The monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1
What is compound interest?
When you earn interest on both the money you've saved and the interest you've earned, this is known as compound interest.
what is the monthly payment?
The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.
Here,
We know that the monthly payment is given as
MP = [Pr(1 + r)¹²ⁿ] / [(1 + r)¹²ⁿ - 1]
Where MP monthly payment, P is the initial amount, r is the rate of interest, and n is the number of years.
we have
r = 0.0115
P = $150,000
n = 25 * 12
n = 300
Then we have
MP = $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1
Hence, the monthly payment for a 25-year loan is $150,000 · 0.01115(1 + 0.0115)^300 / (1 + 0.0115)^300 - 1
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A pe class has 484848 students. one group of 242424 students chooses to play volleyball. the teacher then divides the remaining students into as many groups of 555 as possible to shoot baskets. after that, the remaining students (not on a volleyball or basketball team) climb the rock wall. how many students climb the rock wall?
444 students will climb the rock wall.
Given, that A class has 484848 students, one group of 242424 students chooses to play volleyball.
Then the teacher divides the remaining students into as many groups of 555 as possible to shoot baskets.
After that, the remaining students (not on a volleyball or basketball team) climb the rock wall.
Now, we are asked that the students who climb the rock wall
So, from a class of 484848 students if One group of 242424 students is made to play volleyball then there will be 242424 students remaining.
Now, to divide 242424 students into groups of 555 students,
we need to divide 242424 by 555, then we get
242424/555 = 436.8
Now there will be 436 groups of 555 students who will shoot basket and remaining 444 students who will climb the rock wall.
Hence, 444 students will climb the rock wall.
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whats the answer.......................
The statement that describes the x-intercept of the graph is: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.
What is the X-intercept of a Linear Relationship?The x-intercept of a linear relationship between variable x and y can be described as the value of x when the value of y is zero.
On a graph, the x-intercept is the point on the graph where the line intercepts the x-axis. The value of y at this point is 0.
in the graph that shows a linear relationship between the number of monthly payments made and the remaining balance left on a loan, the line intercepts the x-axis at 60.
Therefore, it means: c. the x-intercept is 60 and it represents the number of monthly payment that is needed to repay the loan.
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Halp for a cookie :) ♥ ♥❣ ❣
*Piece-Wise Defined Functions*
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The function shown in the graph above is a discontinuous function, at x = -2
For values of x less than -2, the left side of the graph is applicable. whose equation is :
[tex]\qquad \sf \dashrightarrow \: y - 0 = \cfrac{1 - 0}{ - 3 - ( - 2)} (x - ( - 2))[/tex]
[tex]\qquad \sf \dashrightarrow \: y = \cfrac{1}{ - 3 + 2} (x + 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - 1(x + 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - x - 2 \:\: ; \:\:x<-2[/tex]
For values of x greater than -2, the right side of the graph is applicable. whose equation is :
[tex]\qquad \sf \dashrightarrow \: y - 4= \cfrac{4 - 2 }{0 - (-2)} (x -0)[/tex]
[tex]\qquad \sf \dashrightarrow \: y - 4 = \cfrac{2}{2} (x)[/tex]
[tex]\qquad \sf \dashrightarrow \: y - 4 = x[/tex]
[tex]\qquad \sf \dashrightarrow \: y = x + 4 \: \: ;\: \: x > - 2[/tex]
So, the correct choice will be Option " A "
Answer:
[tex]\textsf{A.} \quad \begin{cases}-x -2 \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]
Step-by-step explanation:
When graphing piece-wise functions:
An open circle indicates the value is not included in the interval.A closed circle indicates the value is included in the interval.An arrow show that the function continues indefinitely in that direction.From inspection of the given graph:
The equation for the line on the left side of the function has a negative slope and an x-intercept at x = -2.There is an open circle at x = -2 and the line continues to the left.Therefore, the definition of the function is:
[tex]\begin{cases}-x + a \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}[/tex]
where a is some constant.
The only answer option that matches the given parameters is option A.
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
-4, (-2 , 1)
0, (-1, 21)
The equation of straight line having
(a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7
(b) gradient 0 and coordinates (-1,21) is y = 21 .
