The total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.
What is compound interest?Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the compound interest formula can be given as,
[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]
Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.
Gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and Gertrude makes monthly payments.
Put the values in the above formula as,
[tex]5500=P_{mt}\times\left(1-\dfrac{6.8}{12\times100}\right)^{-12\times10}\\P_{mt}=63.29[/tex]
In the 10 years, the refund she gets,
[tex]A_r=63.29\times12\times100\\A_r=7594.8[/tex]
Interest paid by her is,
[tex]I=7594.8-5500\\I=2094.8[/tex]
Thus, the total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.
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Answer: D
Step-by-step explanation:
50 POINTS 50 POINTS please help me with these 5 questions attached pictures
Step-by-step explanation:
the first graph
0=|x+2| f(0)=|0+2|
|x+2|=0 f(0)=|2|
x+2=0 f(0)=2
x=-2
Answer:
First graph X=-2
Which statements are true? select three options. the population density for city b can be found using the ratio 48,592 : 26. the population density for city d can be found using the ratio 258 : 196,429. city a has the greatest population density of the four cities. the population density of city b is greater than that of city c. city d has the lowest population density of the four cities.
The three statements truly define the conditions are 1,3 and 4.
What is population density?The number of individuals of a species in a certain geographic location is known as population density.
Data on population size may be used to quantify demographic information as well as to analyze links with habitats, people's health, and transportation.
The population density is given as the ratio of population per unit area;
[tex]\rm population \ density= \frac{population}{Area}[/tex]
For the different cities the population density is found as;
For city a
[tex]\rm P_A = \frac{2,19514}{1553} \\\\ \rm P_A = 1413.98[/tex]
For city b
[tex]\rm P_B =\frac{48,592 }{26} \\\\ \rm P_B =1868.15[/tex]
For city c
[tex]\rm P_C = \frac{ 1,257,676}{999} \\\\ \rm P_C = 999[/tex]
For city d
[tex]\rm P_D = \frac{196,429}{258} \\\\ \rm P_A = 761.35[/tex]
The three statements defining the condition will be;
The population density for city b would be 48,592:26.
The population density for city b is more than city c.
The city d contains the lowest population density
Hence the three statements true will be 1,3 and 4.
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What are the new coordinates of the figure above if it is rotated 90 degrees clockwise about the origin ?
A. A’(1,-3), B’(1,-7),C’(-3,-7),D’(-3,-3)
B. A’(-3,-1),B’(-7,-1), C’(-7,3) D’(-3,3)
C. A’(-3,-1),B’(-7,-1),C’(-7,3),D(-3,3)
D.A’ (1,-3),B’(1,-7),C’(3,-7),D’(3,-3)
Answer: A
Step-by-step explanation:
Rounding please help! Math
it is just still 5 I believe :P hope this helps
Erin wants to fill the jewelry box with beads. One package of beads is 120 cubic inches. How many packages of beads should Erin purchase to fill the jewelry box completely?
Answer:
9 packages of beads
Step-by-step explanation:
volume of cuboid = area of base × height
⇒ volume of jewelry box = (15 × 12) × 6
= 180 × 6
= 1080 in³
Given:
1 package of beads = 120 in³Number of packages of beads = volume of box ÷ volume of 1 package of beads
⇒ Number of packages of beads = 1080 ÷ 120
= 9
Which expression is equivalent to (q^6)^2
○ q^3
○ q^8
○ q^12
○ q^36
btw, its not q^36
round 763 to the nearist ten
Answer:
760
Step-by-step explanation:
Answer:
760 of course
Step-by-step explanation:
3 is below 5 so its 760
If the last digit was a 5 or higher,it'll be 770
Angelina’s family owns a mini-golf course. When discussing the business with a customer, she explains there is a relationship between the number of visitors and hole-in-one winners. If x is the number of visitors and y is the number of winners, which conclusion is correct?
The ordered pair (–3, 7) is viable.
The ordered pair (0, 4) is viable.
The ordered pair (7, 0) is non-viable.
The ordered pair (12, 3) is viable.
