QUESTION 20
Find the rate of interest required to achieve the conditions set forth.
A = $32,000
P = $8,000
t = 20 years
compounded annually
3.5265%
8%
5.6467%
7.1773%
The rate of interest required to achieve the conditions set forth is 7.1773%.
What is the interest rate?The interest rate is the rate at which the investment increases. The formula that can be used to determine interest rate is:
g = (FV / PV)^(1/N) - 1
Where:
FV = future value = $32,000PV = present value = $8000 n = number of years4^(1/20) - 1 = 7.1773%
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Gabe planted 15 sunflower seeds, and 40% of them have sprouted. How many of the sunflower seeds have sprouted?
Answer:
hello
15 x 0.4 = 6
6 sunflower
Step-by-step explanation:
Answer:
6 of them have sprouted
Step-by-step explanation:
(15/100)x40
0.15x40
6
Jessica has 300 cm³ of material. She uses 12.6 cm³ to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 3. How much more material does Jessica need in order to make the second prism? Select from the drop-down menu to correctly complete the statement. Jessica needs an additional Choose... cm³ of material to make the second prism.
Answer:52.8
Step-by-step explanation:
Answer:
The answer is indeed 52.8
Step-by-step explanation:
Here is proof: I got the same answer.
A culture started with 3000 becteria. after 4 hours it grew to 3600 becteria. Predict how many bacteria will be present after 10 hours. Round your answer to the nearest whole number. p=ae^kt
Answer:
You can solve this by setting up an exponential growth equation.
Now we solve for b
Now that we have found b, we can use the equation to predict how many bacteria will be present after 10 hours.
t = 10
Answer = 4732
Step-by-step explanation:
F(x)=4x^2 and g(x)=x+1, find (f x g)(x)
Answer:
option b
Step-by-step explanation:
It is option b
Your answer is 4(x+1)²
Answer:
B
Step-by-step explanation:
Given functions:
[tex]f(x)=4x^2[/tex][tex]g(x)=x+1[/tex][tex](f \circ g)(x) & =f[g(x)][/tex]
This means substitute the x of f(x) with the function g(x).
[tex]\implies f[g(x)]=4(x+1)^2[/tex]
Which of the numbers below is greater than 36.785 Select all that apply
A) 36.78
B) 36.79
C) 41.2
D) 36.789
a shopkeeper bought a pair of shoes at sh 480 he wished to make a profit of 30 percent after selling what was his marked price
Answer:
624
Step-by-step
480+(480(30%))
=624
Answer:
162
30/100 * 480
3/10 * 480
3/1 * 48
3 * 48
162
Can someone help me with this question please?
Answer:
a) 96 = 3.57√h
b) h ≈ 723.11 m
Step-by-step explanation:
a)The equation you want to solve is the model with the given values filled in.
D(h) = 3.57√h . . . . model
96 = 3.57√h . . . . . equation for seeing 96 km to the horizon
__
b)We solve this equation by dividing by the coefficient of the root, then squaring both sides.
96/3.57 = √h
h ≈ 26.891² ≈ 723.11 . . . . meters above sea level
Dustin would need to have an elevation of 723.11 meters above sea level to see 96 km to the horizon.
Noah's Diner offers its clients a choice of regular and diet soda. Last night, the diner served
18 regular sodias and 57 diet sodas. What percentage of the sodas served were regular?
Answer: 24%
Step-by-step explanation:
for these problems you can use this equation: [tex]\frac{x}{n} *100=p[/tex]
where x=given quantity, n=total amount, and p is your answer.
for this problem x=18 (regular sodas)
we add the amount of regular and diet sodas to get n=75 (18+57)
when we plug it in we have [tex]\frac{18}{75} *100[/tex] which gives us our answer, p, 24%
hope this helped ♡
Michelle is fishing from a small boat. A fish swimming at the same depth as the hook at the end of her fishing line is 16 meters away from the hook. If Michelle is 20 meters away from the fish, how far below Michelle is the hook?
