Find the volume of the given solid.Round to the nearest 10th, If necessary. In cubic inches
Answers
ANSWER
33.5 cubic inches
EXPLANATION
This is a cone with radius r = 2 in and height h = 8 in. The volume of a cone is,
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]Replace the known values and solve,
[tex]V=\frac{1}{3}\cdot\pi\cdot2^2in^2\cdot8in=\frac{32}{3}\pi\text{ }in^3\approx33.5\text{ }in^3[/tex]Hence, the volume of the cone is 33.5 in³, rounded to the nearest tenth.
Related Questions
Write the slope intercept equation through the point (1,2) and it’s parallel to the line y=1+4x
Answers
Given:
Line equation, y=1+4x
The point, (1,2)
To find the slope intercept form:
The general slope intercept form is, y=mx+b.
First to find m:
From the line equation,
y=4x+1
We have, m=4
Next to find b:
Substitute m=4, and (1,2) in the general intercept form is,
[tex]\begin{gathered} (2)=4(1)+b \\ 2=4+b \\ b=-2 \end{gathered}[/tex]Now, substitute m=4 and b=-2 in the slope intercept form
Thus, the slope intercept form is,
[tex]y=4x-2[/tex]Find an equation of the line.Write the equation in the standard form.Through (8,4); parallel to 7x-y= 2.
Answers
Answer:
7x-y=53
Explanation:
Given the line
[tex]7x-y=2[/tex]Making y the subject of the equation, we have:
y = 7x-2
Therefore, the slope of the line, m=7
• If two lines are parallel, their slopes are equal.
Therefore, the slope of the parallel line = 7
The equation of the parallel line through (8,4) will then be:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-4=7(x-8) \\ y-4=7x-57 \\ 7x-y=-4+57 \\ 7x-y=53 \end{gathered}[/tex]A bag contains 5 red and 3 blue marbles. Two marbles are drawn simultaneously from the bag. DETERMIN the probability that at least one is red.
Answers
total number of balls = 5 + 3 = 8
The possibilities are:
RR (two red) and RB (one red and one blue)
RR and RB are mutually exclusive
P(RR) =
Shandar rents a pickup truck for her house move. She has to pay $96 for the first day, $88 for each additional day she keeps the truck, and 45 cents for each mile she drives. She will also be able to use a $25 coupon. Write an expression that represents the total cost when Shandar keeps the truck for h days and travels a total of p miles.Simplify the expression completely.List the terms in your expression.For each term, identify the coefficient and variable.
Answers
96 first day
88 for each additional day (h)
0.45 for each mile driven (p)
$25 coupon
Expression
Total cost = 96 + 88h + 0.45p - 25
Simplify:
Combine like terms:
TC = 96 - 25 + 88h + 0.45p
TC = 71 + 88h + 0.45p
Terms:
71 = constant
88h = coefficient 88 , variable h
0.45p= coeficcient 0.45 , variable p
Which inequality is represented by the graph?
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Answer:
it's option c ............
if the growth factor is 1.2, what is the growth rate
Answers
SOLUTION
Step 1 :
In this question, we are meant to know the relationship between Growth factor and Growth Rate.
Growth factor is the factor by which a quantity multiplies itself over time.
Growth rate is the addend by which a quantity increases ( or decreases ) over time.
Step 2 :
From the question, if the growth factor is 1.2 which is also 120 %,
then the growth rate will be ( 120 - 100 ) % = 20 % = 0. 2
CONCLUSION:
The Growth Rate = 0. 2
which of the following lines is perpendicular to the equation given below?
Answers
Given data:
The given equation of the line is y=-2x+8.
The slope of the given line is -2.
The slope of the line perpendicular to it is,
[tex]\begin{gathered} m\times-2=-1 \\ m=\frac{1}{2} \end{gathered}[/tex]The standard equation of the line is,
[tex]y=mx+c[/tex]Here, m is the slope of the line.
The second option can be written as,
[tex]\begin{gathered} x-2y=8 \\ 2y=x-8 \\ y=\frac{1}{2}x-4 \end{gathered}[/tex]Thus, option (B) is correct.
