The interest paid for the loan is $1748
Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,
We need to find the interest paid for the same.
So,
Simple Interest = principal × time × rate / 100
= 28654 × 1 × 6.1 / 100
= 28654 × 0.061
= 1747.894
= 1748
Hence the interest paid for the loan is $1748
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Stuck on question number 3
Answer:90
Step-by-step explanation:
A small rectangular prism has a length of 5 inches, a width of 4 inches, and a volume of 100 cubic inches. A large rectangular prism also has a length of 5 inches and a width of 4 inches, but its volume is 200 cubic inches.
How much taller is the large prism than the small prism?
Write your answer as a whole number or decimal. Do not round.
the volume of a prism is
length × width × height
so, for the small prism we have
5 × 4 × height = 100 in
height = 100/20 = 5 i
for the large prism we have
5 × 4 × height = 200 in³
height = 200/20 = 10 in
the larger prism is 10/5=2 times taller than the small prism.
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Dos ángulos de un cuadrilátero miden 60° y 80°. Los otros dos ángulos están en una
proporción de 2:9. ¿Cuáles son las medidas de esos dos ángulos?
Answer:
La suma de los cuatro ángulos de un cuadrilátero es igual a 360 grados. Entonces, si dos ángulos miden 60° y 80°, la suma de esos ángulos es de 140 grados.
Los otros dos ángulos están en una proporción de 2:9, lo que significa que la suma de sus medidas es de 11 partes. Si representamos las medidas de estos ángulos como 2x y 9x, respectivamente, entonces podemos escribir la ecuación:
2x + 9x = 11 partes
11x = 11 partes
x = 1 parte
Por lo tanto, el ángulo más pequeño mide 2x = 2 partes o 2 × 1 = 2 grados, y el ángulo más grande mide 9x = 9 partes o 9 × 1 = 9 grados.
En resumen, los dos ángulos faltantes miden 2° y 9°.
Step-by-step explanation:
Given △HJK ~ △RST, what is cos T?
Answer:
cos T = 5/9-------------------
As per definition, the cosine function is:
cosine = adjacent / hypotenuseSince triangles are similar, the ratio of corresponding sides is same:
cos T = ST / RTcos T = cos K = JK / HK = 5/9Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x+2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x-7.
Calculate the limit as 1.
The correct statement is:
"Divide out a common factor of x - 7." The limit of the given expression is 1/6.
Multiply by (√(x + 2) + 3)/(√(x + 2) + 3):
This statement is not correct.
We generally multiply by the conjugate of the expression to eliminate square roots, but in this case, multiplying by (√(x + 2) + 3)/(√(x + 2) + 3) does not help simplify the expression.
Get x - 1 in the numerator:
This statement is not correct. The expression does not involve x - 1 in the numerator.
Get (x - 7)(√(x + 2) - 3) in the denominator:
This statement is not correct. We want to simplify the expression, not introduce a more complex denominator.
Divide out a common factor of x - 7:
This statement is correct. By factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.
Calculate the limit as 1/6:
This statement is not correct. We need to perform further simplification to determine the limit.
After canceling out the common factor of x - 7, the simplified expression becomes:
lim x -> 7 (√(x + 2) - 3)/(x - 7) = lim x -> 7 1/(√(x + 2) + 3)
To find the limit, we substitute the value x = 7 into the simplified expression:
lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6
Therefore, the correct statement is: "Divide out a common factor of x - 7." The limit of the given expression is 1/6.
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An amount of $21,000 is borrowed for 13 years at 8.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Answer: To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the initial principal (the amount borrowed)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time period in years
In this case, we have:
P = $21,000
r = 8.75% = 0.0875
n = 1 (interest is compounded annually)
t = 13 years
So, plugging these values into the formula, we get:
A = 21,000(1 + 0.0875/1)^(1*13)
A = 21,000(1.0875)^13
A = $58,150.51
Therefore, if the loan is paid in full at the end of the 13-year period, $58,150.51 must be paid back, which includes the original principal plus the interest accrued over the 13-year period.
