Given:
Annual interest rate = r%
Growth factor : x = 1 + r
The below function gives the amount in the account after 4 years when the growth factor is x .
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
To find:
The total amount in the account if the interest rate for the account is 3% each year and initial amount.
Solution:
Rate of interest = 3% = 0.03
Growth factor : x = 1 + 0.03 = 1.03
We have,
[tex]A(x)=800x^4+350x^3+500x^2+600x[/tex]
Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.
[tex]A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)[/tex]
[tex]A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609 )+618[/tex]
[tex]A(1.03)=900.407048+382.45445+530.45+618[/tex]
[tex]A(1.03)=2431.311498 [/tex]
[tex]A(1.03)\approx 2431.31 [/tex]
Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.
For initial amount the rate of interest is 0.
Growth factor : x = 1 + 0 = 1
Substitute x=0 in the given function to find the initial amount.
[tex]A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)[/tex]
[tex]A(1)=800+350+500+600[/tex]
[tex]A(1)=2250[/tex]
Therefore, 2250 was put into the account at the beginning.
6th grade math i mark as brainly
Step-by-step explanation:
i mean I never did that in six grade
Which of the following is the equation of the line that is parallel to
y= 3/5x+ 8 and goes through point (-10,4)?
Select one:
a. y = 5/3x + 20 2/3
b. y=-5/3x – 12 2/3
c.y= 3/5x + 10
d. y = -3/5x-2
Answer:
C
Step-by-step explanation:
We want to write the equation of a line that is parallel to:
[tex]y=\frac{3}{5}x+8[/tex]
And also passes through (-10, 4).
Remember that parallel lines have the same slope.
The slope of our old line is 3/5.
Therefore, the slope of our new line is also 3/5.
We know that it passes through (-10, 4). So, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:
[tex]y-(4)=\frac{3}{5}(x-(-10))[/tex]
Simplify:
[tex]y-(4)=\frac{3}{5}(x+10)[/tex]
Distribute on the right:
[tex]y-4=\frac{3}{5}x+6[/tex]
Add 4 to both sides:
[tex]y=\frac{3}{5}x+10[/tex]
So, our answer is C.
And we're done!
Step-by-step explanation:
Hey there!
The equation of a st.line passing through point (-10,4) is ;
(y-y1)= m1(x-x1) [one point formula]
Put all values.
(y - 4) = m1( x + 10)..........(i)
Another equation is; y = 3/5 + 8.............(ii)
From equation (ii)
Slope (m2) = 3/5 [ By comparing equation with y = mx+c].
As per the condition of parallel lines,
Slope of equation (i) = slope of equation (ii)
(i.e m1 = m2 )
Therefore, the value of m1 is 3/5.
Putting value of slope in equation (i).
[tex](y - 4) = \frac{3}{5} (x + 10)[/tex]
[tex](y - 4) = \frac{3}{5} x + \frac{3}{5} \times 10[/tex]
[tex](y - 4) = \frac{3}{5} x + 6[/tex]
[tex]y = \frac{3}{5} x + 10[/tex]
Therefore the required equation is y = 3/5x + 10.
Hope it helps...
What is the equation of the line graphed below?
<1 and <2 form a linear pair. The measure of <2 is six more than twice the measure of <1. Find the measure of <2
Answer:
122 Degrees
Step-by-step explanation:
Since we are given that angle 1 and 2 make a linear pair:
angle 1 + angle 2 = 180 degrees ----------------------------(1)
We have also been told that angle 2 is 6 more than twice the measure of angle 1
Which means: angle 2 = (2*angle1) + 6 -------------------(2)
From putting the value of angle 2 in (1) from (2)
angle 1 + 2*angle 1 + 6 = 180
3*angle 1 = 174
angle 1 = 58 degrees -----------------------(3)
From (1) and (3):
angle 2 + 58 = 180
angle 2 = 122 degrees
Therefore, the measure of angle 2 is 122 degrees
Stan’s Skate Shop is having a sale on skateboards. The original price for its Extreme Skate Board was $84.50. The sale price for the skateboard is $50.70. What is the percent decrease in the price of the skateboard?
Answer:
It is 60%
Step-by-step explanation:
84.50 x 0.60% = 50.7 (also 50.70)
I hope my answer helps even though I am in middle school :)
The required percent decrease in the price of the skateboard is 40%.
