One safe investment pays 8% per year, and a more risky investment pays 12% per year.
a. How much must be invested in each account if an investor of $109,000 would like a return of $9.920
b. Why might the investor use two accounts rather than put all the money in the 12% investment?
Answers
Principal = 109,000
Return - 9,920
Return = (principal x rate x time)/100
X = the amount invested at 12%
Then 102000- x = the amount invested at 8%
9920 = (x*12)/100 + (109000-x*8)100
x = 30,000
a) 30,000 is invested at 12%
79,000 is invested at 8%
b) The 12% investment is riskier so if all the money was in that account the investor could lose all his money.
Related Questions
Use the factor theorem to determine whether or not the first polynomial is a factor of the second
Answers
Answer/Step-by-step explanation:
Based on the factor theorem, a polynomial, x - a, is said to be a factor of another polynomial, f(x), if an only if f(a) = 0.
Using this theorem, let's determine whether each of the given first polynomial, is a factor of the second polynomial.
1. x - 1; x² + 2x + 5
By the factor theorem, x - 1 will be a factor of f(x) = x² + 2x + 5, if and only if f(1) = 0.
f(1) = 1² + 2(1) + 5
= 1 + 2 + 5
= 8
Since f(1) ≠ 0, therefore the first polynomial, x - 1, is NOT a factor of the second polynomial, x² + 2x + 5.
2. x + 1; x³ - x - 2
By the factor theorem, x + 1 will be a factor of f(x) = x³ - x - 2, if and only if f(-1) = 0.
f(1) = -1³ - (-1) - 2
= -1 + 1 - 2
= -2
Since f(-1) ≠ 0, therefore the first polynomial, x + 1, is NOT a factor of the second polynomial, x³ - x - 2.
3. x - 4; 2x³ - 9x² + 9x - 20
By the factor theorem, x - 4 will be a factor of f(x) = 2x³ - 9x² + 9x - 20, if and only if f(4) = 0.
f(4) = 2(4)³ - 9(4)² + 9(4) - 20
= 128 - 144 + 36 - 20
= 0
Since f(4) = 0, therefore the first polynomial, x + 4, is a factor of the second polynomial, 2x³ - 9x² + 9x - 20.
4. a - 1; a³ - 2a² + a - 2
By the factor theorem, a - 1 will be a factor of f(a) = a³ - 2a² + a - 2, if and only if f(1) = 0.
f(1) = 1³ - 2(1)² + 1 - 2
= 1 - 2 + 1 - 2
= -2
Since f(1) ≠ 0, therefore the first polynomial, a - 1, is NOT a factor of the second polynomial, a³ - 2a² + a - 2.
5. y + 3; 2y³ + y² - 13y + 6
By the factor theorem, y + 3 will be a factor of f(y) = 2y³ + y² - 13y + 6, if and only if f(-3) = 0.
f(-3) = 2(-3)³ + (-3)² - 13(-3) + 6
= -54 + 9 + 39 + 6
= 0
Since f(-3) = 0, therefore the first polynomial, y + 3, is a factor of the second polynomial, 2y³ + y² - 13y + 6.
what is the pythagoras theorum in terms of shakespear?
Answers
Answer:*
Step-by-step explanation:
PLEASE HELP!!!!
Suzie made a mistake in the following problem.
The mistake was made in Line ___. Only input the number of the first incorrect line.
Line 1
7(6) ÷ 5 + 42
Line 2
7(6) ÷ 5 + 16
Line 3
42 ÷ 5 + 16
Line 4
42 ÷ 21
Line 5
2
Answers
Answer:
1
Step-by-step explanation:
i say line 1 cuz she jus switched the number from 42 to 16
so i say line 1.
hope this helps :p
Harry places a ladder against his house to fix the roof, leaving 5 feet between the edge of the house and the ladder. The roof is 18 feet off the ground. Using the Triangle Inequality Theorem, determine the range of heights his ladder should have.
Answers
Using the Triangle Inequality Theorem, the range of heights his ladder should have would be greater than or = 23 feet.
