Let a(n) denote the n-th term in the GP. We're given
a(6) = 8a(10)
a(7) + a(8) = 192
In a geometric progression, consecutive terms are scaled up or down by a fixed ratio r such that
a(n) = r a(n - 1)
By substitution, we get
a(n) = r (r a(n - 2)) = r ² a(n - 2)
and we can continue the pattern down to the first term,
a(n) = r a(n - 1) = r ² a(n - 2) = r ³ a(n - 3) = … = rⁿ ⁻¹ a(1)
So we can rewrite the first two equations in terms of the first term of the GP a(1) and the common ratio r :
r ⁵ a(1) = 8r ⁹ a(1)
r ⁶ a(1) + r ⁷ a(1) = 192
Solve the first equation for r :
r ⁵ a(1) = 8r ⁹ a(1) → 1 = 8r ⁴ → r = 1/∜8 ≈ 0.5946
Solve the second equation for a(1) :
r ⁶ a(1) + r ⁷ a(1) = r ⁶ a(1) (1 + r ) = 1/(16√2) a(1) (1 + 1/∜8) = 192
→ a(1) = 6144 ∜2 / (1 + ∜8) ≈ 2724.48
Find the distance from point X to line p.
Answer:
[tex]\sf 2\sqrt{17}[/tex]
Step-by-step explanation:
To find the distance of a line using distance formula:
The line from point X intersect the line p at (0 , -3).
( -2 , 5) ⇒ x₁ = -2 & y₁ = 5
(0 , -3) ⇒ x₂ = 0 & y₂ = -3
[tex]\boxed{\bf Distance = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}}[/tex]
[tex]\sf = \sqrt{-2-0)^2+(5-[-3])^2}\\\\=\sqrt{(-2-0)^2 + (5+3)^2}\\\\=\sqrt{(-2)^2+(8)^2}\\\\=\sqrt{4+64}\\\\=\sqrt{68}\\\\=\sqrt{2*2*17}\\\\=2\sqrt{17}[/tex]
Solve: log 3 (3x) + log 3 (3) = 5
Answer: x=27
Step-by-step explanation:
Assumption the 3's are the bases
[tex]log_{3} 3x +log_{3} 3=5[/tex] >combine using multiplication log rule (logs with
same base, that are being added can be
combined with multiplication)
[tex]log_{3}( 3x)(3) =5\\[/tex] >simplify
[tex]log_{3}( 9x) =5\\[/tex] >rewrite into exponent form
[tex]3^{5} = 9x[/tex] >simplify
243 = 9x
x=27
Answer:
x = 27
Step-by-step explanation:
using the rules of logarithms
• [tex]log_{b}[/tex] b = 1
• [tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
then
[tex]log_{3}[/tex] (3x) + [tex]log_{3}[/tex] 3 = 5
[tex]log_{3}[/tex] (3x) + 1 = 5 ( subtract 1 from both sides )
[tex]log_{3}[/tex] (3x) = 4
3x = [tex]3^{4}[/tex] = 81 ( divide both sides by 3 )
x = 27
What is the interquartile range for data set? 27,4,54,78,27,48,79,64,5,6,41,71
The Interquartile range for the given data set is 51.
The interquartile range for a given data set, the values of the first quartile (Q1) and the third quartile (Q3). The interquartile range is the difference between Q3 and Q1.
First, let's arrange the data set in ascending order:
4, 5, 6, 27, 27, 41, 48, 54, 64, 71, 78, 79
To find Q1, which represents the lower quartile, we need to locate the median of the lower half of the data set. Since the data set has 12 values, the lower half consists of the first 6 values:
4, 5, 6, 27, 27, 41
The median of this lower half is the average of the middle two values, which are 6 and 27:
Q1 = (6 + 27) / 2 = 33 / 2 = 16.5
To find Q3, the upper quartile, we need to locate the median of the upper half of the data set. Again, since the data set has 12 values, the upper half consists of the last 6 values:
48, 54, 64, 71, 78, 79
The median of this upper half is the average of the middle two values, which are 64 and 71:
Q3 = (64 + 71) / 2 = 135 / 2 = 67.5
Finally, we can calculate the interquartile range by subtracting Q1 from Q3:
Interquartile range = Q3 - Q1 = 67.5 - 16.5 = 51
Therefore, the interquartile range for the given data set is 51.
