Which of these expressions can be used to calculate the monthly payment for
a 30-year loan for $195,000 at 6.6% interest, compounded monthly?
O A.
$195 000 0.0055 (1+0.0055) 360
(1+0.0055)300 +1
OB.
$195 000 0.0055 (1+0.0055) 360
(1+0.0055) 300-1
O C.
$195 000 0.0055(1-0.0055)300
(1-0.0055) 300-1
Answer:
B
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
PMT = monthly paymentP = loan amounti = interest rate per month (in decimal form)n = term of the loan (in months)Given:
P = $195,000i = 6.6% = 0.066n = 12 × 30 = 360[tex]\implies \sf PMT=\dfrac{195000(0.066)(1+0.066)^{360}}{(1+0.066)^{360-1}}[/tex]
Let X1, Xn be i.i.d. random variables with probability density function,
fx (x) = { 1/0 0 0 < x < 0 otherwise.
(a) Let X₁, X denote a bootstrap sample and let X = n
Find: E(XX1, , Xn), V(XX1, , Xn), E(X), V(X₂).
Hint: Law of total expectation: E(X)= E(E(XY)).
Law of total variance: V(X) = E(V(XY))+ (E(X|Y)).
Sample variance, i.e. s² = (X; - X)2 is an unbiased estimator of population variance.
The expected value of the assumed probability density function is 3/4 and the variance is 3/80
How to solve for E(x) and V(x)?The probability density function is not properly stated.
So, I will provide a general explanation on how to determine E(x) and V(x) of a probability density function
Assume that the probability density function is given as:
[tex]f(x)= \left[\begin{array}{ccc}3x^2 &0 \le x \le 1\\0&Otherwise\end{array}\right[/tex]
The expression E(x) is calculated using:
[tex]E(x) = \int\limits^a_b {x \cdot f(x)} \, dx[/tex]
So, we have:
[tex]E(x) = \int\limits^1_0 {x \cdot 3x^2 \ d(x)[/tex]
Evaluate the product
[tex]E(x) = \int\limits^1_0 { 3x^3 \ d(x)[/tex]
Integrate
[tex]E(x) = \frac34x^4 |\limits^1_0[/tex]
Expand
[tex]E(x) = \frac34(1-0)^4[/tex]
Evaluate
[tex]E(x) = \frac34[/tex]
The variance is then calculated using:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Calculate [tex]E(x^2)[/tex] using:
[tex]E(x^2) = \int\limits^a_b {x^2 \cdot f(x)} \, dx[/tex]
This gives
[tex]E(x^2) = \int\limits^1_0 {x^2 \cdot 3x^2} \, dx[/tex]
Expand
[tex]E(x^2) = \int\limits^1_0 {3x^4} \, dx[/tex]
Integrate
[tex]E(x^2) = \frac{3}{5}x^5|\limits^1_0[/tex]
Expand
[tex]E(x^2) = \frac{3}{5}(1 - 0)^5[/tex]
Evaluate
[tex]E(x^2) = \frac{3}{5}[/tex]
Substitute [tex]E(x^2) = \frac{3}{5}[/tex] and [tex]E(x) = \frac34[/tex] in [tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = \frac 35 - (\frac{3}{4})^2[/tex]
Evaluate the exponent
[tex]Var(x) = \frac 35 - \frac{9}{16}[/tex]
Evaluate the difference
[tex]Var(x) = \frac{3}{80}[/tex]
Hence, the variance of the probability density function is 3/80
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How many liters of 70% alcohol solution and 30% alcohol solution must be mixed to obtain 8 liters of 60% alcohol solution?
a. Complete the table below with the expressions needed to solve this problem. Then solve it in part b.
70% solution 30% solution Final solution
Number of Liters x y
Liters of Alcohol
b. You need
liters of 70% solution and
liters of 30% solution.
rotate the figure 90 degrees clockwise then translate 4 units left
Answer:
If I am not mistaken, the new figure will be here (view attachment, bright blue figure is the new transformation)
Answer:
For each of the following equations determine the output values Corresponding to the input value
(-2;-1;0;1;2;3)
Identify the 17th term in the arithmetic sequence.
a1 = 11, d = −2
The arithmetic sequence has a common difference, and a first term and the 17th term in the arithmetic sequence is -21
How to determine the 17th term?The given parameters are:
First term, a = 11Common difference, d = -2The nth term of an arithmetic progression is:
Tn = a + (n - 1)d
So, we have:
T17 = a + 16d
Substitute the given values
T17 = 11 - 16 * 2
Evaluate
T17 = -21
Hence, the 17th term in the arithmetic sequence is -21
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somebody helpppp i beg
root*324=18
441=21
529=23
hope it helps
please mark as brainliest
-4+2(3m+7)
Explain please
Answer:
6m + 10
Step-by-step explanation:
Distributive Property
a(b + c) = ab + acSolving
-4 + 2(3m + 7)-4 + 2(3m) + 2(7)-4 + 6m + 146m + 10You are a salesman for company Z. Total sales for company Z last year were
R900 000,00. You were responsible for obtaining R300 000,00 worth of these
sales. As a fraction, what was your share of the total sales?