4. Sales tax in a certain state is 5%. If the sales tax on a new boat was $400, what was the selling price of the boat?
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Sales tax percentage = 5% = 5/100 = 0.05 (decimal form)
Sales tax amount = $400
Multiply the selling price of the boat (x) by the sales tax percentage in decimal form. That expression must be equal to 400.
0.05x = 400
Solve for x:
x = 400/ 0.05
x= $8,000
I inserted a picture of the question Please don’t ask tons of questions. & please state whether it’s a b c or d
Answers
As given by the question
There are given that the graph of the triangle.
Now,
According to the properties,
If the point (x, y) or (-x, y) rotated about the origin by the angle of 360 degrees.
That means,
There is no difference between rotating 360 degrees clockwise or anti-clockwise around the origin.
Then,
From the vertices of the triangle ABC is:
[tex]\text{A is (-6, 3), B is (-5, 7) and C is (-4, 3).}[/tex]Since the triangle map onto itself
[tex]\begin{gathered} A=A^{\prime} \\ B=B^{\prime} \\ C=C^{\prime} \end{gathered}[/tex]So, the triangle is rotated 360 degrees about the origin
Hence, the correct option is D.
How do you convert 313313 yards to inches? Use the drop-down menus to explain your answer.Since there are inches in 11 yard, 313313 by .So, 313313 yards = inches.
Answers
Given:
[tex]3\frac{1}{3}\text{yards}[/tex]Aim:
We need to convert yards into inches.
Explanation:
[tex]3\frac{1}{3}\text{yards}=\frac{3\times3+1}{3}\text{ yards}[/tex]
[tex]3\frac{1}{3}\text{yards}=\frac{10}{3}\text{ yards}[/tex]
Recall that
[tex]1\text{ yard =}36\text{ inches}[/tex]Multiply 10/3 on both sides, we get
[tex]\frac{10}{3}\text{ yards =}\frac{10}{3}\times36\text{ inches}[/tex][tex]\frac{10}{3}\text{ yards=}120\text{ inches}[/tex][tex]3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]We know that
[tex]3\frac{1}{3}\times36=120[/tex]Final answer:
Since there are 36 inches in 1 yard.
[tex]\text{ multiply 3}\frac{1}{3}\text{ by 36.}[/tex][tex]\text{ So, }3\frac{1}{3}\text{ yards =}120\text{ inches}[/tex]Indicate the transformation that has occurred.2.A. (x,y)-->(-x+3.y-5) C. (x,y) --> (-x,y-5)B. (x,y) --> (x +3,y-5) D. (x,y) --> (x-1,-y)
Answers
So we have a transformation that maps a triangle into another one. This is made by transforming the points X, Y and Z into X', Y' and Z'. In order to find out which of the four options is the correct one we must verify that points X, Y and Z actually transform into X', Y' and Z'.
We have:
[tex]X=(2,5)\rightarrow X^{\prime}=(1,0)[/tex]Let's see which of the four transformations do this. So for A:
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x+3,y-5)=(-2+3,5-5) \\ X^{\prime}=(1,0) \end{gathered}[/tex]So transformation A is a possible answer, let's see the rest.
For C:
[tex]\begin{gathered} (x,y)\rightarrow(-x,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(-x,y-5)=(-2,5-5) \\ X^{\prime}=(-2,0)\ne(1,0) \end{gathered}[/tex]So the X' that we calculate with transformation C is different that the one we are looking for so we discard this option.
For option B we have:
[tex]\begin{gathered} (x,y)\rightarrow(x+3,y-5) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x+3,y-5)=(2+3,5-5)=(5,0) \\ X^{\prime}=(5,0)\ne(1,0) \end{gathered}[/tex]Like what happened with C, transformation B is discarded.