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We mixed 5l of 45% alcohol, 4l of 82% and 1l of 92% alcohol. How many percent alcohol does the resulting mixture contain? I got 58.6% and im wondering IF that's correct.
The resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.
To solve this problemWe can calculate the weighted average of the alcohol percentages based on the volumes of each component.
Let's figure out how much alcohol there is overall in the mixture:
Total alcohol is calculated as follows: (Volume of 45% alcohol) * (Property of 45% alcohol) + (Volume of 82% alcohol) * (Property of 82% alcohol) + (Volume of 92% alcohol) * (Property of 92% alcohol).
Total alcohol = (5 liters) * (45%) + (4 liters) * (82%) + (1 liter) * (92%)
Total alcohol = 2.25 liters + 3.28 liters + 0.92 liters
Total alcohol = 6.45 liters
Let's now determine the amount of alcohol included in the final mixture:
Alcohol content is calculated as (total alcohol / total mixture volume) * 100.
The mixture's total volume is = 5 liters + 4 liters + 1 liter = 10 liters
Alcohol content: (6.45 liters / 10 liters) x 100 = 64.5%
Therefore, the resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.
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evaluate 5x - 2y + 4z when x=3 , y=2 and z=4 (a)5 (b) 16 (c) 27 (d) 20
When x = 3, y = 2, and z = 4, the value of the expression 5x - 2y + 4z is 27.
The correct answer is (c) 27.
To evaluate the expression 5x - 2y + 4z when x = 3, y = 2, and z = 4, we substitute the given values into the expression and perform the arithmetic calculations. Here's the step-by-step process:
Step 1: Replace x with 3, y with 2, and z with 4 in the expression:
5(3) - 2(2) + 4(4)Step 2:
Perform the multiplications first:
15 - 4 + 16
Step 3: Perform the additions and subtractions from left to right:
15 - 4 + 16 = 11 + 16 = 27.
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Please solve this question
The solution to the given composite function is calculated as: 12
How to solve Composite functions?Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, the function f of g of x is said to be the composition of the two functions.
We are given the functions:
f(x) = 2[tex]x^{\frac{1}{3} }[/tex]
g(x) = -[tex]x^{\frac{4}{3} }[/tex]
Thus:
(f - g)(-8) = 2[tex]x^{\frac{1}{3} }[/tex] + [tex]x^{\frac{4}{3} }[/tex]
= 2∛-8 + (∛-8)⁴
= (2 * -2) + (-2)⁴
= -4 + 16
= 12
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Can someone please answer and provide an explanation for these problems?
The center and radius for each equation are as follows:
40. Center: (3, 2), Radius: 8
41. Center: (-8, 4), Radius: 6
42. Center: (-4, 12), Radius: 2
43. Center: (4, -15), Radius: 3
What is the center and radius of the equations?The standard equations of a circle is given as (x - h)² + (y - k)² = r²
Where the center are (h, k) and the radius of the circle is r.
40. (x - 3)² + (y - 2)² = 64
Center: (3, 2)
Radius: √64 = 8
41. (x + 8)² + (y - 4)² = 36
Center: (-8, 4)
Radius: √36 = 6
42. (x + 4)² + (y - 12)² = 4
Center: (-4, 12)
Radius: √4 = 2
43. (x - 4)² + (y + 15)² = 9
Center: (4, -15)
Radius: √9 = 3
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Please help due soon
Stmt of cash flows problem
Balance Sheet for Stand Corp Dec 31st:
Cash
Accounts Receivable
Inventory
Total Current Assets
2022
$177,000
$180,000
$100,000
$457,000
2021
$78.000
$185.000
$100.000
$363,000
Investments
Equipment
Accumulated Deprec
Total Non-Current Liabs
$52,000
$298,000
($106,000)
$244.000
$74,000
$240,000
($89.000)
$225,000
Total Assets
$701.000
$588.000
Current Liabilities
$134.000
$151.000
Common Stock
Retained Earnings
$260.000
$307,000
$260,000
$177,000
Total Liabs & Equity
$701.000
$588,000
OTHER INFORMATION:
-Investments were sold in 2022 at a loss of $10.000
-No equipment was sold in 2022
-Cash dividends were paid in 2022
-Net Income for 2022 was $160,000
REQUIRED:Prepare the Statement of Cash Flows:
1. Prepare the Statement of Cash Flows
2. Calculate Free Cash Flow
The Free Cash Flow based on the information given will be $115,000
How to explain the cash flowStatement of Cash Flows for Stand Corp for the year ended December 31, 2022
Cash flows from operating activities:
Net income $160,000
Adjustments to reconcile net income to net cash provided by operating activities:
Depreciation expense $17,000
Loss on sale of investments $10,000
Changes in current assets and liabilities:
Increase in accounts receivable ($5,000)
Increase in inventory ($20,000)
Increase in accounts payable $17,000
Increase in accrued expenses $11,000
Net cash provided by operating activities $190,000
Cash flows from investing activities:
Sale of investments $52,000
Purchase of equipment ($75,000)
Net cash used in investing activities ($23,000)
Cash flows from financing activities:
Payment of cash dividends ($25,000)
Net cash used in financing activities ($25,000)
Net increase in cash $142,000
Cash at beginning of year $78,000
Cash at end of year $220,000
Free Cash Flow = Net cash provided by operating activities - Purchase of equipment
Free Cash Flow = $190,000 - $75,000
Free Cash Flow = $115,000
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Find the area of the stained glass window shown if the diameter of the semi-circle is 61 inches. Use 3.14 for , round your answer to the nearest square inch, and enter the number only.
