The borrower owes $14,760.82 at the end of 8 years
What is compounding interest?
Compounding interest means that earlier interest would earn more interest in the future alongside the loan principal.
Note that in this case the loan continues to accumulate interest because there no repayments, in other words, the loan balance after 8 years, which comprises of the principal and interest for 8 years can be computed using the future value formula of a single cash flow(the single cash flow is the principal) as shown thus:
FV=PV*(1+r/n)^(n*t)
FV=loan balance after 8 years=unknown
PV=loan amount=$5,000
r=annual interest=14%
n=number of times in a year that interest is compounded=2(twice a year)
t=loan period=8 years
FV=$5000*(1+14%/2)^(2*8)
FV=$5000*(1.07)^16
FV=$5000*2.95216374856541
FV=loan balance after 8 years=$14,760.82
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Find the missing length indicated
Step-by-step explanation:
there is a nice formula for the height in a right-angled triangle :
h = sqrt(p×q)
h being the height to the 90° angle, p and q being the segments (left and right of the height) of the Hypotenuse.
so, in our case
x = sqrt(25×144) = 5×12 = 60
For each ordered pair, determine whether it is a solution to the system of equations.
=+−9x2y6=−5x3y8
Is it a solution?
x, y Yes No
7, 9
0, 3
−5, 4
−−2, 6
The only ordered pair that is a solution to the given system of equations is (-2, -6)
System of Linear EquationsFrom the question, we are to determine if each ordered pair is a solution to the given system of equations
The given system of equations is
-9x + 2y = 6
5x - 3y = 8
For (7, 9)That is,
x = 7, y = 9
Putting the values into the first equation
Is -9(7) + 2(9) = 6
-63 + 18 = 6
-45 ≠ 6
Thus, (7,9) is not a solution
For (0, 3)That is,
x = 0, y = 3
Putting the values into the first equation
Is -9(0) + 2(3) = 6
0 + 6 = 6
6 = 6
The ordered pair satisfies the first equation
Testing for the second equation
Is 5(0) - 3(3) = 8
0 - 9 = 8
-9 ≠ 8
Thus, (0, 3) is not a solution
For (5, -4)That is,
x = 5, y = -4
Putting the values into the first equation
Is -9(5) + 2(-4) = 6
-45 - 8 = 6
-53 ≠ 6
Thus, (-5,4) is not a solution
For (-2, -6)That is,
x = -2, y = -6
Putting the values into the first equation
Is -9(-2) + 2(-6) = 6
18 - 12 = 6
6 = 6
The ordered pair satisfies the first equation
Testing for the second equation
Is 5(-2) -3(-6) = 8
-10 + 18 = 8
8 = 8
The ordered pair satisfies the second equation
∴ The ordered pair that is a solution to the system of equations is (-2, -6)
Hence, the only ordered pair that is a solution to the given system of equations is (-2, -6)
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Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship.
Enter the correct answer in the box by replacing the values of a and b
f(x) = a(b)^x
(PLATO)
The exponential equation modeling this relationship is given as follows:
f(x) = 8(0.5)^x.
What is an exponential equation?An exponential equation is modeled by:
f(x) = a(b)^x
In which:
a is the initial value, that is, the value of y when x = 0.b is the rate of change.For this problem, we have that when x = 0, y = 8, hence a = 8. Then:
f(x) = 8(b)^x.
When x = 1, y = 4, hence b is found as follows:
f(x) = 8(b)^x.
4 = 8b
b = 0.5.
Hence the equation is:
f(x) = 8(0.5)^x.
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Find X:
J:58
K:70
L:111
M:121
Answer: 111
Step-by-step explanation:
Angles in a quadrilateral add to 360 degrees, so:
[tex]121+58+70+x=360\\\\x=111[/tex]
Answer:
111
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 360:
121 + 58 + 70 + x = 360 add like terms
249 + x = 360 subtract 249 from both sides
x = 111 is the measure of the angle represented with x
Make a table for each function rule. Then graph each equation using the points you created.
