Since the two cylinders are congruent, it means that their dimensions are exactly the same thing.
In other words, the radius of cylinder 1 is the same as that of cylinder 2, and the height of cylinder 2 is the same as that of cylinder 1. This is what it means for two solid shapes to be congruent.
Now, to find the volume of cylinder 2, we apply the frmula for the volume of a tyical cylnder:
[tex]\text{Volume}=\pi\times r^2\times h[/tex]Now,
radius of cylinder 2 = radius of cylinder 1 = 3
height of cylinder 2 = 8
Thus: r = 3, h= 8
Therefore:
[tex]\begin{gathered} \text{Volume}=\pi\times r^2\times h \\ \text{Volume}=\pi\times3^2\times8 \\ \text{Volume}=\pi\times9^{}\times8 \\ \text{Volume}=\pi\times72 \\ \text{Volume}=72\pi\text{ cubic units} \end{gathered}[/tex]Therefore the volume of cylinder 2 is 72pi cubic units (Option D)
Wade and Ida are salespeople who earned the same amount this week, although Ida made 4 more sales than Wade. Wade earns a base of $153 plus $22 per sale. Ida earns a base of $17 plus $24 per sale. Write the equation for the number of sales Wade made this week
Answer:
y = 24x + 17 20
Step-by-step explanation:
Firstly, let's say that 153 and 17 are both the y-intercepts of their respective equations, while 22 and 24 are the slope. With this we can create the following set of equations:
y = 24x + 17
y = 22x + 153
So your answer would be y = 24x + 17
Now let's find the sales answer!
Since we know that Ida made 4 more sales than Wade this week, we could say:
y = 24(x+4) + 17
y = 22x + 153
Now since we know that they earned the same amount we can do the following:
24(x+4) + 17 = 22x + 153
Simplify...
24x + 96 + 17 = 22x + 153
Simplify again:
24x + 113 = 22x + 153
subtract 22x and 113 from both sides...
2x = 40
Then:
x = 20
So this means that Wade made 20 sales this week!
So let's check if we are right:
Now that we know that x = 20, we need to plug it into Wade's equation!
y = 22(20) + 153
y = 440 + 153
y = 593
Wade made $593 this week!
To check if we are right, let's plug it into Ida's equation:
y = 24x + 113
y = 24(20) + 113
y = 480 +113
y = 593
Ida also made $593 this week!
MEANING we are right!
I hope I helped :P
State the domain and range for the graph and tell if it is a function.
The arrows indicate that the graph of the function continues beyond what can be seen in the image.
Notice that the graph does not appear to have asymptotes; then, the domain of the function is:
[tex]\text{domain}=(-\infty,\infty)[/tex]And the range is:
[tex]\text{range}=(-\infty,\infty)[/tex]Since the graph seems to continue towards the +y-direction and the -y-direction
Finally, notice that for each value of x, the graph has only one value of y. This is the key characteristic of a function; the graph is a function.
Maggie's brother is 3 years younger than four times her age. The sum of their ages is 42.How old is Maggie?Maggie isyears old.
The age of Maggie is 9 years and her brother whose age 3 years less than four times Maggie's age is 33 years old.
What is age?
Age is the difference in days, months, and years between the day, month, and year of birth and the day, month, and year of the event, expressed in the largest completed unit of solar time, such as years for adults and children and months, weeks, days, hours, or minutes of life, as appropriate, for infants under one year of age (Gregorian calendar).
Let the ages of Maggie and her brother be X and Y.
There are two condition given in the question through which we can form a system of equation containing two equations.
First condition: The sum of their ages is 42.
Therefore,
X + Y = 42
Second Condition: Maggie's brother is 3 years younger than four times her age.
Therefore,
4X - 3 = Y
We get the system of equation:
X + Y = 42
4X - 3 = Y
Solving this system of equation
4X - 3 = Y
4X - 3 = 42 - X
X = 45/5
X = 9
Putting the value of X in one of the equation:
Y = 42 - X
Y = 42 - 9
Y = 33
Therefore, age of Maggie is 9 years and age of her brother is 33 years.
