Answers
From the table it can be seen that when r=3, V(r=3) =113
On the other hand, when r=7, V(r=7)=1436 and when r=2, V(2)=33.5, therefore,
[tex]\begin{gathered} V(7)-V(2)=1436-33.5 \\ =1402.5 \end{gathered}[/tex]Related Questions
You are the financial planner for Johnson Controls. Assume last year's profits were $700,000.
The board of directors decided to forgo dividends to stockholders and retire high-interest outstanding bonds that were issued 5 years ago at a face value of $1,250,000. You have been asked to invest the profits in a bank. The board must know how much money you will need from the profits earned to retire the bonds in 10 years. Bank A pays 6% Compounded
quarterly, and Bank B pays 61.5% compounded annually. Which bank would you recommend, and how much of the company's profit should be placed in the bank? If you recommended that the remaining money not be distributed to stockholders but be placed in Bank B, how much would the remaining money be worth in 10 years? Show your work.
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A financial concept known as future value (FV) assigns a value to an asset based on anticipated factors like future interest rates or cashflows.
The answer is as follows:
a-1: Bank B
a-2: Profit $665875
b. Future Value $64056.04
What is meant by Future Value?A financial concept known as future value (FV) assigns a value to an asset based on anticipated factors like future interest rates or cashflows. Knowing how much their investment would be in five years, given a projected rate of return, may be valuable for an investor. Future value is the idea of taking the investment's current value, applying anticipated growth, and estimating what the investment will be in the future.
For planning purposes, future value is used to estimate what an investment, cash flow, or expense might be in the future. Given the future worth of an investment, investors utilize the future value to decide whether or not to proceed with it.
Future value can also be used to assess risk, calculate the rate at which a specific expense will increase if interest is paid, or set a savings goal to see whether adequate reserves will be made in light of the present savings rate and the anticipated rate of return.
Therefore, the answer is as follows:
a-1: Bank B
a-2: Profit $665875
b. Future Value $64056.04
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The table below shows the balance of a savings account b after t weeks where money is being withdrawn at a constant rate Peter can find the balance of the account based on how many weeks have passed.
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B
1) Examining the table we can say the more the independent variable, in this case, t increases by 1 unit, the dependent variable, in this case, b decreases by 50 dollars.
2) Hence the answer is
B. As the independent variable increases by 1, the dependent variable decreases by 50
Find The Measurement Of <6
Answers
The measure of ∠6 from the given figure is 45°.
From the given figure, the measure of angle is 135°.
What are Co-interior angles?Co-interior angles occur in between two parallel lines when they are intersected by a transversal. The two angles that occur on the same side of the transversal always add up to 180°.
From the given figure,
135° + ∠6 = 180° (Co-interior angles adds upto 180°°)
⇒ ∠6 = 180°-135°
⇒ ∠6 = 45°
Therefore, the measure of ∠6 from the given figure is 45°.
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4. If D is the midpoint of CE, CD=4x-19 and DE=2x-1, Find the value of x. Find CE.
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ANSWER
EXPLANATION
We have that D is the midpoint of CE.
We are given that:
CD = 4x - 19
If a car travels for 0 hours, it will travel
0 mile(s). This means it will pass through the point
0. Use the slope to move 3 units to the right of the origin and
enter your response here unit(s) up to find the point
enter your response here that can be used to graph the relationship.
just need to solve bottom part i already did the top
Answers
The correct statement will be;
⇒ If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0, 0). Use the slope to move 3 units to the right of the origin and 3 units up to find the point (3, 3) that can be used to graph the relationship.
What is Equation of line?
The equation of line with slope m and passes through the point
(x₁, y₁) defined as;
⇒ y - y₁ = m (x - x₁).
Given that;
The relation between the distance and time is shown in graph.
Now,
When we move 3 units to the right then, the graph is meet at point 3 up to, for the distance and time.
This point is meet at point (3, 3).
Thus, The correct statement will be;
⇒ If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0, 0). Use the slope to move 3 units to the right of the origin and 3 units up to find the point (3, 3) that can be used to graph the relationship.
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Find
152.87+35.4
. Express your answer in decimal form.
