Based on the number of years that Peter and Blair have till retirement, the total amount that they need to save to completely fund their income shortfall is $65,545.72.
What amount do Peter and Blair need to save?First, find the income shortfall:
= 75,017 - 54,000
= $21,017
The amount they need to save to cover this shortfall is the future value of this amount at retirement. The rate will be the real rate which is:
= 6% - 2% inflation
= 4%
The future value is:
= Income shortfall x future value interest factor, 4%, 29 years
= 21,017 x 3.1187
= $65,545.72
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can someone help me on this question with step by step explaination
and reasoning
Answer: Same
Step-by-step explanation:
Given formula
[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]
Given information
Troop A:
Original (2010) = 14New (2011) = 16Troop B:
Original (2010) = 21New (2011) = 24Substitute values into the formula (Troop A)
[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{(16)~-~(14)}{(14)}*100\%[/tex]
Simplify the fraction
[tex]Percent~of~change~=~\Large\frac{2}{14}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]
[tex]Percent~of~change~\approx~14.29\%[/tex]
Substitute values into the formula (Troop B)
[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{(24)~-~(21)}{(21)}*100\%[/tex]
Simplify the fraction
[tex]Percent~of~change~=~\Large\frac{3}{21}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]
[tex]Percent~of~change~\approx~14.29\%[/tex]
Compare the two percent of change
[tex]Troop~A~v.s.~Troop~B[/tex]
[tex]14.29\%~=~14.29\%[/tex]
Therefore, they are [tex]\Large\boxed{Same}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The answer is same.
Finding the percentage of change for Troop A :
New - Original / Original × 100%
16 - 14 / 14 × 100%1/7 × 100%14.29%Finding the percentage of change for Troop B :
24 - 21 / 21 × 100%1/7 × 100%14.29%Both the troops have the same percent change in membership.
Show all work to write the expression in simplified radical form:
(Assume all variables are positive)
[tex]\sqrt[3]{192x^{5}y^{8}}[/tex]
(Cube root of 192 x to the fifth power y to the eighth power)
Answer:
[tex]\sqrt[3]{192} x^{\frac{3}{5} }y^{\frac{3}{8} }[/tex]
Step-by-step explanation:
You have to simplify all of the terms individually
[tex]\sqrt[3]{192} = 5.769[/tex]
Since that isn't a whole number, it doesn't simplify
Use the root to exponent rule for the variables
[tex]\sqrt[3]{x^{5} } =x^{\frac{3}{5} }[/tex]
[tex]\sqrt[3]{y^{8} } =y^{\frac{3}{8} }[/tex]
Then put them all together to get
[tex]\sqrt[3]{192} x^{\frac{3}{5} }y^{\frac{3}{8} }[/tex]
Make sure the variables aren't under the root when you give your answer
I hope this helps!
pls mark brainliest
Find tan 0.
16
20
12
0
The value of tan 0 as given in question is 0
What are trigonometry identity?Trigonometric identities are equations involving the trigonometric functions that are true for every value of the variables involved. They are written in terms of sine, cosine and tangent.
According to the question, we are to find the value of tan0. This is as shown below;
tan 0 = 0
Note that the tangent angle is positive in the first and third quadrant. Hence the result of the given tangent expression will also be positive.
Hence the value of tan 0 as given in question is 0
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4. A store has 152 bottles of
water. This is 2 times the
number of sodas they
have. How many sodas
does the store have?
Answer:
76 sodas
Step-by-step explanation:
152 divided by 2
Answer: 76 sodas
Step-by-step explanation:
To find the sodas, use the data you see. Bottles of water are twice the sodas. So divided water by 2 to get the sodas.
152 ÷ 2 = 76 ( sodas ) . Hope it helps !
A Ferris wheel with a diameter of 10 m and makes one complete revolution every 80
seconds. Assume that at time t = 0, the Ferris Wheel is at its lowest height above
the ground of 2 m. You will develop the equation of a cosine graph that models your
height, in metres, above the ground as you travel on the Ferris Wheel over time, t in
seconds. To do this, answer the following questions.
1. State the amplitude of the graph.
2. State the value of k in the general form y = a cos [k(x - d)] + c.
3. State the value of d.
4. State the value of c.
5. State the cosine equation of the graph.
The cosine equation of the attached graph is; y = 5 cos [( π/40)(x - (π/2))] + 3
How to plot a trigonometric graph?
