Answer:
Volume of cylinder is: Volume=1808.64 ft³
Step-by-step explanation:
Height of cylinder = 9 ft
Base diameter of cylinder = 16 ft
We need to find volume of cylinder .
The formula used is: [tex]Volume=\pi r^2h[/tex]
We need radius:
The radius = diameter/2 = 16/2 = 8 ft
Putting values and finding volume of cylinder
[tex]Volume=\pi r^2h[/tex]
[tex]Volume=3.14\times (8)^2\times (9) \\Volume=3.14\times 64\times (9) \\Volume=1808.64 \: ft^3[/tex]
So, Volume of cylinder is: Volume=1808.64 ft³
Jack walks around the his schools track field and completes 1 lap in 30seconds.How long does it take Jack to complete 1 mile? How far will he run after 30 min?What is my speed in minutes per hour
The population of a small town was 12,500 in 1995. Since then, the population has
increased at a rate of 4.5% each year.
Write an exponential function to model the situation
Answer:
Step-by-step explanation:
the answer is 6847 if anyone solves it
The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table. What is the relationship between distances biked and distances run?
The relationship between distances biked and distances run is
D(bike) = 2 × D(run)
Here, we have been shown that when distance run is, lets say x then distance run is 2x
When distance run is 2 then distance biked is 4, twice as distance run.
Again in distance run 3[tex]\frac{1}{2}[/tex], distance biked is 7, so this proves that
D(bike) = 2 × D(run)
What is the importance of distance?The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors (e.g. "two counties over").
Since spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to denote a measure of the degree of separation or the statistical distance between two similar objects (such as edit distance between strings of text or statistical distance between probability distributions) (as exemplified by distance between people in a social network).
A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.
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Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks à white marble. In the third attempt, Amy picks a white marble again. Arny has not replaced the marbles she picked.
When Amy picks a black marble in the fourth attempt, the probability that in the fifth attempt she will pick a red or a black marble is 0.7143.
How to calculate the probability?It should be noted that after the 3rd pick we have: 4 white, 3 red and 8 black marbles.
The probability that the 4th marble is black is:
P ( Black ) = 8 / 15 = 0.5333
After the 4th pick we have: 4 white, 3 red and 7 black marbles.
P ( Red or Black ) = 10 / 14 = 5 / 7 = 0.7143.
Therefore, the probability is 0.7143.
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Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks a white marble. In the third attempt, Amy picks a white marble again. Amy has not replaced the marbles she picked. The probability that the fourth marble Amy picks is black is . If Amy picks a black marble in the fourth attempt, the probability that in the fifth attempt she will pick a red or a black marble is____.
What is the domain of the function y = 2√x-5?
THE ANSWER IS IN THE PHOTO
Find all values of $x$ that solves this system.
\begin{align*}
x^2 - 9y^2 &= 72\\
x + 3y &= 9
\end{align*}
All the values of x that solve the given system of equations are as follows:
x = 17/2.
What is a system of equations?A system of equations is when multiple variables are related by equations, which are solved to find the values of each variable. Usually, these relations are linear, but they may also be quadratic, as is the case in this problem.
For this problem, we are given two equations, as follows:
x² - 9y² = 72.x + 3y = 9.From the second equation, we have that:
x = 9 - 3y.
Replacing in the first, we have that:
(9 - 3y)² - 9y² = 72.
9y² - 54y + 81 = 72.
54y = 9.
y = 9/54
y = 1/6, as 9/9 = 1, 54/9 = 6.
Hence the solution for x of the system of equations is found by replacement, as follows:
x = 9 - 3y = 9 - 3/6 = 9 - 1/2 = 18/2 - 1/2 = 17/2.
The solution is x = 17/2.
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5 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids. The winner offers a bid of $72,000 how much will that bidder need to put into a kitty for the other bidders to be compensated?
The amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.
How to calculate the value?It should be noted that 5 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids and the winner offers a bid of $72,000.
