Volume of a cylinder:
[tex]V=h*r^2*\pi[/tex]For cylinder A:
[tex]10\pi cm^3=h*r^2*\pi[/tex]For cylinder B:
[tex]V_B=2h*(2r)^2*\pi[/tex]Simplify the equation for volumen of cylinder B:
[tex]\begin{gathered} V_B=2h*4r^2*\pi \\ V_B=8*(h*r^2*\pi) \end{gathered}[/tex]in the equation for the volume of cylinder A you have the value of h*r^2*π:
[tex]\begin{gathered} V_B=8*(10\pi cm^3) \\ V_B=80\pi cm^3 \end{gathered}[/tex]Then, the volume of cylinder B is 80π cubic centimeters.(−1/2x+7/10)−(−3/4x−1/5)
The expression (−1/2x + 7/10) − (−3/4x − 1/5) has a value of 1/4x + 9/10 when simplified
How to evaluate the expression?From the question, the expression is given as
(−1/2x+7/10)−(−3/4x−1/5)
Rewrite the expression properly to make it legible
So, we have
(−1/2x + 7/10) − (−3/4x − 1/5)
Expression the above parameter as an equation
This is represented as
(−1/2x + 7/10) − (−3/4x − 1/5) = (−1/2x + 7/10) − (−3/4x − 1/5)
Open the brackets
So, we have the following equation
(−1/2x + 7/10) − (−3/4x − 1/5) = −1/2x + 7/10 + 3/4x + 1/5
Collect the like terms in the equation
(−1/2x + 7/10) − (−3/4x − 1/5) = 3/4x − 1/2x + 7/10 + 1/5
Evaluate
(−1/2x + 7/10) − (−3/4x − 1/5) = 1/4x + 9/10
The expression cannot be further simplified
Hence, the solution to the expression (−1/2x + 7/10) − (−3/4x − 1/5) is 1/4x + 9/10
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Evaluate the function f(p) = p2 + 3p + 1 for p = -2.
The result of the function f(p) = [tex]p^2[/tex] + 3p + 1 for p = -2 is -1
The function is
f(p) = [tex]p^2[/tex] + 3p + 1
The function is the expression that represents the relationship between the one variable and another variable. If one variable is dependent variable then the another variable will be independent variable.
The values of p = -2
Substitute the value of p in the function and find the solution
f(p) = [tex]p^2[/tex] + 3p + 1
f(-2) = [tex](-2)^2[/tex] + 3×-2 + 1
f(-2) = 4 - 6 + 1
f(-2) = -1
Hence, the result of the function f(p) = [tex]p^2[/tex] + 3p + 1 for p = -2 is -1
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What is the value of p in the proportion below? 20/6 = p/12O 2 O 10O 40O 72
20/6 = p/12
cross-multiply
p x 6 = 20 x 12
6p = 240
divide both-side of the equation by 6
p = 240/6
p = 40
Two cyclists, 108 miles apart, start riding toward each other at the same time. One cycles 2 times asfast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?
Initial distance: 108 miles
We know that they start riding toward each other, and one of them is 2 times as fast as the other. Then, if the speed of the slowest is v, the speed of the faster cyclist is 2v. The combined speed is:
[tex]v_T=v+2v=3v[/tex]The speed and the distance are related by the equation:
[tex]V=\frac{D}{t}[/tex]They meet 4 hours later, thus:
[tex]\begin{gathered} D=108 \\ t=4 \end{gathered}[/tex]Finally, using the previous equation:
[tex]\begin{gathered} 3v=\frac{108}{4} \\ \Rightarrow v=9\text{ mi/h} \end{gathered}[/tex]The speed of the faster cyclist (2v) is 18 mi/h.