Step-by-step explanation:
Determine if it’s a 1 proportion z interval, 1 proportion z test, 1 sample T interval or 1 sample T test
The type of test used in this problem is given as follows:
1 proportion z test.
How to test the hypothesis?At the null hypothesis, we consider if there is not enough evidence to conclude that the mean is different of 0.55, hence:
[tex]H_0: p = 0.55[/tex]
At the alternative hypothesis, we test if there is enough evidence to conclude that the mean is different of 0.55, hence:
[tex]H_a: p \neq 0.55[/tex]
We are testing a proportion, hence the z-distribution is used, thus the correct option is given as follows:
1 proportion z test.
(in the case of a proportion, a z test is used, for sample means that we can use either z test or t test depending on the problem).
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A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?
The maximum distance of the fire engine from the school is D = 4.5 miles
Given data ,
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the first point be P = P ( -4 , -3 )
Let the second point be Q = Q ( -7 , -3 )
First distance D₁ = √ ( -4 + 7 )² + ( -3 + 3 )
D₁ = √9
D₁ = 3 units
Now , each unit on the grid represents 1/2 mile
And , the distance from P to school is S ( -4 , 3 )
D₂ = √ ( -4 + 4 )² + ( -3 - 3 )²
D₂ = √36
D₂ = 6 units
So , the total distance D = 3 + 6 = 9 units
And , the distance in miles = 9/2 = 4.5 miles
Hence , the distance is 4.5 miles
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The complete question is attached below :
A fire engine takes the shortest possible route when it drives from the firehouse to one of the schools. The route can go only horizontally and vertically on the grid. Each unit on the grid represents 1-half mile. What is the maximum distance, in miles, the fire engine travels to reach one of the schools?
Find the slope and y intercept of the line 5x-9y=45
Answer:
slope = [tex]\frac{5}{9}[/tex] , y- intercept = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
5x - 9y = 45 ( subtract 5x from both sides )
- 9y = - 5x + 45 ( divide through by - 9 )
y = [tex]\frac{-5}{-9}[/tex] x + [tex]\frac{45}{-9}[/tex] , that is
y = [tex]\frac{5}{9}[/tex] x - 5 ← in slope- intercept form
with slope m = [tex]\frac{5}{9}[/tex] and y- intercept c = - 5
Question 5 of 25 The Wildcats and the Leopards are evenly matched football teams. When they play, there is a 0.5 probability that the Wildcats will win. If they play 9 times, what is the probability that the Wildcats will win 4 of the games? Round your answer to the nearest tenth of a percent. O A. 7.0% OB. 24.6% OC. 0.2% O D. 16.4% SUBMITTE
Answer:
24.6%
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
n = 9, r = 4, p = 0.5
P = ₉C₄ (0.5)⁴ (1−0.5)⁹⁻⁴
P = 126 (0.5)⁴ (0.5)⁵
P ≈ 0.246
Pls help asap RSM QUESTION!!!
Write "forty-two thousand, fifteen" as a whole number using digits.
The whole number for "forty-two thousand, fifteen" is 42,015.
We have, "forty-two thousand, fifteen".
To write a sentence as a whole number using digits, you would typically replace the words with their numerical representations. Here's an example:
Sentence: "I have three apples and four bananas."
Whole number: "I have 3 apples and 4 bananas."
Here the numeric terms are forty- thousand and fifteen then the numerical digit will be
= 42, 015.
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if y varies inversely as the same of x, and =7/4 whenx = 1, find y when x=3
if y varies inversely as the same of x, and y=7/4 when x = 1 then value of y is 7/12 when x=3
If y varies inversely as the same of x, we can write the equation:
y = k / x
where k is the constant of proportionality.