What is Triangle Inequality Theorem?The Triangle Inequality Theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
That is c >/= a + b
a = 5 feet
b = 18 feet
C >/ = 5+18 = 23 feet
Therefore, the range of heights his ladder should have would be greater than or = 23 feet.
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Researchers at a medical school conducted a study to test the effectiveness of a new drug for lowering cholesterol. The 52 subjects who volunteered for the study were each given a randomly generated number. Subjects with an odd number were given the new drug, while those with an even number were given a placebo. Cholesterol levels before and after the treatment were measured for each subject, and the differences were computed.
This study is an example of ______________ study. The difference in cholesterol level is _____________ the variable. The treatment with drug or placebo is the ____________ variable.
Answers
Answer:
1. An Experimental
2. Dependent
3. Independent
Step-by-step explanation:
Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol
The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.
The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.
AP TEST QUESTION 1
PLEASE HELP
ILL GIVE BRAINLIST ANSWER
IMAGE ABOVE
Answers
On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .
What is graphs?Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph
by graphs of the function f (x) and g( x).
\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)
from the graphs n f (x) and g( x) are 1 and 5 .
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Find the equation of the line L which is perpendicular to the line 3x - 2y + 6 = 0 and passes through the point (3, -5)
Answers
Answer:
\(\displaystyle y = -\frac{2}{3}\, x - 3\).
Step-by-step explanation:
Rewrite the equation \(3\, x - 2\, y + 6 = 0\) in the slope-intercept form \(y = m_{1} \, x + b\) to find the slope of this given line:
\(\displaystyle y = \frac{3}{2}\, x + 3\).
Thus, the slope of this given line is \(m_{1} = (3/2)\).
Let \(m_{1}\) and \(m_{2}\) denote the slope of the given line and the slope of line \(L\), respectively. Two lines in a plane are perpendicular to one another if and only if the product of their slopes is \((-1)\). Therefore, for these two lines to be perpendicular to one another, \(m_{1} \, m_{2} = (-1)\).
Since \(m_{1} = (3/2)\) according to the equation of the given line, the slope of line \(L\) would be:
\(\begin{aligned} m_{2} &= \frac{(-1)}{m_{1}} \\ &= \frac{(-1)}{(3/2)} \\ &= \frac{(-2)}{3}\end{aligned}\).
If a line in a plane has slope \(m\) and goes through the point \((x_{0},\, y_{0})\), the slope-point equation of that line would be \((y - y_{0}) = m\, (x - x_{0})\).
Since the line \(L\) goes through \((3,\, -5)\), the equation of this line in slope-point form would be:
\(\displaystyle y - (-5) = \frac{(-2)}{3}\, (x - 3)\).
Rearrange to find the equation of line \(L\) in slope-intercept form:
\(\displaystyle y = -\frac{2}{3}\, x - 3\).
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
\(3x-2y+6=0\implies 3x-2y=-6\implies -2y=-3x-6 \implies y=\cfrac{-3x-6}{-2} \\\\\\ y=\cfrac{-3x}{-2}-\cfrac{6}{-2}\implies y=\stackrel{\stackrel{\stackrel{m}{\downarrow }}{}}{\cfrac{3}{2}} x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)
therefore then
\(\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}\)
so we're really looking for the equation of a line whose slope is -2/3 and passes through (3 , -5)
\((\stackrel{x_1}{3}~,~\stackrel{y_1}{-5})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y+5=-\cfrac{2}{3}x+2\implies y=-\cfrac{2}{3}x-3\)
Points A and B are on opposite sides of a lake. Another point, C. is 94.4 meters from Angle A. The measure of Angle A is 72° and the measure of Angle C is 30°. Find the distance between A and B.
Answers
To find the distance between points A and B, we can use trigonometry and the given information.
Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.
Using trigonometry, we can use the tangent function to find the value of "d".
tan(72°) = d / 94.4
To solve for "d", we can rearrange the equation:
d = tan(72°) * 94.4
Using a calculator, we can evaluate the expression:
d ≈ 4.345 * 94.4
d ≈ 408.932
Therefore, the distance between points A and B is approximately 408.932 meters.