F (x) = 2x - 5
F (x) =-3x +6
F (x) =2/3x +4
Answer:
1.f(x)=2x-5
i will take the set {-2,-1,0,1,2}
f(-2)=2(-2)-5
=-4-5
=-9
f(-1)=2(-1)-5
=-2-5
=-7
f(0)=2(0)-5
=-5
f(1)=2(1)-5
=-3
f(2)=2(2)-5
=-1
so the coordinates of the function is {-9,-7,-5,-3,-1}
2.f(x)=-3x+6
i will the take the set {-2,-1,0,1,2} too
f(-2)=-3(-2)+6=6+6=12
f(-1)=-3(-1)+6=3+6=9
f(0)=-3(0)+6=6
f(1)=-3(1)+6=-3+6=3
f(2)=-3(2)+6=-6+6=0
{12,9,6,3,0}
3.f(x)=2/3.x+4
{-2,-1,0,1,2}
f(-2)=2/3(-2)+4=-4/3+4=(-4+12)/3=8/3
f(-1)=2/3(-1)+4=-2/3+4=(-2+12)/3=10/3
f(0)=2/3(0)+4=4
f(1)=2/3(1)+4=2/3+4=(2+12)/3=14/3
f(2)=2/3(2)+4=4/3+4=(4+12)/3=16/3
{8/3,10/3,4,14/3,16/3}
you're can graph those coordinates
actually you can take other coordinates...
CMIIW
,
Select the correct answer.
Which equation represents the measure of the unknown angles?
C
E
D
Xº
A.
B.
50°
C.
(x+10)
F
x + x + 10 =
= 130°
x + 10 = 180°
x+10= 130°
D. x + x + 10 = 180°
Step-by-step explanation:
x+x+10+50=180
2x+60=180
2x=180-60
2x=120
x=120/2
x=60
Pls need help 100 points and crown if right!!!
Marlene only has enough ingredients to make a 1/3
batch of cookies. For the smaller batch, she only needs 3/4
cup of sugar. How much sugar does the recipe for a full batch of cookies call for? Include all your work in your answer.
Answer:
[tex]\sf 2\dfrac{1}{4}\ cups \ of \ sugar[/tex]
Explanation:
Let the full batch be x
Here given:
3/4 cup of sugar required to make 1/3 batch of cookies
Build equation:
[tex]\sf \rightarrow \dfrac{1}{3}x = \dfrac{3}{4} \ cup \ of \ sugar[/tex]
Solve:
[tex]\sf \rightarrow x = \dfrac{3(3)}{1(4)}[/tex]
[tex]\sf \rightarrow x = \dfrac{9}{4}[/tex]
[tex]\rightarrow \sf x = 2\dfrac{1}{4}[/tex]
Answer:
2 2\3 cups of sugar.
Step-by-step explanation:
How do you solve 1.023 x 3.5 ?
Answer:
Step-by-step explanation:
3.5805
Hello please help asap!! i will mark brainliest and this is worth 20 points!!!!! tysm
The least number of colors needed to correctly color in the sections of the given picture so that no two touching sections have the same color is 5.
Let's say we begin with a single triangle. This triangle will be the first of a series of seven subsequent triangles, none of which will have any portions contact. If a square were the initial shape, then there are five shapes—three of which are squares and the other two are triangles—that don't have any touching portions. Given that a square takes up twice as much room, this value is probably lower, but location also matters. Therefore, for the given figure, the least number of colored areas you can color in that yet meet the required criteria is 5.
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Explain insurable interest and give an example
The examples of insurable interest is an employer under certain arrangements.
Insurable interest is a investment that protects anything subject to a financial loss. A person or entity has an insurable interest in an item, event, or action when the damage or loss of the object would cause a financial loss or other hardshapes. In order to have an insurable interest a person or entity would take out an insurance policy protecting the person,item, or event in question. The insurance policy is able to mitigate the risk of loss if something happens to the asset-like becoming damaged or lost.
Examples of insurable interest are:
YourselfYour spouse or former spouseYour children or grandchildrenA special needs adult childAn aging parentAn employer (under arrangements)Hence the examples of insurable interest is an employer under certain arrangements.
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Answer: Insurable interest means you must have a financial stake in the risk being insured. You can’t claim insurance for a risk that you don’t face directly.
If Rob’s dad’s car is stolen, his father will receive the insurance money, not Rob.