Let us find the value of constant of proportionality k:
y = 7/4 when x = 1
7/4 = k / 1
Apply cross multiplication we get:
7/4 = k
k=7/4
Now plug in the value of k to find y when x = 3:
y = k /x
y = (7/4) / 3
When a fraction is divided by the whole number then fraction is multiplied with reciprocal of the whole number.
y=7/4×1/3
Multiply the numerators and denominators.
y=7×1/4×3
We know that 7×1 is 7 and 4×3 is 12.
y=7/12
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Find the derivative of the function
thank you guys sm
The derivative of the function is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = log₂ ( 3x + 4 )³
On simplifying , we get
On taking the derivative of the function , we get
f' ( x ) = d/dx ( log₂ ( 3x + 4 )³ )
d/dx ( log₂ ( 3x + 4 )³ ) = 1/ ln ( 2 ) [ d/dx( 3x + 4 )³ ]
On applying chain rule , we get
f' ( x ) = 1/ ln ( 2 ) 1/( 3x + 4 )³ ( 9 ( 3x + 4 )² )
So , cancelling out the similar terms , we get
f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Hence , the derivative is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
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Find the area of a rectangle with a base of 9 feet and a height of 7 feet
Answer:
63
Step-by-step explanation:
b x h = A
9 x 7 = 63
A solid has as its base the region bounded by the curves y = –2x^2 + 2 and y =-x^2+ 1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the xy-plane, upper base equal to 1/2 the length of the lower base, and height equal to 2 times the length of the lower base.
What is the solution to |x-2| + 3 > 17?
Ox<-12 or x > 16
Ox<-14 or x>7
O-12
O-14
Answer:
x<-12 or x>16
Step-by-step explanation:
Answer:
|x - 2| + 3 > 17
|x - 2| > 14
x - 2 < -14 or x - 2 > 14
x < -12 or x > 16
The table below shows the demand for a new bath soap in a shop for each of the last 7 months.
Month 1 2 3 4 5 6 7 8
Demand 23 29 33 40 41 43 49 52
Calculate a 3-month moving average for months two to nine.
An earthquake in Gansu, China, on December 16, 1920, measured 8.6 on the Richter scale and killed 100 000 people. An earthquake that usually causes no damage measures 4 on the Richter scale. Compare the intensities of the two earthquakes. (THE ANSWER IS 40000).
The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.
Let's compare the intensities of the two earthquakes using the Richter scale.
Step 1: Understand that the Richter scale is logarithmic, which means each whole number increase represents a tenfold increase in intensity.
Step 2: Determine the difference between the magnitudes of the two earthquakes. The Gansu earthquake measured 8.6, and the earthquake causing no damage measured 4.
8.6 - 4 = 4.6
Step 3: Calculate the intensity ratio between the two earthquakes using the difference in magnitudes. Since each whole number increase represents a tenfold increase in intensity, we need to raise 10 to the power of the difference.
10^4.6 ≈ 39,810.71705535
Step 4: Round the result to a whole number.
39,810.71705535 ≈ 39,811
The intensity of the Gansu earthquake was approximately 39,811 times greater than that of an earthquake measuring 4 on the Richter scale, which typically causes no damage.
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A path is made of white tiles and grey tiles.
There is a total of 56 tiles.
Work out the number of grey tiles.
The number of tiles that would be grey tiles out of the total tiles given would be = 28 tiles.
How to calculate the number of grey tiles?To calculate the number of grey tiles, the total number of tiles given should be divided into two since the path is made up of only white and grey tiles.
The total number of tiles = 56 tiles.
Therefore the grey and the white tiles have the same number of tiles = 56/2 = 28 grey tiles
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I ne table below represents the function r, and the tonowing grapn represents the function g.
0 1
-6 -5 -4 -3 -2 -1
-10 -8
-2
22
X
f(x) 8-2-8
Complete the following statements.
The functions / and g have
The y-intercept of fis
the y-intercept of g.
Over the interval [-6, -3), the average rate of change of fis
9
-4 -2
6
4
the average rate of change of g.
Since the average rates of change of f and g cannot be determined from the given information provided.
