Answer:
Interest earned at 3.9 percent rate is $31.2
Interest earned at 2 percent rate is $5.8
Step-by-step explanation:
A = P(1 + rt)
Where 'A' is the amount, 'r' is the rate and 't' is the time in years
When;
P = $1200
r = 3.9%
t = [tex]\frac{8}{12}[/tex] years
Then,
A = $1200(1 + 0.039([tex]\frac{8}{12}[/tex]))
A = $1200 + $31.2 = $1231.2
Interest = Amount - Principal
Interest earned at 3.9 percent rate is $1231.2 - $1200 = $31.2
When;
P = $580
r = 2%
t = [tex]\frac{6}{12}[/tex] years
Then,
A = $580(1 + 0.02([tex]\frac{6}{12}[/tex]))
A = $580 + $5.8 = $585.8
Interest earned = Amount - Principal
Interest earned at 2 percent rate = $585.8 - $580 = $5.8
Thesimple interest, you use the formula I = PRT, with P representing principal, R the annual interest rate in decimal form, and T the time in years. For $1200 at 3.9% over 8 months, the interest is $37.20. For $580 at 2% over 6 months, the interest is $5.80.
The simple interest earned on two separate principals with different interest rates and time periods. To calculate simple interest, we use the formula I = PRT, where I is the interest earned, P is the principal amount, R is the annual interest rate (in decimal form), and T is the time in years. If the time is given in months, we must convert it into years by dividing by 12.
Example 1:
Principal (P) = $1200
Annual Interest Rate (R) = 3.9% = 0.039
Time (T) = 8 months = ({8}{12}) years
Simple Interest (I) = $1200 (times) 0.039 (times) \(frac{8}{12}) = $37.20 to the nearest cent
Example 2:
Principal (P) = $580
Annual Interest Rate (R) = 2% = 0.02
Time (T) = 6 months = ({6}{12}) years
Simple Interest (I) = $580 (times) 0.02 (times) \({6}{12}) = $5.80 to the nearest cent
In conclusion, we have two amounts of simple interest for the different principals, rates, and times provided. To find the total future amount with simple interest, we would add the interest earned to the principal amount.
At the Rolling Ridge School spelling bee, 75% of the
contestants advanced to the second round and 60% advanced
to the third round. What is the probability that a randomly
selected contestant advanced to the third round given the same
contestant advanced to the second round?
A. 3/20
B. 9/20
c. 7/15
D. 4/5
Answer: Option D
[tex]P (B | A) =\frac{4}{5}[/tex]
Step-by-step explanation:
Call A to the event in which a student advances to the second round.
We know that:
[tex]P (A) = 75\% = 0.75[/tex]
Call B the event in which a student advances to the third round.
We know that:
[tex]P (B) = 60\% = 0.6[/tex]
We then look for the probability of B given A. This is:
[tex]P (B | A) =\frac{P(B\ and\ A)}{P(A)}[/tex]
In this case, the probability of B and A is equal to the probability of B, since the students who advance to the third round also advanced to the second round before
[tex]P (B | A) =\frac{P(B)}{P(A)}[/tex]
[tex]P (B | A) =\frac{0.6}{0.75}[/tex]
[tex]P (B | A) =\frac{4}{5}[/tex]
Solve the inequality 3(x-1)<-3(2-2x)
i believe the answer would be x > 1?
Answer:
x > 1
Step-by-step explanation:
3(x-1)<-3(2-2x)
=> 3x +3 < 6x
=> 1<x
find the slope (4,4) (4,9)
Answer:
Undefined
Step-by-step explanation:
Slope form:
m (slope) = (y₂ - y₁)/(x₂ - x₁)
Let:
(x₁ , y₁) = (4 , 4)
(x₂ , y₂) = (4 , 9)
Plug in the corresponding numbers to the corresponding variables.
m = (9 - 4)/(4 - 4)
Simplify
m = (5)/(0)
m = undefined
Undefined is your answer, for there cannot be a 5/0. You cannot have 5 parts of nothing.
~
Find the approximate area of a circle thet has a diameter of 17 inches. Round your answer to the nearest hundredth
A. 26.69 in 2
B. 106.76 in 2
C. 226.87 in 2
D. 53.38 in 2
For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
A: It is the radius of the circle.
