Answers
Answer:
Step-by-step explanation:
Exponential function representing final amount with compound interest compounded continuously,
[tex]A=Pe^{rt}[/tex]
Here, A = Final amount
P = principal amount
r = Rate of interest
t = Duration of investment
For P = $9600
r = 6%
A = 2 × 9600 = $19200
By substituting these values in the formula,
[tex]19200=9600(e)^{0.06\times t}[/tex]
[tex]2=e^{0.06t}[/tex]
[tex]ln(2)=ln(e^{0.06t})[/tex]
ln(2) = 0.06t
t = [tex]\frac{0.693147}{0.06}[/tex]
t = 11.55245
t ≈ 11.5525 years
Any amount will get doubled (with the same rate of interest and duration of investment) in the same time.
Therefore, $960000 will get doubled in 11.5525 years.
Related Questions
A grocer wants to mix two kinds of coffee. One kind sells for $0.85 per pound, and the other sells for $2.70
per pound. He wants to mix a total of 21 pounds and sell it for $0.95 per pound. How many pounds of
each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)
Answers
Answer:
x = $0.85 per pound = 19.85 pounds
y = $2.70 per pound = 1.14 pounds
Step-by-step explanation:
Let
x = $0.85 per pound
y = $2.70 per pound
x + y = 21 (1)
0.85x + 2.70y = 19.95 (2)
From (1)
x = 21 - y
Substitute x = 21 - y into (2)
0.85x + 2.70y = 19.95 (2)
0.85(21 - y) + 2.70y = 19.95
17.85 - 0.85y + 2.70y = 19.95
- 0.85y + 2.70y = 19.95 - 17.85
1.85y = 2.1
y = 2.1 / 1.85
y = 1.14
Substitute y = 1.14 into (2)
0.85x + 2.70y = 19.95
0.85x + 2.70(1.14) = 19.95
0.85x + 3.078 = 19.95
0.85x = 19.95 - 3.078
0.85x = 16.872
x = 16.872 / 0.85
x = 19.85
x = $0.85 per pound = 19.85 pounds
y = $2.70 per pound = 1.14 pounds
Question 10 of 10
Which is not a characteristic of an exponential parent function?
A. It passes through (0,1).
B. It goes through the origin.
C. The domain is all real numbers.
D. The range is positive real numbers (y > 0).
SUBMIT
Answers
It does not pass through origin.
Answer and explainaction please. End of course test is next week and I want to make sure I can work out answers on my own! :)
Answers
Answer: This is what I get.
Step-by-step explanation:
What is the probability of choosing a king of hearts or a queen of spades from a deck of cards? Type your answer as a fraction
Answers
Answer:
[tex]Pr = \frac{1}{26}[/tex]
Step-by-step explanation:
Given
In a deck of card, we have:
[tex]Cards = 52[/tex]
[tex]King[Heart] = 1[/tex]
[tex]Queen[Spade] = 1[/tex]
Required
The probability of obtaining a king of heart or a queen of spade.
The probability of king of heart is:
[tex]P(King[Heart]) = \frac{n(King[Heart])}{Cards}[/tex]
[tex]P(King[Heart]) = \frac{1}{52}[/tex]
The probability of queen of spade is:
[tex]P(Queen[Spade]) = \frac{n(Queen[Spade])}{Cards}[/tex]
[tex]P(Queen[Spade]) = \frac{1}{52}[/tex]
The required probability of obtaining a king of heart or a queen of spade. is:
[tex]Pr = P(King[Heart]) + P(Queen[Spade])[/tex]
[tex]Pr = \frac{1}{52}+ \frac{1}{52}[/tex]
Take LCM
[tex]Pr = \frac{1+1}{52}[/tex]
[tex]Pr = \frac{2}{52}[/tex]
Simplify
[tex]Pr = \frac{1}{26}[/tex]
What is c? This is pythgreomthryrom a=8 b=6 c=?
Answers
Answer:
4
Step-by-step explanation:
What is the surface area of the right cone below?
Answers
Answer:
176π [tex]units^{2}[/tex]
Step-by-step explanation:
SA = B + LA where B is the area of the base (circle) and LA is the lateral area
LA = radius of the circle times the slant height
= 8π(14) = 112π
B = [tex]8^{2} \pi[/tex] = 64π
SA = 112π + 64π = 176π
The surface area of the right cone is 176π square units.
How to calculate the surface area of a composite figure?
Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, cone etc.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
Thus, we have:
[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]
That ∑ sign shows "sum"
We are given that;
The surface area of a right cone is given by the formula:
Surface area=πr(r+l)
where r is the radius of the base and l is the slant height of the cone12.
In this case, r=8 and l=14, so we can plug these values into the formula and simplify:
Surface area=π×8(8+14)
Surface area=π×8×22
Surface area=176π
Therefore, the surface area will be 176π square units.
Learn more about area of a composite figure here:
https://brainly.com/question/10254615
#SPJ7
what is -5/3 as an equivalent fraction
Answers
Answer:
-20/12 as an example there are many others
1. -1 2/3
2. -10/6
3. - 15/9
To find an equivalent fraction you need to multiply the denominator and the numerator by the same number. For example:
1/3 — 1*3/3*3 — which equals 3/9
Hope this helps!!
How many odd numbers are between 10 and 50?
Answers
Answer:
There are 20 odd numbers between 10 and 50
Step-by-step explanation:
Here are all the odd numbers! Hope this helps!
11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49
It's Pythagorean theorem
Answers
Answer:
6root3
Step-by-step explanation:
Answer:
6 radical 3
Step-by-step explanation:
En una caja hay 10 monedas de $50, 20 monedas de $20 y $20 de 10. La probabilidad de sacar una moneda de $10 es:
A 20/20
B 1/2
C 4/10
D 2/5
DOY CORONITA SI RESPONDEN BIEN PLIS
Answers
Answer:
tha answer is c
Step-by-step explanation:
Melanie invested $9,800 in an account paying an interest rate of 4 1 2 4 2 1 % compounded quarterly. Amelia invested $9,800 in an account paying an interest rate of 4 3 4 4 4 3 % compounded continuously. After 20 years, how much more money would Amelia have in her account than Melanie, to the nearest dollar?
Answers
After 20 years, the amount of Money Amelia would have more than Melanie would be $181,551.37.
What is the future value of Melanie's account?The formula for calculating future value:
FV = P (1 + r) nm
FV = Future value P = Present value R = interest rate = 4 1/2 ÷ 4 = 1.125%m = number of compounding = 4N = number of years9800(1 + 0.0125)^80 = 23,983.29
What is the future value of the amount in Amelia's account?the formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate9800 e^0.0475 x 20 = 205,534.66
Difference = 205,534.66 - 23,983.29 = $181,551.37
To learn more about future value, please check: https://brainly.com/question/18760477
A new pair of shoes is advertised for $110. The sales tax is 7.5%. What is the total cost of the shoes?
Answers
Answer:
118.25
Step-by-step explanation
If the tax is in percent, divide the tax rate by 100. You do this by moving the decimal point two spaces to the left. In this, there's 7.5/100 = 0.0
Find the tax value by multiplying tax rate by the item value:
tax = 110 × 0.075
tax = 8.25
Plsssss help me with this angle circle problem what is x
Answers
Answer:
x = 3
Step-by-step explanation:
Once again we want to use the relationship stated earlier
Where A * B = C * D
Once again imagine that the segments in the given problem have letters
A = x
B = 12
C = x + 1
D = 9
Now we create an equation using the relationship
12 * x = 9(x+1)
now we solve using basic algebra
step 1 distribute the 9 to the x and the 1
9 * x = 9x
9 * 1 = 9
now we have 12x = 9x + 9
step 2 subtract 9x from each side
12x - 9x = 3x
9x - 9x cancels out
now we have 3x = 9
step 3 divide each side by 3
3x/3=x
9/3=3
we're left with x = 3
Answer:
x = 3 / C. 3
Step-by-step explanation:
Hope this helps
Find the area
10 yd
12 yd
13 yd
Answers
Answer:
138
Step-by-step explanation:
a+b/2xh
Amit Almor, a psychology researcher at the University of South Carolina, conducted a series of experiments on conversation and attention level. He found that subjects were four times more distracted while preparing to speak or speaking than when they were listening. This research has many implications, including those for the issue of using cell phones while driving.
You decide to explore this issue by having three different groups try tracking a fast-moving target on a computer screen. The first group is preparing to speak, the second group is speaking, and the third group is listening to a conversation.
The sample mean and sum of squares of the scores for each of the three groups are presented in the following table.
Group Sample Mean Sum of Squares
Preparing to speak 98.3 7,2810.0900
Speaking 101.5 6,6156.8100
Listening 103.2 70,277.7600
After collecting the data, you analyze the data using an ANOVA. The results of your analysis are presented in the following ANOVA table.
