[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]
[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]
how much will it be in interest alone?
well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned
[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]
Alexa lives 4 kilometers away from school. She leaves home and rides her bicycle toward school at a speed of 0.25 kilometer per minute.Enter the function f(x) that represents Alexa's distance in kilometers from school after x minutes. I NEED ANSWERS SO I DONT FAIL THIS SCHOOL YEAR PLEASE
Alexa lives 4 kilometers away from school.
Distance between Alexa house and school = 4km
She leaves home and rides her bicycle toward school at a speed of 0.25 kilometer per minute
Speed of Alexa = 0.25km/min
The relation between speed, distance and time is express as:
[tex]\text{Speed}=\frac{Dis\tan ce}{Time}[/tex]Let time = x minutes
Substitute the value, time = x, Distance = f(x), speed = 0.25km/min
[tex]\begin{gathered} \text{Speed}=\frac{Dis\tan ce}{Time} \\ 0.25=\frac{f(x)}{x} \\ f(x)\text{ = 0.25x} \end{gathered}[/tex]Answer: f(x) = 0.25x
write the equation of the line passing through the given points write your awnser in slope intercept form Y=mx+b (5 1) and (-3 17)
The given points are (5, 1) and (-3, 17).
First, we have to find the slope using the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} x_1=5 \\ x_2=-3 \\ y_1=1 \\ y_2=17 \end{gathered}[/tex]Let's use the coordinates above to find the slope.
[tex]m=\frac{17-1}{-3-5}=\frac{16}{-8}\Rightarrow m=-2[/tex]The slope is -2.
Now, we use the point-slope formula to find the equation.
[tex]y-y_1=m(x-x_1)[/tex]Let's use the same coordinates x_1 and y_1, and the slope m = -2.
[tex]y-1=-2(x-5)[/tex]Now, we solve for y to express the equation in slope-intercept form.
[tex]y-1=-2x+10\Rightarrow y=-2x+10+1\Rightarrow y=-2x+11[/tex]Therefore, the slope-intercept form of the equation is[tex]y=-2x+11[/tex]Is 5/6 equivalent to 0.832
Answer: No
Step-by-step explanation:
1 divided by 6 would be 16 and 4/6. So you would have to multiply 16 and 4/6 by 5, add them together, and then divide by 10 to get the decimal. 16 * 5 = 80. 4/6 * 5 = 20/6. 80/10 = 8. 20/6 divided by 10 = 10/6. 8+10/6 is not equal to .832
Do you know how to solve? I got 3.99 for the mean (it was correct)For the sample standard deviation I got 1.1285 ( but it was wrong)
Explanation
Given the sample below, we are asked to find the mean and the standard deviation.
Part A
We can find the mean below using the formula
[tex]\begin{gathered} \text{Mean}=\frac{\sum ^{}_{}x}{n} \\ \text{where x is the sample value and n is the sample size} \end{gathered}[/tex]Therefore,
[tex]\text{Mean }=\frac{79.8}{20}=3.99[/tex]Answer =3.99
Part B
The standard deviation of the sample size can be found using the formula below;
[tex]\begin{gathered} S.D=\sqrt[]{\sum ^{}_{}\frac{(x-\bar{x})^2}{N-1}} \\ =\sqrt[]{\frac{20.938}{19}} \\ =\sqrt[]{1.102} \\ =1.05 \\ \end{gathered}[/tex]Answer: 1.05
A linear equation written in the form y = mx + b is in ?
A linear equation is written in the form
[tex]y=mx+b[/tex]it is the Slope-intercept form
If Nintendo had sold 12.2 million games in March and they had thought that they had sold 20.9 million how off was there percent error?
First let's calculate the absolute error by subtracting both values:
[tex]20.9-12.2=8.7[/tex]So the absolute error is 8.7 millions.
Now, in order to find the percent error, we just need to divide the absolute error by the number of games sold:
[tex]\frac{8.7}{12.2}=0.7131=71.31\text{\%}[/tex]So the percent error is 71.31%.