Answer:
1460 square inches
Step-by-step explanation:
You want the area of a semicircle with diameter 61 inches.
AreaThe area of a circle is given by ...
A = (π/4)d²
The area of a semicircle is half that, so is ...
A = (π/8)d²
A = (3.14/8)(61 in)² ≈ 1460 in²
The area of the semicircular window is about 1460 square inches.
<95141404393>
Part A: Jan INCORRECTLY finds the surface area of the cone using the following work. Explain Jan's error and find the
correct volume AND surface area of the cone.
Therefore, Jan has taken the wrong slant height, he has taken height, h is a place of slant height, l. That's why he has got the wrong answer.
How to solveGiven:,
r= d/2
22/2= 11m
Using the Pythagorean theorem, we can find the length:
l =[tex]11\sqrt{5}\\ = 24.6m[/tex]
Therefore, to find the surface area:
SA= 3.14(270.56 + 121)
=[tex]1229.5m^2[/tex]
Therefore, to find the volume:
V= [tex]1/3 \pi.r^2h[/tex]
V= [tex]2786.23m^3[/tex]
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The Complete Question
Jan INCORRECTLY finds the surface area of the cone using the following work. Explain Jan's error and find the correct volume AND surface area of the cone. 22 m SA = = url + ar?
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O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth.
Answer:
80.4 square units.
Step-by-step explanation:
solution Given:
apothem(a)=5
no of side(n)= 12
Area(A)-?
The area of a regular polygon can be found using the following formula:
[tex]\boxed{\bold{Area =\frac{1}{2}* n * s * a}}[/tex]
where:
n is the number of sidess is the length of one sidea is the apothemIn this case, we have:
n = 12s = ?a = 5First, we need to find S.
We can find the length of one side using the following formula:
[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]
substituting value:
[tex]\bold{s = 2 * 5 * tan(\frac{\pi}{12})=2.679}[/tex] here π is 180°
To find the area substituting value in the above area's formula:
[tex]\bold{Area = \frac{1}{2}* 12 * 2.679 * 5=80.37\: sqaure\: units}[/tex]
in nearest tenth 80.4 square units.
Therefore, the area of the regular polygon is 80.4 square units.
Answer:
80.4 square units (nearest tenth)
Step-by-step explanation:
The given diagram shows a regular dodecagon (12-sided polygon) with an apothem of 5 units.
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.
We can calculate the side length of a regular polygon given its apothem using the following formula:
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Substitute n = 12 and a = 5 into the equation to create an expression for s:
[tex]5=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{12}\right)}[/tex]
[tex]s=10\tan \left(15^{\circ}\right)[/tex]
Now we can use the standard formula for an area of a regular polygon:
[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]
Substitute the found expression for s, n = 12 and a = 5 into the formula and solve for A:
[tex]A=\dfrac{12 \cdot 10\tan \left(15^{\circ}\right) \cdot 5}{2}[/tex]
[tex]A=\dfrac{600\tan \left(15^{\circ}\right)}{2}[/tex]
[tex]A=300\tan \left(15^{\circ}\right)[/tex]
[tex]A=80.3847577...[/tex]
[tex]A=80.4\; \sf square\;units\;(nearest\;tenth)[/tex]
Therefore, the area of a regular dodecagon with an apothem of 5 units is 80.4 square units, rounded to the nearest tenth.
a quadratic function is defined by f(x) = x*2 - 8x - 4.