Answers
In XYZ, XY=14, YZ=22, and XZ=28. What is the measure of angle Z to the nearest degree? *Law of Cosines
Answers
Solution
Draw the diagram
So using cosine rule
[tex]\begin{gathered} z^2=x^2+y^2-2xycosZ \\ \\ cosZ=\frac{x^2+y^2-z^2}{2xy} \\ \\ cosZ=\frac{22^2+28^2-14^2}{2(22)(28)} \\ \\ cosZ=\frac{67}{77} \\ \\ Z=30\degree\text{ \lparen to the nearest degree\rparen} \end{gathered}[/tex]In a certain Algebra 2 class of 30 students, 8 of them play basketball and 10 of them
play baseball. There are 18 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?
Answers
The probability that a classmate picked at random will participate in both basketball and baseball is 0.2.
What in mathematics is a probability?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.
Given: In a particular Algebra 2 class of 30 students, 8 play basketball and 10 play baseball. There are 18 students who participate in neither sport.
Let n denote the number of students who participate in basketball and baseball.
The number of students that play both games: 30 = 18 - n + 8 - n + 10 + n
30 = n + 36
n = 36 - 30 = 6
Probability = 6/30 = 0.2
Therefore, the probability that a student chosen at random from the class will play both basketball and baseball is 0.2.
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The following graphs have no scales assigned to them. Which of them couldbe density curves for a continuous random variable if they were provided withthe right scale?Check all that apply.A. Graph AB. Graph BC. Graph CD. Graph DE Graph E
Answers
Given that:
- The graphs have no scales assigned to them.
- You have to identify the ones that could be density curves for a continuous random variable assuming that they have the right scale.
Then, in order to solve this exercise, you need to remember the following:
1. A Probability Density Function is useful to define the probability of a random variable within a distinct range of values.
2. It is also known as PDF.
3. The Probability Density Function is always positive in all its Domain.
4. The total enclosed area under the curve of the function is:
[tex]A=1[/tex]Knowing all these concepts, you can identify that:
- In graph B the area under the curve is 0. Therefore, this cannot be the graph asked in the exercise.
- In Graph C, the function is not positive in its Domain. Therefore, this does not satisfy the properties mentioned before.
Hence, the answers are:
- Option A.
- Option D.
- Option E.
i need help on this question
Answers
Given the figure below, find the values of x and z.
95°
z°
(6x-23)
Answers
Answer: z=95 and x=18
Step-by-step explanation: the lines are both straight and the whole 6x blahb blah blah is not needed since the line is 180 degrees and 180-95=85 so 6x-23=85 which x=18 and it also has to be 95 so z=95
The rectangle below has an area of x^2-15x+56x
2
−15x+56x, squared, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters.
What expression represents the width of the rectangle?
Answers
The rectangle below has an area of x²-15x+56. (x-7) and are the binomials (x-8). Given that the length is (x-7) and the width is, respectively (x-8).
Given that,
The rectangle below has an area of x²-15x+56.
We have to find the width of the rectangle.
A quadrilateral (4-sided polygon) with two sets of parallel and equal sides called length and width is what is meant by the term "rectangle." The sum of these two is equal to the area of a rectangle. A quadratic equation represents the area. When a quadratic equation is factored, the result is a product of two binomials, such as (x-q)(x-r) = 0, where q and r are the equation's roots or zeros. Making use of the quadratic formula, you may determine this:
x=[tex]\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
Here, a is 1 b is -15 and c is 56.
x=[tex]\frac{-15\pm\sqrt{15^{2}-4(1)(56) } }{2(1)}[/tex]
x=[tex]\frac{-15\pm\sqrt{225-224 } }{2}[/tex]
x=[tex]\frac{-15\pm\sqrt{1} }{2}[/tex]
[tex]x=\frac{-15\pm1 }{2}[/tex]
Take the plus 1st
x=-15+1/2
x=-14/2
x=-7
Now take minus
x=-15-1/2
x=-16/2
x=-8
Therefore, (x-7) and are the binomials (x-8). Given that the length is (x-7) and the width is, respectively (x-8).
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2. Stephanie will be sending 2 parcels of personal items to her niece. The big parcel weighs 12
lbs 11 oz and the smaller parcel is 3 lbs 1 oz lighter than the big parcel. What is the combined
weight of the two parcels?
Answers
Weight of the two parcels 22lbs 5oz.
What is Weight?
The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.
Given,
The weight of big parcel = 12lbs 11oz
The weight of small parcel = 12lbs 11oz - 3lbs 1oz
= 9lbs 10oz
The weight of total parcel = big parcel + small parcel
= 12lbs 11oz + 9lbs 10oz
= 21lbs 21oz = 22lbs 5oz
Hence, The weight of the 2 parcels is 22lbs 5oz.
