The rate of growth of the amount invested with time in Plan 1 is slightly higher than the amount invested in Plan 2.
The option most beneficial to Kevin by comparison is Plan 1Reasons:
The number of years for the investment = 30 years
The amount he plans to save = $250,000
The investment plan options are;
Plan 1: Compounded monthly investment with APR, r = 3.5%
The formula for monthly contributions is presented as follows;
[tex]\displaystyle FV = \mathbf{\frac{PMT \cdot \left( 1 + \frac{r}{n}\right)^{n\cdot t} - 1}{\frac{r}{n} }}[/tex]
Which gives;
[tex]\displaystyle 250,000 = \mathbf{\frac{PMT \cdot \left( 1 + \frac{0.033}{12}\right)^{360} - 1}{\frac{0.033}{12} }}[/tex]
Solving gives;
The amount he needs to deposit each month, PMT ≈ $256.18The total deposit = 360 × $256.18 = $92,224.2
Total interest accrued = $250,000 - $92,224.2 ≈ $157,775.78Plan 2: Compounded quarterly, with APR, r = 3.3
Which gives;
[tex]\displaystyle 250,000 = \mathbf{\frac{PQT \cdot \left( 1 + \frac{0.035}{4}\right)^{120} - 1}{\frac{0.033}{4} }}[/tex]
The amount he needs to deposit each quarter ≈ $769.34The total deposit = $769.34 × 120 = $92,321.3336
Total interest accrued = $250,000 - $92,321.3336 ≈ $157,678.67
The total interest accrued by investing in plan 1 which is approximately
$157,775.78 is larger than the interest accrued on Plan 2 which is
approximately $157,678.67
The option most beneficial to Kevin is Plan 1, due to the higher total interest accruedLearn more here:
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10:8 as a equivalent ratio
What is f(g(-1)) for f(x) = 2x - 3 and g(x) = x2 + 11?
A) 12
B) 21
0.32
D) 36
E) 45
Answer:
I think it is c I hop I'm right
Simplify c+c+7+5c-3-6c.
Help
Answer:
c+4
Step-by-step explanation:
Simplification of the expression c+c+7+5c-3-6c is c+4.
What is an expression?In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.
Given, the expression
c+c+7+5c-3-6c
Simplifying,
c+c+7+5c-3-6c
= 7c-6c + 7-3
= c+4
Therefore, after the simplification expression is c+4.
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If a = 4 and c = 2 then what is 5ac
Answer:
40
Step-by-step explanation:
by replacing the value and multiplying the numbers and the answer will come 40
Answer:
5ac = 40
Step-by-step explanation: When the letters and the numbers are toghether without a symbol they multiply each other.
So 5 x 4 x 2 = 40
mrs.graves gave her class 12 minutes to read. carrie read 5 and 1/2 pages in that time .at what rate , in pages per hour ,did carrie read?
A. 1 1/0
B. 22
C. 27 1/2
D. 66
Answer:c
Step-by-step explanation:
Graph one function of:y=-3sinx
Step-by-step explanation:
Here is our graph of the function [tex]y=-3\sin x[/tex]
Solve 6x+23=1y for y.
Answer:
y = 6x + 23
Step-by-step explanation:
Flip 6x + 23 = 1y into 1y = 6x + 23
Also, 1y is the same as just saying y.
I feel like this question isn't in depth or is the full question. If you made a typo or you want to be more clear for what you need please comment! :)
2. What is the interpretation of the constant of proportionality?
0.001 kilometers per meter
0.001 meter per kilometer
Pls
Answer: It would be the first one, 0.001 kilometers per meter.
Step-by-step explanation: is 1,000 meters is equal to 1 kilometer, you would have to move the decimal on each until one is at one and the other is at 0.001. This would leave you with the first answer. Hope this helps!
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4.
A small box holds 80 stuffed toys. A large box
holds 155% as many stuffed toys as than a
small box. How many stuffed toys does the large
box hold?