Let's see what happens with D:
[tex]\begin{gathered} (x,y)\rightarrow(x-1,-y) \\ X=(2,5)=(x,y) \\ \text{Then} \\ X^{\prime}=(x-1,-y)=(2-1,-5)=(1,-5) \\ X^{\prime}=(1,-5)=(1,0) \end{gathered}[/tex]So D is also discarded. This would mean that A is the correct option but just in case, let's check if it tansform points Y=(0,2) and Z=(3,1) into Y'=(3,-3) and Z'=(0,-4):
[tex]\begin{gathered} (x,y)\rightarrow(-x+3,y-5) \\ \text{If} \\ Y=\mleft(0,2\mright) \\ \text{Then} \\ Y^{\prime}=(-0+3,2-5)=(3,-3) \\ \text{If} \\ Z=\mleft(3,1\mright) \\ \text{Then} \\ Z^{\prime}=(-3+3,1-5)=(0,-4) \end{gathered}[/tex]So Y' and Z' are (3,-3) and (0,-4) which definetely means that option A is the correct one.
In the figure shown, what is mzA? Explain.57°; AABC is an isosceles triangle with base angles A and C. m2A = mc.B. 66; AABC is an isosceles triangle with base angles B and C. m2B = m_C = 57, and m2A + m2B + m2 = 180.C. 57. AABC is an equilateral triangle.
Answers
Since ABC is an isosceles triangle with sides AB=AC, then the angle ABC is the same as ACB, an it's equal to 57º.
Since all three internal angles should add up to 180º, then the angle BAC should have a measure of 180-2(57)=66º.
Reduce to lowest term10\25
Answers
Answer:
2/5
Step-by-step explanation:
10 and 25 can both be divided by 5
10 divided by 5 equals 2
25 divided by 5 equals 5
x = -1,0,1,2,3.
P(X = x) 0.2, 0.2, 0.2, 0.2, 0.2. Find the value of P(X<3).
Answers
The value of the probability P(x < 3) is 0.8
How to determine the probability value?From the question, the table of values is given as
x = -1,0,1,2,3.
P(X = x) 0.2, 0.2, 0.2, 0.2, 0.2
To calculate the probability P(x < 3). we make use of the probability values where x is less than 3
This means that
P(x < 3) = P(-1) + P(0) + P(1) + P(2)
Substitute the known values in the above equation
So, we have
P(x < 3) = 0.2 + 0.2 + 0.2 + 0.2
Evaluate the sum
P(x < 3) = 0.8
Hence, the probability value is 0.8
Read more about probability at
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Can you evaluate 3 + (a + 4)(8- b ) when a= 5 and b=6
Answers
The expression to evaluate is:
[tex]3+a+4\mleft(8-b\mright)[/tex]When
a = 5 and b = 6
We simply plug in the values of 5 and 6, into a and b respectivly. And do algebra to get our answer. The process is shown below:
[tex]\begin{gathered} 3+a+4\mleft(8-b\mright) \\ 3+5+4\mleft(8-6\mright) \\ 3+5+4(2) \\ 3+5+8 \\ 16 \end{gathered}[/tex]The answer is 16.
Jake and Joshua have new jobs selling gift cards at a local convenience store at the cash register, but their pay is different. Jake earns a foundational wage of $6 per hour, as well as $8 for each gift card sold. Joshua gets $4 for each gift card sold and earns a foundational wage of $6 per hour. If they each sell a certain number of gift cards in one hour, they will end up earning the same amount of pay. How many gift cards would that make up to?Write a system of equations, graph them, and type the solution.
Answers
Let x be the number of cards Jake and Joshua sell within one hour. Therefore, their earnings are given by the following expressions,
[tex]\begin{gathered} Ja=6+8x \\ Jo=6+4x \end{gathered}[/tex]Then, set Ja=Jo (both earn the same amount),
[tex]\begin{gathered} Ja=Jo \\ \Rightarrow6+8x=6+4x \end{gathered}[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow8x=4x \\ \Rightarrow4x=0 \\ \Rightarrow x=0 \end{gathered}[/tex]Then, they will earn the same within one hour only if both sell zero cards within the hour.
Graphing the system of equations,
As one can see, the intersection point is (0,6), which stands for 0 cards and $6
QuestionGiven that cot(0)- 1 and 0 is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.Provide your answer below:sin (O)=
Answers
Given:
The trigonometric ratio is given as,
[tex]\cot \theta=-\frac{1}{2}[/tex]The value of θ lies in the second quadrant.
The objective is to find the value of sinθ.