The original price for its Extreme Skate Board was $84.50. The sale price for the skateboard is $50.70. What is the percent decrease in the price of the skateboard is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Original price = $84.50
sale price = $50.70
Percent decrese = 84.50-50.70/84.50 × 100 = 40%
Thus, the required percent decrease in the price of the skateboard is 40%.
Learn more about percentages here:
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You have discovered another alien. Find the correct rescue path before answering this question. When the spaceship starts from a point on the y axis, what is the y-intercept of the line of travel? the x-coordinate of the spaceship the y-coordinate of the spaceship the y-coordinate of the alien the distance from the spaceship to the alien
Answer:
the y-coordinate of the spaceship
Step-by-step explanation:
It's what it said on edge
Answer
b
Step-by-step explanation:
Find g(6) when g(x) = x2-5
Answer:
g(6) = 31
Step-by-step explanation:
If g(x) = x^2 - 5, that means to solve for g(6) you just have to replace the x in the equation with 6.
g(6) = 6^2 - 5
g(6) = 36 - 5
g(6) = 31
Write the expanded form of the expression.
y(0.75+4)
Answer:
25
Step-by-step explanation:
Answer:4.75y
Step-by-step explanation:
3 questions on percentage ❤️
Answer:
Question 1: 131.25 Question 2: 83.33 Question 3. 133.33
Step-by-step explanation:
1. 131.25% x 150
2. Trial and error
3. 60 ÷ 45%
How do you know if a sum or product will result in a rational or irrational number?
Do you like a newspaper has letters to the editor for 60 people. If it’s number represents 5% of all the newspaper readers how many readers of the newspaper have
Answer:
5÷100
=0.05
0.05×60
=3
Answer:
1200 readers
Step-by-step explanation:
Let x = number of readers
x* 5% = 60
Change to decimal form
x* .05 = 60
Divide each side by .05
x * .05/.05 = 60/.05
x =1200
Molly is planting the flowers using the proportional relationship of 18 pink flowers to 12 white flowers per row.
Find the ratio of pink flowers per white flower per row
Answer:
3 : 2.
Step-by-step explanation:
18 : 12 Divide both values by 6:
= 3 : 2.
Answer:
Step-by-step explanation:1.5
Can someone explain how to solve these? I have 10 questions I need to answer for problems like this & I can't go on until I solve it, so I just need the answer for this one and how to solve it. I need it finished fast because I need to bring up a low grade. Any help would be appreciated.
A certain test preparation course is designed to help students improve their scores on the MCAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 7 students' scores on the exam after completing the course: 37,12,12,17,13,32,23 Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Step 1 of 4 : Calculate the sample mean for the given sample data. Round your answer to one decimal place.
Answer:
The 80% confidence interval for the average net change in a student's score after completing the course is (15.4, 26.3).
Step-by-step explanation:
The net change in 7 students' scores on the exam after completing the course are:
S = {37 ,12 ,12 ,17 ,13 ,32 ,23}
Compute the sample mean and sample standard deviation as follows:
[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{7}\times 146=20.857\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}}=\sqrt{\frac{1}{7}\times 622.8571}=10.189[/tex]
As the population standard deviation is not known, a t-interval will be formed.
Compute the critical value of t for 80% confidence interval and 6 degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.20/2, (7-1)}=t_{0.10,6}=1.415[/tex]
*Use a t-table.
Compute the 80% confidence interval for the average net change in a student's score after completing the course as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times\frac{s}{\sqrt{n}}[/tex]
[tex]=20.857\pm 1.415\times\frac{10.189}{\sqrt{7}}\\\\ =20.857\pm 5.4493\\\\=(15.4077, 26.3063)\\\\\approx (15.4,26.3)[/tex]
Thus, the 80% confidence interval for the average net change in a student's score after completing the course is (15.4, 26.3).
Which lists all the multiples of 8 that are less than 50?
A. 2, 4, 8
B. 4, 8, 12, 16, 24, 32, 40, 48
C. 8, 16, 24, 32, 40, 48
D. 8, 16, 24, 32, 40, 48, 56
Answer:
Its the third one 8, 16, 24, 32, 40, 48
Step-by-step explanation:
They all are multiples of 8 and are not more than 50
Amanda has completed 68 deliveries so far this week. She needs to make 85 deliveries for the week. What percentage of her deliveries has Amanda completed?
0
She has completed 80%
What is five times the difference of a number and three?
Btw I need answer immediately
Answer:
t=x+3
y = (x+3)^2 + 5
y = x^2+6x + 9 + 5
y= x^2 + 6x + 14
Answer:
5 times x-3?