Answer:
The large box would hold 124 this is because 155 percent of 80 is 124
Find the angle between u and v, rounded to the nearest tenth degree.
u = (4, 0, 2), v = (6, −3, 0)
Answer:
The angle between vectors u and v is [tex]\theta\approx36.9^\circ[/tex]
Step-by-step explanation:
Recall:
Angle between vectors u and v --> [tex]\theta=cos^{-1}(\frac{u\bullet v}{||u||*||v||})[/tex]Dot product (three-dimensional) --> [tex]u\bullet v=u_1v_1+u_2v_2+u_3v_3[/tex]Magnitude (three-dimensional, vector u) --> [tex]||u||=\sqrt{u_1^2+u_2^2+u_3^2}[/tex]Magnitude (three-dimensional, vector v) --> [tex]||v||=\sqrt{v_1^2+v_2^2+v_3^2}[/tex]Calculation:
Dot product --> [tex]u\bullet v=(4)(6)+(0)(-3)+(2)(0)=24[/tex]Magnitude (u) --> [tex]||u||=\sqrt{4^2+0^2+2^2}=\sqrt{16+0+4}=\sqrt{20}=2\sqrt{5}[/tex]Magnitude (v) --> [tex]||v||=\sqrt{6^2+(-3)^2+0^2}=\sqrt{36+9+0}=\sqrt{45}=3\sqrt{5}[/tex]Plug dot product and magnitudes into formula:
[tex]\theta=cos^{-1}(\frac{u\bullet v}{||u||*||v||})=cos^{-1}(\frac{24}{2\sqrt{5}*3\sqrt{5}})=cos^{-1}(\frac{24}{6*5})=cos^{-1}(\frac{24}{30})\approx36.9^{\circ}[/tex]
Conclusion:
The angle between vectors u and v is [tex]\theta\approx36.9^\circ[/tex]
Not 9 the one on top
Can someone help me do this problem and explain it to me step by step? If so I’ll mark you brainliest
Answer:
-21
28
Step-by-step explanation:
1) if r = -4
Substitute r = -4 in 3r - 9
= 3 * (-4) - 9
= -12 - 9
= -21
2) ( 4 / 7 ) * x = 16
4 * x = 16 * 7
x = 4 * 7
x = 28
are the two sides of congress the Senate and the Supreme Court?
Answer:
Step-by-step explanation:
Legislative—Makes laws (Congress, comprised of the House of Representatives and Senate) Executive—Carries out laws (president, vice president, Cabinet, most federal agencies) Judicial—Evaluates laws (Supreme Court and other courts)
Evaluate 4-7[(3-8)-(-5-8)]
Step-by-step explanation:
The Answer is 52
Hope it's Helpful
1% of the parts produced by a factory are defective. Suppose the test for defective parts has a 99.5% accuracy and a 0.6% false positive rate. SUppose you pick a part and receive a positive test result. WHat is the probability that the part is indeed defective
Using conditional probability, it is found that there is a 0.6262 = 62.62% probability that the part is indeed defective.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Positive test result.
Event B: Defective.
For the probability of a positive test result, we consider two scenarios.
99.5% of 1%(defective).0.6% of 100 - 1 = 99%(false positive).Hence:
[tex]P(A) = 0.995(0.01) + 0.006(0.99) = 0.01589[/tex]
The probability of a positive test result and being defective is:
[tex]P(A \cap B) = 0.995(0.01)[/tex]
The conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.995(0.01)}{0.01589} = 0.6262[/tex]
0.6262 = 62.62% probability that the part is indeed defective.
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State the theorem or postulate that proves a||b . (Picture included )
7. Theorem : When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.
8. Postulate : When a transversal cuts two lines, such that pairs of alternate interior angles are equal, the lines have to be parallel.
Good Luck
if 7p-4=8 what is the value of P? Can someone give me example so I can answer my question. Thanks!
Answer:
p=[tex]1\frac{5}{7}[/tex]
Step-by-step explanation:
7p-4=8
7p=8+4
=12
p=12÷7
=[tex]\frac{12}{7}[/tex]
=[tex]1\frac{5}{7}[/tex]
3. Solve x/5 = 15
о x = 20
O x = 75
O x = 10
O x = 3
Answer:
3
Step-by-step explanation:
cross multiple and divide the two variables
Admission to the movies is $10 for adults and $7 for children. Find the
total admission for 4 adults and 8 children.