Answer:
D
Step-by-step explanation:
X must be positive as you cannot have a negative amount of people and neither X and Y could be 0. (In this case (7, 0) could have been viable but the choice says non-viable.) This means the answer is (12,3).
The ordered pair (12, 3) is viable is correct answer.
What is ordered pair?"Ordered pair is defined as the two numbers or variables which is written in form of pair using parenthesis."
According to the question,
Number of visitors = x
Number of winners = y
Relationship given,
Number of visitors and hole in one winners.
Negative value cannot be part of number of visitors or winners.
Therefore,
(-3,7) is not the correct ordered pair.
'x' and 'y' value cannot be equals to zero as per the condition given.
(7,0) is non viable.
Therefore,
(0,4) and (7,0) is not the correct ordered pair.
(12,3) represent both positive value as per the condition.
Hence, the ordered pair (12, 3) is viable is correct answer.
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A figure is made up of three triangles. Each triangle has a base of 5 feet and a height of 4.5 feet. What is the total area of the figure?
Group of answer choices
33.75 ft²
43.75 ft²
67.5 ft²
22.5 ft²
Answer:
Step-by-step explanation:
3 * 1/2 * 5 * 4.5
= 33.75 fT^2.
it is 3 kilometers from Linda's house to the nearest mailbox. How far is it in meters? Be sure to include the correct unit in your answer.
Answer:
1km=1000m... thats basically the answer so the nearest mail box is 3000M
Please help! I don't know what answer b is, but i know a, thank you.
They are corresponding angles
Step-by-step explanation:
We know that x=75⁰ because
[tex]180 - 105 = 75[/tex]
75⁰ is angle EFB
Since we know this, and because we know that AD//EH,
We can conclude that x=75⁰(AD is parallel to EH and angle CBA or x and angle EFB are corresponding angles)
If ∠GHJ≅∠IHJ and GJ=99, what is IJ?
Answer:
99
Step-by-step explanation:
Triangles GJH and IJH are congruent, so GJ=IJ=99.
compute (5 2/3)^2-(4 1/3)^2
Answer:
40/3
Step-by-step explanation: If you have a calculator type in (5 2/3)^2-(4 1/3)^2. To get 40/3. So in short, square (5 2/3)^2 to get 289/9 and square (4 1/3)^2 to get 169/9. Then subtract the two 289/9-169/9 to get 40/3.
For each of the figures, write an absoulute value equation that has the following solution set.
The solution set -18 and 0 are the true values of the absolute value equation
The absolute value equation that has the a solution set of -18 and 0 is |x + 9| = 9
How to determine the absolute value equation?From the figure, the solution sets of the absolute value equation are given as:
x = {-18, 0}
Calculate the mean of the solution set
Mean = 0.5 * (-18 + 0)
Mean = -9
Calculate the difference of the solution set divided by 2
Difference = (0 + 18)/2
Difference = 9
The absolute value equation is the represented as:
|x - Mean| = Difference
Substitute known values
|x + 9| = 9
Hence, the absolute value equation that has the a solution set of -18 and 0 is |x + 9| = 9
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Answer:
|x+9|=9
Step-by-step explanation:
simplified?
0.0007 - (4.9 × 10^-7)
A.
4.8993 × 1^0-7
B.
6.9951 × 10^-7
C.
2.1 × 10^-4
D.
6.9951 × 10^-4
Answer:
Option B
Step-by-step explanation:
Given the following question:
In order to find the answer, we need to convert the scientific notation into standard notation and then simplify by subtracting the decimals. Then we convert the standard notation back into scientific notation.
[tex]0.0007 - (4.9\times 10^{-7} )[/tex]
[tex]4.9\times10^{-7} =0.00000049[/tex]
[tex]0.0007-0.00000049[/tex]
[tex]0.0007-0.00000049=0.00069951[/tex]
[tex]=0.00069951[/tex]
[tex]0.00069951=6.9951 \times10^{-7}[/tex]
[tex]=6.9951 \times10^{-7}[/tex]
Your answer is "6.9951 × 10^-7" or option B.
Hope this helps.
How do you do this problem:
1- 3 (4 - 3) + (27- 2 x 3)
Answer:
19
Step-by-step explanation:
Do what is in parenthesis first.