The given parameters are:
Diameter = 10 m
Thus;
Radius; r = 5 m
Time; t = 80 s
Height above the ground, h = 2 m
The above means that:
Amplitude; A = 5 m
Period, T = 80 s
Minimum = 2 m
The cosine function is represented as:
y = a cos [k(x - d)] + c.
where;
A is amplitude
B is cycles from 0 to 2π
period = 2π/k
d is horizontal shift
c is vertical shift (displacement)
Thus;
2π/k = 80
k = 2π/80 = π/40
Where
c = Amplitude - Minimum
c = 5 - 2
c = 3
Shift to the left by π/2 gives;
d = π/2
Thus, the equation of the cosine graph is;
y = 5 cos [( π/40)(x - (π/2))] + 3
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Khan Academy Question
Answer:
84
Step-by-step explanation:
Since we are given line OP perpendicular to line DR, then angles PDR and ODR are right angles.
Angles PDA and ADR are complementary.
Angles ODU and UDR are complementary.
Angles ADR and UDR are given as congruent.
We can conclude that angles PDA and ODU are congruent.
By AA Similarity, triangles APD and UMD are similar.
DP/DM = PA/MU
3.75/10 = 4.5/MU
3.75MU = 10 × 4.5
MU = 12 (altitude of triangle DUO)
OD = OM + MD = 4 + 10 = 14 (base of triangle DUO)
area = base × height / 2
area = 14 × 12 / 2
area = 84
Answer:
84
Step-by-step explanation:
correct me if im wrong
What are the major requirements for a group of individuals and organizations to be a market? How does a consumer market differ from a business-to-business market?
The major requirements for a group of individuals and organisations to be a market as evident from the definition big a market is that; there must be an exchange of goods or services in which case, there are sellers and buyers.
Which requirements ascertain that a group of individuals are a market?The occurrence of the exchange of goods and services represents the qualifying requirement for a market.
The distinctive property between a consumer market and a business-to-business market is the that former, involves the end user of the good or service while the latter involves the use of the good or service exchanged to facilitate the production of other goods.
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Which expression is equivalent to (9x8)^4
QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Central angle in the circle is: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. measure of arc BEC is: 260°
e. m(BC) = 100°
What is a Central Angle?A central angle has two of its sides as radii of the circle, forming an angle at the center of the circle, where the vertex is at the center of the circle.
What is a Major Arc?A major arc has a measure that is greater than 180 degrees. That is, it is more than half a circle (semicircle). Thus, measure of major arc > 180 degrees.
What is a Minor Arc?A minor arc has a measure that is less than 180 degrees. That is, it is not more than half a circle (semicircle). Thus, measure of minor arc < 180 degrees.
a. Central angle in the circle is: Angle BAC
b. A major arc in circle A is: Arc BEC
c. A major arc in circle A is: Arc BC.
d. Measure of arc BEC = 360 - 100 [according to the central angle theorem]
Measure of arc BEC = 260°.
e. Measure of angle BAC = 100° [given]
Measure of arc BC = angle BAC [according to the central angle theorem]
Measure of arc BC = 100°
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help me find the answer that bests best
represents this relationship
Answer:
c
Step-by-step explanation:
consider points (0,2) and (-4,0)
slope=(0-2)/(-4-0)=-2/-4=1/2
y-intercept=2
y=mx+c
y=1/2 x+2
Answer:
y=1/2x+2
Step-by-step explanation:
The graph of the absolute value parent function
By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)
How to find a resulting function by applying rigid transformations
Herein we must modify a parent function to get a resulting function by the use of rigid transformations, defined as those transformations applied on geometric loci, including functions, such that Euclidean distance is conserved.
Based on the statement seen in the picture, the enlargement of the parent function can be done by a rigid transformation known as dilation, whose definition is shown below:
g(x) = k · f(x), where k is the stretch factor and is greater than 1. (1)
If we know that f(x) = |x| and k = 5, then the resulting function is:
g(x) = 5 · |x| (1)
This expression is also equivalent to the expression g(x) = |5 · x| by definition of absolute value.
By the definition and properties of absolute value, there are two possible resulting functions: (i) g(x) = 5 · |x|, (ii) g(x) = |5 · x|. (Correct choices: B, D)
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sketch the graphs of equations:
a) y=x
b) y= -x
c) y=x+5
sketch the graphs:
a) y=3x+2
b) y=3x-2
The graphs of the equations are:
In fig. 1:
a) y = x (red line)
b) y = -x (blue line)
c) y = x + 5 (green line)
In Fig. 2:
a. y = 3x + 2 (red line)
b. y = 3x - 2 (blue line)
What is the Graph of a Linear Equation?A linear equation can be expressed in slope-intercept form as, y = mx + b, where m is the slope of the line and b is the y-intercept where the line cuts across the vertical axis (y-axis).