Which expression also defines f and best reveals the max and mini of the function?
a) (x-4)*2 - 20
B) (x-4)*2 + 12
c) x(x-8) -4
d) (x-4)*2 + 20
The expression that best reveals the maximum and minimum of the function[tex]f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.[/tex] Option A
How to find the expressionThe vertex form of a quadratic function is given by[tex]f(x) = a(x - h)^2 + k[/tex] where (h, k) represents the coordinates of the vertex.
In the given quadratic function [tex]f(x) = x^2 - 8x - 4[/tex], we can rewrite it in the vertex form by completing the square:
[tex]f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20[/tex]
From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).
The term[tex](x - 4)^2[/tex] tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.
The expression that best reveals the maximum and minimum of the function[tex]f(x) = x^2 - 8x - 4[/tex] is [tex](x - 4)^2 - 20.[/tex]
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Math
Language arts
Seventh grade> Y.7 Circles: word problems P56
Submit
Recommendations
millimeters
Y
The button on Jasmine's pants has a radius of 5 millimeters. What is the button's
diameter?
9
Answer:
10 millimeters
Step-by-step explanation:
The diameter of the button is twice the radius. Therefore, the diameter of Jasmine's pants button is 10 millimeters.
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The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.
Answer:
444523.45 square miles
Step-by-step explanation:
By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.
Let,
Side a: Distance from Miami to Bermuda = 1042 miles
Side b: Distance from Bermuda to San Juan = 965 miles
Side c: Distance from San Juan to Miami = 1038 miles
Now we can use Heron's formula to find the area of the triangle:
s =[tex]\frac{a+b+c}{2}[/tex]
s = [tex]\frac{1042 + 965 + 1038}{2}=1522.5[/tex] miles
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
A = [tex]\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}=444523.45[/tex]
Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.
Answer:
444,523.45 square miles (2 d.p.)
Step-by-step explanation:
To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):
a = 1042 milesb = 965 milesc = 1038 milesTo find the half perimeter, s, half the sum of the three side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{1042+965+1038}{2}=1522.5[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}\\&=\sqrt{1522.5(480.5)(557.5)(484.5)}\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.
Maxine's credit card has an APR of 27.99%. If her current monthly balance, before interest, is $1,834.50, what will her monthly interest charge be? (4 points) $42.78 $42.79 $51.67 $65.54
Answer:
(b) $42.79
Step-by-step explanation:
You want the monthly interest charge on a balance of $1834.50 when the annual rate is 27.99%.
Monthly rateThe monthly interest rate is the annual rate divided by 12. This means the interest charge is ...
I = Prt . . . . . interest on P at annual rate r for t years
I = $1834.50 × 0.2799 × 1/12 ≈ $42.79
Her monthly interest charge will be $42.79.
If Shawn rides his bike ¾ mile every ½ hour, how many miles does he bike per hour?
Answer:
1 1/2 miles per hour
Step-by-step explanation:
We can use a ratio to solve
3/4 mile
--------------
1/2 hour
Double the top and the bottom to get to 1 hour
3/4 * 2 miles
--------------
1/2 *2 hours
1 1/2 miles
-------------------
1 hours
1 1/2 miles per hour
Answer:1 1/2 mile or 6/4 mile
Step-by-step explanation:
Every half hour he rides 3/4Just multiply 3/4 by 2 which equals 6/4 or 1 1/2.
D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI
The property used to calculate x in (x + 2)(x + 6) = 0 is (a) the zero product property
How to determine the property used to calculate xFrom the question, we have the following parameters that can be used in our computation:
(x + 2)(x + 6) = 0
The equation when expanded becomes
x + 2 = 0 or x + 6 = 0
In algebra, the zero product property states that
if ab = 0, then a = 0 or b = 0
using the above as a guide, we have the following:
The property used to calculate x is (a) the zero product property
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The graph of a sine function has an amplitude of 4, a midline of y=2, and a period of 10.
There is no phase shift. The graph is reflected over the x-axis.
What is the equation of this function?
The equation of the given sine function is y = 4 × sin((π/5)x) + 2.
The equation of the given sine function can be determined based on the given information. We know that the general form of a sine function is:
y = A × sin(Bx - C) + D,
where A represents the amplitude, B represents the frequency, C represents the phase shift, and D represents the vertical shift.