If they tell us that the diameter is 17 inches, then the radius is 8.5 inches. Substituting:
[tex]A = \pi * (8.5) ^ 2\\A = 226,865[/tex]
If we round up, we have that the area is:
226.87 square inches
Answer:
Option C
If ƒ(x) = 2x, then ƒ -1(x) =
-2x
½x
x - 2
Answer: second option
Step-by-step explanation:
To find the inverse function of the given function f(x):
[tex]f(x)=2x[/tex]
You need to:
Substitute [tex]f(x)=y[/tex] into the function:
[tex]y=2x[/tex]
Now, you need to solve for "x", to do this, you must divide both sides of the function by 2:
[tex]\frac{y}{2}=\frac{2x}{2}\\\\\frac{y}{2}=x[/tex]
Now, replace "x" with "y" and replace "y" with "x":
[tex]\frac{x}{2}=y[/tex]
Therefore, substituting [tex]y=f^{-1}(x)[/tex] you get:
[tex]f^{-1}(x)=\frac{x}{2}[/tex] or [tex]f^{-1}(x)=\frac{1}{2}x[/tex]
A ball is dropped from the top of a building. the height of the ball after x bounces can be represented by the expression 40(0.75)^x.
What does the in the expression 40 represent??
Answer:
I believe 40 is the height from which the ball was dropped
In the expression \( 40(0.75)^x \), the number 40 represents the initial height from which the ball is dropped. This initial height refers to the height of the ball above the ground before it experiences any bounces.
The expression itself describes a geometric sequence where the height of the ball after each bounce is a certain fraction of the height from the previous bounce. In this particular case, after each bounce, the ball reaches a height that is 75% (or 0.75 times) of the height of the previous bounce.
To break it down further:
- \( 40 \) is the initial height (in meters, feet, or another unit of measurement) where the ball was dropped from the top of the building.
- \( 0.75 \) is the common ratio, representing the fact that the ball loses 25% of its height with each bounce. It means that the ball only reaches 75% of the height it reached after the previous bounce.
- \( x \) is the number of bounces.
So, after the first bounce (when \( x = 1 \)), the height of the ball would be \( 40 \times 0.75 \). After the second bounce (when \( x = 2 \)), the height would be \( 40 \times 0.75^2 \), and so on for each subsequent bounce, following the pattern of a geometric sequence.
what is (24-6)+19÷2
27.5
Follow the order of operations and start by solving the parentheses.
18 + 19 / 2
Now, do the division.
18 + 9.5
Finally, solve the addition.
27.5
ANSWER QUICKLY PLEASE ITS URGENT
Solve the equation.
X^2 = 0.49
Answer:
x = 0.7
Step-by-step explanation:
To solve this, simply find the square root of 0.49
x^2 = 0.49
(Finding the square root will cancel out the ^2 on x, to get x alone)
x = 0.7
You can double check this too to see if this is the right answer.
0.7 x 0.7 = 0.49
I hope this helps!!! :)
0.7 x 0.7 = 0.49 i think this is it
A recipe for cake needs to 1/4 cup of cake you are making 1/2 of the recipe how many cups of flour do you need?
Answer:
1/8
Step-by-step explanation:
If you need 1/4 cup for the full recipe and you're making half, you have to divide 1/4 by 2. Dividing 1/4 by 2 is the same as multiplying 1/4 by 1/2 since you take the reciprocal (opposite or flip) of 2. 1/4 times 1/2 is 1/8. I hope this helps!
Answer:
1/8
Step-by-step explanation
(1/4)÷2 is the same as saying (1/4)×(1/2)
Multiply the numerators (1×1)
Multiply the denominator (4×2)
and you get (1/8)
Linda Young opened up a computer service company. To pay for start up cost Linda borrowed $79,000 from a bank at 15% for 1 year. Find the interest for the year
Interest=Principal×Rate×Time
I=PRT/100
I= 79000×15×1
100
I= 1185000
100
I= $11850
To confirm
11850/79000 ÷ 100
= 0.5 ×100
= 15% (rate)
The interest of one year is $11850.
What is simple interest?
easy interest is based on the essential amount of a loan or the primary deposit in a savings account.
calculation:-
Amount of money borrowed by Linda = $79000
rate of interest =15%
Interest amount= $79000*15/100
The interest of the year =$11850
Learn more about simple interests here:-https://brainly.com/question/2294792
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What is the equation of the line that passes through the points (2,-1) and (6,1)?
The answer is y=1/2x-2
Write an addition equation or a subtraction equation to describe the diagram
The addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have a line graph shown in the picture.
The small arrow represents the length of 4 but as it is indicating negative direction, so we take -4
Similarly, the big arrow represents the length of 9 as it is indicating negative direction, so we take -9
The sum of the lengths:
(-9)—(-4) = -13
Thus, the addition equation or a subtraction equation to describe the diagram is (-9)—(-4) = -13
Learn more about the arithmetic operation here:
brainly.com/question/20595275
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See attachment below. Please answer. Thank you.
Hi
The probability of landing a green side up is 2 / 6 .
Hope this helps
Answer:
C. 2/6
Step-by-step explanation:
We know that a block has 6 sides.
There are 2 green sides.
Now all we do is put the number of green sides over the number of sides the block has.
2/6 is our answer.
The circumference of heileen’s basketball is 30 inches. What is the approximate diameter of the basketball?