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pls solve this question properly
Answer:
∡BOA ≅ ∡DOC
Step-by-step explanation:
Given a circle O with congruent chords BA and DC, you want the relation between angles BOA and DOC.
CongruenceAll of the radii of circle O are congruent. That means BO≅AO≅DO≅CO. The chords BA and DC are marked as congruent. This means ∆BOA and ∆DOC are congruent by the SSS postulate.
Corresponding parts of congruent triangles are congruent, so ...
∡BOA ≅ ∡DOC
please help me solve,the question is A cylinder with a diameter of 8 feet is cut out of a cube that measures 8 feet on each side.What is the volume of the resulting shape? ( use Pi and round to the nearest tenth.) ______ ft3
Side of cube = 8 ft
Volume of cube = Side x Side x Side
Volume of cube = 8 x 8 x 8
Volume of cube = 512 feet^3
A cylinder with diameter 8feet is cute form the cube
Height of cylinder = Side of cube
Height of cylinder = 8 feet
Diameter of cylinder = 8 feet
Radius of cylinder = 4feet
[tex]\begin{gathered} \text{Volume of cylinder =}\Pi\times radius^2\times Height \\ \text{Volume of cylinder =}\Pi\times4\times4\times8 \\ \text{Volume of cylinder =}401.92ft^3 \end{gathered}[/tex]The volume of resulting shape = Volume of cube - Volume of cylinder
Volume of resulting shape = 512 - 401.92
Volume of resulting shape = 110.08 ft^3
Answer: 110.08 ft^3
the probability that the mean salary of the sample is less than $60,000 is? round 4 decimals if needed.
Answer:
0.26599
Step-by-step explanation:
We will assume a normal distribution for the salaries
We have the following information
Mean μ = 64000
Standard deviation σ = 6400
And we are asked to find P(X < 60000)
First find the z score corresponding to X = 60000
The z score is given by (X - μ) / σ
z score for 60000 with μ = 64000 and σ = 6400 is
z = (60000 - 64000)/6400
z = -40000/6400 = -0.625
We can either look up the P value from the z-tables or simply use a calculator
P(X < 60000) and this works out to 0.26599
What is the value of sec 3pi/2 in simplest form with a rational denominator?
The given expression is
[tex]sec\frac{3\pi}{2}[/tex]Since sec is the opposite of cosine, then
[tex]sec\frac{3\pi}{2}=\frac{1}{cos\frac{3\pi}{2}}[/tex]Since the value of cos(3pi/2) is 0, then
[tex]\begin{gathered} cos\frac{3\pi}{2}=0 \\ \\ sec(\frac{3\pi}{2})=\frac{1}{cos\frac{3\pi}{2}}=\frac{1}{0} \end{gathered}[/tex]Since 1/0 is an undefined value, then
The answer is undefined
Use 3.14 for pi or the pi button and round to the nearest hundredth. The volume of the cone?
Given:-
[tex]r=4.5,h=9[/tex]To find the volume of cone.
So the volume formula for cone is,
[tex]v=\pi r^2\frac{h}{3}[/tex]Substituting we get,
[tex]\begin{gathered} v=3.14(4.5)(4.5)(\frac{9}{3}) \\ v=3.14(4.5)(4.5)(3) \\ v=190.755 \end{gathered}[/tex]So the required solution is 190.76
Find the equation of the line whose slope is 1/6 passing through the point (-9, 3)
The equation of the line whose slope is 1/6 passing through the point (-9, 3) is -x - 6y - 27 = 0
What is slope formula ?To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.
Given slope of equation m =[tex]\frac{1}{6}[/tex]
A point on line (x₁,y₁) = (-9,3)
(y-y₁)= m (x-x₁)
(y-3) = [tex]\frac{1}{6}[/tex] ( x − (-9))
y-3= [tex]\frac{1}{6}[/tex] (x+9)
6(y-3) = x+9
6y - 18 = x +9
-x - 6y - 27 = 0
This is the equation of line
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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 50.2 . You would like to be 90% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required?
The required sample size of the given estimate is 3030.65.
Given that,
The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
For the 90% confidence the value of the z = 1.645
Now the sample size is given as,
n = [z × σ/1.5]²
Substitute values in the above equation,
n = [1.645×50.2/1.5]²
n = 3030.65
Thus, the required sample size of the given estimate is 3030.65.
