The minimum value, the first quartile (Q1), the median, the third quartile (Q3), and the maximum value must all be calculated before we can create a box plot for the rating points data.
The median of the lower and upper halves of the data must be determined in order to determine the first and third quartiles, respectively. The numbers from the minimum to the median make up the lower half of the data, while the values from the median to the highest make up the upper half.
We must first organize the numbers in numerical order: 93.5, 96.3, 97.9, 98.9, 99.3, 101.1, 103.9, 104.8, 105.1, 109.5. This will help us determine the median of the lower half of the data. The lower half's mean, which is (99.3 + 101.1) / 2 = 100.2, is then the average of the fifth and sixth values.
Again, the numbers must be arranged in numerical order to determine the median of the upper half of the data: 93.5, 96.3, 97.9, 98.9, 99.3, 101.1, 103.9, 104.8, 105.1, and 109.5. The average of the sixth and seventh numbers, or (101.1 + 103.9) / 2, equals 102.5, which is the median of the top half.
Following that, Q1 = 100 indicates the first and third quartiles.
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If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows from this?
answer choices
O If you flip three coins 1000 times, you will get three heads exactly 125 times.
O If you flip 3 coins 10 times and never get three heads, the probability of getting three heads in the next set of 10 flips is slightly greater than 0.125.
O If you have 20 sets of three coin flips, then at least one set of flips will be three heads.
O If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
O If you get 3 heads two times in a row, the probability of getting 3 heads again on the next toss of 3 coins is nearly zero.
Using the given provided probability value of getting three heads, The statement which best follow the given condition is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close to 12.5%.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
According to the given question:
Assume you have a fair coin, which means it will likely land tails up 50% of the time and heads up 50% of the time. Let's say you flip it three times, each time independently. What is the likelihood that it will land heads up first, followed by a tails up landing?
The solution is 1/8, or 12.5%.
coin flipped = 3 times.
probability of getting three heads = 0.125
Since, This probability explains the chances of landing three heads which is 0.125 which in terms of percentage is 12.5% .
So, The statement is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
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. construct a finite-state machine that models an oldfashioned soda machine that accepts nickels, dimes, and quarters. the soda machine accepts change until 35 cents has been put in. it gives change back for any amount greater than 35 cents. then the customer can push buttons to receive either a cola, a root beer, or a ginger ale.
We may use the instructions provided to build a finite-state machine that simulates a vintage soda machine and can carry out the specified work.
Nickels (5 cents), dimes (10 cents), and quarters are all accepted by the machine (25 cents).
The states should be s, s1, s2, s3, s4, etc.
If we add a nickel to the machine, we move from state s to state s+1 and so on, and the process is the same for a dime and a quarter.
We can build the necessary finite-state machine to simulate an antique soda machine that takes nickels, dimes, and quarters by using x as the input button for soda pop.
A mathematical model of computation is called a finite-state machine (FSM), often known as a finite automaton or just a state machine.
It is an abstract machine that has a limited number of states that it can only be in at any given time. The FSM can change from one state to another in response to some inputs; this change is known as a transition. A set of states, an initial state, and the inputs that trigger each transition comprise an FSM.
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assume the series can be integrated term by term. use this fact and the result from part a) to find the fourier cosine series of the function f(x)
To find the Fourier cosine series of the function f(x), we first need to find the Fourier coefficients of f(x).
The Fourier coefficients of f(x) are given by:
a0 = (2/L) * integral of f(x) from x=0 to x=L
an = (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L
bn = (2/L) * integral of f(x) * sin(npix/L) from x=0 to x=L
Using the result from part a) and the fact that the series can be integrated term by term, we can find the Fourier cosine series of f(x) as follows:
F(x) = a0/2 + sum from n=1 to infinity of an * cos(npix/L)
Therefore, the Fourier cosine series of the function f(x) is:
F(x) = (1/L) * integral of f(x) from x=0 to x=L + sum from n=1 to infinity of (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L
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19
Select the correct answer.
You work for a carpet company. You sell carpets at these prices: 100 square feet for $67, 200 square feet for $130, 400 square feet for $240, and 800 square feet for $504.
What is the best deal for buying carpet?
A.
B.
C.
D.
100 square feet of carpet for $67
200 square feet of carpet for $130
400 square feet of carpet for $240
800 square feet of carpet for $504
400 square feet of carpet area for $240 is the best deal among the given option.