In this case, we are given the following information:
Amplitude (A) = 4: The amplitude is the distance between the maximum and minimum values of the function. Since the function is reflected over the x-axis, the amplitude is positive 4.
Midline (D) = 2: The midline is the horizontal line around which the graph oscillates. In this case, it is y = 2, indicating a vertical shift of 2 units upwards.
Period = 10: The period is the distance between two consecutive peaks (or troughs) of the function.
Given that there is no phase shift, the phase shift (C) is 0.
From the given information, we can deduce the values of A, B, C, and D to construct the equation.
A = 4 (amplitude)
D = 2 (vertical shift)
C = 0 (no phase shift)
To determine B, we use the formula:
B = 2π / Period
Plugging in the value for Period (10), we can calculate B:
B = 2π / 10 = π / 5
Therefore, the equation of the given sine function is:
y = 4 × sin((π/5)x) + 2.
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Using the image below, answer the following question: you are asked to pick 2
marbles out of the bag, what is the probability of picking a blue marble and then a
green marble, without replacing the blue one?
PLEASE URGENT
The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.
We have,
We see that there are 10 marbles.
Now,
Number of blue marbles = 2
Number of green marbles = 4
Now,
The probability of picking a blue marble first is 2/10, as there are 2 blue marbles out of 10 in total.
After picking a blue marble, there will be 9 marbles left in the bag.
The probability of picking a green marble second, without replacing the blue one, is 4/9, as there are 4 green marbles remaining out of the 9 marbles in total.
Now,
P(blue marble and green marble) = P(blue marble) x P(green marble)
= (2/10) x (4/9)
= 8/90
= 4/45.
Therefore,
The probability of picking a blue marble and then a green marble without replacing the blue one is 4/45.
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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!
Answer:
∆TSU ~ ∆PJM by SAS since 10/14 = 5/7 and 15/21 = 5/7, and angle S is congruent to angle J.
Use the figure to answer the following.
a. What is the surface area of the cylinder? Leave your answer in terms of x.
b. Suppose the diameter and the height of the cylinder are cut in half. How does this affect the surface area of the cylinder? Explain
The diameter of the cylinder is 8 and the height is 11
a. The surface area of the cylinder is 120π square units.
b. Assuming the diameter and the height of the cylinder are cut in half, the surface area of the cylinder would be reduced by a scale factor of 1/4.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.Note: Radius = diameter/2 = 8/2 = 4 m.
By substituting the side lengths into the formula for the surface area (SA) of a cylinder, we have the following;
Surface area = 2πrh + 2πr²
Surface area = 2(π)(4)(11) + 2(π)(4²)
Surface area = 120π square units.
Part b.
Assuming the diameter and the height of the cylinder are cut in half, we have:
Surface area = 2(π)(4/2)(11/2) + 2(π)((4/2)²)
Surface area = 2(π)(2)(5.5) + 2(π)(2²)
Surface area = (π)(2)(11) + 2(π)(4)
Surface area = 22π + 8π
Surface area = 30π square units.
Scale factor = 30π/120π
Scale factor = 1/4.
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Note: "The diameter of the cylinder is 8 and the height is 11"
Donna is thinking about buying a house that costs $125,000. If she puts down $25,000 and is able to get a 5 percent mortgage, she wants an estimate of her total monthly housing expenses. The average annual cost for owning a house, beyond the 5% cost of mortgage interest, is 4.09 percent of the value of the house. Not including the opportunity cost of the down payment, amortization on the loan, or any tax benefits from homeownership, what will be her monthly cost the first month?
A. $206.25
B. $279.60
C. $842.71
D. $746.43
Donna can expect her total monthly housing expenses to be approximately $842.71 for the first month after purchasing the house, assuming no tax benefits or amortization on the loan.
To calculate Donna's monthly housing expenses, we first need to determine the total amount of the mortgage. Since she puts down $25,000 on a $125,000 house, she will need to take out a mortgage for $100,000.
Next, we can calculate the annual cost of owning the house beyond the 5% cost of mortgage interest, which is given as 4.09% of the value of the house. So, 4.09% of $125,000 is:
0.0409 x $125,000 = $5,112.50
This means that Donna can expect to pay approximately $5,112.50 per year in additional expenses associated with owning the house.
