)

= a^4b^24

Answer:

If no time is spent on homework, the test grade is approximately 72.

Step-by-step explanation:

The y-intercept of the line can be interpreted if no time is spent on homework, the test grade is approximately 72.

A graph can be described as a pictorial representation of data. A graph is made up of a x-axis and a y-axis.  The y-intercept is the point where the line crosses the y-axis. The y-intercept is the value of the data set when x is zero.

If x is zero, y = 0 + 72

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Answer:

Ramon will run 1/9 of a mile.

Step-by-step explanation:

The relay race is 1/3 of a mile and there are three of them in his relay squad, himself and his two friends.

If three of them finish each sector and each sector is the same, that means that each of the members will run a third of that distance.

[tex]\frac{1/3}{3}\\=\frac{1}{3} (\frac{1}{3} )\\=\frac{1}{3(3)}\\=\frac{1}{9}[/tex]

9514 1404 393

Answer:

  $7.50

Step-by-step explanation:

Rounded to the nearest $10, the $49.35 bill becomes $50.

We can find 10% of that amount by moving the decimal point to the left. 10% of $50 is $5.00.

Then 5% of $50 is half of 10%, so is $5/2 = $2.50.

The estimated tip of 15% is the sum of 10% and 5% of the bill, so is ...

  15%($50) = 10%($50) +5%($50) = $5.00 +2.50 = $7.50

The estimated 15% tip is $7.50.

Answer:

1) Yes

2) No

Step-by-step explanation:

In the first test  t distribution is  appropriate to use because  in the dot plot the  16 data points can be seen other the the data points clustered round the mean.

Here degrees of freedom = n-1= 74

S. E= s/√n

S.E= 10.1/ √74= 1.17

For t - distribution it is assumed that the sample is approximately normal which is  visible in the dot plot in the first test.

In the second case z test should be applied.

Z test is used when the population standard deviation is not known .

In the second test  t distribution is   not appropriate to use because  in the dot plot only 2 data points can be seen other the the data points clustered round the mean.

For t - distribution it is assumed that the sample is approximately normal which is not visible in the dot plot.

Using the Algebraic tile method we get x=2 solution for equation model

The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.

In the question, we have 3 kinds of tile

Equation will be :

⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1

⇒ 3x - 2 = 4

⇒ 3x = 6

⇒ x = 2

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Answer:

4305

Step-by-step explanation:

The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).

To correctly model the expression -2/6 + (5/6) on a number line, we can use the following steps:

So to model the expression -2/6 + (5/6) on a number line, we start at 0 and move 1/3 to the left, to represent -2/6, and then move 5/6 to the right to represent 5/6. The final point on the number line will be at 2/3 from 0 point, which represents the value of the expression -2/6 + (5/6).

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Answer:

50% for all of em

Step-by-step explanation:

Answer: y = -5x + 6

Step-by-step explanation:

First, we need to find the slope, which would be m in the equation. To find m, we can use the formula called "rise over run". Here's the formula: [tex]m=\frac{y2-y1}{x2-x1}[/tex]

So, to use this formula, you pick two points from the line that you're given and solve for m.

Let's use the points (1,1) and (0,6). x1 would be 1, x2 would be 0, y1 would be 1, y2 would be 6

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

[tex]m=\frac{6-1}{0-1}[/tex]

[tex]m=\frac{5}{-1}[/tex]

[tex]m=-5[/tex]    So, the slope is -5

Then, we need to find the y intercept, which would be b in the formula.

We can see that the point where the line meets the y axis is at (0.6), so the y intercept would be 6.

Now let's put everything together:

y = mx+b

y = -5x + 6

Answer:9/40

Step-by-step explanation:

3/4=10/3x

3/4*3/10=x

9/40=x

Answer:

See below

Step-by-step explanation:

Absolute value is the positive distance from 0, so |-7| = 7 because -7 is 7 from 0, whereas 6 is 6 away from 0. Because 7>6, then -7 has a greater absolute value than 6