Explanation:
The formula of cotθ is,
[tex]\cot \theta=\frac{\text{adjacent}}{\text{opposite}}=-\frac{1}{2}[/tex]Since, the value of θ lies in second quadrant, the triangle formed for cotθ will be,
Then, the value of x can be calculated as,
[tex]\begin{gathered} x^2=2^2+(-1)^2 \\ x=\sqrt[]{4+1} \\ x=\sqrt[]{5} \end{gathered}[/tex]To find the value of sinθ:
The value of sinθ can be calculated as,
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin \theta=\frac{2}{\sqrt[]{5}} \\ \sin \theta=\frac{2}{\sqrt[]{5}}\times\frac{\sqrt[]{5}}{\sqrt[]{5}} \\ \sin \theta=\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]Hence, the value of sinθ is (2√5)/5.
Elena is traveling to visit her grandparents who live 125 miles away.
a. Elena stops for lunch 2/3 of the way. How far has Elena traveled?
b. Elena enters the city where her grandmother lives after 110 miles. Is she more or less than 9/10 of the way there?
PLS PLS PLS HELPP
Answers
Answer:
A. 83 1/3 miles
B. Less than 9/10 of the way there
Step-by-step explanation:
A.
2/3 of the way. "of" means to multiply, so multiply 2/3 and 125.
[tex]\frac{2}{3}[/tex] × [tex]\frac{125}{1}[/tex] = [tex]\frac{250}{3}[/tex]
Simplify by dividing 250 and 3.
250 ÷ 3
[tex]83 \frac{1}{3}[/tex] miles
B.
Multiply 125 by 9/10 then compare the answer to 110 to see if she is more or less than 110 miles.
[tex]\frac{125}{1}[/tex] × [tex]\frac{9}{10}[/tex] [tex]= \frac{1125}{10}[/tex]
Divide 1125 by 10
1125 ÷ 10 = 112.5
Since 9/10 of the distance is 112.5 miles, 110 miles is less than 9/10 of the way there.
I was doing this with a tutor but there was a connection problem.
Answers
ANSWER:
[tex](x-3)^2+(y+7)^2=113[/tex]The point (7,6) is not on the circle
STEP-BY-STEP EXPLANATION:
(a)
The equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ where (h,k) is the center and r is the radius } \end{gathered}[/tex]We replace to calculate the radius of the circle, like this:
[tex]\begin{gathered} \mleft(-4-3\mright)^2+\mleft(1-\mleft(-7\mright)\mright)^2=r^2 \\ (-7)^2+(8)^2=r^2 \\ r^2=113 \end{gathered}[/tex]Therefore, the equation would be:
[tex](x-3)^2+(y+7)^2=113[/tex](b)
We replace the point, and if the value is greater than the radius, it means that this point is not on the circle:
[tex]\begin{gathered} (x-3)^2+(y+7)^2\le113 \\ \text{ replacing:} \\ \mleft(7-3\mright)^2+\mleft(6+7\mright)^2\le113 \\ 4^2+13^2\le113 \\ 16+169\le113 \\ 185\le113 \end{gathered}[/tex]Therefore, the point (7,6) is not on the circle
Question60 is 40% of what number?
Answers
let the required number be x then
[tex]\begin{gathered} \frac{60}{x}\times100=40 \\ x=\frac{60}{40}\times100 \\ x=150 \end{gathered}[/tex]So 60 is 40% of 150.
Question 11:What is the maximum height of the driver off the diving board
Answers
To find the maximun height (y) given a quadratic equation as above you find the coordinates of the vertex (maximum or minimun point of a parabola)
1. Use the next formula to find the x- coordinate of the vertex
[tex]\begin{gathered} y=ax^2+bx+c \\ \\ x=-\frac{b}{2a} \end{gathered}[/tex][tex]\begin{gathered} x=-\frac{\frac{24}{9}}{2(-\frac{4}{9})} \\ \\ x=-\frac{\frac{24}{9}}{-\frac{8}{9}}=\frac{-24}{-8}=3 \end{gathered}[/tex]2. Use the value of x above to find y-coordinate in the vertex:
[tex]\begin{gathered} y=-\frac{4}{9}(3)^2+\frac{24}{9}(3)+12 \\ \\ y=-\frac{4}{9}(9)+\frac{72}{9}+12 \\ \\ y=-4+8+12 \\ \\ y=16 \end{gathered}[/tex]Then, the maximum height of the diver is 16 feetSolve the following system using the substitution method. Enter your answer as an ordered pair in the form (x,y). 3x-2y=55x+10y=35
Answers
System of equations
• Equation 1
[tex]3x-2y=5[/tex]• Equation 2
[tex]5x+10y=35[/tex]Procedure
Solving the system by substitution.