Making an inference usingig a two-way frequency tableA group of 150 college students who took math fost term were interviewed. They were asked whether they passed their math course and whether they live oncampus. Their responses are summarized in the following tablePassed math Failed mathve on campus2466Live off campus392152(a) What percentage of the students passed moth? []%(b) What percentage of the students live off campus? []%(c) What percentage of the students who live off campus passed math? []%(d) Is there evidence that students who live off campus tend to pass math more often than average?Yes, because the percentage found in part (e) is much greater than the percentage found in part (0)Yes, because the percentage found in part() is much greater than the percentage found in part (b)No, because the percentage found in part(e) is about the same as the percentage found in part (a).No, because the percentage found in part (5) is about the same as the percentage found in part (b).
1) Considering that there are 150 students
A) Adding 24+39 we got 63 students
150------------100%
63 ----------- x
x=6300/150
x= 42% of the students passed Math.
B) Adding the number of those students who live off-campus 39 +21
150 ----------------100%
60------------------ y
y=6000/150
y=40%
C) 60 students live off-campus 39 succeded. So we can write
60 --------- 100%
39 --------- z
z= 3900/60
z=65% passed math (off-campus)
D) Comparing that 65% of students who live off-campus passed math and that among those who live on campus and that 58% of all students failed
Then we can state:
A)
Use the order of operations to demonstrate that the Distributive Property holds by showing that both sides of each equation are equal.
2/5(4/3-1/3)=2/5*4/3-2/5*1/3
LHS= 2/5(4/3-1/3)
=2/5(4-1/3)
=2/5( /3)
= /15
= 2/5
RHS= 2/5*4/3-2/5*1/3
= /15-2/15
= -2/15
= /15
=2/5
The Distributive Property holds as both sides of the given equality are equal.
Distributive PropertyThe distributive property means that the outer time of the expression multiplies each of the inner terms of the expression. Then, these terms may be combined, if they contain like-terms.
The left-hand side of the expression is given as follows:
2/5(4/3 - 1/3).
Applying the distributive property, it is found that:
2/5 x 4/3 = 8/15.2/5 x 1/3 = 2/15.Subtracting them, it is found that:
2/5(4/3 - 1/3) = 8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Precedence of operationsThe right-hand side of the expression is:
2/5 x 4/3 - 2/5 x 1/3
Multiplication takes precedence over subtraction, hence:
2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15
Same denominator, hence the numerators can be subtracted as follows:
8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Both sides of the expression have the same value, hence the distributive property holds for this problem.
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Determine the X intercepts of the para bola whose graph is given below write your answer as ordered pairs separated by a comma if necessary
The x-intercepts are (-1, 0) and (4, 0)
Explanation:Given:
A graph of a parabola
To find:
the x-intercepts of the parabola in ordered pairs
The x-intercept is the value of x when y = 0
On a graph, it is the value of x when the line crosses the x-axis
The line crosses the x axis at x = -1 and x = 4
The x intercept in ordered pairs will be in the form (x, y)
when x = -1, y = 0
when x = 4, y = 0
The x-intercepts are (-1, 0) and (4, 0)
35×0.37 ..find out the solution and the reasoning behind the solution
Given:
Given that 35×0.37.
Required:
To find the solution and reasoning behind the solution.
Explanation:
Let us manipulate the multiplication.
[tex]35\times0.37=12.95[/tex]As there are two digits after decimal point in 0.37, we put decimal point after two digits from right to left in the product (solution) obtained after multiplication.
Final Answer:
The solution is 12.95.
in CDE, J is the centroid. If DH=72 find DJ
Answer:
DJ = 24
Explanation:
We are told from the question that J is the centroid of CDE, this means that J is the midpoint of DH, CJ and FE
If J is the centroid of DH, then 2DJ = JH
Also DJ + JH = DH
The equation becomes:
DJ + 2DJ = DH
3DJ= DH
Given
DH = 72
Hence 3DJ = 72
DJ = 72/3
DJ = 24
Hence the measure of DJ is 24
Find a polynomial function P(x)with the given zeros.4, 3, 8
Given the word problem, we can deduce the following information:
The zeroes are: 4, 3, 8
To determine the polynomial function P(x) with the given zeroes, we follow the process as shown below:
[tex]\begin{gathered} (x-4)(x-3)(x-8)=0 \\ \\ \end{gathered}[/tex]We first expand (x-4)(x-3):
[tex](x-4)(x-3)=x^2-7x+12[/tex]Next, we expand (x^2-7x+12)(x-8):
[tex]\begin{gathered} (x^2-7x+12)(x-8)=x^2(x)+x^2(-8)-7x(x)-7x(-8)+12(x)+12(-8) \\ Simplify \\ =x^3-15x^2+68x-96 \end{gathered}[/tex]Hence,
[tex]x^3-15x^2+68x-96=0[/tex]Therefore, the polynomial function is:
[tex]P(x)=x^3-15x^2+68x-96[/tex]Determine the z-intercepts of the parabola whose graph is given below.
The x-intercepts are the points where a curve intercepts the x-axis.
From the picture of the problem, we see that the curve intercepts the x-axis in two points:
Answer
The x-intercepts are at:
• x = -6 at (-6,0)
,• x = -2 at (-2,0)
im having a hard time understanding this could you please help me
Given -
The odds against winning a prize in the raffle = 9:1
To Find -
Probability of winning prize =?
Step-by-Step Explanation -
Total possible outcome = 9 + 1 = 10
Favourable outcome = 9
So,
Probability = Total outcome / Favourable outcome
Probability = 9/10 = 0.9
Final Answer -
Probability of winning prize = 0.9
if I may ask may you help me solve this
Explanation
In the image,
[tex]QT=18[/tex]We can see that line SQ is a perpendicular line that serves as the bisector of RT
This implies that;
[tex]RQ=QT=18[/tex]Since;
[tex]\begin{gathered} RQ+QT=RT \\ 18+18=RT \\ RT=36 \end{gathered}[/tex]Answer: 36
How many solutions does the system formed by x − y = 4 and ay − ax + 4a = 0 have for a nonzero number a? Give your answer and complete the explanation.
Given system of equations have no solutions that is nonzero.
We have been given the system of equations formed by x − y = 4 and ay - ax + 4a = 0
We need to find the number of non-zero solutions the system have for a nonzero number 'a'
x - y = 4 ............(1)
ay - ax + 4a = 0 ............(2)
From equation (1),
x = 4 + y
Substitute x = 4 + y in equation (2),
ay - a(4 + y) + 4a = 0
ay - 4a - ay + 4a = 0
-4a + 4a = 0
0 = 0
This means that the system have no solutions that is nonzero.
Therefore, given system of equations have no solutions that is nonzero.
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Written as a percent, what is the probability of getting an odd number on a spinner with 5 equal parts numbered 1 to 5?A.20%B.40%C.60%D.80%
Given:
There are given that the spinner with 5 equal parts numbered 1 to 5.
Explanation:
In the given spinner, there are given the number: 1, 2, 3, 4, 5.
Now,
From all the given numbers, there are 3 odd numbers: 1, 3, and 5.
So,
From the probability:
[tex]P=\frac{Total\text{ number of odd numbers in the given spinner}}{Total\text{ numbers on the spinner}}[/tex]Then,
[tex]\begin{gathered} P=\frac{3}{5} \\ P=0.6 \end{gathered}[/tex]Now,
For the percentage:
[tex]\begin{gathered} P=0.6\times100\% \\ P=60\% \end{gathered}[/tex]Final answer:
Hence, the correct option is C.
The weight P in pounds that a beam can safely carry is inversely proportional to the distance D in feet between the supports of the beam. For a certain type of wooden beam,
K←
5,400
P= What distance between supports is needed to carry 900 lb?