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Kim's room is an 11 ft by 12 ft rectangle. How many square feet of carpeting does she need to buy to cover the entire floor?
In order to calculate the area of carpet needed to cover the entire floor, we just need to calculate the area of the room.
The area of a rectagle is calculated by the product of its dimensions, so we have:
[tex]\text{Area}=11\cdot12=132\text{ ft2}[/tex]So the area of carpet needed is 132 square feet.
Im not the best at word problems please help.Frank knows that his first four test grades were 74, 76, 77, and 84. Use the formula x‾=x1+x2+…+xnn to find Frank's grade on the fifth test if his test average is 80.6.
Given:
Frank knows that his first four test grades were 74, 76, 77, and 84
We will find Frank's grade on the fifth test if his test average is 80.6.
So, let the fifth grade = x,
The average is the sum of the grades over the number of the grades
So,
[tex]\frac{74+76+77+84+x}{5}=80.6[/tex]Solve the expression to find x:
[tex]\begin{gathered} 74+76+77+84+x=5\cdot80.6 \\ 311+x=403 \\ x=403-311=92 \end{gathered}[/tex]So, the answer will be: the fifth grade = 92
Hi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.Good evening g, thanks for helping meHi, can you please help me with my math? Please help me please that's all I'm asking and thank you so much.The problem is 7.Can you please help and thanks 7. The two lines y=4x+5 and y= 4x-2 are parallel because their slopes are equal (both equal to 4).What happens when you try to algebraically solve for their intersection point?
No solution
Explanation:y = 4x + 5
y = 4x - 2
Solving algebraically:
equate both equations
y = y
4x + 5 = 4x - 2
collect like terms:
4x - 4x = - 2 - 5
0 = -7
When the right hand side is not the same as the left hand side equation, it is a no solution.
Their intersection point gives no solution
I need help with this question but no one is helping me! Can someone please help me
Answer:
when rounding the answer it shouldn't be the exact answer so add or multiply then once you find your product round it off and add a decimal
Bill bought a table on sale for $558. This price was 28% less than the original price,What was the original price?
For the new price to be 28% less than the original price then, therefore, the original price is definitely more than the new price
Let the original price be
[tex]x[/tex]the new price given is
[tex]\text{ \$558}[/tex]It means that the percentage decrease is
[tex]28\text{ \%}[/tex]The formula for percentage decrease is
[tex]\text{percentage decrease=}\frac{\text{original price-new price}}{\text{original price}}\times100\text{ \%}[/tex]By substitution, we will have
[tex]\begin{gathered} 28=\frac{x-\text{ \$558}}{x}\times100 \\ 28x=100x-55800 \\ 55800=100x-28x \\ 72x=55800 \\ \frac{72x}{72}=\frac{55800}{72} \\ x=\text{ \$775} \end{gathered}[/tex]Therefore,
The original price = $775
If F(X) = 5x-7 and G(X)= -2x+9, what is G(F(X))?O A. -10x +23O B. -10X2 +59x-63O C. -10x+38O 10XD. 10x7 - 59x+63
f(x) = 5x - 7
g(x) = -2x + 9
g(f(x)) = -2(5x -7) + 9 = -10x + 14 + 9 = -10x + 23
g(f(x)) = -10x + 23
Answer:
Option A: -10x + 23
Which of the following is not a solution 3x-5<2
SIMPLIFY THE EQUALITY FIRST
[tex]3x \leqslant - 2 + 5 \\ 3x \leqslant 3 \\ \frac{3x}{3} \leqslant \frac{3}{3} \\ x \leqslant 1[/tex]
X CAN BE ALL THE NUMBERS LESS OR EQUAL TO 1
IN THE PICTURE THE ONLY OPTION THAT CONTRAST THE INEQUALITY IS OPTION B BECAUSE IT IS GREATER THAN 1.