(4 - 3) = 1
(27 - 2 * 3) = (27 - 6) = 21
Now the equation looks like this:
1 - 3 (1) + (21) =
1 - 3 + 21 =
19
What is the median age of a group of employees
whose ages are 32, 37, 30, 43, 29 and 31?
A principal of a large high school wants to estimate the true proportion of high school students who use the community's public library. To do so, he selects a random sample of 50 students and asks them if they use the community's public library. The 95% confidence interval for the true proportion of all students who use the community's public library is 0.25 to 0.34. If the principal had used a sample size of 200 students rather than 50 students, how would the length of the second interval compare to the original interval?
O It would be half as wide.
O It would be twice as wide.
O It would be one-fourth as wide.
O It would be four times as wide
ws
Considering the margin of error of a confidence interval, it is found that the correct option is:
It would be half as wide.
What is the margin of error of a confidence interval?It is modeled by:
[tex]M = z\frac{s}{\sqrt{n}}[/tex]
In which:
z is the critical value.s is the standard deviation.n is the sample size.From this, we get that the margin of error is inversely proportional to the square root of the sample size. Then, multiplying the sample size by 4, when it changes from 50 to 200, cuts the margin of error in half, making the interval half as wide.
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Answer: It would be half as wide
Step-by-step explanation:
If the principal had used a sample size of 200 students rather than 50 students, the length of the second interval would be half as wide compared to the original interval.
The width of a confidence interval is inversely proportional to the square root of the sample size. In this case, the sample size is multiplied by 4 (from 50 to 200), so the square root of the sample size is doubled. As a result, the width of the confidence interval is divided by 2, making it half as wide.
Therefore, the correct answer is: It would be half as wide.
SYSTEM OF EQUATIONS- I struggle with this
Person A wants to order a bunch of shirts. One website charges 9.65 per shirt, plus a set up fee for $43. Another company charges 8.40 per shirt plus a $58 fee. But what number of shirts would the cost be the same? Why?
Answer:
12 shirts
Step-by-step explanation:
First, we need to write our equations. Let x be the number of shirts and y be the cost. We will multiply the number of shirts bought (x) by the price and then add the setup fee.
To answer the overall question, we will graph the two equations we create. Their point of intersection is the solution, or where the number of shirts bought would cost the same.
"One website" - 9.65 per shirt, plus a set up fee for $43
y = 9.65x + $43
"Another company" - 8.40 per shirt plus a $58 fee
y = 8.4x + $58
See attached for the graph.
They intersect at point (12, 158.8) meaning that both websites will charge $158.80 for 12 shirts.
18x3 + 6x2y - 9x2 - 3xy
factor completely
Answer:
[tex]\sf 3x(3x+y)(2x-1)[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf 18x^3 + 6x^2y - 9x^2 - 3xy[/tex]
Factor out common term [tex]\sf 3x[/tex]:
[tex]\sf \implies 3x(6x^2 + 2xy - 3x - y)[/tex]
Factor [tex]\sf (6x^2 + 2xy - 3x - y)[/tex]
Rearrange:
[tex]\sf \implies 6x^2 - 3x+ 2xy - y[/tex]
Factor pairs of terms:
[tex]\sf \implies 3x(2x-1)+ y(2x - 1)[/tex]
Factor out common term (2x - 1):
[tex]\sf \implies (3x+y)(2x-1)[/tex]
Final solution:
[tex]\sf \implies 3x(3x+y)(2x-1)[/tex]
Answer:
6x2y(3xy2 − 1)
Step-by-step explanation:
i got it right on my quiz :D
Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30%
chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets if she
catches 2 fish.