D
uestion:
For the beam to support a weight of 900 lb, the distance between the supports needs to be no more than feet.
(Simplify your answer. Round to two decimal places as needed.)
The distance between supports is needed to carry 900 lb is 6 feet.
What is termed as the inversely proportional?Whenever the value with one quantity rises relative to the value of another, the two are referred to as being inversely proportional. It indicates that the two portions behave in nature in opposing ways. For instance, speed as well as time are inversely proportional to one another. The time decreases as the speed increases.For the given question,
The distance of the support of the beam is 'D'.
P ∝ 1/D
Now, weight is inversely proportional to distance.
P is the weight needed to carry = 900 lb.
Thus,
P = K/D
Where is proportionality constant; K = 5400.
D = K/P
Put the values.
D = 5400/900
D = 6 feet
Thus, the distance between supports is needed to carry 900 lb is 6 feet.
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What is the line of reflection for
SOLUTION:
Step 1:
In question 12, we are meant to find the line of reflection for Triangle ABC and its image based on the diagram:
Step 2:
The line of reflection for Triangle ABC and its image is:
[tex]\text{y = x --- OPTION D}[/tex]probleme 1-2 show two Parallel lines and a transversal. Find the values of x
From the blurry picture shown, we can concur that:
x and 123.25 degree angle are interior corresponding angles.
They add up to 180 degrees, thus we can write the equation:
[tex]123.25\degree+x\degree=180\degree[/tex]We can now easily solve for x:
[tex]\begin{gathered} 123.25\degree+x\degree=180\degree \\ x\degree=180-123.25 \\ x=56.75\degree \end{gathered}[/tex]The solution:
[tex]x=56.75\degree[/tex]Find the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We need to find the savings plan balance after 8 months with an APR of 8% and monthly payments of $300.00.
Let 8% is changed to decimal value by dividing with hundred.
8/100=0.08.
Now we are required to find the growth factor.
growth factor = (1 + (0.08 / 12)) per month = 1.00667
After 9 months, the balance is
($300.00)*(1.00667)8
316.21 is the balance after 6 months.
Hence 316.21 is the savings plan balance after 6 months with an APR of 8% and monthly payments of $300.
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Somebody please answer asap for brainlist please
The thing that the change that takes place in Ulrich and Georg suggested that the authors theme may be A. Wild anger can lead to wild deaths.
What is the story about?The Interlopers is a story about two men who met in a forest and we're fighting over a land. They were trapped under a tree. In the end, they wee killed by a wolf.
It should be noted that the theme was illustrated in the story. This was that anger can bring about death. This was depicted ad Georg and rich fired due o their anger.
In conclusion, the correct option is A.
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I need help with my math
Answer:
Histogram Tells you how many pumpkins had mass below 6 kg
The box plot can be used to determine that the median was 8
Explanation:
A histogram is a chart the plots frequency of a certain quantity.
In our case, the histogram given tell us how many pumpkins fall within a certain mass range. Therefore, to find out how many pumpkins are below 6 kg, we use a histogram.
On the other hand, the box plot summarizes the numerical data. In our case, it can be used to find the median weight of the pumpkins by just reading off the position of the median line.
7 ( 7x - 3y) - 6 Expand the expression
The expanded form of the expression is 49x - 21y - 6
Explanation:[tex]\text{Given: }7(7x\text{ - 3y) - 6}[/tex]To expand, we will multiply the terms outside by the terms inside the parentheiss:
[tex]\begin{gathered} U\sin g\text{ distributive property} \\ a(b\text{ + c) = a9b) + a(c)} \\ \\ 7(7x-3y)-6=\text{ }7(7x)\text{ -7(3y) - 6} \\ =\text{ 49x - 21y - 6} \end{gathered}[/tex]The expanded form of the expression is 49x - 21y - 6
Should Clare's or the doctor's measurement be considered the actual height? Explain your reasoning.