We can find the average rate of change of function f over the interval [-6, -3) as:
The average rate of change of f;
= (f (6) - f (3)) / (6 - 3)
= (71 - 59) / 2 = 6
We have the two given points to set up equations:
-53 = a(3)^b - 41
-53 = a(5)^b - 41
0 = a(3^b - 5^b)
Since 3^b ≠ 5^b, we must have a = 0, that means g is not a valid exponential function passing through the given points.
Therefore,
We can conclude, that the average rates of change of f and g cannot be determined.
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Sarah spends 30 minutes reading,20 minutes writing,and 20 minutes doing her math. How many minutes does she spends on school work in all
Answer:
She spends 70 minutes in total or 1h 10min
PLEASE MARK IT THE BRAINLIEST!!!!!
If it rains tomorrow, the probability is 0.7 that John will practice his cello. If it does not rain tomorrow, there is only a 0.6 chance that John will practice.
Suppose the chance of rain tomorrow is 60%.
What is the probability that John will practice his cello?
P(John will practice) =
(Type an integer or a decimal.)
Answer:
0.66
Step-by-step explanation:
please read attachments
La señora Luisa pide un presupuesto para reparar ocho joyas. El encargado de la joyería le dice que cobrará $6 por la primera joya, y por cada pieza sucesiva lo triple que la anterior. ¿Cuánto le cobrará el joyero a la señora Luisa?
The amount that the jeweler would charge Mrs. Luisa, given the prices of the successive jewelry would be $ 19, 680
How to find the total cost ?The charge for repairing the jewelry pieces is calculated in a geometric progression:
= 6, 63, 63 ², 63 ³, ..., 63 ⁷
The sum of the first n terms in such a progression is:
S = a x (r ⁿ - 1) / ( r - 1 )
Seeing as there are 8 pieces of jewelry, the total cost to Mrs. Luisa would be:
S = 6 x ( 3 ⁸ - 1) / ( 3 - 1 )
S = 6 x ( 6561 - 1 ) / 2
S = 6 x 6560 / 2
S = 3 x 6560
S = $ 19, 680
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i need help graphing y=-4/3+2
Indicate which of the following variables are continuous.
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
5. Monthly spendings of a family.
O 1, 2, 3 and 5
O 1, 4 and 5
O 1, 2, 3 and 4
O 1 and 2
The correct variables which are continuous are,
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
We have to given that;
To find correct variables which are continuous.
Since, The number of wheels of a car is a discrete variable, because it can only take certain integer values (2, 3, 4, etc.), while the other variables can take any real value within a certain range.
Hence, The correct variables which are continuous are,
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
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Describe in words each of the transformations
represented by the rules below:
a. (x,y) → (x-5, y + 6)
b. (x,y) → (y, -x)
c. (x, y) (1.2x, 1.2y)
d. (x,y) → (x, y)
What is 5x6 + (5x5-5)
Answer:50
Step-by-step explanation:
write equivalent fraction for 1 1/5 and 1 1/3
Answer:
1 1/5 = 6/5
1 1/3 = 4/3
Step-by-step explanation:
hope this helps, if you’re looking for 1 1/5 + 1 1/3 please tell me and I will solve that for you
MULTIPLE CHOICE QUESTION:
The table shows the amount of time different students studied for an exam and the scores they received. Draw a line that best represents the data, which equation in slope-intercept form best represents the line of best fit?
OPTION 1: y=1/3x +75
OPTION 2: y=3x + 67
OPTION 3: y=1/3x + 67
OPTION 4: y= 3x +75
Answer:
Option 3: y = 1/3x +67
Step-by-step explanation:
You want the equation of the best-fit line in slope-intercept form for the data given.
Best fitThe attached calculator display shows the best-fit line for the data, where x is in minutes, is approximately ...
y = 0.41x + 64
The closest answer choice is ...
Option 3: y = 1/3x +67
__
Additional comment
The second attachment shows a plot of the data (study minutes, test score) with the best-fit line in red, and the Option 3 line in blue.
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