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 16° = ___
We have round of to 100th place means up to 3 places
[tex]\sin (16\text{ degre}e)=0.27563[/tex]Now we will reduce the digit from right side upto 3 places
As last digit is 3 which is less than 5 so it will remove directly
[tex]\sin (16\text{ degr}e)=0.2756[/tex]Now the last digit is 6 which is greater than 5. So and is even so change we will simply remove this
[tex]\sin (16\text{ degre}e)=0.275[/tex]Short steps pleaseFind the mean and variance of the binomial experiment in which n 5 and p 0.7. a. Mean b. Variance
Given
n= 5
p = 0.7
Find:
a. mean
b. variance
sol:
Mean d
[tex]\begin{gathered} mean\text{ =n}\times\text{p} \\ \\ \text{ = 5}\times\text{0.7} \\ \\ \text{ =3.5} \end{gathered}[/tex][tex]\begin{gathered} variance=np(1-p) \\ \\ =\text{ }5\times0.7(1-0.7) \\ \\ =3.5(0.3) \\ \\ =1.05 \\ \\ \end{gathered}[/tex]2. I want to find the area of a basketball free throw lane, and I am trying to use this formula:
Area =(6 ft) + (12 ft)(19 ft).
Clearly explain how you can tell this is wrong without knowing any area formulas.
Answer:
Down Here
Step-by-step explanation:
Hello!
Area is measured in units². Here, the units are feet, so the area would be written as feet² (ft²).
Simplifying the expression:
6ft + (12ft)(19ft)6ft + 228ft²You can't simplify this because the units are not the same, and this can't measure area because all units of the area have to be squared. The term 6ft has non-squared units.
rag the red and blue dots along the x-axis and y-axis to graph 10x - 7y=40
We were given the equation:
[tex]10x-7y=40[/tex]We will proceed to graph this equation as shown below:
[tex]\begin{gathered} 10x-7y=40 \\ \text{Make ''y'' the subject of the equation, we have:} \\ \text{Subtract ''10x'' from both sides, we have:} \\ -7y=-10x+40 \\ \text{Divide through each term by ''-7'' to obtain the equation in terms of ''y'', we have:} \\ y=\frac{-10}{-7}x+\frac{40}{-7} \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ \\ y=\frac{10}{7}x-\frac{40}{7}_{} \\ when\colon x=-7 \\ y=\frac{10}{7}(-7)-\frac{40}{7} \\ y=-10-\frac{40}{7} \\ y=-\frac{110}{7} \\ \\ when\colon x=0 \\ y=\frac{10}{7}(0)-\frac{40}{7} \\ y=-\frac{40}{7} \\ \\ when\colon x=7 \\ y=\frac{10}{7}(7)-\frac{40}{7} \\ y=10-\frac{40}{7} \\ y=\frac{30}{7} \end{gathered}[/tex]We will proceed to plot these ordered pairs on a graph, we have:
Which of the following statements are equivalent to "Some politicians are not crooked"? Select all that apply:All politicians are crooked.Some politicians are crooked.Not all politicians are crooked.All politicians are not crooked.
SOLUTION
The given statement is
"Some politicians are not crooked"
The equivalent statement is
Not all politicians are crooked
And
All politicians are not crooked.
The equivalent statement is
Not all politicians are crooked
And
All politicians are not crooked.
Answer: Not all politicians are crooked
It is equivalent to saying that "Some politicians are not crooked". Both are implying that not every politician is crooked and some of them are good.
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Which of the following is the number of sides a polygon can have to form aregular tessellation?O A. 9B. 3C. 5D.7
From the image, we are asked the number of sides a polygon can have to form a regular tesselation.
The first step is to understand what a regular tessellation is;
A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape. There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons.
This implies that it could either have 3 sides(triangle), four sides(square), six sides(hexagon).
From the given options we can clearly see that 3 sides is the only available option.
ANSWER: Option B
use the graph to complete the ordered pair solution (0,_) for f.
we must look the value of the graph when x=0
the graph trought x=0 when y=-1 so, the point is
[tex](0,-1)[/tex]8 Madison has two plants. She waters the spider plant every 4 days and the cactus every 6 daysShe water bo November 30. What is the next day that she will water both plants?
Two plants
Spider plant 4 days
Cactus plant 6 days
Then find when
4X = 6Y
find m.c.m (minimum common multiple) of 4 and 6
m.c.m (4,6) = 12
SO therefore, if both plants were watered November 30, then
add 12 days to Nov 30
12 days after Nov 30 = December 12
how to find a volume of a cylinder that has a radius of 10 and a base of 4 Khan academy
Question:
Find a volume of a cylinder:
Solution:
Remember that the volume of the cylinder with radius r and height h is given by the following formula:
[tex]V\text{ = }\pi r^2h[/tex]then, replacing the data of the problem into the previous equation, we get:
[tex]V\text{ = }\pi(4^2)(10)\text{ = 3.14 (16)(10) = 502.4}[/tex]thus, we can conclude that the correct answer is:
[tex]V\text{ = 502.4}[/tex]
LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit
The Solution:
Given the graph below:
We are required to find the perimeter of the triangle LMN rounded to the nearest unit.