Answer:
9.55 in
Step-by-step explanation:
The formula for the circumference of a circle (or the circum. of a basketball) is C = πd, where d is the diameter.
Here C =30 in = πd, so
d = (30 in) / π
= 9.55 in, approx.
Answer:
d = 9.554 inches.
Step-by-step explanation:
Formula
C = 2*pi*r
r = the radius
C = the Circumference.
Givens
Circumference = 30 inches.
pi = 3.14
Solution
C = 2*pi * r
30 = (2*r) * 3.14 (you'll see why I've done that in a minute. Divide by pi.
30/3.14 = 2*r
9.554 = 2r
The diameter of the basketball = 2 * radius. So the answer for the diameter = 9.554 inches.
A local clothing shop is marking down all of its summer clothes by 75%. sarah would like to purchase a swimsuit that is originally priced at $80. when she gets to the register, she signs up for a loyalty cars that saves her an additional 10%. how much did she spend on the swimsuit and what total percent did she receive off?
a. Find the markdown price of the swimsuit.
b. Then, find the markdown of the loyalty card.
c. Subtract to find the final price.
Answer:
$18.00
Step-by-step explanation:
75% of 80$ is 60$ .
80$-60$=20$
10%of20$=2$
20$-2$=18$
18$
She spend $18 on the swimsuit and she gets total 77.5 percent off.
Given local clothing shop is marking down all of its summer clothes by 75%.
And Sarah would like to purchase a swimsuit that is originally priced at $80.
So, the markdown price of swimsuit will be ( $80 - 75 % of $80).
Now 75% of $80 is equals to $60.
So the markdown price of swimsuit will be ($80 - $60) or $20.
Again, when she gets to the register, she signs up for a loyalty cars that saves her an additional 10%.
So 2% of $20 dollar will be $2.
Now the final markdown price of swimsuit will be ($20-$2) or $18 .
Total discount she get is of ($80 - $18) or $62.
The percent amount she gets off = [tex]\frac{62}{80} \times100%[/tex] %.
=[tex]0.775 \times100[/tex]%.
[tex]=77.5[/tex]%.
She spend $18 on the swimsuit and she gets total 77.5 percent off.
For more details on percentage follow the link:
https://brainly.com/question/16797504
find the slope of the line that passes through -2 -2 and 2 -4
Answer:
-1/2
Step-by-step explanation:
To find the slope we know that:
Slope = (Y2-Y1)/(X2-X1)
Then, given the two points, we have that:
(X1, Y1) = (-2,-2)
(X2, Y2) = (2, -4)
Then:
m= (Y2-Y1)/(X2-X1) = (-4-(-2))/(2-(-2)) = -4+2/2+2 = -2/4 = -1/2
So the slope of the function that passes through those points is: -1/2
Which of the following statements are true? Select all that apply. This is Algebra Nation
Answer:
241
Step-by-step explanation:
I don’t understand it
So first you have to find the volume of the entire tank using the height of 6cm. Then you have to find the volume of just the water using the height of 4 cm. Then you subtract both of your volumes and that will represent the volume of the part of the tank that isn't filled with water
Answer:
432cm³
Step-by-step explanation:
First we need to find the volume.
Use the volume formula.
[tex]V=l*w*h[/tex]
Plug in the values.
[tex]V=18*12*6\\ \\ V=1296[/tex]
Now find the volume of water we filled up.
[tex]V=18*12*4\\ \\ \\V=864[/tex]
Now we can subtract to find how much more water we need.
[tex]V=1296-864\\ \\ \\V=432[/tex]
432cm³ of water is needed to fill up the tank completely.
If you are going to use the SAS postulate to prove these two triangles congruent what additional information do you need
Answer:
Option D. ET=IT
Step-by-step explanation:
we know that
The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
In this problem
the included angle ∠ETK of triangle TEK is congruent with the included angle ∠KTI of triangle TIK
the side KT is a common side both triangles
therefore
ET must be equal to IT to prove that triangles TEK and TIK are congruent by SAS postulate
Travis just started high school and he wants to manage his time wisely. He schedules 3/2 hours each day for homework, 1/2 of an hour each day for chores at home, and 17/2 hours each day for sleep. How many hours each day are scheduled for these activities?
hw: 3/2hrs = 3×30 = 90mins
chores: 1/2hr = 1×30 = 30mins
sleep: 17/2hrs = 17×30 = 510mins
90+30+510=630mins=10.5hrs/day
Answer:
21/2
Step-by-step explanation:
khan academy got right
Write the word sentence as an equation. Number c increased by 6 is the same as 23
C+6=23 just go step by step dawg
What is the probability of choosing a number from 1-25 that is a multiple of 4
Answer:
6/25, or 0.24
Step-by-step explanation:
There are 25 numbers from which to choose, each equally likely to be chosen.