0. Isolating ,x ,from equation 2:
[tex]5x=35-10y[/tex][tex]x=\frac{35}{5}-\frac{10y}{5}[/tex][tex]x=7-2y[/tex]2. Replacing the expression of x obtained in equation 1:
[tex]3\cdot(7-2y)-2y=5[/tex]3. Simplifying:
[tex]21-6y-2y=5[/tex][tex]-8y=5-21[/tex][tex]y=\frac{-16}{-8}[/tex][tex]y=2[/tex]4. Finally, we replace this value in the isolated expression of x and solve it:
[tex]x=7-2\cdot(2)[/tex][tex]x=7-4[/tex][tex]x=3[/tex]Answer: (3, 2)
The test results for 4 students are 96 83 78 and 83. If one more student's test score of 87 is added, what would increase?A. median B. meanC. modeD. range
Answers
Mean will increase because 87 is greater than 83 and 78, then the eman will be greater
Franklin is drawing a model of a rectangular swimming pool. He marks two points, A and B, on the coordinate plane and connects them to represent one side of the pool. Points C and D are reflections of B and A, respectively, across the x- axis. Each unit in the coordinate plane represents 1 meter. Draw a rectangle in the coordinate plane yo model the swimming pool. What is the area of the swimming pool?
Answers
Area = base x height
A = 8 x 6 = 48 m²
HELLPPPPLLPPPPPPPPPPPPPPP
Answers
Answer:
a²+13a+40
Step-by-step explanation:
Now the x in the function has been replaced into (a+5) :
(a+5)²+3(a+5) =
(a²+10a+25)+(3a+15) =
a²+13a+40
Hope this helped and have a good day
A table is in the shape of a regularhexagon. The perimeter of the table is 12 ftfeet. What is the length of each side ofthe tableA 1 ftB 2 ftC 3 ftD 4 ft
Answers
Solution:
Given the shape of a hexagon;
The perimeter, P, of a hexagon is;
[tex]\begin{gathered} P=6s \\ \\ \text{ Where }s=side\text{ length} \end{gathered}[/tex]Given;
[tex]\begin{gathered} P=12ft \\ \\ s=\frac{12}{6}ft \\ \\ s=2ft \end{gathered}[/tex]CORRECT OPTION: B
13 divided by 10 5/6
Answers
Answer:
the answer is 1 1/5
In the diagram, m/ACB = 55°.
E
What is mZECD?
90°
O 55°
180°
D
O 125°
C
B
80
Answers
Answer:
55°
Step-by-step explanation:
Angle ACB and angle ECD are alternate exterior angles and alternate angles have same angle measurements:
If angle ACB = 55°
then angle ECD is also = 55°
Write the equation for the trigonometric graph.y= 8cos(pi/40x)y= –8sin(pi/40x)y= –8cos(pi/40x)y= 8sin(pi/40x)
Answers
Solution
For this case we can verify the answer using the point x= 0 if we replace we got:
y=8 cos (pi/40* 0) = 8 cos (0) = 8
y= -8 sin (pi/40 *0)= -8 sin(0) = 0
y= -8cos(pi/40*0)= -8 cos (0)= -8
y= 8 sin (pi/40 *0)= 8 sin(0) = 0
Then the correct option would be:
y= -8cos(pi/40*0)
a rectangle with a area of s sq feet and a width of 6 in what is the length of the rectangle
Answers
The area of the reactangle is calculates using the following formula:
[tex]A=w\cdot l[/tex]Where
A: area
w: wisth
l: lenght
You can write this formula in terms of the length by dividing the Area by the width:
[tex]l=\frac{A}{w}[/tex]If the area is A=s feet² and the width is w=6 feet, then the length is
[tex]l=\frac{s}{6}[/tex]