Source of Variation SS df MS F
Between Treatments 3,095.00 2 1,547.50 5.52
Within Treatments 209,244.66 747 280.11
Total 212,339.66 749
These findings are significant at α = 0.05, which tells you that the difference is very unlikely to have occurred just by chance, but it does not tell you the size of the effect. A simple measure of the effect size is given by: ________
Required:
What is the formula for this measure of the effect size?
Answers
Answer:
η²
SSbetween / SStotal
η² = 0.0145757
Step-by-step explanation:
Effect size, η² = SSbetween / SStotal
SSbetween is the sum of square between the groups in the experiment. It is sometimes denoted as SSb.
The sum of square Total, SStotal measures the entire variability in these dataset.
SSbetween = 3,095.00 ; SStotal = 212,339.66
η² = SSbetween / SStotal
Effect size η²= 3,095.00 / 212,339.66
Effect size = 0.0145757
A solid figure is composed of a cube and a pyramid as shown. What is the volume
Answers
Answer:
288 in^3
Step-by-step explanation:
1) find the volume of the cube
V = side^3 = 6^3 = 216 in^3
2) find the base surface of the pyramid:
base surface = side^2 = 6^2 = 36 in^2
3) find the height of the pyramid:
height of the solid - height of the cube = 12 - 6 = 6 in
4) find the volume of the pyramid:
V = (base area x height) / 3 = (36 x 6)/3 = 72 in^3
5) add up the two volumes
V = 216 + 72 = 288 in^3
Jessica's bedroom is 17 feet long and 9 1/2 feet wide. What is the area of the bedroom?
Answers
What is the area of the shape below?
Answers
Answer:
31 1/2 yd 2
Step-by-step explanation:
4*6=24
3*5= 15 15/2 = 7 1/2
24+7 1/2 = 31 1/2
Which of the following points satisfies the linear inequality below? Select all correct answers.
5x + 2y 26
Select all that apply:
(0,5)
(3,1)
(3,-4)
(-4,1)
Answers
Answer:
All points satisfy the inequality
Step-by-step explanation:
Given
[tex]5x + 2y \le 26[/tex]
Required
Select all points that satisfy the above inequality
[tex](a)\ (0,5)[/tex]
This implies that
[tex]x = 0; y = 5[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 0 + 2 * 5 \le 26[/tex]
[tex]0 + 10 \le 26[/tex]
[tex]10 \le 26[/tex]
This satisfy the inequality
[tex](b)\ (3,1)[/tex]
This implies that
[tex]x = 3;\ y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * 1 \le 26[/tex]
[tex]15 + 2 \le 26[/tex]
[tex]17 \le 26[/tex]
This satisfy the inequality
[tex](c)\ (3,-4)[/tex]
This implies that:
[tex]x = 3; y-4[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * -4 \le 26[/tex]
[tex]15 -8 \le 26[/tex]
[tex]7 \le 26[/tex]
This satisfy the inequality
[tex](d)\ (-4,1)[/tex]
This implies that:
[tex]x = -4; y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * -4 + 2 *1 \le 26[/tex]
[tex]-20 + 2 \le 26[/tex]
[tex]-18 \le 26[/tex]
This satisfy the inequality
Natasha goes bowling she pays $5.75 for an admission ticket and $9.25 for each round of bowling she plays the total amount of Tasha pays for admission and the number of rounds who plays is $33.50 which equation can be used to determine the number of rounds X that Natasha bowled
a.) 5.75 x + 9.25=33.50
b.) 9.25 X - 5.75= 33.50
c.) 5.75 + 9.25 X= 33.50
d.) 5.75 x - 9.25=33.50.
Answers
PLS HELP WITH NUMBER 6
Answers
Answer: The answer to this question is A
The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Age 38 41 45 48 51 53 57 61 65 Pressure 116 120 123 131 142 145 148 150 152 What is the best predicted value for blood pressure of an individual who is 64 years old
Answers
Answer:
156
Step-by-step explanation:
Given the data:
Age (X) :
38
41
45
48
51
53
57
61
65
Pressure(Y) :
116
120
123
131
142
145
148
150
152
From the data, we could obtain a regression equation to mod the data Given using a linear regression calculator :
The regression equation obtained is :
y = 1.48769X + 60.46103
Using the model, the predicted blood pressure for a person aged 64 will be :
y = 1.48769(64) + 60.46103
y = 95.21216 + 60.46103
y = 155.67319
y = 156 (nearest whole number)
who was the first Democratic elected president of Nigeria
Answers
Answer:
Alhaji Shehu Shagari
Step-by-step explanation:
Alhaji Shehu Shagari the first Democratic elected president of Nigeria, He was elected in October 1979. He contested under the The National Party of Nigeria. Prior to that time, Nigeria had been under military rule for more than 13 years.