HOPE THIS HELPS
Answer:
option B
Step-by-step explanation:
3x - 5 ≤ -2
add 5 to both sides
3x - 5 + 5 ≤ -2 + 5
3x ≤ 3
divided both sided by 3 to get x alone
3x/3 ≤ 3/3
x ≤ 1
option B is the only choice that is above 1.01 making it not a solution
50 points for this one
Answer:
-1, 0
Step-by-step explanation:
Hello!
We can test each solution for by substituting the value for x, and see if the inequality is true.
x = -1:[tex]\frac{3(-1)^2}{(-1)^2+3} < 1[/tex][tex]\frac34 < 1[/tex]This inequality is true.
x = -2:[tex]\frac{3(-2)^2}{(-2)^2+3} < 1[/tex][tex]\frac{12}{7} < 1[/tex]This inequality is not true because 12/7 is greater than 1.
x = 0:[tex]\frac{3(0)^2}{(0)^2+3} < 1[/tex][tex]0 < 1[/tex]This is inequality is true.
x = 3:[tex]\frac{3(3)^2}{(3)^2+3} < 1[/tex][tex]\frac{27}{12} < 1[/tex]This inequality is not true because 27/12 is greater than 1.
The solutions that work are -1 and 0.
Answer: A
Step-by-step explanation:
2(3x - 1) + 2(4x + 5) = 8
Answer:
0
Step-by-step explanation:
2(3x -1) + 2(4x + 5) = 8 Distribute the 2's
2(3x) + 2(-1) + 2(4x) + 2(5) = 8
6x - 2 + 8x +10 = 8 Combine like terms
14x + 8 = 8 Subtract 8 from both sides of the equaion
14x = 0 Divide both sides by 14
x = 0
help me please if you can i need to know the equation
Following the instructions provided, we shall use a graphing calculator (Desmos) to determine the equation of the circle shown by the "colorful people."
The first step is to determine the radius which we can observe from the circle itself, whose diameter spans from 0 units to 10 units along the x-axis. The radius therefore is 5 units (half of the diameter).
Observe also that the center has now moved away from the origin (0, 0), and if we move the slider very carefully for h, that would be 5 units away from the origin towards the right (along the x-axis), andk would be 7 units away from the origin) towards the bottom (along the y-axis).
After following these steps, we can replicate the circle given in the question and if we now substitute the values of h, k and r into the equation of a circle, we would end up with;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{Where;} \\ h=5,k=-7,r=5 \\ \text{The equation becomes;} \\ (x-5)^2+(y-\lbrack-7\rbrack)^2=5^2 \\ (x-5)^2+(y+7)^2=25 \end{gathered}[/tex]Look at triangle ABC on the coordinate plane. 1 Which coordinate plane shows triangle ABC after a reflection over the y-axis?
We a figure is being reflected over the y-axis, the y-coordinates of its point will not change. However, the x-coordinates will be multiplied by -1.
Given points of the figure:
Point A: -5,-2
Point B: -4,-4
Point C: -6,-4
Let's now determine the new points of the figure once reflected over the y-axis.
Point A: -5,-2 ➜ Point A': (-5)(-1),-2 = 5,-2
Point B: -4,-4 ➜ Point B': (-4)(-1),-4 = 4,-2
Point C: -6,-4 ➜ Point C': (-6)(-1),-4 = 7,-4
Looking at the
Find csco, cose, and tan , where is the angle shown in the figure.Give exact values, not decimal approximations.
Let 'a' represent the unknown side of the triangle.
To solve for the unknown side, we will apply the Pythagoras theorem.
[tex]a^2=b^2+c^2^{}[/tex][tex]\begin{gathered} b=4 \\ c=5 \end{gathered}[/tex][tex]\begin{gathered} a^2=4^2+5^2 \\ a=\sqrt[]{16+25} \\ a=\sqrt[]{41} \end{gathered}[/tex]Let solve for cscθ
[tex]\begin{gathered} \csc \theta=\frac{1}{\sin \theta} \\ \sin \theta=\frac{4}{\sqrt[]{41}} \\ \text{Therefore,} \\ \csc \theta=\frac{1}{\frac{4}{\sqrt[]{41}}}=\frac{\sqrt[]{41}}{4} \end{gathered}[/tex]Let us solve for cosθ
[tex]\cos \theta=\frac{5}{\sqrt[]{41}}[/tex][tex]\begin{gathered} \frac{5}{\sqrt[]{41}} \\ \text{Rationalising} \\ \frac{5}{\sqrt[]{41}}\times\frac{\sqrt[]{41}}{\sqrt[]{41}}=\frac{5\sqrt[]{41}}{41} \end{gathered}[/tex][tex]\cos \theta=\frac{5\sqrt[]{41}}{41}[/tex]Let us solve for tanθ
[tex]\tan \theta=\frac{4}{5}[/tex]C IS BETWEEN A AND D, B IS THE MIDPOINT OF AC . IF BD =15 AND BC= 7, FIND AD
BD= 12
BC=7
Is this from a graded quiz?