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A rectangle is shown belowA(-4,2) B(-2, 2)C(-2, -2)D(-4, -2)The rectangle is rotated 180 about the origin, What are the new coordinates of point D?A (2,-2)B. (4,2)C. (4.-2)D (2,2)
Answers
Answer:
B. (4,2)
Explanation:
The coordinates of point D is (-4, -2)
If a point (x,y) is rotated 180 about the origin, we have the transformation:
[tex](x,y)\to(-x,-y)[/tex]Therefore, the new coordinates of point D will be: (4, 2).
The correct choice is B.
pefume discounted 25% on sale for 27$
Answers
Determine the vertical intercept of h.h(0)=Determine the root(s) of h.x=Determine the vertical asymptote(s) of h.x=Determine the horizontal asymptote of h.y=
Answers
The general equation of line is :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The equation of the function g(x) is:
Consider any two coordinates : (-3,0) & (0,3) So, the equation is:
[tex]\begin{gathered} y-0=\frac{3-0}{0-(-3)}(x-(-3)) \\ y=\frac{3}{3}(x+3) \\ y=x+3 \\ g(x)=x+3 \end{gathered}[/tex]The equation of the function f(x) is:
Consider any two coordinates: (-1,0) & (0,1)
[tex]\begin{gathered} y-0=\frac{1-0}{0-(-1)}(x-(-1)) \\ y=1(x+1)_{} \\ y=x+1 \\ f(x)=x+1 \end{gathered}[/tex]Since, h(x) = f(x)/g(x)
So, the funstion h(x) is express as:
[tex]\begin{gathered} h(x)=\frac{f(x)}{g(x)} \\ h(x)=\frac{x+1}{x+3} \end{gathered}[/tex]a) Vertical intercept of h
Substitute x =0 in h(x)
[tex]\begin{gathered} h(x)=\frac{x+1}{x+3} \\ h(0)=\frac{0+1}{0+3} \\ h(0)=\frac{1}{3} \end{gathered}[/tex]b) Determine the roots of h(x)
[tex]\begin{gathered} g(x)=\frac{x+1}{x+3} \\ \text{ the given expression is the iraationla polynomial } \\ \frac{x+1}{x+3}=\frac{x+1}{x+3} \\ \text{ Roots of h(x) =}\frac{x+1}{x+3} \end{gathered}[/tex]c) Vertical asymptote : Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function
So,
[tex]\begin{gathered} x+3=0 \\ x=-3 \end{gathered}[/tex]The vertical assymptote : x =-3
D) Horizontal assymptote : x - 3
bAnswer: x -3
Answer:
a)h(0)=1/3
b) h(x)=(x+1)/(x+3)
c) x = -3
Hroizontal Assymotote : y =1/3
Hello! I’m trying to figure out this problem but have no idea how.
Answers
Given: Two investments compounded annually as follows-
[tex]\begin{gathered} P_1=4800 \\ R_1=7\% \end{gathered}[/tex]and,
[tex]\begin{gathered} P_2=7900 \\ R_2=5.7\% \end{gathered}[/tex]Required: To find out the time required by smaller investment to catch up to larger investment.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{100})^t[/tex]Putting the values for the first investment (smaller one) we get,
[tex]\begin{gathered} A_1=4800(1+\frac{7}{100})^t \\ =4800(1+0.07)^t \\ =4800(1.07)^t \end{gathered}[/tex]Similarly solving for other investment we get,
[tex]\begin{gathered} A_2=7900(1+0.057)^t \\ =7900(1.057)^t \end{gathered}[/tex]Now lets say in time 't' our investment catch up or becomes equal, i.e.,
[tex]A_1=A_2[/tex][tex]4800(1.07)^t=7900(1.057)^t[/tex][tex](\frac{7900}{4800})=(\frac{1.057}{1.07})^t[/tex][tex]1.65=(0.98)^t[/tex]Taking logarithm both sides and solving for t gives us,
[tex]t\approx40.7599[/tex][tex]\approx40.8[/tex]Final Answer: The investments would catch up after approximately 40.8 yrs.