A rectangle is 1/2 feet long and 3/4 feet wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form
Answers
Answer: 3/8
Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.
Numerators first- 1x3Denominators second 2x4Consider the following graph of two functions.(8-1-2)Step 3 of 4: Find (8.5(-2)Enable Zoom/Pan866) = -3010-35SG) = x + 3
Answers
The question requires that we evaluate the value of:
\((g\cdot f)(-2)\)Recall that:
\(\left(g\cdot \:f\right)\left(x\right)=g\left(x\right)\cdot \:f\left(x\right)\)Therefore, we have that:
\(\left(g\cdot\:f\right)\left(-2\right)=g\left(-2\right)\cdot\:f\left(-2\right)\)We can get the values of g(-2) and f(-2) from the graph as shown below:
Therefore, we have:
\(\begin{gathered} g(-2)=5 \\ f(-2)=1 \end{gathered}\)Hence, we can calculate the composite function to be:
\(\begin{gathered} (g\cdot f)(-2)=5\times1 \\ (g\cdot f)(-2)=5 \end{gathered}\)
please help me, i will give points
Answers
Part A
(20)(35)+(15)(15)-125
Part B
Multiply the sale price of each item by the number of items, and subtract the cost.
Part C
\((20)(35)+(15)(15)-125 \\ \\ =700+225-125 \\ \\ =700+100 \\ \\ =800\)
A) The profit he made from the sales is expressed as; 20(35) + 15(15) - 125
B) The way I know the expression in A above is correct is because the formula for profit is; Profit = Selling Price - Cost Price
C) Profit = $350
How to solve algebra word problems?
We are told that;
Selling price of each keyboard = $35
Selling price of each charger = $15
A) Now, we are told that he bought 20 keyboards and 15 chargers for a total of $125. Thus;
The profit he made from the sales is;
20(35) + 15(15) - 125
B) The way I know the expression in A above is correct is because the formula for profit is;
Profit = Selling Price - Cost Price
C) The profit made is;
20(35) + 15(15) - 125 = 700 - 225 - 125 = $350
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What’s the answer to 2x+3x+9 < 5x-7 with step by step explanation
Answers
Answer:
no solution.
Step-by-step explanation:
2x + 3x + 9 < 5x - 7
5x + 9 < 5x - 7
5x + 9 - 9 < 5x - 7 - 9
5x < 5x - 16
5x - 5x < 5x - 16 - 5x
0 < - 16 - ∅ (no solution).
Trina has a credit card that uses the adjusted balance method. For the first 10
days of one of her 30-day billing cycles, her balance was $780. She then
made a purchase for $170, so her balance jumped to $950, and it remained
that amount for the next 10 days. Trina then made a payment of $210, so her
balance for the last 10 days of the billing cycle was $740. If her credit card's
APR is 17%, which of these expressions could be used to calculate the
amount Trina was charged in interest for the billing cycle?
OA. (30)($780)
365
B.
O C.
D.
0.17
365
0.17
365
0.17
365
30
30
(10 $780+10 $950 +10 $210)
30
10
$780+10$950+10 $740
30
•30) ($570)
Answers
The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is (APR / 365) x 30 days x adjusted balance.
What is the adjusted balance method?The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.
The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.
Credit card interest method = adjusted balance method
Beginning balance = $780
Purchase = $170
Payment = $210
Adjusted balance, AB = $740 ($780 + $170 - $210)
APR = 17% = 0.17 (17/100)
The interest charged = (APR / 365) x 30 days x adjusted balance
= $10.34 [(0.17/365) x 30 x $740]
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i need help!!!! does anyone know this..!!???
Answers
The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.
How to determine the period of the frequency factor b given above?The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.
The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.