Answer:
$96
Step-by-step explanation:
4 times 10 is 40. 7 times 8 is 56. 40 + 56 = 96
Kathy is baking 3 apple pies. Each pie requires 2 3/4 pounds apples. Apples cost $2.49 a pound. About how much will Kathy spend on apples?
Answer:
$20.55
Explanation:
1apple pie needs 2/3/4pounds of apple 1pound cost $2.492/3/4 = ?2/3/4 ×2.49 =$6.85 for one pieFor 3 pies , =$6.85×3 = $20.55The total amount spent on apples is $20.5425.
Given that, Kathy is baking 3 apple pies. Each pie requires 2 3/4 pounds of apples. Apples cost $2.49 a pound.
We need to find out how much will Kathy spend on apples.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the amount spent on apples be x.
Now, 2 3/4=11/4
The total number of apples required to make 3 apple pies=3 × 11/4
=33/4 pounds
Apples cost $2.49 a pound.
So, the amount spent on apples=x=33/4 × 2.49
=$20.5425
Therefore, the total amount spent on apples is $20.5425.
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An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. It may be assumed that the weight loss of participants to the weight-reduction program is normally distributed.
a) set up the competing hypotheses to test the advertisement's claim
b) at the 5% significance level, what is the critical value(s)? specify the decision rule
c) what does the consumer activist conclude?
Testing the hypothesis, it is found that:
a)
The null hypothesis is: [tex]H_0: \mu \leq 10[/tex]
The alternative hypothesis is: [tex]H_1: \mu > 10[/tex]
b)
The critical value is: [tex]t_c = 1.74[/tex]
The decision rule is:
If t < 1.74, we do not reject the null hypothesis.If t > 1.74, we reject the null hypothesis.c)
Since t = 1.41 < 1.74, we do not reject the null hypothesis, that is, it cannot be concluded that the mean weight loss is of more than 10 pounds.
Item a:
At the null hypothesis, it is tested if the mean loss is of at most 10 pounds, that is:
[tex]H_0: \mu \leq 10[/tex]
At the alternative hypothesis, it is tested if the mean loss is of more than 10 pounds, that is:
[tex]H_1: \mu > 10[/tex]
Item b:
We are having a right-tailed test, as we are testing if the mean is more than a value, with a significance level of 0.05 and 18 - 1 = 17 df.
Hence, using a calculator for the t-distribution, the critical value is: [tex]t_c = 1.74[/tex].
Hence, the decision rule is:
If t < 1.74, we do not reject the null hypothesis.If t > 1.74, we reject the null hypothesis.Item c:
We have the standard deviation for the sample, hence the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem, we have that:
[tex]\overline{x} = 10.8, \mu = 10, s = 2.4, n = 18[/tex]
Thus, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{10.8 - 10}{\frac{2.4}{\sqrt{18}}}[/tex]
[tex]t = 1.41[/tex]
Since t = 1.41 < 1.74, we do not reject the null hypothesis, that is, it cannot be concluded that the mean weight loss is of more than 10 pounds.
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11y+7+5(y-3) as binomial forms
Answer:
16y − 8 is your answer!
Step-by-step explanation:
Simplify the expression!
Duidueydheueudhrueyeue
a) suppose {u,v,w} spans the vectore space V.
ptove that {u+v,u+w,v+w} also spans V.
b) suppose that the set of vectors {u,v,w} is linearly independent in a vector space v. prove that the set of vectors {u+v+w, u+v, u+w} must be linearly independentRocket,
Answer:
Victini V
Step-by-step explanation:
Best pokemon v is Victini V so yea ez dubs good luck on test.
I don't understand what do and I am on a time crunch please help
Answer:
Step-by-step explanation:
Decrease % = 4.2% = 0.042
Total area = 1500 km²
[tex]y =(1 -0.042)^{t}*1500\\\\y= 1500*(0.958)^{t}[/tex]
I need help ASAP
Mrs. Stevens deposited $4,500 in a college savings account for her grandson that earns an annual simple interest rate of 6.5%. How much interest will be paid in 10 years?