In the question ,
the gradient and coordinates of the point on the line is given .
we have to find the equation of the straight line .
Part(a)
the gradient of the line [tex]=[/tex] -4 ,
the coordinates of a point on the line = (-2,1)
So , the equation of the line is
(y - 1) = (-4)*(x -(-2))
y - 1 = -4(x + 2)
y - 1 = -4x - 8
4x + y = -8 + 1
4x + y = -7
the equation is 4x + y = -7 .
Part(b)
the gradient of the line = 0 ,
the coordinates of a point on the line = (-1 , 21)
So , the equation of the line is
(y - 21) = 0(x-(-1))
y - 21 = 0
y = 21
the equation of the line is y = 21 .
Therefore , The equation of straight line having (a) gradient -4 and coordinates (-2,1) is 4x + y [tex]=[/tex] -7 and (b) gradient 0 and coordinates (-1,21) is y = 21 .
The given question is incomplete , the complete question is
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
(a) -4, (-2 , 1)
(b) 0, (-1, 21)
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Determine the equation of the line.
(Write the answer in slope-intercept form.)
Answer:
y = 1x + -2
Step-by-step explanation:
Step 1: Calculating Slope (m).
m = y2 - y1 / x2 - x1
m = -4 - 0 / -2 - 2
m = -4 / -4
m = 1
Now put value of m in equation...
y = 1x + b
Step 2: Calculating Y-intercept (b).
Lets choose the first point, ( 2, 0) for calculating y-intercept:
y = m ( x ) + b
0 = 1 ( 2 ) + b
0 = 2 + b
-2 = b
b = -2
Now put value of b in equation for your final answer...
y = 1x + -2
Hope this helps!
A blue whale weighs about 200 tons. It eats only small sea creatures called krill. The blue whale
eats 2% of its body weight each day. How many tons of krill does the blue whale eat each day?
Explain your thinking.
Answer:
4 tons of its body weight
Step-by-step explanation:
In this situation you must find 2% of 200. This is simply 4.
Answer: 4 tons
Step-by-step explanation:
the whale eats 2% of itself everyday, so it would be x/200= 2/100 and the whale would eat x tons, which equals 4 so it eats 4 tons of krill a day
AB has endpoints at A(-4, 4) and B(5, -1).
Find the coordinates
(x, y) of the midpoint.
Answer:
(0.5, 1.5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is
M = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (- 4, 4 ) and (x₂, y₂ ) = B (5, - 1 ) ,then
M = ( [tex]\frac{-4+5}{2}[/tex] , [tex]\frac{4-1}{2}[/tex] ) = ( [tex]\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] ) = (0.5, 1.5 )
Answer:
The midpoint is at ( 1/2, 3/2)
Step-by-step explanation:
Midpoint
To find the x coordinate of the midpoint
Add the x coordinates of the endpoints and divide by 2
( -4+5)/2 = 1/2
To find the y coordinate of the midpoint
Add the y coordinates of the endpoints and divide by 2
( 4+-1)/2 = 3/2
The midpoint is at ( 1/2, 3/2)
HELPPP MEEEEE PLEASEEEE
Answer: 2176 cm^2 i think
Step-by-step explanation:
Answer:
60 cm
Step-by-step explanation:
we can use the Pythagorean theorem:
a^2 = b^2 + c^2 where a is the hypothenuse
so 68^2 = 32^2 + c^2
rearrange: 68^2 - 32^2 = c^2
so 4624 - 1024 = c^2
= 3600
square root of 3600 = 60
missing side = 60 cm
Last year, James earned £2,100 per month.
This year, he's had a 6% increase in his monthly pay.
He worked 35 hours per week for 46 weeks in the year.
What is James' average pay per hour this year?
Give your answer to 2 dp.
James average pay per hour is $17.40
How to find James average pay per hour
information given in the problem are
Last year, James earned £2,100 per month
This year, he's had a 6% increase in his monthly pay
35 hours per week for 46 weeks in the year
The question is a percentage problem
6% increase a factor of 1.16
2100 * 1.16 = 2436
number of hours in a month
35 hours = 1 week
? hours = 4 weeks
? = 4 * 35
? = 140 hours in 4 weeks = 1 month
James average pay per hour is gotten form the calculation below
if 140 hours pays 2436 then1 hour will pay ?