Answer:
12 meters
Step-by-step explanation:
You have to use the inverse of the pythagorean theorem to do this so you do square root of (20x20-16x16) which is 12
The length of a rectangle is 3 inches more than it’s width.If the perimeter is 42 inches,find the dimensions of the rectangle.
Answer: Length = 9 in
Width = 12 in
Step-by-step explanation:
Length L = 3 + W
Perimeter P = 42 in
Perimeter = 2L + 2W
plugin values:
42 = 2(3 + W) + 2W
42 = 6 + 2W + 2W
42-6 = 4W
W = 36 / 4
W = 9
solve L by substituting the value of W=9 into the equation:
L = 3 + W
L = 3 + 9
L = 12
therefore, the dimensions of the rectangle:
Length = 9 in
Width = 12 in
Answer:
Answer:
length = 9 in
width = 12 in
Step-by-step explanation:
You have to use the formula for the perimeter of a rectangle
P=2(l+w)
The following refers to a purchase of a machine by a company on January 1, 2021:
Salvage Value: $7,500
Life: 6 years
Desired Rate of Return 4%
Interest Compounded: semi-annually
Maximum amount the company can pay $32,348
What is the semi-annual net cash flow the company must achieve in order for the purchase to be made?
The semi-annual net cash flow that the company must achieve in order for the purchase to be made is $5041.
How to calculate the cash flow?Maximum amount that can be invested = $32348.
Less: Present value of salvage value = $5927
Present value of cash inflow = $32348 - $5927 = $26421.
Net cash flow will be:
= $26421 / PV factor
= $26421/5.242
= $5041
In conclusion, the correct option is $5041.
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Tim will buy a pair of shoes that cost $120.He received a 35% discount coupon. Luckily his friend Mario gets an additional 15% discount being an employee of the store. If Mario buys the shoes for Tim, how much will Mario pay if the tax is 8%? Round your answer to the nearest centavo
Answer: 55.20$
Step-by-step explanation:
1. Add up 35% with the 15% since Mario is paying for it
2. Multiply 120(the cost without any discount/tax) with the new discount percentage
3. Now with the answer from multiplying subtract it from 120.
4. With the answer, multiply the tax percentage(0.08)
5. Now add It to the discounted price.
6. Round it to the nearest hundredth
what is the volume of the box with a high of 3/2 inches a length of 7/2 inches and a with of 5/2 inches
Answer: It is 105/8, or 13 1/8 (as a mixed number)
Step-by-step explanation:
To find volume, you do length times width times height (l * w * h)
Hope this helps! :D
Pleaseee help!
What is 8^2+x^2=17
Answer:
6.856
Step-by-step explanation:
8² + x² = 17
8² - 17 = -x²
64 - 17 = -x²
-47 = -x²
x² = 47
x = 6.856
A file that is 236 megabytes is being downloaded. If the download is 19.3% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
18.3% x 238 megabytes
0.183 x 238 = 43.554 megabytes = 43.6 megabytes (rounded to the nearest tenth) or 43.55 (rounded to the nearest hundredth).
Step-by-step explanation:
Find the volume of this composite figure
Answer:
381 feet cubed
Step-by-step explanation:
You need to divide the shape into 2.
I would divide the shape so that 8.5ft, 6ft, and 3ft are one.
Now do Length times Width times Height for the first one.
8.5 ft x 6 ft x 3 ft = volume for shape 1
The volume for shape 1 is 153 feet cubed
Now onto the second one.
Since you divide the other shape to have 8.5 feet the measurements are:
4ft, 9.5ft, and 6ft.
Do the formula lwh.
4ft x 9.5ft x 6ft = volume for shape 2
The volume for shape 2 is 228 feet cubed
Finally, you have to add shapes 1 and 2 due to the fact it's a composite figure.
153ft + 228ft = 381ft cubed
The following table summarizes a sample of the wait times at two branches of a bank. The district manager wants to construct a two-sample t test to see if there is a significant difference between the average wait times at the two branches.
Branch A B
Mean (minutes) 4.77 5.13
Standard deviation (minutes) 1.45, 45 1.36
Number of observations 20 20
Which of the following are conditions for this type of test?