30% in 85 209
please
Answers
Answer: 25.5 im pretty sure
Step-by-step explanation:
i need to know minor arc, chord, tangent line, central angle, secant line, major arc, radius, and inscribed angle
Answers
Based on your picture, we can say the following:
- Minor arc: The curve between points B and E
- Chord: AB
- Tangent line: The line which goes through points DE
- Central angle: ECB
- Secant line: The line which goes through points AE
- Major arc: The curve between points B and B going through A
- Radius: CE and CB
- Inscribed angle: EAB
Use slope formula to find the slope of the line between the points (5,3) and (7,0)
Answers
The formula for calculating the slope of a line is
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ Where(x_1,y_1)=(5,3)and_{} \\ (x_2,y_2)\text{ = (7, 0)} \end{gathered}[/tex][tex]\begin{gathered} \text{Substituting the values of }(x_1,y_1)\text{ and }(x_2,y_2),\text{ we have } \\ m=\frac{0-3}{7-5} \\ m=\frac{-3}{2} \end{gathered}[/tex]Hence, the slope of the line is -3/2 or -1.5
Which of the following is the prime factores form of the lowest common denominator of
Answers
We need to find the primed factor form of the lowest common denominator of the fractions 2/15 and 5/12, hence we first need to find the lowest common factor between 15 and 12, let's do that by listing the multiples of each number:
12, 24, 36, 48, 60, 72, ....
15, 30, 45, 60, 75, ....
From the multiples above we notice that the least common denominator will be 60.
Now we need to find the prime factorization of 60, let's do that:
[tex]60=2\times2\times3\times5[/tex]Since we can't have any further factorization of the factors this is the prime factored form of the LCD, therefore, the answer is the third option.
WIL GIVE BRAINLYEST 100 POINTS ACULY 200 BECUS EI GIVE EXTRA
Answers
Answer:
600
Step-by-step explanation:
Vol = length x width x height
(8)(15)(5) = 600
PROBLEM #2A package contains 56 cups of oatmeal. A batch ofcookies requires 2 34 cups of oatmeal. Is thereenough oatmeal to make 21 batches of cookies?Explain. Show your work to prove your answer.
Answers
First, calculate the total amount of cups of oatmeal required to make 21 batches of cookies by multiplying 21 times 2 3/4:
[tex]21\times2\frac{3}{4}=21\times2+21\times\frac{3}{4}[/tex]Simplify that fraction:
[tex]\begin{gathered} =42+\frac{21\times3}{4} \\ =42+\frac{63}{4} \\ =42+\frac{60+3}{4} \\ =42+\frac{60}{4}+\frac{3}{4} \\ =42+15+\frac{3}{4} \\ =57+\frac{3}{4} \\ =57\frac{3}{4} \end{gathered}[/tex]Since a total of 57 3/4 cups of oatmeal are needed to make 21 batches of cookies, but a package contains only 56 cups of oatmeal, therefore, there is not enough oatmeal to make 21 batches of cookies.
A pitcher contains 4 6/8 cups of juice. we pour out 7/8 cup. how much juice is left in the pitcher?
Answers
The amount of juice in a pitcher is 4 6/8 cups and 7/8 cup is taken out.
The amount of juice left in the pitcher is,
[tex]\begin{gathered} 4\frac{6}{8}-\frac{7}{8}=\frac{4\cdot8+6}{8}-\frac{7}{8} \\ =\frac{38}{8}-\frac{7}{8} \\ =\frac{38-7}{8} \\ =\frac{31}{8} \\ =3\frac{7}{8} \end{gathered}[/tex]There are 3 7/8 cups left in the pitcher.
What is an equation of the line that passes through the points (6, 5) and (8, -6)?
Answers
Answer:
y= -11/2 x +38
Step-by-step explanation:
to find slope:
m= -6-5/8-6 m= -11/2
to find the y-intercept:
y= -11/2 x +b
5 = -11/2(6) + b
5 = -33 + b
38 = b
so then:
y= -11/2 x +38
Please do #1 under where it says “Mixed review slide 8”
Answers
The coins are in the shape of a cylinder.
The formula to calculate the volume of a cylinder is given as
[tex]V=\pi r^2h[/tex]where
[tex]\begin{gathered} r=\text{ radius} \\ h=\text{ height} \end{gathered}[/tex]The individual coin has the following dimensions:
[tex]\begin{gathered} r=1\text{ in} \\ h=0.0625\text{ in} \end{gathered}[/tex]Thus, the volume of one coin can be calculated as
[tex]\begin{gathered} V=\pi\times1^2\times0.0625 \\ V=0.196\text{ cubic inches} \end{gathered}[/tex]If there are 225 coins in the chest, the combined volume of all the coins will be
[tex]\begin{gathered} V_T=0.196\times225 \\ V_T=44.1\text{ cubic inches} \end{gathered}[/tex]The combined volume is 44.1 cubic inches.
