If Goran invested his savings in two investment funds. The amount that Goran invest in Fund B, if the total profit from the two funds together was 500?
How to find the amount invested?Amount Invested in Fund A = x
Amount invested in Fund B = x+7000
Profit from fund A = 0.04x
Profit from fund B = 0.02(x+7000)
0.04x +0.02(x+7000) = 500
0.04 +0.02x + 140 =500
Combine like terms
0.06 x =360
Divide both side by 0.06x
x = 360 /0.06
x = 6,000
Amount Invested in Fund A = x =6,000
Amount invested in Fund B = x+7000
Amount invested in Fund B = 6,000 + 7,000
Amount invested in Fund B = 13,000
Therefore the amount invested in Fund A 6,000 and the Fund B is 13,000.
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3/4 of a cup of sugar is needed to make 3 1/3 batches of banana bread.How much is needed to make 1 batch?
Answer:9/40
Step-by-step explanation:
3/4=10/3x
3/4*3/10=x
9/40=x
Gemma has 3 rose bushes, each with the same number or roses. She picks 4 of the roses. There are 20 roses left on the rose bushes. How many roses were on each rose bush?
There were 8 roses on each bushes
How to calculate the number of roses on each bush?
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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find -2/6 + (5/6) model the expression on the number line
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).
Modelling -2/6 + (5/6 on the number lineTo correctly model the expression -2/6 + (5/6) on a number line, we can use the following steps:
Start at 0 on the number line.Move to the left by 1/3. This represents the value of -2/6 which is equivalent to -1/3.Move to the right by 5/6. This represents the value of 5/6.The final point on the number line will be 2/3 to the right of the point (-1/3) which we reached in step 2, this represents the sum of -2/6 and 5/6, which is the final result.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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20 x 321-15 x 141
What is the value of the expression?
Answer:
4305
Step-by-step explanation:
please help me!
Please explain it
Answer:
1,416 cm²Step-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.
To find the area of a triangle, multiply the base and the height, then multiply the product by 1/2.To find the area of a rectangle, multiply the width by the length.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.
The data reflects the amount of time spent on homework (x), paired with a corresponding test grade (y).
How can the y-intercept of the line be interpreted?
The minimum time spent on homework is approximately 72 hours.
The average time spent on homework is approximately 7.9 hours.
If no time is spent on homework, the test grade is approximately 72.
If no time is spent on homework, the test grade is approximately 7.9.
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.
What is the y intercept?
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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A student is graduating from college in 12 months but will need a loan in the amount of $10,958 for the last two semester. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 3.85%, compounded monthly, and a grace period of six months from time of graduation
PLUS loan: annual interest rate of 4.15%, compounded monthly, with a balance of $11,421.51 at the time of repayment
Which loan will have a higher balance, and by how much at the time of repayment?
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:
Find the distance between the two points.
✓ [?]
(-1,-2)
(3,-1)
Enter the number that
goes beneath the
radical symbol.
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]
Ayuda porfa doy corona
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
There was 5/6 of the pizza left,and Malachi ate 1/2 of that.What fraction of the pizza did Malachi eat.
Answer:
She ate 1/10 of the pizza.
Hope this helps!!
I NEED HELP PLS HELP ME ASAP!!! I'LL GIVE YOU 100 POINTS!
Answer:
189 sq mm
Step-by-step explanation:
area = (21×18)/2 = 189 sq mm
100 points Pls help me with the red ones
To calculate the cost of painting his silo, a farmer must find its height. The farmer uses a cardboard square to line up the top and bottom of the silo as shown in the diagram below. Approximate the height of the silo, rounded to the nearest foot.
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.
What's the equation and solution?
Using the Algebraic tile method we get x=2 solution for equation model
What is Algebraic Tile method?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
X tilesunit positive tilesunit negative tilesEquation will be :
⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1
⇒ 3x - 2 = 4
⇒ 3x = 6
⇒ x = 2
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2. Construct Arguments Explain why -7 has a
greater absolute value than the absolute value
of 6.
5.-9
7.1-5
9. --
11.-1
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
The makers of the movie Harry Potter need to
create Hogwarts. The maker created a scale
drawing of Hogwarts before he began building
the model. The length of the drawing for
Hogwarts is 13 inches. The length of the actual
model is 78 feet. What scale did the maker use
to create the scale drawing of Hogwarts?
A.
B.
1 inch represents 13 feet
6 inch represents 13 feet
1 inch represents 78 feet
1 inch represents 6 feet
Answer:
78 ft x 1 in/ 13 in = 6 ft
1 inch represent 6 ft
Can y’all help me on question 4?!
Answer:
D
Step-by-step explanation:
Frank is at point G: (-6,-1)
Jimmy is at point B: (4,1)
Plz help I will give brainiest
Answer:
50% for all of em
Step-by-step explanation:
A kite is flying 24 ft off the ground. Its line is pulled taut and casts a 7-ft shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
The side lengths are;
tan x = e/f
cos x = e/d
sin x = f/d
What is a right angled triangle?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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Need help ASAP! See images below
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)
Find the surface area of the composite figure,
5 cm
10 cm
10 cm
8 cm
4 cm
4 cm
5 cm
12 cm
The surface area of the composite figure is 416 square cm because the composite figure is made up of two figures.
What is a rectangular prism?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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1) Is a t-Distribution Appropriate?
A sample with size n=75 has x¯=18.92, and s=10.1. The dotplot for this sample is given below.
Indicate whether or not it is appropriate to use the t-distribution.
Yes / No
If it is appropriate, give the degrees of freedom for the t-distribution and give the estimated standard error. If it is not appropriate, enter -1 in both of the answer fields below.
Enter the exact answer for the degrees of freedom and round your answer for the standard error to two decimal places.
df=
standard error =
2) Is a t-Distribution Appropriate?
A sample with size n=10 has x¯=508.5, and s=21.5. The dotplot for this sample is given below.
Indicate whether or not it is appropriate to use the t-distribution.
Yes / No
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.
Ramon and 2 of his friends will run a relay race. The length of the race is 1/3 mile. If each person runs the same distance, how far will
Ramon run?
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]
Pls help Whats the equation?
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
4.4) Find the least number by which 768 must be multiplied so as to make it a perfect square
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
Estimate a 15% tip on a dinner bill of $49.35 by first rounding the bill amount to the nearest ten dollars.
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.
PLEASE HELP!!! THANK YOU!!!
You have $1000 to invest in an account and need to have $2000 in one year. What interest rate would you need to have in order to have this if the amount is compounded weekly? Round your answer to the nearest percent.
A. 4%
B. 2%
C. 3%
D. 1%
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)
Which expression is equivalent to (ab6)4?
a4b24
ab24
a5b10
ab28
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
need help asappppppp
can someone help me with this PLEASE ITS KILLING ME!!!!