Step 1:
Find the distance LM, where L(-3,2) and M(3,5)
By the formula for distance between two points, we have
[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]Substituting, we get
[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]Step 2:
Find the distance LN:
[tex]LN=12[/tex]Step 3:
Find the distance MN, where M(3,5) and N(9,2)
[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]Step 4:
The perimeter is:
[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]Therefore, the correct answer is 28 units.
Out of 3500 students at a college 1760 are enrolled in a computer class. What is the per cent of students taking the computer class?
Using percentages we can conclude that 50.2% of students are taking a computer class.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, the percentage of students taking computer classes:
The total number of students is 3500.The number of students enrolled in a computer class is 1760.Now, calculate as follows:
1760/3500 × 1000.502 × 10050.2Therefore, using percentages we can conclude that 50.2% of students are taking a computer class.
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Which postulate or theorem could you use to prove (triangle)XYZ = (triangle)ABC?Choose the correct answer below.AAS theoremSSS postulateASA postulateSAS postulate
From the given figures in the 2 triangles XYZ and ABC
mXZ = AC
m
Since we have two equal angles and the sides between them are equal, then
The 2 triangles are congruent using ASA postulate
The answer is C
Look at the photograph and if you need anything let me know
Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.
Therefore, the answer is the first option.
Solve |x4|+6 = 13.
O A. x
11 and x = -11
OB. x = 11 and x = -3
OC. x = -11 and x = -3
OD. x = -11 and x = 3
Answer:
B
Step-by-step explanation:
| x - 4 | + 6 = 13
x - 4 + 6 = 13
x = 11
Or
4 - x + 6 = 13
x = -3
Which of the following is the position vector for a vector that has an initial point of (10, 2) andterminal point of (-8, -7)?
initial point = (10,2)
Terminal point = (-8,-7)
subtract the coordinates of the initial point from the coordinates of the terminal point
Position vector = ( -8-10 , -7-2 ) = <-18,-9>
Graph transformation of the following line given the transformation: g(x)= -f(x) -2
Transformation of a Function
We are given the function:
[tex]y=f(x)=\frac{2}{3}x+8[/tex]And it's required to find another function g(x) according to the transformation:
g(x) = -f(x) - 2
First, we calculate the negative of f(x):
[tex]-f(x)=-(\frac{2}{3}x+8)=-\frac{2}{3}x-8[/tex]And now we subtract 2 to find g(x):
[tex]g(x)=-\frac{2}{3}x-8-2=-\frac{2}{3}x-10[/tex]The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10
Answer:
[tex]g(x)=-\frac{2}{3}x-10[/tex]Which graph shows the same linear equation shown in the table below?
I'm drawing now
_______________________
Option C
HELP PLEASEEEEE!!!!!!
-1 3/4, 14/8, 1.125 and -0.875 correspond to points 1, 8, 6 and 4 respectively on the number line.
How can we match -1 3/4, 14/8, 1.125 and -0.875 on the number line?Looking at the number line, there are 8 divisions between two points e.g 0 to 1.
To know the value of 1 division, we divide the value of the distance between two points by the number of divisions:
= 1/8 = 0.125
To find the locations, we just divide the value of the locations with the value of 1 division:
-1 3/4 / 0.125 = -14 (Count 14 divisions to the left of 0) = point 1
14/8 / 0.125 = 14 (Count 14 divisions to the right of 0) = point 8
1.125/ 0.125 = 9 (Count 9 divisions to the right of 0) = point 6
-0.875 / 0.125 = -7 (Count 7 divisions to the left of 0) = point 4
Therefore, the positions of -1 3/4, 14/8, 1.125 and -0.875 on the number line are points 1, 8, 6 and 4 respectively.
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The equation of a curve is y=f(x)
The vertex of the curve is at (2,-3)
Write down the coordinates of the vertex of the curve with the equation
a) f(x)+5
b) -f(x)
The rigid transformations of the vertex of the curve are listed below:
(i) (2, 2).
(ii) (2, 3).