Hey can anyone pls answer these problems!!! find the area and perimeter pls show work
Answers
The areas of each figure are listed below:
Case 2 - Triangle: 20 in²
Case 3 - Composite figure: 72 ft²
Case 4 - Parallelogram: 45
Case 5 - Rhombus: 39 m²
Case 6 - Composite figure: 94 cm²
Case 9 - Composite figure: 101 m²
How to calculate the areas of triangles, quadrilaterals and composite figures
In this problems we must calculate the areas of triangles, quadrilaterals and composite figures formed by triangles and quadrilaterals. Now we proceed to present the areas for each case:
Case 2
The area of the triangle is the sum of the areas of the two right triangles:
A = (1 / 2) · (3 in) · (4 in) + (1 / 2) · (7 in) · (4 in)
A = 6 in² + 14 in²
A = 20 in²
Case 3
The area of the composite figure is the sum of the areas of the rectangle and two right triangles:
A = (1 / 2) · (6 ft) · (6 ft) + (8 ft) · (6 ft) + (1 / 2) · (2 ft) · (6 ft)
A = 18 ft² + 48 ft² + 6 ft²
A = 72 ft²
Case 4
The area of the parallelogram is the product of the length of its base and the length of its height:
A = b · h
A = 9 · 5
A = 45
Case 5
The area of the irregular rhombus is equal to the sum of the areas of the four triangles:
A = 2 · (1 / 2) · (4 m) · (3 m) + 2 · (1 / 2) · (3 m) · (9 m)
A = 12 m² + 27 m²
A = 39 m²
Case 6
The area of the composite figure is the sum of the areas of the three rectangles:
A = (10 cm) · (5 cm) + (8 cm) · (4 cm) + (4 cm) · (3 cm)
A = 50 cm² + 32 cm² + 12 cm²
A = 94 cm²
Case 9
The area of the composite figure is the sum of the areas of a right triangle and two rectangles:
A = (1 / 2) · (3 m) · (10 m) + (3 m) · (10 m) + (8 m) · (7 m)
A = 15 m² + 30 m² + 56 m²
A = 101 m²
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how do you put [tex]y = - \frac{3}{2} x + 3[/tex]on a graph
Answers
The equation to graph is:
[tex]y=-\frac{3}{2}x+3[/tex]Let's break it down and see how can we EASILY graph this!!
The first point is to always put x = 0 and find the y-value. This way, we graph the y-intercept. Thus,
[tex]\begin{gathered} y=-\frac{3}{2}x+3 \\ y=-\frac{3}{2}(0)+3 \\ y=3 \end{gathered}[/tex]So, y-intercept is (0, 3).
Now, look at the slope, the constant before "x". It is -3/2.
The numerator is rise and denominator is run.
Thus, from the y-intercept, we move "-3" units "rise" (y-direction) and "2" units "run" (x-direction).
We will arrive at (2,0).
Then we can make this move again!
We will arrive at (4, -3).
That's it!!
We can now graph the 3 points found, draw a smooth line through these points and that's our line!!
The graph of the line is shown below:
Please help because I'm pretty sure I got the right answer but making sure.
Answers
Jim walked 1/2 of a mile in 1/4 of an hour. at this rate how many miles will he walk in one hour
Answers
Answer:
2 miles
Explanation:
Jim walked 1/2 of a mile in 1/4 of an hour.
[tex]\begin{gathered} \text{In }\frac{1}{4}\text{ of an hour, Jim walked }\frac{1}{2}\text{ miles} \\ \text{Then:} \\ \text{In 1 hour, Jim will walk }\frac{1}{2}\div\frac{1}{4}\text{ miles} \end{gathered}[/tex]We simplify our result:
[tex]\begin{gathered} \frac{1}{2}\div\frac{1}{4}=\frac{1}{2}\times\frac{4}{1} \\ =\frac{4}{2} \\ =2\text{ miles} \end{gathered}[/tex]At this rate, Jim will walk 2 miles in one hour.