What is Area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
Detailed explanation:The carpets were sold for the following prices:
1) $67 for 100 square feet.
2) $130 for 200 square feet.
3) $240 for 400 square feet
4) $504 for 800 square feet.
Calculation:
For each of them, we would calculate the unit cost per square foot. It develops
1) The price per square foot is 67÷100 = $0.67
2) The price per square foot is 130÷200 = $0.65.
3) The price per square foot is 240÷400 = $0.6.
4) The price per square foot is 504÷800 = $0.63.
Comparing the unit costs per square foot the best deal costs $0.6 per square foot per unit, which is 400 square feet of carpet for $240.
400 square feet of carpet area for $240 is the best deal among the given option.
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build a binary search tree with the following values. what is the leftmost value on the 3rd level? reminder, the root is the 1st level. 47, `b, 38, 66, 57, 19, 31, 45, 88
The leftmost value on the 3rd level of the binary tree with given elements 47, 38, 66, 57, 19, 31, 45, 88 is 19
To build a binary tree first we have to insert 47 into the tree as the root of the tree. The read the next element if it is smaller than the root node, insert it as the left subtree and if it is larger than the root node, insert it as the subtree.
The next element is 38 which is smaller than 47 so it will become the left subtree. The next element is 66 which becomes the right subtree. The next element is 57 is greater than 47 and 38 so it becomes the right subtree below 38. Similarly we go ahead and build a binary tree to find the leftmost value at 3rd level of the binary tree.
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What was the approximate difference
between the highest and lowest oil
production between 1960 and 2010?
4,500 barrels per day
3,500,000 barrels per day
3,500 barrels per day
O4,500,000 barrels per day
The approximate difference between the highest and lowest oil production is 4,500,000 barrels per day
What is approximation?An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.
Given is a graph of oil production between 1960 and 2010
The lowest oil production was in year 2010 = 5000,000 barrels per day
The highest oil production was in year 1970 = 9500,000 barrels per day
The difference between highest and lowest oil production = 9500,000 - 5000,000 = 4,500,000 barrels per day
Hence, The approximate difference between the highest and lowest oil production is 4,500,000 barrels per day
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Solve the following equation for x
KADS, Incorporated has spent $490,000 on research to develop a new computer game. The firm is planning to spend $290,000 on a machine to produce the new game. Shipping and installation costs of the machine will be capitalized and depreciated using bonus depreciated; they total $59,000. The machine has an expected life of three years, a $84,000 estimated resale value, and falls under the MACRS seven-year class life. Revenue from the new game is expected to be $690,000 per year, with costs of $340,000 per year. The firm has a tax rate of 21 percent, has an opportunity cost of capital of 12 percent, and expects net working capital to increase by $145,000 at the beginning of the project. What will the cash flows for this project be? Note: Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.
Year 0 1 2 3
FCF ___ ___ ___ ___
Answer:
To find the cash flows for this project, we need to calculate the net income for each year and then subtract any investments in net working capital and capital expenditures.
In year 0, the firm will incur the following expenses:
- Research and development costs: $490,000
- Cost of the machine: $290,000
- Shipping and installation costs: $59,000
- Increase in net working capital: $145,000
Total expenses in year 0: $490,000 + $290,000 + $59,000 + $145,000 = $984,000
The net income in year 0 is equal to the revenue minus the costs: $690,000 - $340,000 = $350,000.
Therefore, the cash flow in year 0 is:
FCF0 = $350,000 - $984,000 = -$634,000
In years 1, 2, and 3, the firm will incur the following expenses:
- Cost of goods sold: $340,000
- Depreciation: (This can be calculated using the MACRS depreciation schedule. For the first year, the depreciation will be 14.29% of the cost of the machine, or 0.1429 * $290,000 = $41,461. The depreciation in subsequent years can be calculated using the same method.)
- Increase in net working capital: $145,000
Total expenses in each of years 1, 2, and 3: $340,000 + Depreciation + $145,000
The net income in each of these years is equal to the revenue minus the costs: $690,000 - (Total expenses)
The cash flow in each of these years is equal to the net income minus any investments in net working capital and capital expenditures: Net income - Increase in net working capital - Depreciation
Substituting the appropriate values, we get:
Year 1: FCF1 = $690,000 - ($340,000 + $41,461 + $145,000) = $163,539
Year 2: FCF2 = $690,000 - ($340,000 + Depreciation + $145,000)
Year 3: FCF3 = $690,000 - ($340,000 + Depreciation + $145,000)
Note that the depreciation in years 2 and 3 can be calculated using the same method as in year 1.
So, the cash flows for this project are:
Year 0 1 2 3
FCF -$634,000 $163,539
I hope this helps!
The mean s recorded by 27 candidates happened to be 64%. During inspection it was found that one candidate actually scored 74% s instead of 47% recorded in the result sheet. What will be the correct mean?
Step-by-step explanation:
the mean score is the sum of all scores divided by the number of scores.
64 = (s1+s2+s3+...+s26+s27)/27
64×27 = (s1+s2+s3+...+s26+s27)
1728 = (s1+s2+s3+...+s26+s27)
now, one of the scores changes from 47 to 74. that means the sum of all scores is increased by 74-47 = 27.
so, we get
1728 + 27 = (s1+s2+s3+...+s26+s27+27)
1755 = (s1+s2+s3+...+s26+s27+ 27)
we still have 27 scores, so for the updated mean we have to divide both sides by 27 again :
1755/27 = (s1+s2+s3+...+s26+s27+27)/27
65 = (s1+s2+s3+...+s26+s27+27)/27
the correct mean is therefore 65%.
A rock falls from a tower that is 352 feet high. As it is falling, its height is given by the formula h=352-16t^(2). How many seconds (in tenths ) will it take for the rock to hit the ground (h)=(0)?
The rock will take 10.25 seconds to hit the ground, as the amount determined by the formula h=352-16t^(2).
The given equation is h=352-16t^(2). This equation can be used to calculate the time it will take for a rock to hit the ground after it has been dropped from a tower that is 352 feet high. The equation states that the rock's height (h) is equal to 352 minus 16 times the square of the time (t). To find the time it will take for the rock to hit the ground (h=0), we can rearrange the equation to solve for t. The rearranged equation is t=sqrt((352-0)/16), which simplifies to t=10.25. This means that the rock will take 10.25 seconds to hit the ground. This can also be expressed in tenths of a second as 102.5, which is the same as 10.25 seconds.
t= sqrt((352-0)/16)
t= sqrt(22)/4
t= 10.25
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What is the equation of this function after it is reflected over the x-axis?
Answer:
Below
Step-by-step explanation:
Multiplying the equation by -1 will flip it around the x - axis
so 3(x-2)^3
Let X1,82 be independent random variables representing lifetimes (in hours) of two key components of a device that fails when and only when both components fail. Say each Xi has an exponential distribution with mean 1000. Let Y1 = min(X1,X2) and Y2 = max(X1,X2), so that the space of Y1,Y2 is 0 < y1 < y2 <. (a) Find G(y1, y2) = P(Y1 = 71,Y2 = y2).
To find the probability that Y1 = 71 and Y2 = y2, we can write G(y1, y2) = P(Y1 = 71, Y2 = y2).
To find the probability that Y1 = 71 and Y2 = y2, we need to consider the possible values of X1 and X2 that could lead to these values of Y1 and Y2. The probability density functions (PDFs) of an exponential distribution with mean 1000 is f(x) = 1/1000 * e^(-x/1000). Therefore, the probability of this event is
P(X1 = 71, X2 = y2) = f(71) * f(y2) = 1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000).Another possibility is that X1 = y2 and X2 = 71. The probability of this event is
P(X1 = y2, X2 = 71) = f(y2) * f(71) = 1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000).Since these two events are mutually exclusive and exhaust all possible ways that Y1 can equal 71 and Y2 can equal y2, the probability of these events occurring is the sum of these probabilities. Therefore,
G(y1, y2) = P(Y1 = 71, Y2 = y2) = P(X1 = 71, X2 = y2) + P(X1 = y2, X2 = 71) = (1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000)) + (1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000)) = 2/1000^2 * e^(-(71 + y2)/1000).Note that this expression is only valid when 0 < 71 < y2 < ∞ since these are the conditions under which Y1 can equal 71 and Y2 can equal y2.
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Find the solution of the inequality 5 > r – 3.