How to determine the coordinates of the vertex
In this problem we find the value of a point of a curve f(x), this point (the vertex) must be transformed by using rigid transformations. There are two cases: (i) Vertical translation, (ii) Reflection about the x-axis. The formulas for each case are described below:
Vertical translation
P'(x, y) = P(x, y) + (0, k)
Reflection about the x-axis
P'(x, y) = P(x, y) + (0, - 2 · p)
Where p is the y-coordinate of point P.
If we know that P(x, y) = (2, - 3), then the coordinates for each case are, respectively:
Vertical translation
P'(x, y) = (2, - 3) + (0, 5)
P'(x, y) = (2, 2)
Reflection about the x-axis
P'(x, y) = (2, - 3) + (0, 6)
P'(x, y) = (2, 3)
The transformations of the vertex of the curve are (i) (2, 2) and (ii) (2, 3).
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What is 2 2/3 - 3/5? 7/154 4/152 1/15 1 2/5
The Ruiz family took a summer trip.
In 4 days, they drove 1,600 miles. If they drove an equal
number of miles each day, how many miles did they drive
each day? Describe the basic fact you use to find your
answer and how many zeros you add from the dividend.
Answer:
400 miles each day
Step-by-step explanation:
You have 1600 miles divided into four days.
1600 / 4
We can use the basic fact that multiplying a number by ten simply means shifting everything to the left, for example 2 x 10 = 20, we just shifted 2 to the left and inserted a 0.
So for this problem, we can do the same. Divide 1600 by 100, or 10 x 10, then divide by 4.
1600/16 = 100
16/4 = 4.
Now, since we divided by ten twice before, we can get the right answer by multiplying by ten twice.
4 x 10 = 40
40 x 10 = 400
Event A, Event B, and Event Care provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the union of A and B?
Given data:
The probability of A is P(A)=0.45.
The probability of B is P(B)=0.30.
The expression for the mutually exclusive events is,
[tex]P(A\cap B)=0[/tex]The expression for the probability of A union B is,
[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =0.45+0.30-0 \\ =0.75 \end{gathered}[/tex]Thus, the probability of (AUB) is 0.75.
Michael bought groceries and spent $46.85 before including the sales tax of 7%. What is the total purchase price after tax?
We are told that a 7% tax is applied to the original sales price, in order to determine the tax amount we just have to multiply the original price ($46.85) by the tax percentage (0.07 as 7% in decimal form), then we get:
Tax amount = 0.07×46.85 ≈ 3.28
By adding the tax amount to the original price we should get the final price, like this:
Total purchase price = 46.85 + 3.28 = 50.13
Then, the total purchase price after tax is $50.13
This table shows the top athletes that play both basketball and track. What is the intersection between the set of basketball players and the set of track athletes? Basketball Track Arnold Berenson Nickerson Eaton Yun Tadesse McDonald Jones Tadesse Nickerson Yang Martin
The intersection between the set of basketball players and the set of track athletes is given by:
{Tadesse, Nickerson}
What is the intersection between two sets?The intersection between two sets is the set containing the elements that belong to both sets which we are calculating the intersection.
In the context of this problem, the sets are given as follows:
List of basketball players: {Arnold, Nickerson, Yun, McDonald, Jones, Tadesse}List of track athletes: {Berenson, Eaton, Tadesse, Nickerson, Yang, Martin}.The intersection is composed by athletes that are both basketball players and track athletes, hence it is given as follows:
{Tadesse, Nickerson}
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If lines L=4x and M=x are perpendicular, what is the value of x?
Those angles are complementary, therefore, we can conclude:
[tex]\begin{gathered} 4x+x=90 \\ add_{\text{ }}like_{\text{ }}terms: \\ 5x=90 \\ Solve_{\text{ }}for_{\text{ }}x: \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]Answer:
x = 18
Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000How much should they deposit now if they assume that they can earn 8.5% compounded annually?
Compound interest formula:
[tex]A\text{ = }P(1+i)^n[/tex]where:
A is the final amount, here = $250,000
P is the principal amount
i is the interest rate per year (in decimal form), here = 0.085
n is the number of years invested, here = 14
Replacing into the equation and solving for P, we get:
[tex]250000=P(1+0.085)^{14}[/tex][tex]\frac{250000}{1.085^{14}}=P[/tex]
P = $79,785.5