Choose all answers that apply:
A. The samples are both randomly selected.
B. The wait times within each sample are independent of each other.
C. The wait times within each group are approximately symmetric without outliers.
The conditions for this type of sampling test regarding the wait times at two branches of a bank include:
The samples are both randomly selected.The wait times within each group are approximately symmetric without outliers.What is sampling?It should be noted that sampling simply means a statistical process where a predetermined number of observations are taken from a larger population.
In this case, the samples are both randomly selected and the wait times within each group are approximately symmetric without outliers. When there's a symmetric distribution with no outliers, the mean and standard deviation will be used.
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R (-3,1) and S (-1,3) are points on a circle. If RS is a diameter, find the equation of the circle.
Answer:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Step-by-step explanation:
If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.
[tex]\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)[/tex]
[tex]\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)[/tex]
[tex]\sf =(-2, 2)[/tex]
Equation of a circle: [tex]\sf (x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the center and r is the radius)
Substituting found center (-2, 2) into the equation of a circle:
[tex]\sf \implies (x-(-2))^2+(y-2)^2=r^2[/tex]
[tex]\sf \implies (x+2)^2+(y-2)^2=r^2[/tex]
To find [tex]\sf r^2[/tex], simply substitute one of the points into the equation and solve:
[tex]\sf \implies (-3+2)^2+(1-2)^2=r^2[/tex]
[tex]\sf \implies 1+1=r^2[/tex]
[tex]\sf \implies r^2=2[/tex]
Therefore, the equation of the circle is:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the explicit rule for this sequence in simplified form?
Answer:
d
Step-by-step explanation:
The explicit rule for this sequence in simplified form is,
⇒ [tex]a_{n}[/tex] = 500n + 30,000
Where, n is number of months.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Mr. Red's first year salary is $30,000 and it increases by $500 each year.
Now, Let number of months = n
We can formulate explicit rule for this sequence in simplified form as,
⇒ [tex]a_{n}[/tex] = 500n + 30,000
Therefore, The explicit rule for this sequence in simplified form is,
⇒ [tex]a_{n}[/tex] = 500n + 30,000
Where, n is number of months.
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75 POINTS IF U GET THIS RIGHT !!!!!Every June 1, an ecologist takes a census of the number of wrens in a state park. She noticed that the number is decreasing by $40\%$ each year. If this trend continues, in what year will the census show that the number of wrens is less than $10\%$ of what it was on June 1, 2004?
Answer:
In 2009
Step-by-step explanation:
If the wren population is going down by 40% each year, that means the following year's population is just 60% of what was in the previous year. This means that what we have to do is multiply the previous year's number by 0.6 to get the current year's population. If we take the data from 2004 as 100%, we have the following numbers:
2004 = 100%
2005 = 60 % (100 * .6)
2006 = 36 % (60 * .6)
2007 = 21.6 % (36 * .6)
2008 = 12.96 % (21.6 * .6)
2009 = 7.776% (12.96 * .6)
This means that 2009 will show that the wren population is less than 10% (7.776%) than what it was in the year 2004.
I hope this helps! :D
Answer:
2009
Step-by-step explanation:
On June 1, 2004 we can say that there were 100% of the wrens.
If the number decreases by 40% each year, then each year there will be 60% of the previous years number. To find 60%, multiply by 0.6 (since 60% = 60/100 = 0.6)
June 1, 2004 = 100%
June 1, 2005 = 100% x 0.6 = 60%
June 1, 2006 = 60% x 0.6 = 36%
June 1, 2007 = 36% x 0.6 = 21.6%
June 1, 2008 = 21.6% x 0.6 = 12.96%
June 1, 2009 = 12.96% x 0.6 = 7.776%
Therefore, the census shows that the number of wrens is less than 10% in the year 2009.
Need help with his geometry question. Find the value of x
Answer:
Step-by-step explanation:
The fourth term of a geometric series is 10 and the seventh term of the series is 80. Find the sum to 10 terms of the series.