Given the equations:
a) y = x, the slope is 1, while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the red line on the graph plotted).
b) y= -x, the slope is -1 (declining slope), while the y-intercept is 0. This means the line of the graph passes through the point of origin (0, 0). (It is the blue line on the graph plotted).
c) y = x + 5, the slope is 1 (rising slope), while the y-intercept is 5. This means the line of the graph passes the y-axis at 5. (It is the green line on the graph plotted).
In Figure 2, we have the second graph with the following equations:
a. y = 3x + 2, the slope is 3 (rising slope), while the y-intercept is 2. This means the line of the graph passes the y-axis at 2. (It is the red line on the graph plotted).
b. y = 3x - 2, the slope is 3 (rising slope), while the y-intercept is -2. This means the line of the graph passes the y-axis at -2. (It is the blue line on the graph plotted).
In summary, the graphs of the equations are:
In fig. 1:
a) y = x (red line)
b) y = -x (blue line)
c) y = x + 5 (green line)
In Fig. 2:
a. y = 3x + 2 (red line)
b. y = 3x - 2 (blue line)
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Use the ANOVA analysis tool Base on the given data uploaded, will you conclude that the number of bathroom of houses is a significant factor for house price? I your answer is affirmative, then explain how the house price is influenced by the number of bathroom?
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the points with their polar coordinates. HELPPPPP!!
The points would be matched with their polar coordinates as follows:
(-4, -3π/4) → E.(4, 7π/4) → F.(4, 3π/4) → C.(- 4, - 7π/4) → D.What is a polar coordinate?A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).
How to transform polar coordinates to rectangular coordinates?In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:
a = rcos(θ) ....equation 1.
b = rsin(θ) ....equation 2.
Where:
θ is the angle.r is the radius of a circle.In Mathematics, a negative vector for a given vector has the same magnitude but acts in an opposite direction while an antiparallel vector for a given vector refers to any vector that acts in an opposite direction.
This ultimately implies that, a negative vector equals to an antiparallel vector, but an antiparallel vector isn't always a negative vector.
In this context, we can infer and logically deduce that the points would be matched with their polar coordinates as follows:
(-4, -3π/4) → E.(4, 7π/4) → F.(4, 3π/4) → C.(- 4, - 7π/4) → D.Read more on polar coordinates here: https://brainly.com/question/2193539
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Graph the hyperbola using the transverse axis, vertices, and co-vertices:
12x2−3y2−108=0
Use the green key point to change the orientation of the transverse axis, and the red key points to adjust the locations of the vertices and co-vertices.
See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0
How to graph the hyperbola?The equation of the hyperbola is given as:
12x^2 - 3y^2 - 108 = 0
Start by calculating the transverse axis
So, we have:
Transverse axis
The vertices of the given hyperbola are (0, 0)
This means that
(h, k) = 0
Where
a = 3 and b = 6
The transverse axis is calculated as:
y = ±b/a(x - h) + k
So, we have:
y = ±6/3(x - 0) + 0
Evaluate the difference and sum
y = ±6/3x
Evaluate the quotient
y = ±2x
This means that the transverse axes are y = 2x and y =-2x
The vertices
In the above section, we have:
The vertices of the given hyperbola are (0, 0)
This means that
(h, k) = 0
The co-vertices
In the above section, we have:
The vertices of the given hyperbola are (0, 0)
This means that
(h, k) = 0
And
a = 3 and b = 6
The co-vertices are
(h - a, k) and (h + a, k)
So, we have:
(0 - 3, 0) and (0 + 3, 0)
Evaluate
(-3,0) and (3, 0)
See attachment for the graph of the hyperbola
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ASAP HELPPP PLEASE ANSWER CORRECT QUESTION!! GIVING OUT BRAINLY Stars!!!
Silas is researching the cost of a specific souvenir he wants to buy on his international trip.
Use the table to answer the question.
Country Currency Name Exchange Rate Per US Dollar Average Cost of Souvenir: Britain pound 0.83 British pounds 17. British pounds Egypt pound 18 Egyptian pounds 288 Egyptian pounds
Determine which country the souvenir would be less expensive in in US dollars. Show your work. (10 points)
Using proportions, it is found that due to the smaller division of the exchange rate by the cost, the souvenir would be less expensive in Egypt.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The souvenir would be less expensive in the country in which the division of the exchange rate by the cost is smaller.