W = # of walleye 0
1
2
P(W)
0. 49
0. 42
0. 09
Calculate the mean of W.
walleye
Uw =
Answer:
Answer: 1.4
Step-by-step explanation:
P(Northern pike) = 0.7
P(walleye) = 0.3
If 2 fishes are caught :
Number of northern pike (x) :
X = 0
P(walleye 1 st) * p(walleye 2nd) = (0.3 * 0.3) = 0.09
X = 1
P(walleye 1st)*P(Northern pike 2nd) OR P(Northern pike 1st)*P(Walleye 2nd)
= (0.3 * 0.7) + (0.7 * 0.3)
= 0.21 + 0.21
= 0.42
P(x = 2)
P(northern pike 1st) * P(northen pike 2nd)
0.7 *0.7 = 0.49
X: _ 0 _ 1 __ 2
P(x): ___ 0.09 ___ 0.42 ____ 0.49
Expected value of northern pikes :
(0* 0.09) + (1 * 0.42) + (2 * 0.49)
0 + 0.42 + 0.98
= 1.4
Expected value of the number of walleye is 0.5.
What is the expected value?
The expected value exists as a long-run average value of random variables. It also demonstrates the probability-weighted average of all possible values. Expected value exists as a generally utilized financial concept.
W = # of walleye 0, 1, 2
P(W) 0. 49, 0. 42, 0. 09
To estimate the expected value of the number of walleye.
E(X) = number of walleye
E(X) = (0 [tex]\times[/tex] 0.49) + (1 [tex]\times[/tex] 0.42) + (2 [tex]\times[/tex] 0.09)
E(X) = 0 + 0.42 + 0.08
E(X) = 0.5
Therefore, the number of walleye expected value = 0.5.
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Angle A and angle B form a vertical angle pair. The measure of angle A is six less than twice times the measure of angle B. Find the measure of each angle.
Angle A and Angle B are vertical angle pairs. The measure of angle A and B are equal because they are vertical pairs. Therefore, the measure of each angle is 6 degrees.
What is vertical angles?Vertical angles are a pair of opposite angles formed by intersecting lines.
Vertical angles are congruent to each other . Vertical angles share the same vertex.
Therefore, angle A and angle B are congruent because they are vertical angle pair.
Therefore,
∠A≅∠B
let
∠B = x
Therefore,
∠A = 2x - 6
Therefore,
x = 2x - 6
x - 2x = - 6
-x = - 6
x = 6
The measure of each angle is 6 degrees.
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Bo needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged him $63 for parts. The total was $551.75. What was the cost of labor, per hour?
If v is the circumcenter of pqr ,pr =46 ,tv=15,and vr=25 find each measure
Answer:
1. a) SR = 23
b) QV = 25
c) QT = 20
d) PQ = 40
e) VS = 4·√6
2. a) LH = 16
b) EL = 2·√185
c) JG = 30
d) EK = 22
e) KG = 30
3. a) XT = 37
b) TZ = 34
c) ZW = 17
d) XZ = 21
e) SY = 69
Step-by-step explanation:
The circumcenter ΔPQR is the center of the circle that circumscribes ΔPQR
The length of the radius of the circle ≡ VR = VP = QV = 25
a) Given that VR ≅ VP - Radius of circumcircle
VS ≅ VS Reflective property
∠VPS ≅ ∠VRS - Base angles of an isosceles triangle
Right triangle VPS ≅ Right triangle VRS -Hypotenuse and one Leg HL congruency
Therefore, SR ≅ PS -Corresponding parts of congruent triangles are congruent CPCTC
SR + PS = PR = 46
SR + PS = SR + SR = 2·SR = 46
∴ SR = 46/2 = 23
b) QV = VR = 25 = Radius of circumcircle of ΔPQR -Given V = center and Q = vertices of the triangle circumscribed by the circle referred to in the question
c) QT = √(QV² - TV²) = √(25² - 15²) = √400 = 20
d) TV ≅ TV - Reflexive property of congruency
ΔTQV ≅ ΔTVP - Hypotenuse and one Leg (HL) congruency
QT ≅ TP -Corresponding parts of congruent triangles are congruent CPCTC
PQ = QT + TP Given
∴ PQ = QT + QT since QT = TP
PQ = 2·QT = 2 × 20 = 40
e) VS = √(VR² - SR²) = √(25² - 23²) = √96 = 4·√6
2. The incenter is the center of the incircle of ΔEFG
a) LH = LK = JL = 16 -Radius of incircle of ΔEFG
b) EL = Hypotenuse of right triangle LHE = √(LH² + EH²) = √(16² + 22²) = √740 = 2·√185
c) JG = Leg length of right triangle JGL = √(LG² - JL²) = √(34² - 16²) = √900 = 30
d) EK = Leg length of right triangle LKE = √(EL² - LK²) = √(740 - 256) = 22
e) KG = Leg length of right triangle LKG = √(LG² - LK²) = √(34²- 16²) = √900 = 30
3. Point Z id the centroid of ΔRST
a) XT = XS - point X on ST bisected by median line RX
ST = XT + XS = XT + XT = 2.XT = 74
XT = 74/2 = 37
b) TZ = 2/3×TW - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
TZ = 2/3×51 = 34
c) TZ + ZW = TW
∴ ZW = TW - TZ = 51 - 34 = 17
d) RZ = 42 = 2/3×RX - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
∴ RX = 3/2×42 = 63
RZ + XZ = RX - Given
XZ = RX - RZ = 63 - 42 = 21
e) SZ = 2/3×SY - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
SZ + ZY = SY
∴ ZY = SY - SZ = SY - 2/3×SY = 1/3×SY = 23
Which gives;
SY = 3 × 23 = 69.