Answer:
8<r
Step-by-step explanation:
5 > r – 3
+3 +3
add 3 to both sides
8>r
move variable to the left and flip the sign
8<r
Evaluate the given integral by changing to polar coordinates. yex dA, where R is the region in the first quadrant enclosed by the circle x2 y2 = 64
After evaluating the given integral by changing to polar coordinates we get [tex]7 e^8-31[/tex]
As per the details shared in the above question it is given that,
[tex]$x^2+y^2=64$[/tex]
[tex](x, y)=r(\cos \theta, \sin \theta)[/tex]
[tex]d A=r d r d \theta.[/tex]
Further solving above we get,
[tex]r^2=64 \\\Rightarrow & r=8 . \\0 \leq r \leq 8 ; & 0 \leq \theta \leq \pi / 2[/tex]
The polar coordinate,
[tex]\iint_{R} y e^x d A=\int_0^{\frac{\pi}{2}} \int_0^8 r^2 \sin \theta e^{r \cos \theta} d r d \theta[/tex]
[tex]& =\int_0^8 \int_0^{\frac{\pi}{2}} r^2 \sin \theta e^{r \cos \theta} d \theta ; \\& =\int_0^8\left[-r e^{r \cos \theta}\right]_0^{\pi / 2} d r[/tex]
[tex]=\int_0^8 r\left[-e^{r \cos \left(\frac{\pi}{2}\right)}+e^\alpha\right] d r .[/tex]
[tex]=\int_0^8 r e^r d r-\left.\frac{r^2}{2}\right|_0 ^8[/tex]
Now substituting the value we get,
[tex]7 e^8-31[/tex]
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Note the correct question should be ,
Evaluate the given integral by changing to polar coordinates.
[tex]\iint_R y e^x d A[/tex] , where R is the region in the first quadrant enclosed by the circle [tex]x^2+y^2=64[/tex].
Food Mart is having a sale on Hot Cheetos, selling 8 bags for $4.00. What is the cost of one bag at the sale price?
Answer:
Step-by-step explanation:
Question 1 of 10
For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it?
A. Increasing linear
B. Decreasing linear
C. Exponential growth
D. Exponential decay
The type of function is it is C . Exponential growth .
Given :
For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value .
If for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.
Option B is incorrect because because y is not decreasing
Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.
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How to add mixed numbers with unlike denominators
Answer:
you multiply to find common denominators. in the example below you multiply the denominators by themselves, and then individually. 1/2 and 1/3 are the fractions your working with. (2x3)=6 and then (1x3)=3 and (1x2)=2 (2+3)=5 and so (5/6)
Step-by-step explanation:
example: 1½+1⅓=2⅚
Answer: You have to find a common denominator.
Step-by-step explanation: Look at this attachment to understand: (Directions included)
I hoped this helped! If you can, may you PLEASE mark me brainliest?
Determine whether the relation is a function. Explain.
(1,3), (2,4), (3,5), (1,5), (4,6)
Answer:
yes it is function.........
What is the value of x?
Enter your answer in the box
___units
The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔRCD is similar to the triangle ΔRAP. Then the equation is given as,
RC / CA = RD / DP
x / 10 = 42 / 15
x / 2 = 14
x = 2 (14)
x = 28
The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.
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Answer:
x = 28 units
Step-by-step explanation:
As AP is parallel to CD (indicated by the arrows on the line segment), triangle APR is similar to triangle CDR.
In similar triangles, corresponding sides are always in the same ratio.
[tex]\implies \sf AP:CD=PR:DR=AR:CR[/tex]
Given
PR = 15 + 42 = 57DR = 42AR = 10 + xCR = xTherefore:
[tex]\implies \sf PR:DR=AR:CR[/tex]
[tex]\implies \sf 57:42=10+x:x[/tex]
[tex]\implies \sf \dfrac{57}{42}=\dfrac{10+x}{x}[/tex]
[tex]\implies \sf 57x=42(10+x)[/tex]
[tex]\implies \sf 57x=420+42x[/tex]
[tex]\implies \sf 15x=420[/tex]
[tex]\implies \sf x=28[/tex]
Type the correct answer in each box. Use numerals instead of words.
If x>0, what values of c and d make the equations true?