140 = 2346
1 = ?
cross multiplying
? * 140 = 2436 * 1
? = 2436 / 140
? = $17.40
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What is 7) 952 divided?
(b) Work out the value of (2.3 × 10³) × (5.9 × 105)
Give your answer in standard form.
Answer: 1424850
Step-by-step explanation:
2.3 x 10³ = 2300
5.9 x 105 = 619.5
2300 x 619.5 = 1424850
Pls thank and rate <3 (and branliest if ok with u :)))
A) A box of mass 9 kg contains x articles each of mass 1.2 kg. Write down an expression for the total mass of the box and its contents.
B) How many articles are there in the box if the total mass of the box and articles is 21 kg?
Step-by-step explanation:
A. total mass = 9 + (x × 1.2)
B. 21 - 9 = 12kg
12 ÷ 1.2 = 10 articles.
hope it helps. :)
Seventh grade > M.6 Percent of a number: tax, discount, and more SPN
A store pays $871 for a gold ring. The store marks up the price by 26%. What is the
amount of the mark-up?
Round your answer to the nearest dollar: $
Submit
Answer:
$1097.46
Step-by-step explanation:
Assume P is the finall price. The markup of 26% can be written in decimal form as 0.26. This is in additon to the full price paid for the gold ring, so we can add 1.00 to 0.26 to arrive at the factor 1.26. Multiply 1.26 times the store cost of $871 to find the amount after 26% markup:
($871)*(1.26) = $1097.46
Suppose that each semester at a particular community college Manuel has to pay $1478 in tuition and $121 in fees.
If Manuel has x semesters remaining, write an algebraic expression representing the total amount he will need for tuition.
If Manuel has x semesters remaining, write an algebraic expression representing the total amount he will need for the fees.
If Manuel has × semesters remaining, write an algebraic expression representing the total amount of money he will spend for tuition and
Answer:
Step-by-step explanation:
Let x be time, in semesters, remaining before Manuel graduates. We find that Manuel's expenses are:
$1478/semester in tuition, and
$121/semester in fees
1. x semesters remaining: fees
Remaining cost for fees, y, is the product of the fee times the number of semesters, x:
y =($121/semester)*x
y = ($121)*x
2. x semesters remaining: tuition
Remaining cost, y, is the product of the tuition (times the number of semesters, x.
y = ($1478/semester)*x + ($121/semester)*x
y = ($1599)*x
3. x semesters remaining: tuition and fees
Remaining cost, y, is the sum of the products of the tuition (times the number of semesters, and the fees (tix.
y = ($1478/semester)*x + ($121/semester)*x
y = ($1599)*x
At 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
If he continues at this rate, at what time will he reach `10000` steps?
Answer:
9:55 a.m.
Step-by-step explanation:
Sothy starts at 8 a.m. and plans for 10,000 steps. At 8:23 a.m., she walked 2000. We are solving for when she reaches 10,000 steps.
This means that she walks 2,000 steps in 23 minutes
If she walks 2,000 steps in 23 minutes, then we can multiply by 5 to get 10,000 steps in 115 minutes.
Now, we need to add 115 minutes to 8 a.m.
we can round 115 minutes to 120 minutes.
If you add 120 minutes to 8 a.m., you get 10 a.m.
Now subtract the 5 minutes you added earlier to get 9:55 a.m.
Rebekah deposited $1500 in a savings account that pays simple annual
interest. After 21 months, she earns $131.25. What is the interest rate
for her account?
The rate of interest for Rebekah's account is 5.25%
Given,
The principal amount deposited by Rebekah, P = $1500
The time period of the deposit, T = 21 months = 5/3 years
The simple interest she got after 21 months, SI = $131.25
We have to find the rate of interest, R;
Simple Interest;
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Here,
Simple interest, SI = PRT/100
131.25 = (1500 × R × 5/3) / 100
131.25 = 15R × 5/3
131.25 = 25R
R = 131.25/25
R = 5.25%
That is,
The rate of interest for Rebekah's account is 5.25%
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4) What type of slope does the following line have?