In Britain, the cost is of 17, with an exchange rate of 0.83, hence the cost in US dollars is:
c = 17/0.83 = $20.48.
In Egypt, the cost is of 288, with an exchange rate of 18, hence the cost in US dollars is:
c = 288/18 = $16.
16 < 20.48, hence the souvenir would be less expensive in Egypt.
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Write the following number in scientific notation. 788,000
Answer:
7.88 x 10^5 is 788,000 is scientific notation
at the beginning of the week, a particular stock sold for 29 3/8 per share. at the end of the same week it sold for 31 2/8. what was the amount of increase per share ?
Answer:
2 1/8
Step-by-step explanation:
I counted from 29 to 31 and then saw that for 29 it was 3/8 and for 31 it was 2/8 so i knew that the answer would be 2 1/8
Uncle Bill has planted fruits in the farm and 7/12 is watermelon.2/3 of the watermelon section is ruined from the storm.The rest is planted with lemon which isn’t ruined.What is the fraction of his farm which isn’t ruined?
The fraction of his farm which isn’t ruined is 11/18
Fractions and proportionFractions are written as a ratio of two integers. The given question will be solved using the method of proportion.
If Uncle Bill has planted fruits in the farm and 7/12 is watermelon, and 2/3 of the watermelon section is ruined from the storm, the fraction ruined from the storm is;
Fraction ruined from the storm = 2/3* (7/12)
Simplify to its lowest term to have:
Fraction ruined from the storm = 7/18
Determine the fraction of the firm that is not ruined
Fraction not ruined = 1 - 7/18
Fraction not ruined = 11/18
Hence the fraction of his farm which isn’t ruined is 11/18 if uncle Bill has planted fruits in the farm and 7/12 is watermelon.
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SV is angle bisector of
Answer:
Sv is angle bisector of rst.In the similar quadrilaterals below, what angle corresponds to ∠C
HURRY PLEASE!!!
∠H
∠G
∠F
∠E
Answer:
angle G
Step-by-step explanation:
the quadrilateral did not change position or ration, it only shrank, so all the angles are in the same place and angle C = angle G
Answer:
2
Step-by-step explanation:
695 is a hundred times smaller than
Answer:
69500
Step-by-step explanation:
695 x 100 = 69500
to check answer divided 69500 by 100
which is equals to 695
695 is a hundred times smaller than 69500
What is Multiplication?multiplication is a method of finding the product of two or more numbers.
We need to find the number which 695 is a hundred times smaller than
Six hundred ninety five times smaller than
Let us consider the number to be x.
Let us multiply 695 with 100 to get the value or answer of the above question.
Six hundred ninety five into hundred is sixty nine thousand five hundred
695 x 100 = 69500
To verify the answer is correct or not , divide 69500 by 100. if we get 695 out answer is correct
69500/100=695
Hence 695 is a hundred times smaller than 69500
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a linear equation is an equation whose graph is a straight line
Answer:
True
Step-by-step explanation:
Plotting the point of any linear equation on a graph gives a straight line
Tyson uploaded 500 videos to the Internet. Sarita uploaded fewer videos than Tyson. Write an inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded.
→WILL MARK BRAINLIEST←
The inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
Inequalitynumber of videos Sarita uploaded = vnumber of videos Tyson uploaded = 500Total videos updated = yInequality for number of videos Sarita uploaded:
v - 500 < y
Therefore, the inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y
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Answer:
- v < 500
Step-by-step explanation:
what is 6x ≥ 6 inequalities
Answer:
[1 , +∞)
Step-by-step explanation:
Solving the inequality 6x ≥ 6
6x ≥ 6
⇔ x ≥ 1 (Divide both sides by 6)
⇔ x ∈ [1 , +∞)
will give brainliest
-(×+3)=-8+10× is what
Answer: 5/11
Solution: x = 5/11
Step-by-step explanation:
Question: -(x+3)=-8+10x
Result -x-3=10x-8
Hope this help :)
Please give brainless
-(×+3)=-8+10× is a math equation with the solution of 5/11
ejercicio de estadistica
Answer:
no habla espanol
Step-by-step explanation:
3. Working with Percent: Determine each amount. a) 1.6% of $150 b) 11.3% of $950 c) 0.29% of $2000 (3)
Answer:
a) (1,6 x 150)/100 = 2,4 dollars
b) (11,3 x 950)/100 = 107,35 dollars
c) (0,29 x 2000)/100 = 5,8 dollars
What is the value of the last digit in 3,500.45
Answer:
five-hundredths
Step-by-step explanation: