The top thing is question my answer is in the box am I correct and can you show me how to do it right if not
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Formula
[tex]M=\frac{pm(1+m)^{na}}{(1+m)^{na}-1}[/tex]Given parameters
[tex]\begin{gathered} p=3,500 \\ m=\frac{8}{12\times100}=\frac{0.08}{12} \\ n=12\text{ } \\ a=2 \end{gathered}[/tex]Substitute the given parameters into the formula
[tex]M=\frac{3500(\frac{0.08}{12})(1+\frac{0.08}{12})^{24}}{(1+\frac{0.08}{12})^{24}-1}[/tex][tex]\begin{gathered} M=\frac{3500(\frac{0.08}{12})(1+\frac{0.08}{12})^{24}}{(1+\frac{0.08}{12})^{24}-1} \\ \\ \text{Remove the parent}heses\text{ (a)=a} \\ \frac{3500\cdot\frac{0.08}{12}\left(1+\frac{0.08}{12}\right)^{24}}{\left(1+\frac{0.08}{12}\right)^{24}-1} \\ \\ \text{Now} \\ \frac{3500\cdot\frac{0.08}{12}\mleft(\frac{0.08}{12}+1\mright)^{24}}{1.0066^{24}^{}-1} \\ \text{Multiply the numerator} \\ \frac{27.367}{1.00666^{24}-1} \\ \text{simplify} \\ =\frac{27.36738}{0.17288}=158.296 \\ \end{gathered}[/tex]The final answer
[tex]\text{ \$158.30}[/tex]Related Questions
a bag contains 6 black marbles and 6 white marbles. What is the least number of marbles that you must choose, without looking, to be certain that you have chosen two white marbles?
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Given:
Number of black marbles = 6
Number of white number marbles = 6
Both marbles have an equal chance of being selected :
[tex]\begin{gathered} P(\text{black marble) = }\frac{Number\text{ of black marble}}{Total\text{ number of marbles}} \\ =\text{ }\frac{6}{12} \\ P(\text{white marble) = }\frac{6}{12} \end{gathered}[/tex]The least number of marbles that must be chosen to be certain that you have chosen 2 white marbles is 8 marbles.
Fill in the table using this function ruley=24-4x
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The values of y is obtained by replacing the corresponding values of x in the equation y = 24 - 4x
x workings y
1 24 - 4(1) = 24 -4 20
3 24 - 4(3) =24 - 12 12
5 24 - 4(5) =24 - 20 4
6 24 - 4(6) =24 - 24 0
Score: 0 of 1 pt X 12.2.17 The data to the right represent the population of 20 of the most populous cities in the world, in millions of people (rounded to the nearest 100,000). 13.7 12.7 10.4 8.7 8.1 13.4 12.3 10.2 8.4 7.4 13.1 11.6 9.5 8.4 7.4 12.9 10.5 8.9 8.1 7.3 Use these data to construct a frequency distribution with a first class of 7.0-7.9. Fill in the Population (millions of people) 7,0 = 7.9 Number of Cities 10.0 - 10.9 110-11.9 20
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Data:
Organice the data from least to largest:
From 7.0 to 7.9
[tex]7.3,7.4,7.4[/tex]From 8.0 to 8.9
[tex]8.1,8.1,8.4,8.4,8.7,8.9[/tex]From 9.0 to 9.9
[tex]9.5[/tex]From 10.0 to 19.9
[tex]10.2,10.4,10.5[/tex]From 11.0 to 11.9
[tex]11.6[/tex]From 12.0 to 12.9
[tex]12.3,12.7,12.9[/tex]From 13.0 to 13.9
[tex]13.1,13.4,13.7[/tex]To make the frequency distribution you need to stablish the groups in millions of people, and then count the number of data that fit in that data range.
Find the volume of a pyramid with a square base, where the perimeter of the base is10.7 ft and the height of the pyramid is 9.8 ft. Round your answer to the nearesttenth of a cubic foot.
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The volume of a pyramid is one third of the product between the base area and the height:
[tex]V=\frac{1}{3}\cdot A_{base}\cdot h[/tex]We already know the height of the pyramid, however we need to estimate the base area from the information given.
The base is a square. Squares have their four sides with the exat same length.
The perimeter is the sum of the length of the sides of a polygon, then, the perimeter of the square is four times its side:
[tex]P=4\cdot L[/tex]Where L is the length of the side. Now, knowing the perimeter we can estimate the lenght of the sides of the base, from which we can calculate the base area:
[tex]\begin{gathered} 4\cdot L=P \\ L=\frac{P}{4} \\ L=\frac{10.7ft}{4} \\ L=2.675ft \end{gathered}[/tex]Now we know the sides of the base have a length of 2.675 ft each. To estimate the area of the base we just need to square this lenght:
[tex]A_{\text{base}}=L^2[/tex]Then, to calculate the volume of the pyramid:
[tex]\begin{gathered} V=\frac{1}{3}\cdot A_{base}\cdot h \\ \\ V=\frac{1}{3}\cdot L^2\cdot h \end{gathered}[/tex]Let's replace values:
[tex]\begin{gathered} V=\frac{1}{3}\cdot(2.675ft)^2\cdot9.8ft \\ V\approx23.375ft^3 \\ V\approx23.4ft^3 \end{gathered}[/tex]The volume of the pyramid is approximately 23.4 cubic feet.
which of the following is the correct factorization of the polynomial below?1331x^3-64
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Given:
[tex]1331x^3-64[/tex]Find: correct factor of the given expression
Explanation: (a)
when we divide 11x-4 to the given expression we got 0 remainder.
and quotient will be
[tex]121x^2+44x+16[/tex]hence the correct factor of the given expression is
[tex](11x-4)(121x^2+44x+16)[/tex]thirteen more than half of a number
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The given statement thirteen more than half of a number can be expressed as
[tex]13+\frac{x}{2}[/tex]Remember that a number means the variable x, half means we divide by 2.
Hi can you help me find the correct answer to this?
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The formula for calulating the period is expressed as
T = 2π√(L/32)
where
T is the period
L is the length of the pendulum
π is a constant whose value is 3.14
From the information given,
T = 3.14
By substituting these values into the formula, we have
3.14 = 2 x 3.14√(L/32)
3.14 = 6.28√(L/32)
3.14/6.28 = √(L/32)
Square both sides of the equation. It becomes
(3.14/6.28)^2 = (√(L/32))^2
(3.14/6.28)^2 = L/32
By cross multiplying,
L = 32 x (3.14/6.28)^2
L = 32 x 0.25
L = 8
The length is 8 feet
Mark the two points on the graph:A(-2,5) B(3,-7)Draw a line between them, what is that distance?ML231451678maMark points on the graph A(-2,5) B(3,-7)
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The graph is plotted in the explanation section below
The distance = 13 units
Explanations:The given points are A(-2, 5) and B(3, -7)
The graph showing the line joining the two points is shown below:
The distance between two points is given as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]For the points A(-2,5) B(3,-7)
[tex]\begin{gathered} D\text{ = }\sqrt[]{(3-(-2))^2+(-7-5)^2} \\ D\text{ = }\sqrt[]{5^2+(-12)^2} \\ D\text{ = }\sqrt[]{25+144} \\ D\text{ = }\sqrt[]{169} \\ D\text{ = 13} \end{gathered}[/tex]The distance between the points A(-2,5) B(3,-7) = 13
77, 71, 65, 59, 53, ....what is the 23rd term
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77, 71, 65, 59, 53, ....
what is the 23rd term
we have
a1=77
a2=71
a3=65
a4=59
a5=53
so
a2-a1=71-77=-6
a3-a2=65-71=-6
a4-a3=59-65=-6
therefore
Is an aritnetic sequence
the common difference is d=-6
the nerela expression is
an=a1+d(n-1)
substitute the given values
an=77-6(n-1)
For n=23
substitute
a_23=77-6(23-1)
a_23=77-6(22)
a_23=77-132
a_23=-55Answer:
a_23=-55
Step-by-step explanation:
Determine the intercepts of the line. y-intercept: 2-intercept: ( y 1 3 2 1 -1413121110-9-8-16-5-4-3-2 1 2 3 4 دا ب ر ا ت -8 -9 -10 -11 -12 -13 -141
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Y-intercet
it is when the line touches the y-axis(vertical axis)
From the graph is
[tex](0,-6)[/tex]X-intercept
It is when the line touches the x-axis(horizontal axis)
From the graph is
[tex](-8,0)[/tex]What is a valid conclusion that can be reached by reading the graph?A.Most of the first ladies came from Ohio.B.Most of the first ladies came from Georgia and Massachusetts.C.The same number of first ladies came from Massachusetts and Virginia as came from New York.D.Most of the first ladies are from New York.
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Solution:
Given the graph below:
The above graph represents the number of first ladies from each state (Georgia, Ohio, New York, Massachusetts, and Virginia).
The state having the longest horizontal bar is the state having the highest number of first ladies, and the state having the shortest horizontal bar is the state having the least number of first ladies.
From the graph, New York has the longest bar. This implies that Newyork has the highest number of first ladies.
Hence, we can conclude that most of the first ladies are from New York.
The correct option is D.
for particular event 686 tickets were sold for a total 2276
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Solution
For this case 686 tickets for 2766$
Students paid x=3$ and non students y=$5
Then we can set up this equations:
686 = x+y
3x + 5y = 2766
Solving for x we got:
x = 686 -y
Replacing in the second equation we got:
3(686-y) +5y =2766
2058 -3y +5y =2766
Solving for y we got:
2y = 2766-2058 =708
y= 354
And solving for x we got:
x= 686- 354 = 332
And we have:
x= 332 student tickets were sold
what are the new vertices of quadrilateral DEFG, if the quadrilateral is translated downward one unit?
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ANSWER
• D'(-5, 0)
,• E'(-3,4)
,• F'(5,0)
,• G'(3,-4)
EXPLANATION
When the quadrilateral is translated 1 unit down, only the y-coordinates change,
Hence, the new vertices of the translated quadrilateral are:
• D'(-5, 0)
,• E'(-3,4)
,• F'(5,0)
,• G'(3,-4)
11. Use each similarity statement to write thecorresponding sides of the triangles as proportions.a. ACGJ- AMKP
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Two shapes that are similar triangle CGJ and triangle MKP
to understand the following statements, lets draw the triangles first.
lets compare ratios :
line CG /MK = GJ/KP=CJ/MP
[tex]\begin{gathered} \angle C\cong M \\ \angle G\cong K \\ \angle J\cong\angle P \\ corresponding\text{ angles are congruent } \end{gathered}[/tex]Round your answers to five significant digits. Write your answers for angle measures in decimal degrees.
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We will have the following:
We first determine "b", that is:
[tex]\begin{gathered} b=\sqrt{42766^2-35276^2}\Rightarrow b=24177.14996... \\ \\ \Rightarrow b\approx24177 \end{gathered}[/tex]Now, using the law of sines we determine the measure of the angles, that is:
alpha:
[tex]\begin{gathered} \frac{sin(\alpha)}{35276}=\frac{sin(90)}{42766}\Rightarrow sin(\alpha)=\frac{35276}{42766} \\ \\ \Rightarrow\alpha=sin^{-1}(\frac{35276}{42766})\Rightarrow\alpha=55.5743883... \\ \\ \Rightarrow\alpha\approx55.574 \end{gathered}[/tex]Beta:
[tex]\begin{gathered} \frac{sin(\beta)}{24177.14996}=\frac{sin(90)}{42766}\Rightarrow sin(\beta)=\frac{24177.14996}{42766} \\ \\ \Rightarrow\beta=sin^{-1}(\frac{24177.14996}{42766})\Rightarrow\beta=34.42561171... \\ \\ \Rightarrow\beta\approx34.426 \end{gathered}[/tex]Which unit is the largest?decametermillimetermetercentimeter
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The largest unit will be meter.
On a map that shows the location of movie stars' houses, two Hollywood actors' houses are 8 centimeters apart. If the map uses a scale of 2 centimeters = 1 kilometer, how far apart are the actors' houses in real life?
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Answer
The actors' houses in real life will be 4 kilometers apart.
Explanation
If the two Hollywood actors' houses are 8 centimeters apart, and the map uses a scale of 2 centimeters = 1 kilometer, then the actors' houses in real life will be
[tex]\frac{8\text{ centimeters }\times1\text{ kilometer}}{2\text{ centimeters}}=4\text{ kilometers}[/tex]Divide Give the quotient 34,334÷7 give the quotient and remainder
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Given the expression:
34,334÷7
The quotientcan be said to be the number of times a division is fully completed while the remainder is the amount amount left that doen't go in the divisor.
To find the quotient and remainder, we have:
[tex]undefined[/tex][tex]\frac{34334}{7}=4904\text{ remainder }6[/tex]The quotient is 4904 ehilr the remainder is 6
Thus, we have:
Quotient = 4904
Remainder = 6
ANSWER:
Quotient = 4904
Remainder = 6
Bob has $700 in a savings account at thebeginning of October. If he wants to keep atleast $300 in the account for Christmas gifts andhe withdraws $25 every week for spendingmoney, how many weeks can he withdrawmoney?
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Bod has $700 in his savings account.
He wants to keep at least $300
Then $700 - $300= $400
Now, $400 is the total of money that he can withdraw.
Every week he withdraws $25.
Divide $400 by 25 to find the total of weeks:
$400/$25 = 16 weeks
Hence, Bob can withdraw money for 16 weeks.
Which expression is equivalent to (4.5j + 6)(-2.3j)?
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The simplified equivalent expression of ( 4.5j + 6 ) (- 2.3j ) is 10.35 - 13.8j
How to find equivalent expression?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them
In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.
The expression to find the equivalent is as follows:
( 4.5j + 6 ) (- 2.3j )
Hence, let's simplify the expression to get the equivalent.
( 4.5j + 6 ) (- 2.3j ) = - 10.35j² - 13.8j
Hence,
j² = -1
Therefore,
- 10.35(-1) - 13.8j = 10.35 - 13.8j
Therefore, ( 4.5j + 6 ) (- 2.3j ) is equivalent to 10.35 - 13.8j
learn more on equivalent expression here; https://brainly.com/question/24242989
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simplify. write the expression using only positive exponents 8x ^-3
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
10. 8 x ^ - 3
simplify ===> positive exponents
Step 02:
We must apply the laws of exponents.
[tex]8x^{-3}=8\frac{1}{x^3}=\frac{8}{x^3}[/tex]That is the solution.
8 / x ^ 3
Evaluate the expression. 9C5/9P5
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SOLUTION:
Step 1:
In this question, we are given the following:
Evaluate the expression.
[tex]\frac{^9C_5}{^9P_5}[/tex]Step 2:
The details of the solution are as follows:
Are the rectangles similar?Use ratios to justify your answer?
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Similar Rectangles: Two rectangles are similar when the corresponding adjacent sides have the same ratio
Taking the ratios of the Length to breadth
rectangle 1: rectangle 2
[tex]\begin{gathered} \frac{CD}{AD}\text{ :}\frac{GH}{EH} \\ \frac{5\operatorname{cm}}{4\operatorname{cm}}\text{ : }\frac{3\operatorname{cm}}{2\operatorname{cm}} \end{gathered}[/tex][tex]\begin{gathered} \frac{5}{4}\text{ : }\frac{3}{2} \\ 1.25\text{ : 1.5} \end{gathered}[/tex]The ratio of the sides is 1.25 : 1.5
Since the values are different, the rectangles are not similar
2Question 5 Multiple Choice Worth 5 points)(01.04 MC)What is the sign of the product (8)-231-21)(-29)Positive, because the products (8)(-23) and (-21) (-29) are negative, andthe product of two negative numbers is positivePositive, because the products (8)(-23) and (-21)(-29) are positive, and theproduct of two positive numbers is positiveNegative, because the product (8)(-23) is positive and the product (-21)(-29) is negative, and the product of a positive number and a negative numberis negativeNegative, because the product (8)(-23) is negative and the product (-21)-29) is positive, and the product of a negative number and a positive numberIs a negative number
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The produt of two negative numbers is positive
The produt of a positive number and a negative number is negative
Thus, for the product of (8)(-23)(- 21)(-29),
the product of 8 and - 23 would be negative(positve and negative numbers)
the product of - 21 and - 29 would be positive(negative and negative numbers)
Thus, the product of the negative and positive results would be negative. Thus, the correct option is the last option
whats the value of _ sqrt( 9/16)
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Given the following expression:
[tex]\sqrt[]{\frac{9}{16}}[/tex]remember that we have the following property when we have a square root of a fraction:
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]then, in this case we have the following:
[tex]\sqrt[]{\frac{9}{16}}=\frac{\sqrt[]{9}}{\sqrt[]{16}}=\frac{3}{4}[/tex]therefore, the simplified expression is 3/4
Calculate the six trigonometric function values of an angle θ in standard position whose terminal side goes through the point (−12,16). Make sure your fractions are fully reduced.