Step-by-step explanation: Edmentum
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
What is a Chord in Geometry?In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.
What is the Congruent Chords Theorem?In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.
In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.
According to the congruent chords theorem, NS = PS, thus:
8 = 2x - 6
8 + 6 = 2x
14 = 2x
Divide both sides by 2
14/2 = 2x/2
7 = x
x = 7
LP = 1/2(12)
LP = 6 units.
In summary, applying the congruent chords theorem, the value of x is: 7.
Length of segment LP is: 6 units.
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In a survey of 2035 workers, 73% reported working out 3 or more days a week. What is the margin of error? What is the interval that is likely to contain the exact percent of all people who work out 3 or more days a week? Show all work.
Your work needs to be your own. If you need help, reach out to your teacher. Use this formula:
The margin of error is 1.9%. and the interval that likely contains the true percent of all people who work out 3 or more days a week is: (71.1%, 74.9%)
What is the Margin of Error?Margin of error is the critical value (t score or z score) multiplied by the standard error (standard deviation of the sample). Thus;
ME = Critical value × S.E
Since n > 30, we can use the z-score as the critical value.
Assuming 95% confidence level, then z = 1.96
The standard error for a proportion is given by the formula:
s = √(p (1 − p) / n)
We are given;
p = 0.73
n = 2035:
Thus;
s = √(0.73 (1 − 0.73) / 2035)
s = 0.0098
Thus, the margin of error is:
ME = 1.96 × 0.0098
ME = 0.019
The margin of error is 1.9%.
The interval that likely contains the true percent of all people who work out 3 or more days a week is:
73% ± 1.9% = (71.1%, 74.9%)
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find dy/dx when y =
[tex] \sqrt{(1 + cosx)/( 1 - cosx)} [/tex]
Answer:
cos(x)
Step-by-step explanation:
(1 + cos(x))(1 - cos(x)) = 1 - cos²(x) = sin²(x)
sqrt(sin²(x)) = sin(x)
sin'(x) = cos(x)
elsa sold 24 drawings for $12 each at the art fair. She is going to use 1/3 of the money to buy books. The rest of the money is going into her savings account. How much money will she put into her savings account?
Anu is a photographer and was recently hired to photograph a wedding in Hawaii. While there, Anu had some time to
explore the island and capture other beautiful pictures.
During the trip, Anu took a total of 1,200 photographs. Of these, 25% were wedding photos, 35% were pictures of Lanikai
Beach, and the rest of the pictures were taken at the Honolulu Zoo. How many of Anu's pictures were taken at the Honolulu
Zoo?
ANSWER: 480 out of 1200 were taken at the Honolulu Zoo.
jake made some tarts. He sold 3/5 of them and gave 1/4 of the remainder to his friends. If he had 150 tarts left, how many did he sell?
Check what other students also ask
Answer:
300 tarts
Step-by-step explanation:
we must solve this equation by going backwards
3/4 of something (as 1/4 was given away) is 150
150 / 3/4 is what you must do
or
150 * 4/3
that is
200
3/5 was sold so 2/5 was left
2/5 of something is 200
200 / 2/5
200 * 5/2
that is
500
3/5 of that was sold
so
500 * 3/5 is 300
300 tarts were sold
=
Use the Fundamental Counting Principle to solve.
A television programmer is arranging the order that three movies will be seen between the hours of 6 P.M. and 12
A.M. Two of the movies have a G rating, and they are to be shown in the first two time blocks. One of the movies is
rated NC-17, and it is to be shown in the last of the time blocks, from 10 P.M. until 12 A.M. Given these restrictions,
in how many ways can the three movies be arranged during the indicated time blocks?
The number of different ways the three movies can be arranged during the indicated time blocks is.
(Type a whole number.)