Answer:
1/3 or 33.33%
Step-by-step explanation:
30000000/90000000
The area of a rectangle is 24 cm² and the perimeter is 22 cm .What is the lenth and width of this rectangle?
Step-by-step explanation:
length × width = 24
2×length + 2×width = 22
length + width = 11
length = 11 - width
this we use in the first equation again :
(11 - width) × width = 24
11×width - width² = 24
width² - 11×width + 24 = 0
the general solution to an quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = width
a = 1
b = -11
c = 24
and so we get
width = (11 ± sqrt((-11)² - 4×1×24))/2×1) =
= (11 ± sqrt(11² - 96))/2 = (11 ± sqrt(121-96))/2 =
= (11 ± sqrt(25))/2 = (11 ± 5)/2
width1 = (11 + 5)/2 = 16/2 = 8 cm
width2 = (11 - 5)/2 = 6/2 = 3 cm
and teenaged to this is then
length1 = 11 - width1 = 11 - 8 = 3 cm
length2 = 11 - width2 = 11 - 3 = 8 cm
so, it is clear. one dimension has to be 8 cm, and the other one 3 cm. it does not matter which is which.
Interest = $821.25, time = 1 year, rate = 12.42%. Find the principal
Step-by-step explanation:
P = l.100/t.r = $821.25×100/12.42×1 = $6612.318
hope this helps you.
Write the tangent, cosine and sine ratios of angles X & Y. Write each answer as a (reduced) fraction. Not a decimal.
The tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.
What are the trigonometry ratios?For a right angle triangle, the trigonometry ratios can be given as,
[tex]\rm \sin \theta=\dfrac{b}{c}\\\rm \cos \theta=\dfrac{a}{c}\\\rm \tan \theta=\dfrac{b}{a}[/tex]
Here, a is base side, b is perpendicular side and c is the hypotenuse side of the triangle.
In the given triangle, the length of base side is 8 units, perpendicular side is 6 units and hypotenuse side is 10 units.
[tex]a=8\\b=6\\c=10[/tex]
Thus, the tangent, cosine and sine ratios of angles X & Y are,
[tex]\rm \sin \theta=\dfrac{6}{10}=\dfrac{3}{5}\\\rm \cos \theta=\dfrac{8}{10}=\dfrac{4}{5}\\\rm \tan \theta=\dfrac{6}{8}=\dfrac{3}{4}[/tex]
Thus, the tangent, cosine and sine ratios of angles X & Y in the reduced faction form is 3/4, 4/5 and 3/5 respectively.
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PLEASE HELP ME! Find the 10th term of the geometric sequence that has a1 = 400 and A2 = 200.
Answer:
I believe the answer is 0.7813
Step-by-step explanation:
Find the difference between 400 and 200, as they are first and second terms. This is going to be 0.5 since it is being divided.
The formula is: a∨n=a∨1(r)^(n-1)
n= the number of the sequence you are looking for
r=0.5
a∨1=400
a∨2=200
400(0.5)^(10-1)
The volume of a sphere is
[tex]125\pi[/tex] cm3. What is the radius?
Last question.
Hi!!
Answer:
I'm not 100% sure, but I think it's 3.1.
Step-by-step explanation:
I took your volume, which is 125[tex]\pi[/tex], then a formula, which is
V=[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex], then I just plugged in the 125 and I got 3.1. I'm so sorry if it's wrong! <3
The figure below shows the graph of f’ the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.
find the x-value where f attains it’s absolute maximum value on the closed interval x=-2 to x=6. justify your answer
Answer:
x = -2
Step-by-step explanation:
The function is decreasing where the first derivative is negative.
That is, the function is decreasing on the interval (-2, 5), except at x=2, where there is a flat spot. That means the maximum value is found at the left end of that interval, at x=-2.
__
The maximum value might be found at x = 6, at the right end of the interval (5, 6) on which the function is increasing. However, we judge the area under the first derivative curve between x=5 and x=6 to be less than the total area under the curve between x=-2 and x=5. That means the function does not increase enough from its minimum at x=5 to make up for the decrease over the longer interval.
__
The attachment shows an approximation of the derivative function given in the problem statement (dashed line) and its integral (solid line). Not all of the curvature of f'(x) is accounted for in the approximation, but the overall result is consistent with the above analysis.