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GIven:
[tex]x=-12\text{ ;y=16}[/tex][tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ r=\sqrt[]{(-12)^2+(16)^2} \\ r=\sqrt[]{144+256} \\ r=\sqrt[]{400} \\ r=20 \end{gathered}[/tex][tex]\begin{gathered} \sin \theta=\frac{y}{r} \\ \sin \theta=\frac{16}{20} \\ \sin \theta=\frac{4}{5} \end{gathered}[/tex][tex]\begin{gathered} \cos \theta=\frac{x}{r} \\ \cos \theta=-\frac{12}{20} \\ \cos \theta=-\frac{3}{5} \end{gathered}[/tex][tex]\begin{gathered} \tan \theta=\frac{y}{x} \\ \tan \theta=-\frac{16}{12} \\ \tan \theta=-\frac{4}{3} \end{gathered}[/tex][tex]co\sec \theta=\frac{5}{4}[/tex][tex]\sec \theta=-\frac{5}{3}[/tex][tex]\cot \theta=-\frac{3}{4}[/tex]A.whats is its surface area B. how would the surface area change if the top two cubes are remove
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A. The green face of the figure is 6 square units. It is congruent with the contrary face which is obscured from view.
The back face, also non viewed, is 6 square units.
Blue faces total also is 6 square units, and the yellow also 6 square units.
Then, the surface area of this figure is:
(6x2)+6+6+6=30 square units.
B. So, if the top two cubes are removed, then the green face and its contrary would be 5 square units each.
The back face would be 4 square units, the blue faces still being 6 square units.
And the yellow faces would be 4 square units.
So, the surface area of the new figure would be:
(5x2)+4+6+4=24 square units.
A parabola opening up or down has vertex (0, 1) and passes through (8, -3). Write its equation invertex form.
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Explanation
The parabola in vertex form is given as
[tex]y=a(x-h)^2+k[/tex]Where (h,k) is the vertex.
[tex]y=a(x-0)^2+1[/tex]Therefore, since the parabola passes through (8,-3)
We will have;
[tex]\begin{gathered} -3=a(8)^2+1 \\ -3=64a+1 \\ 64a=-4 \\ a=-\frac{4}{64} \\ a=-\frac{1}{16} \end{gathered}[/tex]Therefore;
Answer:
[tex]y=-\frac{1}{16}(x-0)^2+1[/tex]"The more miles a person runs, the more calorles the person burns." Which scatter plot supports this statement?
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The scatter plot that supports this statement has to be a linear function (direct proportional relationship), with a positive slope.
I have snapped a picture of the question I am needing help with. Thank you.
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Given :
The length of the metal is 20 inches longer than the width.
But we fold up 4-inch flaps on each side, so the height of the box is 4 inches, and the length and width will each decrease by 8 inches (4 inches on each side). Since the length and width decrease by the same amount, the length will still be 20 inches longer than the width.
Explanation :
So the equations would be:
[tex]l=w+20[/tex]
The volume is determined as
[tex]V=l\times w\times h[/tex]Substitute the values
[tex]\begin{gathered} 2304=(w+20)\times w\times4 \\ 2304=(w^2+20w)4 \\ 2304=4w^2+80w \\ 4w^2+80w-2304=0 \end{gathered}[/tex]Solve the quadratic equation.
[tex]\begin{gathered} (w-16)(w+6)=0 \\ w=16,-6 \end{gathered}[/tex]Since the width can't be negative, the width of the box is 16 and the length is l= (16 + 20)=36.
But remember, the length and width of the piece of metal are each 8 inches longer than the box, so it was 24 inches by 44 inches.