Equation A √448 x⁽=8 x³ √7 x
Equation B ∛576 xᵃ=4 x ∛9 x²
In equation A, c is
In equation B, d is
The value of c in the equation A is 7 and the value of d in the equation B is 5
The first equation is
[tex]\sqrt{448x^c}=8x^3\sqrt{7x}[/tex]
Move the term 8x^3 inside the square root
[tex]\sqrt{448x^c}=\sqrt{7x(8x^3)^2}[/tex]
Multiply the terms in the equation
[tex]\sqrt{448x^c} = \sqrt{448x^7}[/tex]
Here the both terms are equal. Therefore the value of x^c and the x^7 will be equal.
Then the value of c = 7
Part 2
The second equation is
[tex]\sqrt[3]{576x^d}=4x \sqrt[3]{9x^2}[/tex]
Move the term 4x inside the square root
[tex]\sqrt[3]{576x^d}=\sqrt[3]{9x^2(4x)^3}[/tex]
Multiply the terms in the equation
[tex]\sqrt[3]{576x^d}=\sqrt[3]{576x^3}[/tex]
Here the both terms are equal. Therefore the value of x^d and the x^5 will be equal
Then the value of d = 5
Therefore, the value of c = 7 and the value of d = 5
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A worker has 3 bags of pebbles to use in a garden. The mass of each bag is
9 kilograms. What is the total mass, in kilograms, of all of the bags of pebbles?
Answer:
D). 27
Step-by-step explanation:
The mass of each bag is 9 kilograms
We have 3 bags
Let's add the mass of all 3 bags to find our answer.
9 kilograms + 9 kilograms + 9 kilograms = 27 kilograms
The solution is, D). 27 is the total mass, in kilograms, of all of the bags of pebbles.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
A worker has 3 bags of pebbles to use in a garden. The mass of each bag is 9 kilograms.
so, we have,
The mass of each bag is 9 kilograms
We have 3 bags
i.e. total mass = 9 * 3 =27
here, we have to multiply 9 by 3 we get the total mass,
i,e. 27 kg.
similarly, we have,
Let's add the mass of all 3 bags to find our answer.
9 kilograms + 9 kilograms + 9 kilograms = 27 kilograms
Hence, The solution is, D). 27 is the total mass, in kilograms, of all of the bags of pebbles.
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suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. the time t is measured in seconds and the units for r(t) are measured in tonnes (metric tons) per second. note that r(t) is increasing over the interval [0, 6]. t 0 1 2 3 4 5 6 r(t) 2 10 18 32 44 54 60 (a) give upper and lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds. (use six equal subintervals.)
The upper and the lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds is 224 and 166 metric tons respectively.
The volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table
Assuming that r(t) is increasing for all t in [0,6], a lower estimate is obtained by using left endpoints and an upper estimate is achieved by using right endpoints.
Lower estimate: r(0)(1)+r(1)(1)+r(2)(1)+r(3)(1)+r(4)(1)+r(5)(1)
= 2+12+20+36+44+52 = 166 metric tons
Upper estimate: r(1)(1)+r(2)(1)+r(3)(1)+r(4)(1)+r(5)(1)+r(6)(1)
= 12+20+36+44+52+60 = 224 metric tons
Midpoint estimate: r(1)(2)+r(3)(2)+r(5)(2)
= 24+72+104 = 200 metric tons
Therefore, the upper and the lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds is 224 and 166 metric tons respectively.
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Alfonso bought 4 movie tickets for $29. Write an equation relating the total cost, y, to the number of tickets bought, x. Write the equation in the form ykx.
Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
The volume of the composite solid that is made up of hemisphere and cylinder will be 7,121.52 cubic feet.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The shape is the combination of the hemisphere and cylinder. Then the volume of the composite solid is calculated as,
V = Volume of hemisphere + Volume of cylinder
V = (2/3) πr³ + πr²h
Simplify the equation, then we have
V = (2/3) π(9)³ + π(9)²(22)
V = 486π + 1782π
V = 2268 x 3.14
V = 7,121.52 cubic feet
The volume of the composite solid will be 7,121.52 cubic feet.
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What is the scale factor of the geometric sequence?
200, 100, 50, 25, . . .
Enter your answer as a decimal in the box.
The scale factor of the geometric sequence 200, 100, 50, 25 is ½
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Therefore scale factor= new dimension/ original dimension.