Therefore, the fair share will be:
= Bids / Number of people
= 72000 / 5
= 14400
Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be:
= $72000 - $14400
= $57600
Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.
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R6000 is deposited into a savings account. Four years later, R7000 is added to the savings. The interest rate for the first three years is 8% per annum compounded annually. Thereafter, the interest rate changes to 9% per annum compounded annually. Calculate the value of the savings at the end of the seventh year.
Answer:
R 19734.32
Step-by-step explanation:
If an amount P is deposited at R% interest compounded annually for n years, the amount at the end of n years is given by the formula
[tex]P = P(1 + r)^t[/tex]
r = R/100
Note
Interest rate 8% = 8/100 =0.08 for computation
Interest rate 9% = 8/100 =0.09 for computation
Since the interest rate changes after 3 years, the first thing to do is to find out how much the value is after 3 years
[tex]V(3 years) = 6000(1 + 0.08)^3[/tex] = 6000 x1.08³ = 6000 x 1.259712 = 7558.27
After 3rd year interest changes to 9%(0..09) but an additional amount is deposited
Let's find the value after the 4th year at 9% compounded annually using the general formula with r = 0.09 and t =1
V (after 4th year) = 7558.27(1.09)¹ = 7558.27 x 1.09 = 8238.51
We are depositing 7000 at the end of the 4th year so the principal becomes 8238.51 + 7000 = 15,238.51
This new amount accrues interest at 9% for 3 more years (7-4)
So value of savings at end of 7th year is
V = 15238.51(1+0.09)³ = 15238.51 x 1.259712 = 19734.32
Answer:
R19734.32
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Years 1-3Given:
P = R6000r = 8% = 0.08t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=6000(1+0.08)^3[/tex]
[tex]\implies \sf A=6000(1.08)^3[/tex]
[tex]\implies \sf A=6000(1.259712)[/tex]
[tex]\implies \sf A=7558.272[/tex]
Therefore, the amount in the account after 3 years was R7558.272.
Year 4The interest rate changed to 9%.
Given:
P = R7558.272r = 9% = 0.09t = 1Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=7558.272(1+0.09)^1[/tex]
[tex]\implies \sf A=7558.272(1.09)[/tex]
[tex]\implies \sf A=8238.51648[/tex]
Therefore, the value of savings at the end of the 4th year was R8238.51648.
Years 5-7After four years, R7000 was added to the account.
Given:
P = R8238.21648 + R7000 = R15238.21648r = 9% = 0.09t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=15238.21648(1+0.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.295029)[/tex]
[tex]\implies \sf A=19734.3207...[/tex]
Therefore, the value of the savings at the end of the seventh year is R19734.32.
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Find the midpoint of points A(-1,-7) and B (3,-4) graphically
(0,0) because that is the center
1. The table represents a quadratic function. Write an equation of the function in standard form. X f(x) -4 -3 -2 0 0 1 2 0
An equation of the function in standard form is equal to -x²/4 + 1 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-3 = a(-4)² + b(-4) + c ⇒ -3 = 16a - 4b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
1 = a(0)² + b(0) + c ⇒ 1 = c .......equation 3.
Substituting the value of c into eqn. 1 and eqn. 2, we have:
-4 = 16a - 4b .......equation 4.
-1 = 4a - 2b .......equation 5.
Multiplying eqn. 5 by 2 and solving simultaneously, we have:
-4 = 16a - 4b
-2 = 8a - 4b
-2 = 8a
a = -2/8
a = -1/4
For the value of b, we have:
-1 = 4a - 2b
-1 = 4(-1/4) - 2b
-1 = -1 - 2b
2b = 0
b = 0
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-1/4x² + (0)x + 1 = 0
-x²/4 + 1 = 0
Check:
When x = 2, we have:
-x²/4 + 1 = 0
-2²/4 + 1 = 0
-4/4 + 1 = 0
-1 + 1 = 0
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Find the weighted average of the points on the line.
The weighted average of the points on the line is 3/5 after applying the concept of the weighted average.
What is average?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that:
The number line is shown in the picture:
The number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.
From the number line:
The weighted average = [2(-5) + 8(2)]/(2 + 8)
The weighted average = [-10 + 16]/(10)
The weighted average = [6]/(10)
The weighted average = 3/5
Thus, the weighted average of the points on the line is 3/5 after applying the concept of the weighted average.
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Right angle ABC is taken by a dilation with center P and scale factor 1/2 to angle A'B'C'. What is the measure of angle A'B'C'?
Answer: 90 degrees
Step-by-step explanation:
Dilations preserve angle measure.
write your answers in Arabic numerals XXXV-VIII
Step-by-step explanation:
٨-٥٢.....................
What is the y-intercept of f(x) =
700- (2)* ?
A. (0, 1)
B. (1,0)
C. (0,0)
(14)
D.
Answer:
its A
Step-by-step explanation:
Annenbaum Corporation uses the weighted-average method in its process costing system. This month, the beginning inventory in the first processing department consisted of 400 units. The costs and percentage completion of these units in beginning inventory were:
1. The cost per equivalent unit for materials for the month in the first processing department of Annenbaum Corporation is $20.50.
2. The cost per equivalent unit for conversion costs for the month in the first processing department of Annenbaum Corporation is $34.208.
How is the cost per equivalent unit determined?The cost per equivalent unit is the quotient of the total costs to be accounted for divided by total equivalent units of production.
The equivalent units of production are a mathematical equivalent of completed units based on their degrees of completion.
Data and Calculations:Beginning work in process:
Materials costs = $5,700 65%
Conversion costs = $6,800 45%
Started units = 6,500 units
Transferred out units = 5,900 units
Ending inventory:
Material costs = 50%
Conversion costs = 35%
Costs incurred during the period:
Materials costs......... $125,500
Conversion costs...... $207,000
Physical units to be accounted for:Beginning inventory = 400 units
Started during period = 6,500 units
Total units processed = 6,900 units
Units transferred out = 5,900 units
Ending inventory = 1,000 units
Equivalent Units (Weighted Average):Physical Units Material Conversion
Transferred out 5,900 5,900 (100%) 5,900 (100%)
Ending inventory 1,000 500 (50%) 350 (35%)
Total equivalent units 6,400 units 6,250 units
Total Production Costs:Material Conversion
Beginning WIP $5,700 $6,800
Costs for the period 125,500 207,000
Total production costs $131,200 $213,800
Total equivalent units 6,400 units 6,250 units
Cost per equivalent unit $20.50 $34.208 ($213,800/6,250)
Thus, the cost per equivalent unit of materials is $20.50, while it is $34.208 for conversion costs.
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Question Completion:Cost Percent Complete Materials costs......... $5,700 65% Conversion costs...... $6,800 45% A total of 6,500 units were started and 5,900 units were transferred to the second processing department during the month. The following costs were incurred in the first processing department during the month: Materials costs......... $125,500 Conversion costs...... $207,000 The ending inventory was 50% complete with respect to materials and 35% complete with respect to conversion costs. Required: 1. What's the cost per equivalent unit for materials for the month in the first processing department? 2. What's the cost per equivalent unit for conversion costs for the month in the first processing department?
Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs $22 per share and Stock Y, which costs $35 per share. His budget for buying stock is no more than $4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?
The option which represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased is:
D. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≥ 20
b ≥ 15
What does at least and no more than mean in this instance?
At least is interpreted in inequalities as greater than or equals to whereas "no more than" implies that it cannot be greater, hence, can be less than or equals to, as a result, the following relationships are determined:
a≥20(the least number of X shares is a, which is 20)
b≥ 15(the least number of Y shares is a, which is 15)
total amount spent on X=22*a=22a
total amount spent on Y=35*b=35b
maximum amount to invest=4500(less than or equals to)
22a+35b≤ 4500
sum of X and Y shares altogether(least)=100
a+b≥100
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Full question:
Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs $22 per share and Stock Y, which costs $35 per share. His budget for buying stock is no more than $4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?
A. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≤ 20
b ≤ 15
B. 22a + 35b ≤ 4,500
a + b ≤ 100
a ≤ 20
b ≤ 15
C. 22a + 35b ≤ 4,500
a + b ≤ 100
a ≥ 20
b ≥ 15
D. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≥ 20
b ≥ 15
A solid lies between planes perpendicular to the y-axis at [tex]y=0[/tex] and [tex]y=4[/tex]. The cross-sections perpendicular to the y-axis are circular disks with diameters running from the y-axis to the parabola [tex]x=\sqrt{10} y^2[/tex]. Find the volume of the solid.
For any given [tex]0\le y\le4[/tex], a cross section in that plane is a circle whose diameter is [tex]x=\sqrt{10}\,y^2[/tex] with thickness [tex]\Delta y[/tex]. Such a cross section contributes a volume of [tex]\pi \left(\frac x2\right)^2 \, \Delta y = \frac{5\pi}2 y^4 \, \Delta y[/tex].
As [tex]\Delta y\to0[/tex] and the number of cross sectional cylindrical disks increases without bound, the infinite sum of their volumes converge to the volume of the solid, given by the definite integral
[tex]\displaystyle \frac{5\pi}2 \int_0^4 y^4 \, dy = \frac{5\pi}2 \cdot \frac{4^5}5 = \boxed{512\pi}[/tex]
11. Convert the number to scientific notation.
0.000001019
1.02 x 10-⁹
1.02 x 10-6
10.19 x 10-7
1.02 x 106
The mean monthly rent of students at Oxnard University is $910 with a standard deviation of $216. (a) John’s rent is $1,355. What is his standardized z-score? (Round your answer to 3 decimal places.)
Answer:
maybe if you learn you will know
Step-by-step explanation:
3x+18+4x+15=180 what is x
Answer:
x = 21
Step-by-step explanation:
Adding numbers:
3x+ 18 + 4x + 15 = 180
3x + 33 + 4x = 180
Combine Like terms:
3x + 33 + 4x = 180
7x + 33 = 180
Subtract:
7x + 33 - 33 = 180-33
7x = 147
Divide:
[tex] \frac{7x}{7} = \frac{147}{7} [/tex] x = 21rewrite this expression using a positive exponent
[tex]\frac{1}{2^{-6} }[/tex]
Answer:
1/5 needs to be 20 words long
If f(x)=3x-2 determine the value of y for each x value -4, 2, 3
Answer:
Step-by-step explanation:
y = f(x) = 3x -2
When x = -4,
y = 3(-4) -2 = -12-2 = -14
When x = 2,
y = 3(2) -2 = 6-2 = 4
When x = 3,
y = 3(3) -2 = 9-2 = 7
1)
**
16 yd
A
8 yd
12 yd What is the area of the shape
Answer:
35 yd
Step-by-step explanation:
Manuel made $20,000 in taxable income last year.
Suppose the income tax rate is 10% for the first $7000 plus 16% for the amount over $7000.
How much must Manuel pay in income tax for last year?
$0
Check
X
S
Answer:
$2780
Step-by-step explanation:
Given an income tax of 10% of the first $7000 and 16% of all after that, you want the tax on $20,000.
Piece-wise functionManuel's income is more than $7000, so the tax is computed in two parts.
First $7000
The tax on the first $7000 of income is 10%:
tax = $7000 × 0.10 = $700
Amount Over $7000
The amount over $7000 is ...
$20,000 -7,000 = $13,000
The tax on that amount is 16%:
tax = $13,000 × 0.16 = $2080
Total tax due
The tax Manuel must pay is the total of these two amounts:
$700 +2080 = $2780
Manuel must pay $2780 in income tax for last year.
I didn’t understand this question please help and thank u
-87.55% rounded to one decimal place
Answer:
-8756 %
Step-by-step explanation:
Because 5 is a strong number
Evaluate the expression 3.8 +0+ y for the given values of y value value of expression -4.3 -1.6 0 5.2 -0.5
The answers are -0.5, 2.2, 3.8, and 9.0
We need to evaluate the expression 3.8 + 0 + y for the given values of y.