The image shows a circle centered at point O angle AOB Measures at 42 degrees.
What is the Measure of the angle acb explain your reasoning
The measure of angle ACB for circle centered at point O is 21°
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
∠AOB = 2 * ∠ACB (angle at center is twice the angle at circumference)
42 = 2 * ∠ACB
∠ACB = 21°
The measure of angle ACB for circle centered at point O is 21°
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In the following diagram, what is the value of x?
x=[x]
Answer:
x=90°
Step-by-step explanation:
Too much work............. ....
An electric bulb is sold in a box measuring 5 cm by 4 cm by 4 cm. If the shopkeeper receives them in a carton measuring 50 cm by 20 cm by 20 cm, how many bulbs would be packed in one carton ?
Answer:
250
Step-by-step explanation:
Bulb box and carton both are of cuboidal shape.
For bulb box the dimensions are:
l = 5 cm, w = 4 cm, h = 4 cm[tex]V_{Bulb\: box} =lwh[/tex][tex]\implies V_{Bulb\: box} =5(4)(4)[/tex][tex]\implies V_{Bulb\: box} =80\: cm^3[/tex]For Carton the dimensions are:
l = 50 cm, w = 20 cm, h = 20 cm[tex]V_{Carton} =lwh[/tex][tex]\implies V_{Carton} =50(20)(20)[/tex][tex]\implies V_{Bulb\: box} =20,000\: cm^3[/tex]To find the number of bulbs packed in the carton, divide the [tex]V_{Carton}[/tex] by [tex] V_{Bulb\: box}[/tex]
[tex] Number \:of \:bulbs =\frac{V_{Carton}}{V_{Bulb\: box}}[/tex][tex] \implies Number \:of \:bulbs =\frac{20,000}{80}[/tex][tex] \implies Number \:of \:bulbs = 250[/tex]So, 250 bulbs will be packed in one carton.
MARKING BRAINLEST IF CORRECT
Solve for x.
66
6
7
110
Answer:
x =6
Step-by-step explanation:
17x + 8 + 66 + 74 +110 = 360
17x + 258 =360
17x = 360 -258
17x =102
x =6
Apply angle sum property
17x+8+66+74+110=36017x+258=36017x=102x=6Find the volume of the solid.
PLS HELP
Find the value of x and y.
Answer:
x= 27.71281 = 16√3
y= 13.85641 = 8√3
Step-by-step explanation:
hope it helps :)
Which shows a true comparison? Select all that apply. A. 32. 03 > 32. 3 32.03>32.3 B. 3. 114 > 3. 112 3.114>3.112 C. 4. 003 < 3. 996 4.003<3.996 D. 0. 541 > 0. 145 0.541>0.145 E. 0. 141 < 0. 19
Answer:
B. 3.114 > 3.112
D. 0.541 > 0.145
E. 0.141 < 0.19
Step-by-step explanation:
In order to determine which decimal is greater or less than another, compare the place values from left to right. First, compare the whole numbers to the left of the decimal point. If they are not the same, the smaller decimal number is the one with the smaller whole number. This applies to the rest of the places.
----------------------------------------------------
32.3 has a greater tenths value than 32.03, so 32.03 < 32.3. Option A is false.
----------------------------------------------------
3.114 has a greater thousandths value than 3.112, so 3.114 > 3.112. Option B is true.
----------------------------------------------------
4.003 has a greater whole number than 3.996, so 4.003 > 3.996. Option C is false.
----------------------------------------------------
0.541 has a greater tenths value than 0.145, so 0.541 > 0.145. Option D is true.
----------------------------------------------------
0.19 has a greater hundredths value than 0.141, so 0.141 < 0.19. Option E is true.
hope this helps!
The inequalities which are truly compared are B, D and E.
Given certain inequalities.
We have to find the true comparisons.
We have to look at the corresponding digits of numbers which are compared from left to right. Greater numbers on the left will be the greater number.
A. 32. 03 > 32. 3
This is false since 32.3 is greater. In 32.03, 0 is in the tenth place, while 3 is in the tenth place for 32.3.
B. 3. 114 > 3. 112
This is true since in the thousandths place, 4 is greater than 2.
C. 4. 003 < 3. 996
This is clearly false, since in the whole part, 4 is greater than 3.
D. 0. 541 > 0. 145
This is true, since in the tenths place, 5 is greater than 1.
E. 0. 141 < 0. 19
This is also true, since in the hundredths place, 9 is greater than 4.
Hence the true comparisons are B, D and E.
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round 2.577681 to 4 decimal places
Answer:
2.5777
Step-by-step explanation:
Answer: 2.5777
Step-by-step explanation:
Given:
2.577681
Find the fourth decimal place:
2.577681
Round:
2.5777
Rounding:
Is the place to the right greater than or less than 5?