The area of a circle is 36π cm². What is the circumference, in centimeters? Express your answer in terms of π
Answer: [tex]12\pi[/tex]
Step-by-step explanation:
The formula for area of a circle is [tex]\pi r^2=A[/tex]
The formula for circumference of a circle is [tex]2r\pi=C[/tex]
Where r is the radius
A is area
C is circumference
Knowing this we can sub our values in and solve for r in the formula for area
Divide both sides by [tex]\pi[/tex] to isolate r
[tex]\pi r^2=A\\\pi r^2=36\pi \\\frac{\pi r^2}{\pi } =\frac{36\pi }{\pi } \\r^2=36[/tex]
Take the square root of both sides
[tex]r^2=36\\\sqrt{r^2} =\sqrt{36} \\r=6[/tex]
Now sub the value of r into the formula for circumference
[tex]2r\pi =C\\2(6)\pi =C\\12\pi[/tex]
Answer:
[tex]12\pi \: c \: m[/tex]
step by step explanation:
[tex]area \: of \: a \: cirle = \pi \: r {}^{2} \\ circmferene \: of \: a \: circle = 2 \:\pi \: r \\ 36\pi = \pi \: r {}^{2} \\ 36 = r {}^{2} \\ r = 6 \\ for \: circmference \\ 2 \times \pi \: \times 6 = 12\ \: \pi \: cm [/tex]
The camp has two fire pits. One is a rectangular fire pit with a perimeter of 20 inches. The
other is a circular fire pit with a circumference of 7 inches. Shakir will place stones along
the outside edges of both fire pits. If each stone is the same size, which pit will require more
stones? Use the space below for your work. Explain how you know.
Please help!!
A company that produces cell phones has a cost function of C = 4x^2 - 107x + 4322, where C is the
cost in dollars and c is the number of cell phones produced in thousands). How many units of cell phone
(in thousands) minimizes the cost function?
Based on the cost function, the company that produces cell phones can minimize the cost function at 13.4 cell phones.
What number of cell phones are sold at the minimized cost function?To minimize the cost function, you should differentiate it.
= 4x² - 107x + 4322
dC/dx = 0
8x - 107 = 0
Solving gives:
8x = 107
x = 107 / 8
= 13.4 cell phones
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3
14) There are seven million, eight hundred and fifty-four thousand,
three hundred and eight people in a country. i lleda
Round this number to the nearest ten thousand people.
Answer:
7,854,000
because the 308 people would have to be at least 500 to round up to 7,855,000
what is the way to find inverse of matrix?
Formula for inverse of matrix:
matrix → inverse matrix
[tex]A = \bold{ \sf { \begin{pmatrix}a&b\\ c&d\end{pmatrix} \ \ \ \rightarrow \ \ A^{-1} = \dfrac{1}{(ad-bc)} \begin{pmatrix}d&-b\\ -c&a\end{pmatrix} }}[/tex]
Quadrilateral ABCD is similar to Quadrilateral EFGH. The scale factor is 3:2 if AB = 18, find EF
Answer:
A... 12
Step-by-step explanation: