To calculate the volume, w will use the formula:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question,
diameter = 10
This implies that; r=d/2 = 10/2 = 5
h = 17
susbtitute the values into the formula
[tex]V=\pi\times5^2\times17[/tex][tex]=425\pi\text{ cubic feet}[/tex]If we substitute the value of pie= 22/7
[tex]V=\frac{22}{7}\times425[/tex][tex]\approx1335.71\text{ cubic f}eet[/tex]If there are 40 seats per row how many seats are in 90 rows?
Answer:
3,600 seats
Step-by-step explanation:
If you have 40 seats in a row, and there are 90 rows, you simply take the amount of seats, and multiply that by the amount of rows.
-Hope this helps
Answer:
Step-by-step explanation:
3600
If you were to multiply 40 seats by 90 rows, you would result with 3600 seats!
Triangle UVW, with vertices U(-5,5), V(-4,7), and W(-9,8), is drawn on the coordinate grid below.
The area formula of a triangle given the coordinates of the vertices :
[tex]U(-5,5),V(-4,7),W(-9,8)[/tex][tex]A=\lvert\frac{U_x(V_y-W_y)+V_x(W_y-U_y)+W_x(U_y-V_y)}{2}\rvert[/tex]Using the formula above, the area will be :
[tex]\begin{gathered} A=\lvert\frac{-5(7-8)-4(8-5)-9(5-7)}{2}\rvert \\ A=\lvert\frac{5-12+18}{2}\rvert \\ A=\lvert\frac{11}{2}\rvert \\ A=\lvert5.5\rvert \\ A=5.5 \end{gathered}[/tex]The answer is 5.5 square units
How many angles and sides are there in a Heptagon?ANGLES:SIDES:
The heptagon is a polygon of 7 sides and 7 angles
The heptagon is a closed figure formed from 7 sides
Since every 2 sides connected to form an angle, then
It contains also 7 angles
Then the answer is :
Angles: 7
Sides: 7
Mr.Gonzalez spent $50 more than Mr.Silva on school supplies. together, they spent $174. How much money did each of them spent?
Answer: You need to spend more than $5.00
Step-by-step explanation:
Write an expression to determine the surface area of a cube-shaped box, S A , in terms of its side length, s (in inches).
The cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
What is a cube?A three-dimensional object with six equal square faces is called a cube. The cube's six square faces all have the same dimensions.
A cube is become by joining 6 squares such that the angle between any two adjacent lines should be 90 degrees.
A cube is a symmetric 3 dimension figure in which all sides must be the same.
The cube has six equal squares.
It is known that the surface area of a square = side²
Therefore, the surface area of the given cube is 6 side².
Given cube has side length = s
So,
Surface area = 6s²
Hence the cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
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two systems of equations are given below. for each system, choose the best description of its solution. if applicable, give the solution.
Let:
[tex]\begin{gathered} x-4y=8_{\text{ }}(1) \\ -x-4y=8_{\text{ }}(2) \\ \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (1)+(2) \\ x+(-x)+(-4y)+(-4y)=8+8 \\ -8y=16 \\ y=\frac{16}{-8} \\ y=-2 \end{gathered}[/tex]Replace the value of y into (1):
[tex]\begin{gathered} x-4(-2)=8 \\ x+8=8 \\ x=8-8 \\ x=0 \end{gathered}[/tex]The system has unique solution:
[tex](x,y)=(0,-2)[/tex]Solve the inequality: -1 <= x - 3 > 7
-1 ≤x-3>7
So:
-1≤x-3
x-3>7
Solve each
-1≤x-3
Add 3 to both sides:
-1+3≤x-3+3
2≤x
x-3>7
add 3 to both sides:
x-3+3>7+3
x>10
Solution:
2≤x or >10
The given diagram shows the steps for constructing a parallel line to line AB and passing through point P, but an error has occurred in the construction
Given:
Constructing a parallel line to line AB and passing through point P.
To find:
The error occurred in the construction.
Explanation:
The procedure is,
The first arc must be drawn centred at C.
The second must be drawn centred at P.