If greater than or equal to, round up. If less than, it stays the same.
In this case, 8 > 5
John is making apple pies and apple cobblers to sell at the farmer’s market. A pie uses 4 cups of apples and 3 cups of flour. A cobbler uses 2 cups of apples and 3 cups of flour. When John sells the pies and cobblers at the farmer’s market, he will make $3.00 profit per pie and $2.00 profit per cobbler. Let x = the number of pies John makes. Let y = the number of cobblers John makes. Interpret the meaning of the vertex with the maximum profit in context of john’s baking.
Step-by-step explanation:
there are some pieces of information missing like the price of apples and flour. or the selling prices. or any restrictions like a fixed budget to buy ingredients or how many pies and cobblers he can make in a certain available time.
all we can say based on the given information :
one pie = 4a + 3f (a = apples, f = flour)
one cobbler = 2a + 3f
P(x, y) = 3x + 2y =
= x(selling price - 4a - 3f) + y(selling price - 2a - 3f)
the max. of P(x, y) is the maximum profit by selling pies and cobblers, which is without any further information +infinity.
the more pies and cobblers he sells, the bigger the profit - no limit.
if mÃc=170° Find mLB
Answer:
∠ B = 85°
Step-by-step explanation:
the inscribed angle B is half the measure of its intercepted arc AC , then
∠ B = [tex]\frac{1}{2}[/tex] × 170° = 85°
Gretta is 2 1/2 kilometers tall. Which of the followings is equivalent to 2 1/2 kilometers in meters
Answer:
Gretta would be 2500 meters tall
Step-by-step explanation:
2km=2000 and the 1/2 would be 1/2=500 so the answer it 2500
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Alex buys 30 shares of Walmart at the close price if $48.80. His broker charges him 3% of each share. How much did Alex spend in total to buy this stock?
Alex spend $1507.92 in total to buy this stock at 3% charges on each shares.
What is shares?
Shares represent equity ownership in a corporation or financial asset, owned by investors who exchange capital in return for these units.
Alex buys 30 shares of Walmart at the close price of $48.80.
His broker charges him 3% of each share.
Purchasing of 30 shares =48.80 *30
=$1464
Now we have to find the 3% of total purchasing of shares.
So,
Broker's fees =[tex]\frac{3}{100}*1464[/tex]
= 0.03 * 1464
= 43.92
So, total cost of stock= 1464+43.92
= 1507.92
Hence, Alex spend $1507.92 in total to buy this stock.
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NEED HELP FAST! 50 POINTS see the image below
Answer:
90 in²
Step-by-step explanation:
First,check the figure I provided .
Area of the figure = area1 + area2 + area3 + area4
= (3×2) + (7×7) + (7×2) + (7×6)÷2
= 6 + 49 + 14 + 21
= 90
Convert 4 3/5 to a fraction greater than one
Answer:
23/5
Step-by-step explanation:
* means multiply
4 3/5
5 * 4 = 20
20 + 3 = 23
23/5
Answer:
[tex]\frac{23}{5}[/tex]
Step-by-step explanation:
The type of fraction we are dealing with is called a mixed fraction
In order to convert this fraction into a fraction greater than 1, we will have to convert it into an improper fraction
So we keep the denominator
Multiply the whole number by the denominator and add that to the numerator
Some of the most important nutrients in the ocean include:
A. Nitrates, carbonic acid, and oxygen.
B. Carbon dioxide, oil, and gold.
C. Phosphate, phytoplankton, and potassium.
D. Phosphates, nitrates, and carbon.
Answer:
D one is the answer
Step-by-step explanation:
Segment AB has coordinates A(-4, 7) and B(5, 1). Find AP/AB and the coordinates of P that partitions AB such that AP:PB = 1:2. AP/AB= [Select] Coordinates of P: ( [Select] [Select] Hint: (x₁+ m/n (x2-x1). Y₁+ m/n (y2-V₁))
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-4,7)\qquad B(5,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-4,7)=1(5,1)[/tex]
[tex](\stackrel{x}{-8}~~,~~ \stackrel{y}{14})=(\stackrel{x}{5}~~,~~ \stackrel{y}{1})\implies P=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-8 +5}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{14 +1}}{1+2} \right)} \\\\\\ P=\left(\cfrac{-3}{3}~~,~~\cfrac{15}{3} \right)\implies P=(-1~~,~~5)[/tex]
now, the segment AB cut by P in a 1:2 ratio, makes 3 thirds, so the ratio AP/AB is
[tex]\cfrac{AP}{AB}\implies \cfrac{1}{1+2}\implies \cfrac{1}{3}[/tex]