Let x = 3.8 + 0 + y
The values of y are -4.3, -1.6, 0, and 5.2
Let's substitute the value of y in the expression and calculate the values of x.
When y = -4.3, x = 3.8 + 0 + (-4.3) = 3.8 - 4.3 = -0.5When y = -1.6, x = 3.8 + 0 + (-1.6) = 3.8 - 1.6 = 2.2When y = 0, x = 3.8 + 0 + 0 = 3.8When y = 5.2, x = 3.8 + 0 + 5.2 = 3.8 + 5.2 = 9.0Refer to the attached image for the values of the expression corresponding to the values of y.
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Answer:
-0.5, 2.2, 3.8, and 9.0
Step-by-step explanation:
Solve the system by back substitution.
-4x - 8y - 2z - 6w = 5
3y + 18z + 6w = 24
z + w =2
-2w = -6
Solution should be set like {( _ , _ , _ , _ )}
The values of all the variables are:
w = -3z = 5y = -16x = 33 approxWhat are equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.Given equations:
-4x - 8y - 2z - 6w = 53y + 18z + 6w = 24z + w =2-2w = -6To find the values of x, y, w, and z:
-2w = -6w = -6/2w = -3Substitute (w = -3) in z + w = 2:
z + w = 2z -3 = 2z = 2 + 3z = 5Substitute (w = -3) and (z = 5) in 3y + 18z + 6w = 24:
3y + 18z + 6w = 243y + 18(5) + 6(-3) = 243y + 90 - 18 = 243y + 72 = 243y = 24 - 723y = - 48y = - 16Substitute (y = - 16), (w = -3) and (z = 5) in -4x - 8y - 2z - 6w = 5
-4x - 8y - 2z - 6w = 5-4x - 8(-16) - 2(5) - 6(-3) = 5-4x + 128 - 10 + 18 = 5-4x + 118 + 18 = 5-4x + 136 = 5-4x = 5 - 136-4x = - 131x = 131/4x = 32.75Rounding off: x = 33Therefore, the values of all the variables are:
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I need help asap please!
Answer:
5x+10
Step-by-step explanation:
[tex](f \circ g)(x)=f(g(x)) \\ \\ =f(-5x-6) \\ \\ =-(-5x-6)+4 \\ \\ =5x+6+4 \\ \\ =5x+10[/tex]
Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = 0.5 x + 2 intersect the circle with radius 5 and center (0, 2)?
At (4.472 , 4.236) in the first quadrant , the line with equation y = 0.5 x + 2 intersect the circle with radius 5 and center (0, 2) .
The equation of circle with center (h,k) and radius r can be written as
(x-h)²+(y-k)²=r²
In the given question
the center of the circle is (0,2) and the radius of the circle is 5 .
So the equation of circle become
(x-0)²+(y-2)²=5²
x²+(y-2)²=25 ...(i)
It is given that y=0.5x+2 intersects the circle
y = 0.5x+2
Rewriting the equation we get
y-2=0.5x
(y-2)=0.5x
x=(y-2)/0.5
x = 2(y-2) ...(as 0.5=1/2) ....(ii)
Squaring both sides
x² = (2(y-2))²
x² = 2²(y-2)²
x² = 4(y-2)² ...(iii)
Substituting the value of equation (iii) in equation (i) we get ,
4(y-2)²+(y-2)²=25
5(y-2)²=25
(y-2)²=25/5
(y-2)²=5
Taking Square root both the sides , we get
√(y-2)²=√5
y-2 = √5
y=(√5)+2
y=2.236+2
y=4.236
Substituting the value of y in (ii) we get
x=2(4.236-2)
x=2*2.236
x=4.472
Therefore , the circle with radius 5 and center (0, 2) will intersect the line with equation y = 0.5 x + 2 in the first quadrant at (4.472 , 4.236).
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