The interest that will be paid in 10 years is = $2,925
The total amount of money deposited as savings (p)
= $4,500,
The annual simple interest rate (r) = 6.5%.
The time to collect the interest expected (t) = 10 years.
There the simple interest generated =
[tex] \frac{p \times t \times r}{100} [/tex]
[tex] \frac{4500 \times 10 \times 6.5}{100} [/tex]
[tex] \frac{292500}{100} [/tex]
Therefore simple interest = $2,925
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(1,4) and (6,-1)
find the point slope asap plsssssss
Answer:
(5,-5)
Step-by-step explanation:
-1-4
------ = (5,-5)
(6-1)
Answer:
Slope intercept form: y = -x + 5
Point slope form: y - 4 = -1 (x - 1)
Step-by-step explanation:
First we need to find slope by using this formula⤵⤵⤵
[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]
(Sorry if it's a bit small btw)
-1 - 4 = -5
6 - 1 = 5
Simplify -5/5 by dividing, and your slope is -1.
Now we plug in one of the points and the slope into the point slope formula⤵⤵⤵
[tex]y - y _{1} = m(x - x _{1})[/tex]
We'll use point (1,4) for this:
y - 4 = -1 (x - 1)
To solve this, start by distributing the -1 among everything inside the parenthesis to get
y - 4 = -x + 1. Next, add 4 on both sides to get
y = - x + 5.
Hope this helps you :)
Find the distance between the following points: (0,0,0) and (-2,6,3)
1. √7
2. √41
3. 7
4. 36
PLEASE HELP ASAP
9514 1404 393
Answer:
3. 7
Step-by-step explanation:
The distance formula applies in 3 dimensions as well as 2.
d = √((x2 -x1)² +(y2 -y1)² +(z2 -z1)²)
d = √((-2)² +6² +3²) = √(4 +36 +9) = √49
d = 7
The distance between the two points is 7 units.
Find the coordinates of point p along the directed line segment AB, from A (-2,-4) to B (6,1), so that the ratio of AP to PB is 3 to 2
Answer:
Step-by-step explanation:
x distance from A to B
6 - (-2) = 8
3/5(8) = 24/5 = 4.8 or 2/5(8) = 16/5 = 3.2
-2 + 4.8 = 2.8 6 - 3.2 = 2.8
y distance from A to B
1 - (-4) = 5
3/5(5) = 3 or 2/5(5) = 2
-4 + 3 = -1 1 - 2 = -1
P = (2.8, -1)
The coordinates of point P (rounded to one decimal place) along the directed line segment AB are approximately (2.8, -1).
Given that the line segment has been divide into ratio 3:2 by a point P, we need to find the coordinates of the point P.
To find the coordinates of point P along the directed line segment AB, such that the ratio of AP to PB is 3 to 2, we can use the concept of section formula in coordinate geometry.
Let's assume the coordinates of point P are (x, y). According to the given information, the ratio of AP to PB is 3 to 2. This means that the distance between A and P (AP) is three times the distance between P and B (PB).
The section formula states that if a point P(x, y) divides the line segment joining points A(x₁, y₁) and B(x₂, y₂) in the ratio m:n, then the coordinates of point P can be calculated as:
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
In this case, m = 3 and n = 2.
Coordinates of A: (x₁, y₁) = (-2, -4)
Coordinates of B: (x₂, y₂) = (6, 1)
Ratio m:n = 3:2
Now, let's plug the values into the section formula to find the coordinates of P:
x = (3 · 6 + 2 · (-2)) / (3 + 2)
= (18 - 4) / 5
= 14 / 5
= 2.8
y = (3 · 1 + 2 · (-4)) / (3 + 2)
= (3 - 8) / 5
= -5 / 5
= -1
So, the coordinates of point P is (2.8, -1).
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A recipe calls for 2/3 cup of milk. How much milk should be used to make 1/6 of the recipe?
________________
The answer is 1/9
_________________