Answer: Should Clare's or the doctor's measurement be considered the actual height? In this scenario I believe its the doctors measurements. This is because she could have used a measuring tape and had someone measure her height. The measuring tape may not be accurate due to how it would be used to measure her height. So the doctor's should because they don't measure you, they use a measuring tape/ stick that is attached to the wall. That is why I think the doctor's is the actual height.
(I used RACE format)
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 3.0, b = 4.0, C = 58°
Answer
A = 46.3°
B = 75.7°
c = 3.5
Explanation
We will be using both Cosine and Sine rule to solve this.
For Cosine rule,
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the Cosine rule is given as
c² = a² + b² - 2ab Cos C
a = 3.0
b = 4.0
C = 58°
c² = 3² + 4² - 2(3)(4)(Cos 58°)
c² = 9 + 16 - (24)(0.5299)
c² = 25 - 12.72 = 12.28
c = √12.28 = 3.50
To find the other angles, we will now use Sine Rule
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
[tex]\frac{\text{ Sin A}}{a}=\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]So, we can use the latter parts to solve this
[tex]\frac{\text{ Sin B}}{b}=\frac{\text{ Sin C}}{c}[/tex]B = ?
b = 4.0
C = 58°
c = 3.5
[tex]\begin{gathered} \frac{\text{ Sin B}}{4}=\frac{\text{ Sin 58}\degree}{3.5} \\ \text{ Sin B = }\frac{4\times\text{ Sin 58}\degree}{3.5}=0.9692 \\ B=Sin^{-1}(0.9692)=75.7\degree \end{gathered}[/tex]We can then solve for Angle A
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 75.7° + 58° = 180°
A = 180° - 133.7° = 46.3°
Hope this Helps!!!
Please help me with this question! Will give brainliest !!! I need it ASAP
Answer:
The number is not a square number because the exponent is an odd number.
Step-by-step explanation:
Square numbers or perfect squares are any numbers that once put to the square root equals a whole number. Such as 4 is a square number because the square root of 4 is 2 or 2 to the second power. Numbers that are raised to even powers also fall under this rule. For example, 16 is a square number as it is equal to 2 to the fourth power, or 16 to the fourth root is 2. Since 1953125 can also be written by 5 to the ninth power it does not go under this rule due to the power being 9. 9 is an odd number. For it to be a perfect square the exponent would have to be an even number.
Which options show polynomial 1 bring divided into polynomial 2? SELECT ALL THAT APPLY
Hello. This is an exercise about polynomials.
In this specific question, we will see about the division of polynomials:
We have two polynomials:
• First: 2x
,• Second: 6x²-10x
Now, we'll have to divide the first by the second. We have some ways to write this:
The third and fourth options are wrong because it divides the second polynomial by the first, while the question asks the first divided by the second.
20% of blank = 100 I suck at math
Answer:
20% means divide by 5 so 100 * 5 = 500
Step-by-step explanation:
because 20% of 500 is 100
Hello!
Original Question: 20% of blank = 100
⇒ 20% = [tex]\dfrac{20}{100} =0.2[/tex]
⇒ 0.2 of blank ⇒ 0.2 * blank = 100
Let's solve:
[tex]0.2 *\text{blank}=100\\\\blank = \dfrac{100}{0.2} = 500[/tex]
Thus blank is 500!
Answer: 500
Hope that helps!
a washer and dryer cost 1001 combined the washer costs 51 more the than the dryer how much does the dryer cost
we can write equations from the statements
a washer and dryer cost 1001 combined
[tex]w+d=1001[/tex]where w is the price of the washer and d the price of the dryer
the washer costs 51 more the than the dryer
[tex]w=51+d[/tex]then we can replace the value of w from the second equation to the first equation
[tex]\begin{gathered} (51+d)+d=1001 \\ 51+d+d=1001 \\ 51+2d=1001 \end{gathered}[/tex]and solve for d
[tex]\begin{gathered} 2d=1001-51 \\ 2d=950 \\ d=\frac{950}{2} \\ \\ d=475 \end{gathered}[/tex]the cost of the dryer was $475