To calculate the monthly cost, we simply divide this by 12:
$5,112.50 / 12 = $426.04
So, Donna can expect to pay approximately $426.04 per month in additional expenses associated with owning the house.
Adding the cost of the mortgage interest, we can calculate her total monthly housing expenses as follows:
Total monthly housing expenses = Mortgage interest + Additional annual costs / 12
Mortgage interest = 5% of $100,000 = $5,000 per year or $416.67 per month
Total monthly housing expenses = $416.67 + ($5,112.50 / 12) = $416.67 + $426.04 = $842.71
Hence, Donna can expect her total monthly housing expenses to be approximately $842.71
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Select the values that are solutions to the inequality x2 + 3x – 4 > 0.
Answer: To solve the inequality x^2 + 3x - 4 > 0, we can use the method of factoring.
First, we can factor the quadratic expression:
x^2 + 3x - 4 = (x + 4)(x - 1)
Now we can find the values of x that make the expression greater than zero by looking at the sign of the expression for each factor and applying the sign rules of multiplication:
If both factors are positive, the expression is positive.If both factors are negative, the expression is positive.If one factor is positive and one factor is negative, the expression is negative.
Using this method, we can create a sign chart:
x x + 4 x - 1 x^2 + 3x - 4
-4 0 -5 +6
-1 + - -
1 + + +
0 + - -
2 + + +
From the sign chart, we can see that the expression is greater than zero for x < -4 or x > 1. Therefore, the solutions to the inequality are all real numbers x such that x < -4 or x > 1. We can write this as:
x < -4 or x > 1
Angel works at a small shop that sells candy
bars. She oversees ordering more boxes of
candy bars. A box of candy bars (p) costs
$64 and Angel has no more than $230 to
spend on the order. What inequality
represents her situation?
Op 64 >= 230
Op 64 <= 230
O p/64 <= 230
O p/64 >= 230
Answer:
p/64 <= 230
Step-by-step explanation:
The inequality that represents Angel's situation is:
p/64 <= 230
This inequality states that the number of boxes of candy bars, represented by p, divided by 64 (the cost of each box), is less than or equal to 230 (the maximum amount Angel has to spend on the order).
the third term of an arithmetic sequence is 7 and the twelfth term in 106. what is the one hundredth term of the sequence
Answer:
a₁₀₀ = 1074
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₃ = 7 and a₁₂ = 106 , then
a₁ + 2d = 7 → (1)
a₁ + 11d = 106 → (2)
solve the equations simultaneously to find a₁ and d
subtract (1) from (2) term by term to eliminate a₁
(a₁ - a₁) + (11d - 2d) = 106 - 7
0 + 9d = 99
9d = 99 ( divide both sides by 9 )
d = 11
substitute d = 11 into (1) and solve for a₁
a₁ + 2(11) = 7
a₁ + 22 = 7 ( subtract 22 from both sides )
a₁ = - 15
Then
a₁₀₀ = - 15 + (99 × 11) = - 15 + 1089 = 1074
18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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Find the value for the side marked below. Round your answer to the nearest tenth 210 37 degrees
Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.
How to Find the Value of the Marked Side Using the Cosine Ratio?The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:
cos ∅ = length of hypotenuse/length of adjacent side.
From the image attached below, we have the following:
Reference angle (∅) = 37°
length of hypotenuse = 210
length of adjacent side = y
Plug in the values:
cos 37 = y/210
210 * cos 37 = y
y = 167.7
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What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
The domain of function f(x) is given as follows:
{x | 1 ≤ x < 5}.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The values of x of the function given at the end of the answer are as follows:
Starts at x = 1(closed interval).Ends at x = 5 (open interval).Hence the domain is given as follows:
{x | 1 ≤ x < 5}.
Missing InformationThe function is given by the image presented at the end of the answer.
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Answer:
A - {x | 1 < x < 5}
Step-by-step explanation:
took the Quiz
Write and solve an equation to find the value of x.
A spinner has 3 equal sections: red, white, and blue. John spins the spinner and tosses a coin. Which shows the sample space for spinning the spinner and tossing the coin?
The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}. Thus, the correct option is D.
Given that:
A coin is tossed.
A spinner has 3 equal sections: Red, White, and Blue.
The samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The total number of samples is calculated as,
Total samples = 2 x 3
Total samples = 6
The samples are {(H, R), (H, W), (H, B), (T, R), (T, W), (T, B)}.
Thus, the correct option is D.
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