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Only two more questions
Answers
Answer:
60
Step-by-step explanation:
if it has a square in the center of the angle it means it is 90 degrees
so a straight line adds up to 180b
90 +30+x=180
x=60
solve -4 + x = 6 A. -24 B. -10 C. -2 D. 10
Answers
Answer:
D. 10
Step-by-step explanation:
-4+x=6
Add 4 to both sides
x=10
Answer:
x = 10
Step-by-step explanation:
-4 + x = 6
=> x = 6 + 4
=> x = 10
A store manager designs a new accounting system that will be cost effective if the mean monthly charge account balance is more than $50. A sample of 100 accounts is randomly selected. The sample mean balance is $56 and the sample standard deviation is $25.a.Find the t-statistic for a hypothesis test that is designed to answer the question.
Answers
Answer:
The t-statistic for a hypothesis test that is designed to answer the question is 2.4.
Step-by-step explanation:
Our test statistic is:
\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation of the saple and n is the size of the sample.
A store manager designs a new accounting system that will be cost effective if the mean monthly charge account balance is more than $50.
This means that \(\mu = 50\)
A sample of 100 accounts is randomly selected. The sample mean balance is $56 and the sample standard deviation is $25.
This means that \(X = 56, s = 25, n = 100\). So
\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}\)
\(t = \frac{56 - 50}{\frac{25}{\sqrt{10}}\)
\(t = \frac{6}{2.5}\)
\(t = 2.4\)
The t-statistic for a hypothesis test that is designed to answer the question is 2.4.
A bus holds 39 passengers. How many buses will 420 people need
Answers
Answer:
11 buses
Step-by-step explanation:
Solve the system of equations.
2x−9y=14
x=−6y+7
Answers
Answer:{x,y}={7,0}
i hope this is right :)
Step-by-step explanati
Answer:
Step-by-step explanation:
Write and expression using only a whole-number based and a whole-number exponent to model 9•9•9•9•9
Answers
\(9 \times 9 \times 9 \times 9 \times 9 \\ = {9}^{5} \)
how do I write 4.18 as a mixed number
Answers
Answer:
4 18/100
Step-by-step explanation
for each parallel lines. you are given the measure of one angle
Answers
Answer:
The question is not complete
Find the domain and range please!
Answers
Answer:
domain: -2 < x < 4
range: -∞ < y < 9
Step-by-step explanation:
domain: because the domain is all of the x-values, just look for the furthest one to the left, which is -2, and then look for the one that is furthest to the right, it being 4.
range: because the quadratic function has the two arrows continuing downwards, toward the negative portion of the graph, it would be -∞. Then look for the maximum of the graph, which would be considered the most highest part of the graph, which is seen on the graph as 9.
what is the meaning of the following data? 101, 143, 132, 155, 166
Answers
Answer:
it depends on what you're doing
what's the name of the topic
Q1 ? Help Robert is 7 ½ years old. How many months old is he?
Answers
Answer:
Step-by-step explanation:
If Robert is 7 1/2 months old you need to multiply 7 1/2 by 12 because there are 12 months in a year.
7x12=84
1/2x12=6
6+84=90
Find the value of X in the diagram. (See below)
1. 25
2. 10
3. 180
4. 50
Answers
Answer:
17
Step-by-step explanation:
STUDY HARD GUYS I NEED HW HELP
Please help, thanks!
Answers
The change in function values is f(40) - f(10) = 49 - 55 = -6.
The change in x-values is 40 - 10 = 30.
Therefore, the average rate of change is -6/30, which simplifies to -1/5.
The average rate of change of the function over the interval 10 < x ≤ 40 is -1/5.
plz help I'll give u 15 points
Answers
I think the answer should be D
Find the values of x and y in the equation below.
Answers
Answer:
The answer is a^6 b^18
Step-by-step explanation:
If p = 7, q = 2, r = 4; find the value of q (5p - r).
Answers
Answer: 62
Step-by-step explanation:
Given
p = 7, q = 2, r = 4
Solve
q ( 5p - r )
Substitute
(2) (5(7) - (4))
Simplify
(2) (35 - 4)
(2) (31)
62
Hope this helps!! :)
Please let me know if you have any questions