there are about 6*10^24 molecules in a litre of water. it is estimated that a person drinks about 2.2 *10^3 litres of water a year. how many molecules of water does a person drink in a year?
Based on the concept of multiplication, the amount of molecules consumption of water does a person drink in a year is 1.32 x 10²⁸.
Molecules:
A molecules is the group of two or more atoms linked together by sharing electrons in a chemical bond
Given,
There are about 6 x 10²⁴ molecules in a liter of water. it is estimated that a person drinks about 2.2 x 10³ liters of water a year.
Here we have to find the amount of molecules consumption of water does a person drink in a year.
To find the total amount of molecules consumption for the year we have to use the following formula,
Total molecules consumption per year = amount of water x molecules.
Here we know the values of the following,
Water consumption per year = 2.2 x 10³ liters
Molecules of one liter water = 6 x 10²⁴
Apply the values on the formula, then we get,
=> total molecules consumption = (2.2 x 10³) x (6 x 10²⁴)
=> (2.2 x 6) x (10³ x 10²⁴)
=> 13.2 x 10³⁺²⁴
=> 13.2 x ²⁷
It can be further simplified as,
=> 1.32 x 10²⁸
Therefore, the amount of molecules consumption of water does a person drink in a year is 1.32 x 10²⁸.
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I only need help with part "b." I have provided the answer for "a" to help.
Part b.
If we want to dilate a figure we simply multiply each x- and y-coordinate with the scale factor we want to dilate with. Therefore:
Factor of 3
[tex]3\begin{bmatrix}{2} & {4} & {1} \\ {-1} & {3} & {5} \\ {} & {} & {}\end{bmatrix}[/tex]Multiply:
[tex]\begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix}[/tex]Answer:
[tex]\begin{equation*} \begin{bmatrix}{6} & {12} & {3} \\ {-3} & {9} & {15} \\ {} & {} & {}\end{bmatrix} \end{equation*}[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: .25x + 75.00 = C(x)
Step-by-step explanation:
Can I get help in #5 ? I don’t get it
Step 1
The selection formula is;
[tex]\begin{gathered} ^nc_r=\frac{n!}{r!(n-r)!} \\ n=10 \\ r=5 \end{gathered}[/tex][tex]=\frac{10!}{5!(10-5)!}=\frac{3628800}{120(120)}=252\text{ groups}[/tex]Answer; 252 groups
Write an expression describing all the angles that are coterminal with 346°. (Please use the variable k in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)
______ degrees
Answer:
346 + 360k
You can get coterminal angles by adding intervals of 360 degrees
please help with this practice question, thank you
What is the quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in
scientific notation?
The quotient of 7.7 x 10^8 and 5.5 x 10^2 expressed in scientific notation is 1.4x10^6.
What is quotient?
A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is used to describe the integer component of a division (when Euclidean division), as well as a fraction or a ratio (when proper division). A quotient in the second sense is only the proportion of a dividend to its divisor.
Lets calculate the quotient for the value given in question:
[tex]7.7 \times 10^8[/tex]
[tex]5.5 \times 10^2[/tex]
Now we divide the 7.7 by 5.5
[tex]\frac{7.7}{5.5} = 1.4[/tex]
we get value 1.4.
on dividing [tex]\frac{10^8}{10^2}[/tex] we get, [tex]10^6[/tex]
Combining both the value, we get
quotient = [tex]1.4 \times 10^6[/tex]
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