Step-by-step explanation:
Sorry if its wrong i didn't really understand what you wanted.
What is 1 over 4 multiplied by 7 over 2
Answer:
7/8
Step-by-step explanation:
Answer:
1/4 x 7/2
First, let's convert each fraction into percentages.
1/4= 25%
7/2= 350%
Now just multiply them together.
25x350= 8750
Convert it back into a fraction.
8750% = 175/2 = 871/2 as a fraction.
Hope this helps!
44 plus 48 distributive property
Answer:
92
Step-by-step explanation:
44 plus 48 can be rewritten as:
4(11 + 12), which, in turn, simplifies to:
4(23), or 92
Next time, please include all of the instructions. Thank you.
Find the common difference of the arithmetic sequence 4,2,0,...
Answer:
d=-2 is the difference
At an archeological site, the remains of two ancient step pyramids are congruent. If ABCD~=EFGH, find AD
(Diagrams are not to scale)
AD= ? ft
Answer: 300ft
Step-by-step explanation:
Coach Brown made 50 pints of Gatorade for his team. How many gallons did he make?
Answer:
6.25 gallons
Step-by-step explanation:
Answer:
6.25
Step-by-step explanation:
Most universities and colleges require an SAT score as one of the inputs to an admissions decision. Is it a good predictor of college success? Total SAT scores for 10 students are given, along with their college GPAs.
what letter grade is a 38/49
Answer:77%
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
because if you multiply 38/49, it would be 76/98. and 76 is a letter c, but if i am wrong its b.
6200 divided by 163 i need the answer or ill fail
Answer:
38.04
Step-by-step explanation:
6200/163= 38.036809816
Since after the 3 is a 6 which is over 5 you can round the 3 up to a 4 and cut everything else off.
Hope this helps. Plz give brainliest.
6200 divided by 163 is equal to 38 with a remainder of 6.
We have,
The concept used to divide 6200 by 163 is a long division.
Long division is a method of dividing two numbers by repeatedly subtracting multiples of the divisor from the dividend until the remainder becomes smaller than the divisor.
It involves dividing digit by digit, starting from the leftmost digits of the dividend and moving towards the right.
Now,
To divide 6200 by 163, we perform a long division.
Here's how it works:
38
__________
163| 6200
4890
______
1310
1304
______
6
The quotient is 38, and the remainder is 6.
Therefore,
6200 divided by 163 is equal to 38 with a remainder of 6.
Learn more about expressions here:
https://brainly.com/question/3118662
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A model rocket is launched from the roof of a building. Its flight path is modeled
by h = -5t^2 +30t +10 where h is the height of the rocket above the ground in
metres and r is the time after the launch in seconds.
What is the rocket's maximum height?
Answer:
55
Step-by-step explanation:
This is the equation of a parabola. To make things simpler, we can replace [tex]h[/tex] with [tex]y[/tex] and [tex]t[/tex] with [tex]x[/tex]. Therefore, [tex]y=-5x^2+30x+10[/tex]. Because the coefficient of the [tex]x^2[/tex] term is negative, we know the parabola points down, and the maximum height is the vertex. The x coordinate of the vertex of a parabola can be found with the equation [tex]-\frac{b}{2a}[/tex], or [tex]-\frac{30}{-10} = 3[/tex]. Plugging in [tex]3[/tex] into the equation gives us [tex]y = -5(3)^2+30(3)+10 = \boxed{55}[/tex]
A local road rises 15 feet for every 309 feet of highway . What is the slope of the highway
(x-y)(x-y+1)² -2(x-y)(x-y+1)+x-y
help ASAP pleasee!!
Step-by-step explanation:
If u are looking for factorization this is the way
(x-y)(x-y+1)² -2(x-y)(x-y+1)+(x-y)=
(x-y)[(x-y+1)^2-2(x-y+1)+1]=
(x-y)[(x-y+1)^2-2(x-y+1)+1^2]=
(x-y)[(x-y+1)-1]^2=(x-y)(x-y+1-1)^2
(x-y)(x-y)^2=
(x-y)^3
Find the measure of the third angle of a triangle given the measures of two angles.
34 and 88
Answer:
58
Step-by-step explanation:
All three angles of a triangle have to add up to 180. Given this we can do the following problem:
180-34-88 = 58
how to solve
2(x+4)=2x+5
Step-by-step explanation:
2x+8=2x+5
2x-2x=15-8
0x=7