Answer: zero slope
Step-by-step explanation:
When the slope of a line is zero it creates a horizontal line.
PLS HURRY!!!Juan divided 12 jar of fish food into 7 equal parts. He feeds his fish one part each day.
What fraction of the jar of food will Juan will feed his fish each day?
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:1/14
Step-by-step explanation:He divides 1/2 of the jar into sevenths, but if he had the whole jar it would be fourteen parts because 2x7=14, or 14÷2=7
Find the value of X. Find the m
Answer:
Step-by-step explanation:
all angles of a triangle add up to 180 degrees, so:
3x-40+x+60 = 180
4x = 180 - 60 + 40
4x = 160
x = 40
Check:
LS: RS:
3(40)-40+40+60 180
= 180
because LS = RS,
x = 40
Hope this helps and you understand!!
Please answer as quick as possible (timed)
Table C is the only table that represents a function
How to identify a function?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Based on the definition of function as seen above. Let's check the tables:
Table A has two inputs with the same value (4) but with different outputs. So Table A is not a function
Table B also has two inputs with the same value (9) but with different outputs. Thus, Table B does not represent a function
In Table C each input has exactly one output. Table C represents a function
Table D also has two inputs with the same value (8) but with different outputs. So Table D does not represent a function
Therefore, Table C represents a function
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Please help me with this (ASAP) 15 POINTS
Given that x is a nonnegative number, a student conjectured that x+4
Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
(x equals negative one fourth)
B. x=−4
C. x = 1
D. x = 4
The value of x that is a counterexample to the student's conjecture is (a) x = -1/4
How to determine the value of x?From the question, we have the following statement that can be used in our computation:
x = Non-negative number
Student's conjecture:
x + 4 < x²
Using the options, we have:
(a) x = -1/4
x + 4 < x²
-1/4 + 4 < (-1/4)²
3.75 < 1/16 -- false
(b) x = -4
x + 4 < x²
-4 + 4 < (-4)²
0 < 16 -- true
(c) x = 1
x + 4 < x²
1 + 4 < (1)²
5 < 1 -- false
This cannot be used because x is non-negative
(c) x = 4
x + 4 < x²
4 + 4 < (4)²
8 < 16 -- true
The false statements are the counterexamples
Hence, the value of x is (a) x = -1/4
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Complete question
Given that x is a nonnegative number, a student conjectured that x + 4 < x². Which value of x is a counterexample to the student's conjecture?
Responses
A. x=−1/4
B. x=−4
C. x = 1
D. x = 4
Use the "Insert Line" Tool to construct the line
showing the given distance. If you need to extend
the line outside the shape, use a dotted line.
The distance from B to AC can be constructed as
The distance from G to EF can be constructed as
The distance from Q to SR can be constructed as
What is the distance of a line from a point?
A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.
For the first figure,
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the ages of five randomly choose cars in the parking lot are determined to be 7, 9, 3,4, and 6 years old. if we consider these 5 cars in groups of 3, how many groups can be formed?
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3. Is this graph a function?
This is a function.
This is not a function.
This cannot be determined from this graph.
Answer:
that is a quadratic function so yes it is a function
Step-by-step explanation:
it is a function becausr you can write an equation with it. Hope I could help!
a large company states in its promotional literature that 74% of its employees have college degrees. assume this claim is true. if 3 employees are selected at random from this company, what is the probability that at least 1 of the selected employees will not have a college degree?
The probability of having at least one employee not have a college degree is 0.595
Here it is given that the 74% of employees have a college degree.
Hence, the probability of one employee having a college degree is
74/100
= 0.74
The probability that an employee does not have a college degree is
1 - 0.74
= 0.26
Hence
The above problem is clearly a Binomial distribution. with n = 120 and p = 0.26
"success" is when one employee does not have a college degree.