In the sequence 200, 100, 50, 25...., as we take 200 as the original dimension and 100 as the new dimension. From these we can discover that the object is decreasing in shape
Therefore the scale factor = new dimension/ original dimension
scale factor = 100/200
scale factor = ½
therefore the scale factor of the sequence is ½
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observe that {b}->{a} appears to hold with respect to the given instance. does {a}->{b} holds with respect to the instance? g
false, {b}->{a} appears to hold with respect to the given instance.
what is instance?A variable created in a class that has a unique copy, or instance, for each instantiated object of the class is known as an instance variable in class-based, object-oriented programming. Although not static, an instance variable resembles a class variable.
A variable specified within a class but outside of constructors, methods, or blocks is known as an instance variable. All the constructors, methods, and blocks in the class have access to instance variables, which are created when an object is instantiated. To the instance variable, access modifiers can be applied.
false, {b}->{a} appears to hold with respect to the given instance.
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y-2x=4 please help i’m
stuck
Answer:
To find x and y intercept .... y = 4, and x = -2
Step-by-step explanation:
y-2x=4
y = 4
-2x=4
-2x/-2 = 4/-2
x = -2
Is this equation for solving y and x
Jessica puts away $200 a month for 20 years. How much will she have if she puts it into an annuity paying 6% interest compounded monthly? How much interest does she earn?
The amount after 20 years is $662.04.
The interest does she earn is $240.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the addition of interest to the loan or deposit principal.
One plus the annual interest rate raised to the number of compound periods minus one is multiplied by the initial loan amount, or principal, to determine compound interest.
Given:
Jessica puts away $200 a month for 20 years.
P = $200
t = 20 years
r = 6% = 0.06
n = 12 (compounded monthly)
Consider the compound interest formula,
[tex]A = P(1+\frac{r}{n})^n^t[/tex]
Plug the values of P, r, n and t in the above equation.
⇒
[tex]A = 200(1+\frac{0.06}{12})^1^2^*^2^0\\ A = 200(1+0.005)^2^4^0\\A = 200(1.005)^2^4^0\\A = 662.04089\\A = 662.04[/tex]
Hence, the amount after 20 years is $662.04.
Now to find the interest does she earn.
Interest = Principle x time x rate
= 200 x 20 x 0.06
Interest = $240
Hence, the interest does she earn is $240.
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in triangle pqr pq equals 39 inches, pr equals 17 inches, and hte altitude pn equals 15 inches. find ar. consider all cases, two answers
In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 in.
How did we figure this out?Solution:[tex]\boxed{\bold{= > (39)^2=(15)^2+(QN^2}}\\\boxed{= > QN=\bold{\sqrt{(39)^2-(15)^2}} }\\\boxed{= > QN=\bold{36}}[/tex]
Now we have to determine the side RN.
Side PR = 17Side PN = 15Now put all the values in the above expression, we get the value of side RN.
[tex]\boxed{\bold{= > (17)^2}=(15)^2+(RN)^2}\\\boxed{= > RN=\bold{\sqrt{(17)^2-(15)^2} }}\\\boxed{= > RN=\bold{8}}[/tex]
Side QR = 36 + 8Side QR = 44Therefore, In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 inches.
[tex]\text{The correct answer is QR is, 44 in.}[/tex]
Using Pythagoras theorem in ΔPNQ:
[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PQ)^2=(PN)^2+(QN)^2}}[/tex]
PQ = 39PN = 15[tex]\boxed{(39)^2=(15)^2+(QN)^2}\\\boxed{\bold{QN=\sqrt{(39)^2-(15)^2} }}\\\boxed{QN=\bold{36}}[/tex]
[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PR)^2=(PN)^2+(QN)^2}}[/tex]
PR = 17PN = 15[tex]\boxed{\bold{(17)^2=(15)^2+(RN)^2}}\\\boxed{\bold{RN=\sqrt{(17)^2-(15)^2} }}\\\boxed{RN=\bold{8}}}[/tex]
Adding the numbers:
36 + 8 = 44
[tex]\text{Hence, The correct answer is QR is, 44 in.}[/tex]
twice the sum of a number and 3 is equal to three times the diffrence of the number and 3 find the number.
When "twice the sum of a number and 3 equals three times the difference of the number and 3," the value of expression is 6.
What is expression?In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.
Here,
let x be the number,
2x+3=3x-3
x=6
The value of expression is 6 when "twice the sum of a number and 3 is equal to three times the difference of the number and 3."
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