In December 1983, there was a military coup and he was overthrown.
The volume of a cuboid is 176cm
The length is 11 cm and the width is 20mm
Work out the height of the cuboid in cm.
Answers
Answer:
.08cm or 0.08cm
Step-by-step explanation:
First of all, we can see that 20mm is in millimeters, not centimeters.
If we convert the ones in centimeters to millimeters, it will result in decimals, which I want to avoid, but you could also do it that way.
There are 10 mm in 1 cm, so I multiply all of the values in cm by 10.
So now, we have that the volume is 1760mm, the length is 110mm, and the width is 20mm.
The formula for the volume of a cuboid is: [tex]w*l*h = volume[/tex]
We have the width, length, and volume, so let's plug it in.
[tex]20*110*h=1760[/tex]
To solve for h:
1. Multiply 20 and 100
[tex]2200*h=1760[/tex]
2. Divide both sides by 2200
[tex]h = 1760/2200[/tex]
3. Divide right side
h = 0.8
Keep in mind that this is in millimeters. In centimeters, it would be .08
A company produces remote-controlled helicopters. The company’s profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company’s profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week.
The function that models the scenario, where h is the number of helicopters produced per week, is
f(h) = –2(h – 4)2 + 22.
When 6 helicopters are produced weekly, the company’s profit is (blank)
thousand dollars.
Answers
Explanation:
I took this in 9th grade so I know how to do this kind of stuff
Answer:
the answer is B
Step-by-step explanation:
4^?=1024? i know the answer is 5 but is there an easier way to find that out instead of guessing?
Answers
Answer:
here you go............
Step-by-step explanation:
I hope it helped
what is the measure of angle 2
Answers
Answer:
45
Step-by-step explanation:
180 - 135 = 45
The measure of angle 2 is 45.
Find the exact value for the expression under the given conditions.
cos(α+β), sin α= -8/17 for α in Quadrant lll and cosβ= -8/15 for β in Quadrant ll.
Answers
Answer:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
Step-by-step explanation:
We are given the conditions:
[tex]\displaystyle \sin(\alpha)=-\frac{8}{17}\text{ and } \cos(\beta)=-\frac{8}{15}[/tex]
Where α is in QIII and β is in QII and we want to find the exact value of cos(α + β).
The first ratio gives us the opposite side and the hypotenuse with respect to α . Then the adjacent side is (we can ignore negatives):
[tex]a=\sqrt{(17)^2-(8)^2}=15[/tex]
The second ratio gives us the adjacent side and the hypotenuse with respect to β. Then the opposite side is:
[tex]o=\sqrt{(15)^2-(8)^2}=\sqrt{161}[/tex]
Therefore, for α, ignoring negatives, the adjacent side is 15, the opposite side is 8, and the hypotenuse is 17.
And for β, ignoring negatives, the adjacent side is 8, the opposite side is √(161), and the hypotenuse is 15.
We can rewrite our expression as:
[tex]\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]
Since α is in QIII, sin(α), cos(α) < 0, and tan(α) > 0.
And since β is in QII, cos(β), tan(β) < 0, and sin(β) > 0.
Using this information, substitute:
[tex]\displaystyle \cos(\alpha+\beta)=\left(-\frac{15}{17}\right)\left(-\frac{8}{15}\right)-\left(-\frac{8}{17}\right)\left(\frac{\sqrt{161}}{15}\right)[/tex]
Therefore:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
How many cities could have an annual rainfall of 28.5 in 32.5 in
Answers
Answer:
A) 6
Step-by-step explanation:
Answer:
2. A) 6
Step-by-step explanation:
#CarryOnLearning
The perimeter of a triangle is 29. One side of a triangle is 5 less than twice the side of the shortest length. The third side is 6 more than the shortest side. What are the lengths of the triangle?
Answers
Answer:
7, 9, 13Step-by-step explanation:
Let the sides of the triangle be a, b and c.
We have:
P = a + b + c = 29a = 2b - 5c = b + 6Substitute values and solve for b:
2b - 5 + b + b + 6 = 294b + 1 = 294b = 28b = 7Find a and c:
a = 2*7 - 5 = 14 - 5 = 9c = 7 + 6 = 13The sides are: 7, 9, 13