Therefore the probability that at least 1 employee does not have a college degree is
P(X≥1)
= 1 - P(X = 0)
A binomial distribution with sample n and probability p has a PMF
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
where x is a random variable
Here
n = 3
p = 0.28
x = 0
Hence we get
³C₀ X 0.26⁰ X (0.74)³
0.405
Therefore,
P(X≥1)
= 1 - 0.405
= 0.595
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the sales force for a publishing company is constantly on the road trying to sell books. as a result, each salesperson accumulates many travel-related expenses that he or she charges to a company-issued credit card. to prevent fraud, management hires an outside company to audit a sample of these expenses. for each salesperson, the auditor prints out the credit card statements for the entire year, randomly chooses one of the first 20 expenses to examine, and then examines every 20th expense from that point on. which type of sampling method is the auditor using for each salesperson?
Systematic random sampling is the sampling method is the auditor using for each salesperson.
Define sampling method.Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study. If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.
Given,
The sales force for a publishing company is constantly on the road trying to sell books. as a result, each salesperson accumulates many travel-related expenses that he or she charges to a company-issued credit card. to prevent fraud, management hires an outside company to audit a sample of these expenses. for each salesperson, the auditor prints out the credit card statements for the entire year, randomly chooses one of the first 20 expenses to examine, and then examines every 20th expense from that point on.
Systematic random sampling is the sampling method is the auditor using for each salesperson.
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A 7-pound box of strawberries costs $12.32. What is the price per ounce?
Step-by-step explanation:
Answer: 9.090909090909091
Step-by-step explanation: Knowing this we can solve. We have 7 pounds, and there are 16oz in 1 pound so we multiply the number of pounds by the number of ounces in 1 pound. 7 x 16 = 112 ounces. So there are 112oz total, which costs $12.32. Now we divide $12.32 by 112oz to find the price per ounce which would be roughly 9.09
9x + 7y = 3
x - 7y=-8
Answer:
The point at which these lines intersect is (-0.50, 1.07). We can solve this in two ways: mathematically or graphically. Both are described.
Step-by-step explanation:
We have 2 equations, so we'll assume that the question is to find if they intersect, and if they do, where is the point of intersection.
Let's rewite the equations in slope-intercept format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
1) 9x + 7y = 3
7y = -9x + 3
y = -(9/7)x + (3/7) This line has a slope of -(9/7) and a y-intercept of +(3/7).
2) x - 7y=-8
-7y = -x - 8
y = (1/7)x + (8/7) This line has a slope of (1/7) and an intercept of (8/7)
The line have different slopes, so they will intersect. We can find the intersection point by either graphing or by substitution. We'll do both:
Substitution
We'll rearrange one equation in terms of x and then use that value of x in the second equation. Thuis has the effect of eliminating one of the variables (x or y) so that we can solve for the remaining value of x or y,
We've rearranged both equations so that they have y equal to an expression involving x. If the lines intersect, we know that y in both equations will be the same at that point, so set the equations equal to each other and solve for x:
y = -(9/7)x + (3/7)
y = (1/7)x + (8/7)
Therefore: -(9/7)x + (3/7) = (1/7)x + (8/7)
-(9/7)x -(1/7)x = + (8/7) - (3/7)
-(10/7)x = +(5/7)
x = (5/7)*(-7/10)
x = (-35/70)
x = -0.50
Now we can use this value of x to find y:
9x + 7y = 3
9(-0.50) + 7y = 3
-4.5 + 7y = 3
7y = 3+4.5
y = (7.5/7)
y = 1.07
The point at which these lines intersect is (-0.50, 1.07)
Graphing:
We can also graph the two equations and then look for the intersection. See the attached graph. The lines intersect at (-0.50, 1.07)
The mathematical approach has more certainty, since it does not require interpreting the intersection point on a graph. Use the graphing approach to check the conclusion from the substitution approach.
jeremiah is testing the impact of different fertilizers on crop yields. six different fertilizers have been applied to one field. suppose he uses an anova to test whether or not there are differences in yields. how many treatments are in this test?
The impact of different fertilizers on crop which yields six different fertilizers have been applied to one field. here, the number of treatments in the test are 6.
Treatments are the numerous values of the factor.
The factor here is the effect of various fertilizers on crop yields.
Six different fertilizers were used.
As a result, the number of treatments equals the number of different fertilizers used = 6.
Fertilizers supply essential nutrients such as nitrogen to crops, allowing them to grow larger, faster, and produce more food. However, overfertilization can be a problem because it causes greenhouse gas emissions and eutrophication.
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