Multiples of 4 that are between 1 and 25 are {4, 8, 12, 16, 20, 24}
There are 6 such multiples of 4, out of 25 numbers total.
Thus, the probability of choosing a number from 1-25 that is a multiple of 4 is 6/25, or 0.24.
the slope of the line below -5 which of ths following is the point slope form of the line?
The right answer is y + 8= -5 (x-2).
Answer:
[tex]y+8=-5(x-2)[/tex]
Step-by-step explanation:
Slope of the line =-5
To get point slope form of the line , we use the point that passes through the line. LEts pick the point (2,-8)
Point slope form of a line is
[tex]y-y_1=m (x-x_1)[/tex]
(x1,y1) is (2,-8) and slope m = -5
[tex]y-(-8)=-5(x-2)[/tex]
[tex]y+8=-5(x-2)[/tex] is the equation of the line in point slope form.
What is the sum of 1/9, 2/3, and 5/18?
A. 4/15
B. 19/18
C. 8/30
D. 12/9
The correct answer is B.
1/9 can be converted into 2/18. 2/3 can be converted into 12/18. 2/18 + 12/18 + 5/18 = 19/18. The answer is B
The graph below shows three different normal distributions which statement must be true
Answer:
4th option is correct; Each distribution has a different mean and a different standard deviation
Step-by-step explanation:
For the mean to be same in all three distributions, all graphs must be centered around the same number, so mean is not same.
The width of each graph shows how much data deviate from the mean. Since the width is different in all three distributions, standard deviation is different in all three distributions
Answer:
D
Step-by-step explanation:
E2020
PLEASE HELP!!!!
Mike says that if he doubles each dimension of any rectangular prism, the surface area also doubles. Is Mike correct? Give an example to support your answer.
Answer:
Mike is not right
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z----> the scale factor
x----> surface area of the enlarged rectangular prism
y-----> surface area of the original rectangular prism
[tex]z^{2}=\frac{x}{y}[/tex]
so
In this problem we have
[tex]z=2[/tex]
substitute
[tex]2^{2}=\frac{x}{y}[/tex]
[tex]4=\frac{x}{y}[/tex]
[tex]x=4y[/tex]
so
The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism
therefore
Mike is not right
Verify with an example
we have a rectangular prism
[tex]L=5\ m[/tex]
[tex]W=2\ m[/tex]
[tex]H=3\ m[/tex]
The surface area of the prism is equal to
[tex]SA=2(LW)+(2L+2W)H[/tex]
substitute the values
[tex]SA=2*(5*2)+(2*5+2*2)*3=62\ m^{2}[/tex]
If he doubles each dimension of any rectangular prism
then
the new dimensions will be
[tex]L=5*2=10\ m[/tex]
[tex]W=2*2=4\ m[/tex]
[tex]H=3*2=6\ m[/tex]
The new surface area will be
[tex]SA=2*(10*4)+(2*10+2*4)*6=248\ m^{2}[/tex]
[tex]248/62=4[/tex]
therefore
The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism
Find -8 * -1/2
1/16
16
-1/4
-4
Answer:
4
Step-by-step explanation:
Given in the questions
-8 * [tex]\frac{-1}{2}[/tex]
Step 1
[tex]\frac{-(-1)8}{2}[/tex]
Step 2
[tex]\frac{8}{2}[/tex]
Step 3
4
Answer:
16
Step-by-step explanation:
I had it on a test and i got it right this is 100% correct.
Find the value of x.
Answer:
x=60
Step-by-step explanation:
As the sides of the triangle are doubled (21 to 42 and 44 to 88) that means that the side of 30 is doubled to 60
Answer:
x=60
Step-by-step explanation:
-6x+5y=14
-6x+7y=-11
-6x+7y=11
-7x+6y=-11
Anything helps owo
Answer:
-6x + 7y = 11Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, -1) and (1/2, 2). Substitute:
[tex]m=\dfrac{2-(-1)}{\frac{1}{2}-(-3)}=\dfrac{3}{3\frac{1}{2}}=\dfrac{3}{\frac{7}{2}}=3\cdot\dfrac{2}{7}=\dfrac{6}{7}\\\\y-(-1)=\dfrac{6}{7}(x-(-3))\\\\y+1=\dfrac{6}{7}(x+3)}[/tex]
Convert to the standard form Ax + By = C:
[tex]y+1=\dfrac{6}{7}(x+3)[/tex] multiply both sides by 7
[tex]7y+7=6(x+3)[/tex] use the distributive property
[tex]7y+7=6x+18[/tex] subtract 7 from both sides
[tex]7y=6x+11[/tex] subtract 6x from both sides
[tex]-6x+7y=11[/tex]
Solve Y-37 equals 82
you can use inverse operations and add 37 to 82 and get y=119
Y= 119 because if you add 82 and 37 you get 119
To check: 119-37=82