The geometric series with 4th term as 10 and 7th term as 80 has the sum of the first tenth terms as 1278.75.
How to find sum of terms in geometric series?aₙ = arⁿ⁻¹
where
a = first termr = common ration = number of termsTherefore,
10 = ar³
80 = ar⁶
Hence,
a = 10 / r³
80 = (10 / r₃) r⁶
80 = 10r³
r³ = 80 / 10
r = ∛8
r = 2
a = 10 / 2³
a = 10 / 8 = 5 / 4
The sum of 10 terms can be calculated as follows:
Sₙ = a(rⁿ - 1) / r - 1
Sₙ = 5 / 4 (2¹⁰ - 1) / 2 - 1
Sₙ = 5 / 4 (1024 - 1) / 1
Sₙ = 1.25(1023)
Sₙ = 1278.75
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What is the measure of angle x?
Enter your answer in the box.
X=
Answer:
Step-by-step explanation:
y + 47° = 90° {Complementary angles}
y = 90° - 47°
y = 43°
x = y {Vertically opposite angles}
x = 43°
Answer:
x = 43°
Step-by-step explanation:
[tex] \sf{Y + 47° = 90° } [/tex]Substract 47° from both sides
[tex] \sf{Y + 47° - 47° = 90° - 47°} [/tex][tex] \sf{Y = 43°} [/tex]since X and y are vertically opposite angles
[tex] \sf{x = 43°} [/tex]Miko has 3 cakes.
She cuts each cake into 4 equal pieces.
How many pieces of cake does Miko have?
Answer:
12 pieces of cake
Step-by-step explanation:
4 pieces for each cake
there is a total of three cakes
needed to find total pieces of cakes
multiply 4 by 3 and you will get 12 pieces of cake.
Answer:
Miko has 12 pieces of cake
5/6 of a number is 65.
Find the number.
Answer:
78 is the number
Step-by-step explanation:
(65*6)÷5 = 78.
5/6 of a number is 65.
And the number is 78.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
A phrase: 5/6 of a number is 65.
To find the number:
Let the number be n.
Applying multiplication operation,
5/6 of n is 65.
(5/6)n = 65.
Applying cross multiplication,
n = 65 x 6/5
n = 390/5
n = 78.
Therefore, the number is 78.
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7. Assessment Practice Tiffany buys a stuffed animal for 84¢. She pays with 8 dimes and I nickel. Which shows hov much change Tiffany should get? A A C) BO D
Answer:
1 cent
Step-by-step explanation:
Dime = 10 cents
8 Dimes = 8 * 10 = 80 Cents
1 Nickel = 5 Cents
80 + 5 = 85
85 - 84 = 1 Cent
Luke's house is due west of Toronto and due south of Barrie. Toronto is 16 kilometres from Luke's house and 20 kilometres from Barrie. How far is Barrie from Luke's house, measured in a straight line?
Using the Pythagorean Theorem, it is found that Barrie is 12 miles from Luke's house, in a straight line.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
This problem can be modeled by a right triangle, with [tex]l_1 = 16, l_2 = d, h = 20[/tex], hence:
[tex]h^2 = l_1^2 + l_2^2[/tex]
[tex]16^2 + d^2 = 20^2[/tex]
[tex]d^2 = 144[/tex]
[tex]d = 12[/tex]
Barrie is 12 miles from Luke's house, in a straight line.
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What is the area, in square inches, of the isosceles trapezoid below?
Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn from point C to a point on side A B to form a right angle. The length of A B is 17 and the length of A C is 8.
What is the length of Line segment B C?
9 units
11 units
15 units
16 units
Answer:
15 unit that is the answer
Step-by-step explanation:
hope it is help you
The length of the line segment BC is 15 units
Pythagoras theoremIn order to determine the length of BC, we will use the Pythagoras theorem as shown;
AB² = AC² + BC²
Substitute the given parameters
17² = 8² + BC²
BC² = 289 - 64
BC² = 225
BC=. 15 units
Hence the length of the line segment BC is 15 units
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