[tex]number \: of \: movies = 3 \\ permutations = 2 \\ \\ c( \gamma ) = 2! \times 1 = 2 \: ways[/tex]
[tex]g(1) \: \: \: \: g(2) \: \: \: \: nc(17) \\ g(2) \: \: \: \: g(1) \: \: \: \: nc(17)[/tex]
(1+m)²= (1-m)²+ 4lm,
The expression is simplified to give 2 ( m² + m + 2Im ) = 0
How to simplify the expression
Given the expression;
(1+m)²= (1-m)²+ 4lm,
Expand the expression
( 1 +m) ( 1 + m) = ( 1 + m) ( 1 - m) + 4Im
1 + m + m + m² = 1 - m + m - m² + 4Im
collect like terms
1 + 2m + m² = 1 - m² + 4Im
1 - 1 + m² + m² + 2m + 4Im
2m² + 2m + 4lm = 0
simplify
2 ( m² + m + 2Im ) = 0
Thus, the expression is simplified to give 2 ( m² + m + 2Im ) = 0
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:
Find the intercepts and graph the following linear equations:
3x+4y-12=0
x - intercept:
y - intercept:
Answer:
x-intercept: (4, 0)
y-intercept: (0, 3)
Step-by-step explanation:
The intercepts of the equation can be found by setting each variable to zero and solving for the other. The graph will be a line through the intercept points.
InterceptsSetting x=0 and solving for y, we have ...
4y -12 = 0 ⇒ y = 12/4 = 3
Setting y=0 and solving for x, we have ...
3x -12 = 0 ⇒ x = 12/3 = 4
The intercepts are ...
x-intercept: (4, 0)
y-intercept: (0, 3)
GraphThe line will go through these intercept points.
Let a be an even integer number, b be an odd integer number and c be an integer number.
Which of the following statements is NOT true?
a.
If a+b=c, then c is odd integer.
b.
If b+b=c, then c is even integer.
c.
If b×b=c, then c is even integer.
d.
If a×b=c, then c is even integer.
The false statement is given by:
c. If b×b=c, then c is even integer.
When is the addition of two integers even or odd?It both numbers are even or both are odd, the addition is even.It one number is even and the other is odd, the addition is odd.When is the multiplication of two integers even or odd?It at least one of the numbers is even, the multiplication is even.If the two numbers are odd, the multiplication is odd.Hence, since b is odd, b x b = c is odd, hence statement c is false.
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Sasha does push-ups each day for five days. The numbers of push-ups she does each day or shown below.
22, 36, 21, 25, 27
The mean average of push ups Sasha does in 5 days is 26.2.
Mean averageNumber of days = 5Day 1 = 22 push upsDay 2 = 36 push upsDay 3 = 21 push upsDay 4 = 25 push upsDay 5 = 27 push upsMean average = Total push ups done / number of days
= (22 + 36 + 21 + 25 + 27) / 5
= 131 / 5
= 26.2
Therefore, the mean average of push ups Sasha does in 5 days is 26.2.
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A right triangle has a base of 8 1/2 inches and a height of 12 1/2. If the height is reduced to 4 inches, how many inches is the new base?
The length of the new base is 26.56 inches or [tex]26\frac{14}{25}[/tex] inches. Using the area of a right triangle, the required base is calculated.
How the area of a right triangle is calculated?The area of the right triangle is given by
A = [tex]\frac{1}{2}[/tex] × b × h sq. units
Where A -area; b -base; h -height;
Calculation:It is given that,
The right triangle has a base of length b = 8 1/2 = 8.5 inches and a height of length h = 12 1/2 = 12.5 inches.
So, its area is
A = [tex]\frac{1}{2}[/tex] × 8.5 × 12.5 = 53.125 sq. inches
When the height of the right triangle is reduced to 4 inches,
53.125 = [tex]\frac{1}{2}[/tex] × b × 4
⇒ b = 53.125/2
∴ b = 26.56 or [tex]26\frac{14}{25}[/tex] inches
Thus, the length of the new base is 26.56 or [tex]26\frac{14}{25}[/tex] inches.
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A random sample of 80 tires showed that the mean mileage per tire was 41,400mi, with a standard deviation of 4700mi
Question 14
Part (a)
[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]
Part (b)
[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]
Emily thinks the perfect tomato sauce has 15 cloves of garlic in every 6 L end text of sauce. Raphael's tomato sauce has 25 cloves of garlic in every 9 L end text of sauce. What will Emily think of the amount of garlic in Raphael's tomato sauce? Choose 1 answer: Choose 1 answer: (Choice A) A Raphael's tomato sauce has too much garlic. (Choice B) B Raphael's tomato sauce has too little garlic. (Choice C) C Raphael's tomato sauce is perfect.