Finally, the third arc must be drawn centred at F.
But here, the third arc is drawn centred at D. This is wrong.
Therefore, the correct step is that the third arc must be centred at F.
Final answer:
The third arc should be drawn centred at F.
graph a line that is parallel to the given line. determine the slope of the given line and the one you graphed in simplest form. click and drag on the graph to draw a line. Click and drag to plot a parallel line. The line will change colors when a parallel or perpendicular line is drawn accurately.
Choosing two points of the line given ( Lg ):
• A( ,0, -4, )
,• B( -,1.5, 0, )
Procedure:
0. Finding the slope ( ,m ,) of ,Lg:
[tex]m_{Lg}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m_{Lg}=\frac{0_{}-(-4)_{}}{-1.5_{}-0_{}}=\frac{4}{-1.5}=-\frac{8}{3}[/tex][tex]m_{Lg}=-\frac{8}{3}[/tex]Also, based on point (0, -4), we can determine the intersection in y - axis ( b = -4). Therefore, the equation of the line given is:
[tex]y=mx+b[/tex][tex]y=-\frac{8}{3}x-4[/tex]To determine the parallel slope ( mp ), we know that parallel lines have the same slope:
[tex]m_p=m_{Lg}=-\frac{8}{3}[/tex]For the new graph, you would have to choose a different parameter b, all the equation would be the same except b. Choosing b = 3 as an example:
[tex]y=-\frac{8}{3}x+3[/tex]Answer:
• Original slope: -8/3
,• Parallel slope: -8/3
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of AC.A. 8B. 6C. 2D. 4
Answer:
the length of the diagonal AC is;
[tex]8[/tex]Explanation:
Given the parallelogram ABCD, diagonals AC and BD intersect at point E.
[tex]\begin{gathered} AE=2x \\ CE=x+2 \\ BE=y+10 \\ DE=4y+8 \end{gathered}[/tex]Recall that the diagonals of a parallelogram bisect each other;
So;
[tex]AE=CE[/tex]substituting AE and CE;
[tex]\begin{gathered} 2x=x+2 \\ 2x-x=2 \\ x=2 \end{gathered}[/tex]To calculate the length of AC;
[tex]\begin{gathered} AC=2x+x+2=3x+2 \\ since\text{ x=2} \\ AC=3x+2=3(2)+2 \\ AC=6+2 \\ AC=8 \end{gathered}[/tex]Therefore, the length of the diagonal AC is;
[tex]8[/tex]Rob earns $4200 per month at his new job. He pays the following taxes: 6.2% for social security 1.45% for Medicare 16% for federal income tax • 5.5% for state income tax Calculate his annual net income.
Answer:
$35,708.4
Explanation:
His net income will be the total that he earns less the taxes.
So, we need to calculate how much money does Rob pays for each tax.
Therefore, 6.2% of 4200 is equal to:
[tex]4200\times6.2\text{ \% =4200 }\times\frac{6.2}{100}=260.4[/tex]It means that Rob pays $260.4 each month for social security,
In the same way, 1.45% of 4200 is equal to:
[tex]4200\times1.45\text{ \% = 4200}\times\frac{1.45}{100}=60.9[/tex]16% of 4200 is equal to:
[tex]4200\times16\text{ \% = 4200}\times\frac{16}{100}=672[/tex]5.5% of 4200 is equal to:
[tex]4200\times5.5\text{ \% = 4200}\times\frac{5.5}{100}=231[/tex]Now, we can calculate the net income per month as:
$4200 - $260.4 - $60.9 - $672 - $231 = $2975.7
Finally, his annually net income will be the net income per month multiplied by 12 months:
$2975.7 x 12 = $35,708.4
So, the answer is $35,708.4
The functions f(x) and g(x) are shown on the graph.f(x)=x^2What is g(x)?A. g(x)=(x+3)^2B. g(x)=(x-3)^2C. g(x)=(1/3x)^2D. g(x)=3x^2
Given:
[tex]f(x)=x^2[/tex]Let's find g(x).
From the given graph, we can see the graph of g(x) is compressed horizontally from f(x).
Thus, to find g(x) aply the transformation rules for function.
We have:
Horizontal compression of b units ==> f(bx)
Given the point on g(x):
(x, y) ==> (2, 12)
Let's solve for the value of the compressed factor.
We have:
[tex]\begin{gathered} 12=b(2)^2 \\ \\ 12=b4 \\ \\ \text{Divide both sides by 4:} \\ \frac{12}{4}=\frac{b4}{4} \\ \\ 3=b \\ \\ b=3 \end{gathered}[/tex]This means the graph of f(x) was compressed horizontally by a factor of 3 to get g(x).
Thus, to write the function for g(x), we have:
[tex]g(x)=3x^2[/tex]ANSWER:
[tex]D\text{.}g(x)=3x^2[/tex]If triangular pyramid P and triangular pyramid D are similar, which of the following statements must be true?
When two figures are similar, the relation or proportion between same measures is the same. So answer is option d.
Which quadrant has ordered pairs (-x,-y)?
ANSWER
Quadrant III
STEP-BY-STEP EXPLANATION:
Firstly, we need to draw the cardinal points and label each quadrant on it
Looking at the ordered pair (-x, -y), you will see that the x and y-values both fall on the negative side of the x-ais and y-axis
Hence, it falls on the quadrant III
The original price of a sweater is $48. The sale price is 80%. What is the sale price of the sweater?
what is the slope of the line which goes through the points (-2, -9) and (2, 11) the slope of the line is___
We know the equation of a line is given by:
[tex]y=mx+b[/tex]where m is its slope and b its interpcetion with y - axis.
We know the slope equation is
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]If (x₁, y₁) = (-2, -9) and (x₂, y₂) = (2, 11) then replacing in the slope equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{11-(-9)}{2-(-2)} \\ =\frac{11+9}{2+2} \\ =\frac{20}{4}=5 \end{gathered}[/tex]Answer: the slope of the line is 5There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.
The given statement is true.
This is a question of probability.
It is given in the question that:-
Chance of raining here = 50 %
Chance of raining on Mars = 10 %
The given statement is :-
There is a 45 % chance that it will rain in neither place.
Chance of not raining here = 100 - 50 % = 50 % = 1/2
Chance of not raining on Mars = 100 - 10% = 90 % = 9/10
Hence, chance of raining in neither place = (1/2)*(9/10) = 9/20
9/20 = (9/20)*100 = 45 %.
Hence, the given statement "There is a 45% chance that it will rain in neither place" is true.
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Y=-4 graph each equation by making a table
The graph of the equation and the table is attached below.
Graph:
Graph means the pictorial representation of the given set of data or the equation.
Given,
Here we have the equation
y = -4.
Now, we need to plot the graph for this equation and we have also draw the table for that.
Here we have the equation y = -4. This one can't take any value for the calculation,
Which means it we take any value on the x coordinate, the given equation will result only the value of y as -4.
Which means, if we take x as -2, the value of y is -4.
If we take x as -1, it will also have the value of y as -4.
If we take x as 0, then again we will get the value of y as -4.
Therefore, it will continuous at infinity.
So, the table for this equation is look like the following.
And the graph of the equation is attached below.
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Sarkis OganesyanCombine Like Terms (Basic, Decimals)May 20, 11:02:29 AMA triangle has side lengths of (1.1p + 9.59) centimeters, (4.5p - 5.2r)centimeters, and (5.3r + 5.4q) centimeters. Which expression represents theperimeter, in centimeters, of the triangle?14.89 + 5.6p + 0.2rO 0.1r + 5.6p + 14.99Submit Answer-0.7pr + 10.7qr + 10.6pq9.7qr + 10.9pr
The sides of the triagle have lengths:
1.1 p + 9.5 q
4.5 p - 5.2 r
5.3 r + 5.4 q
Or:
1.1 p + 0 r + 9.5 q
4.5 p - 5.2 r + 0 q
0 p + 5.3 r + 5.4 q
If we want to calculate the perimeter of the triangle, we just need to sum the three lenghts:
(1.1 + 4.5) p + (-5.2 + 5.3) r + (9.5 + 5.4) q
= 5.6 p + 0.1 r + 14.9 q
How many solutions does the equation 5(m + 3) = 6-7m have? Explain how you found your answer.
Expand the left hand side using distributive property:
[tex]\begin{gathered} 5\cdot m+5\cdot3=6-7m \\ 5m+15=6-7m \\ \text{Add 7m to both sides:} \\ 5m+15+7m=6-7m+7m \\ 12m+15=6 \\ \text{subtract 15 from both sides:} \\ 12m+15-15=6-15 \\ 12m=-9 \\ \text{divide both sides by 12:} \\ \frac{12}{12}m=-\frac{9}{12} \\ m=-\frac{3}{4} \end{gathered}[/tex]Triangle ABC lies on the coordinate plane with vertices located at A(7,6), B(-3,5), and C(-4,9). The triangle is transformed using the rule (x,y) -> (2x,y-3) to create triangle A'B'C'. Select all possible answers for the vertices of triangle A'B'C'. Question 1 options: (14,3) (9,3) (-6,10) (-8,6) (-6,2)
All of the possible answers for the vertices of triangle A'B'C' after using this translation rule (x, y) → (2x, y - 3) include the following:
A. (14, 3)
D. (-8, 6)
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure or object in the same direction, as well as for the same distance.
Next, we would transform triangle ABC by using this translation rule (x, y) → (2x, y - 3) to create the vertices of triangle A'B'C' as follows:
(x, y) → (2x, y - 3)
Coordinate A = (7, 6) → Coordinate A' (2(7), 6 - 3) = (14, 3)
Coordinate B = (-3, 5) → Coordinate B' = (2(-2), 5 - 3) = (-4, 2)
Coordinate C = (-4, 9) → Coordinate C' = (2(-4), 9 - 3) = (-8, 6)
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Michelle can wash dry and fold 5 loads of laundry in 3 1/2 hours. what is the average amount of time it takes Michelle to do one load of laundry
Sketch the graph of the polynomial function. Use synthetic division and the remainder theorem to find the zeros.
GIVEN:
We are given the following polynomial;
[tex]f(x)=x^4-2x^3-25x^2+2x+24[/tex]Required;
We are required to sketch the graph of the function. Also, to use the synthetic division and the remainder theorem to find the zeros.
Step-by-step solution;
We shall begin by sketching a graph of the polynomial function.
From the graph of this polynomial, we can see that there are four points where the graph crosses the x-axis. These are the zeros of the function. One of the zeros is at the point;
[tex](-1,0)[/tex]That is, where x = -1, and y = 0.
We shall take this factor and divide the polynomial by this factor.
The step by step procedure is shown below;
Now we have the coefficients of the quotient as follows;
[tex]1,-3,-22,24[/tex]That means the quotient is;
[tex]x^3-3x^2-22x+24[/tex]We can also divide this by (x - 1) and we'll have;
We now have the coefficients of the quotient after dividing a second time and these are;
[tex]x^2-2x-24[/tex]The remaining two factors are the factors of the quadratic expression we just arrived at.
We can factorize this and we'll have;
[tex]\begin{gathered} x^2-2x-24 \\ \\ x^2+4x-6x-24 \\ \\ (x^2+4x)-(6x+24) \\ \\ x(x+4)-6(x+4) \\ \\ (x-6)(x+4) \end{gathered}[/tex]The zeros of this polynomial therefore are;
[tex]\begin{gathered} f(x)=x^4-2x^3-25x^2+2x+24 \\ \\ f(x)=(x+1)(x-1)(x-6)(x+4) \\ \\ Where\text{ }f(x)=0: \\ \\ (x+1)(x-1)(x-6)(x+4)=0 \end{gathered}[/tex]Therefore;
ANSWER:
[tex]\begin{gathered} x+1=0,\text{ }x=-1 \\ \\ x-1=0,\text{ }x=1 \\ \\ x-6=0,\text{ }x=6 \\ \\ x+4=0,\text{ }x=-4 \end{gathered}[/tex]Given a family with four children, find the probability of the event. All are boys. The probability that all are boys
Answer:
0.0625
Explanation:
The number of children in the family = 4
The possible combination of genders:
[tex]|\Omega|=2^4=16[/tex]The event that all are boys, |A|=1
Therefore, the probability that all are boys:
[tex]\begin{gathered} P(A)=\frac{1}{16} \\ =0.0625 \end{gathered}[/tex]2) (3 pt) Write the function from the table and graph.хf(x)-10004122130.52) f(x) =
(x - h)^2 = 4p(y - k)
(-1 - 3)^2 = 4p(8 - 0.5)
(-4)^2 = 4p(7.5)
16 = 30p
p = 16/30
p = 8/15
(x - 3)^2 = 16/15(y - 0.5)
15(x^2 - 6x + 9) = 16y - 8
15x^2 - 90x + 135 = 16y - 8
16y = 15x^2 - 90x + 135 + 8
y = 15/16 x^2 - 90/16 x + 143/16
f(x) = 15/16 x^2 - 90/16x + 143/16
O GRAPHS AND FUNCTIONSGraphing a piecewise-defined function: Problem type 1
Answer:
Explanation:
To get the plot of h(x), we just plot the given values of y at the given values of x.
For example, we are told that between x = -3.5 and -2.5, h(x) = -3. Therefore, the plot gives
The hollow circle tells us that the value x = -3.5 itself is not included. The solid circle tells us that x = -.2.5 is included. All this comes from the fact that the interval given is -3.5 < x ≤ -2.5.
Using the same method for other entries on the graph, we get our desired plot.
What’s the total of all the present values of the payments? $320,640 $787,116 $878,611 $987,116
The total of all the present values of the payments is $2,973,483.
What is the present value?The present value is the future cash flows discounted to the present day's values.
The present value can be determined using an online finance calculator that inputs the future cash flows, the interest rate, and the period.
How is the total present value determined?The total present value is a function of the summation of the four present values.
Since the present values are given, computing the total involves the mathematical operation of addition.
Present Values:1st payment $320,640
2nd payment $787,116
3rd payment $878,611
4th payment $987,116
Total PV $2,973,483
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Answer:
The correct answer is $878,611 for plato users
Step-by-step explanation:
find the following quantity. Do not round your answers 5.4% of 900
The question asks us to find 5.4% of 900.
Percentage is expressed in terms of 100.
5.4% of 900 would be written as
5.4/100 * 900
= 48.6
5.4% of 900 is 48.6
In the diagram below of triangle DEF, G is a midpoint of DE and H is a midpoint of EF. IfGH = 50 -- 87, and DF = 9x + 0, what is the measure of GH? E H D F
GH = 18
Explanations:From the diagram:
DF = 9x + 0
GH = 50 - 8x
Since G is a midpoint of DE and H is a midpoint of EF, using the midpoint theorem:
DF = 2GH
9x + 0 = 2 (50 - 8x)
9x = 100 - 16x
9x + 16x = 100
25x = 100
x = 100/25
x = 4
Substituting the value of x into GH = 50 - 8x
GH = 50 - 8(4)
GH = 50 - 32
GH = 18
Write an expression to show how much Gretchen paid for drama,action, and comedy videos if she paid $4 for each at a sale. Evaluate the expression
explanation
To determine how much Gretchen paid, we will have to list out the number of Video purchases made for drama, action, and comedy videos.
Let the Action videos be represented by A
Let the Comedy videos be represented by C
Let the Drama videos be represented by D
Also,
A has 3 purchases
C has 5 purchases
D has 2 purchases
Therefore, we will have the expression
[tex]3A+5C+2D[/tex]If she paid $4 for each, then
The total videos purchased = 3+5+2=10
Thus, the total amount paid will be
[tex]\begin{gathered} 10p \\ \text{where p is the price she paid for each video} \\ \text{Thus, } \\ \text{she paid} \\ 10(4)=\text{ \$40} \end{gathered}[/tex]Thus, Gretchen paid $40