Answer:
Raphael's tomato sauce has too much garlic.
Step-by-step explanation:
We can use ratios to solve
Emily:
15 cloves
----------------
6L
2.5 Cloves per Liter
Raphael
25 cloves
----------------
9 L
2.7777(repeating) cloves per liter
Raphael has more garlic per liter
Answer:
B
Step-by-step explanation:
perfect tomato sauce
15 cloves → 6 L ( multiply both parts by 1.5 )
22.5 cloves → 9 L← Raphael's tomato sauce
since he used 25 cloves of garlic , then
Emily would think Raphael's sauce has too little garlic
f(x)=cos(2x) and state the amplitude and period. Enter exact answers
The amplitude of function f(x)=cos(2x) is 1 and the period is 2.
Given that the function of x is f(x)=cos(2x).
We are required to find the value of amplitude and period of function f(x) which is given in the question.
Amplitude basically refers to maximum displacement from the equilibrium that an object in periodic motion show. It is a product analytics platform or term that helps businesses to track visitors with the help of collaborative analytics.
Period is basically the time interval between two waves. A function that repeats its values at regular intervals or periods is known as periodic function.
The amplitude of f(x)=cos(2x) is 1 because the highest value that cos Θ can give 1. We can also see in graph that the value of cos 2x is going to 1 and starts decreasing again.
The period of f(x) is 2. From the graph we can say that the vertical distance between upper point and lower point is 2.
Hence the amplitude of function f(x)=cos(2x) is 1 and the period is 2.
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Write a general formula
Answer:
y = [tex]\frac{24}{\sqrt{x} }[/tex]
Step-by-step explanation:
given y varies inversely as [tex]\sqrt{x}[/tex] then th equation relating them is
y = [tex]\frac{k}{\sqrt{x} }[/tex] ← k is the constant of variation
to find k use the condition y = 8 when x = 9 , then
8 = [tex]\frac{k}{\sqrt{9} }[/tex] = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
24 = k
y = [tex]\frac{24}{\sqrt{x} }[/tex] ← equation of variation
Given that m/_a=40 and m/_b=61 find that the measure of angles x and y
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 159°y = 140°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:y + a = 180[/tex]
( linear pair )
[tex]\qquad❖ \: \sf \:y + 40 = 180[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - 40[/tex]
[tex]\qquad❖ \: \sf \:y = 140 \degree[/tex]
And
[tex]\qquad❖ \: \sf \:x = a +( 180 - b)[/tex]
( Exterior angle = sum of opposite interior angles )
[tex]\qquad❖ \: \sf \:x = 40 + (180 - 61)[/tex]
[tex]\qquad❖ \: \sf \:x = 40 + 119[/tex]
[tex]\qquad❖ \: \sf \:159 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 159°y = 140°Find the surface area of the cone in terms of pie 18 height 12 radius
144π cm²
Answer:
Solution given:
diameter (d)= 12cm
radius (r)=12/2=6 cm
slant height(l)=18cm
Now
Total surface area of cone=πr(r+l)π*6(6+18)=144π cm²
The price of an item has risen to $187 today. Yesterday it was $110. Find the percentage increase.
Answer:
Percent increase is 70%.
Step-by-step explanation:
The original price was $110. That will go on the bottom (denominator) in our calculation. On the top (numerator) we put the change in the dollar amount. The new price is $187. So we'll subtract:
187 - 110
= 77
The change in price was $77.
change/original
= 77/110
= 0.7
Change the decimal answer to a percent by multiplying by 100.
0.7 × 100
= 70%
The percent increase is 70%.
Two triangles are similar. The sides of the first triangle are 4,5,and 6. The largest side of the second triangle is 24. Find the perimeter of the second triangle.
Answer:
The perimeter of the second triangle is 60 units.Step-by-step explanation:
If two triangles are similar, their corresponding sides will be k times greater or smaller, where k is the scale factor.
We have two corresponding sides given, 6 and 24 or 6k. Using this info, find the value of k:
k = 24/6 = 4The other sides of the larger triangle are:
4k = 4*4 = 165k = 5*4 = 20The perimeter is the sum of sides:
P = 16 + 20 + 24 = 60