Answer:
160π
Step-by-step explanation:
The surface area of a right circular cylinder can be calculated using the following equation:
[tex]\boxed{\mathrm{Surface \ area = }2 \pi rh + 2 \pi r^2}[/tex] ,
where h is the height and r is the radius of the base of the cylinder.
We are told that the rod is 16 inches tall, therefore h = 16. We are also told that the radius of the base is 4 inches, therefore r = 4. Using this information along with the formula above, we can calculate the surface area of the metallic rod:
Surface area = [tex](2 \times \pi \times 4 \times 16) + (2 \times \pi \times (4)^2)[/tex]
= [tex]128\pi + 32\pi[/tex]
= [tex]\bf 160\pi[/tex]
Therefore the surface area of the metallic rod is 160π.
Answer:
[tex]144\pi \: or \: 145\pi[/tex]
SA to cylinder is
[tex]2\pi \: rh + \pi \: r {}^{2} [/tex]
=2
[tex] 2 \times \pi \times r \\ \times h + \pi \times r {}^{2} [/tex]
2
[tex]2\pi \times 4 \times 16 + \pi \times 4 \times 4[/tex]
answer =
[tex]144\pi \: to \: 145\pi[/tex]
Anursery owner buys 8 panes of glass to fix some damage to his greenhouse. The 8 panes cost $18 80. Unfortunately, he breaks 3 more panes while repaining the damage. What is the cost of another
3 panes of glass?
Another 3 panes of glass cost:
Answer:
Step-by-step explanation:
If 8 panes cost 1880
then 1 pane cost 1880 divided by 8
1 pane = $ 235
3 pane = $235 x 3
= $ 705
$1715 + $705 = $ 2420
The coordinated of point T are (0,4). The midpoint of ST is (4,-5). Find the coordinates of point S
Answer:
(8,-14)
Step-by-step explanation:
mid piont is (4,-5) So let us consider that S(x,y)
Now,
from mid point formula,
[tex]4 = \frac{x + 0}{2} \\ x = 8[/tex]
[tex] - 5 = \frac{y + 4}{2} \\ - 10 = y + 4 \\ y = - 10 - 4 \\ y = - 14[/tex]
ZA and ZB are supplementary angles. If m/A= (2x - 20)° and m
LB = (3x+15)°, then find the measure of ZB.
The required measure for the supplementary angles EB is calculated as 126°.
Given that,
Two supplementary angles are given ZA and ZB.
ZA = 2x - 20 ; ZB = 3x + 15
To determine the measure of ZB.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The sum of the supplementary angle is 180°.
ZA + ZB = 180°
2x - 20 + 3x + 15 = 180
5x - 5 = 180
5x = 180 + 5
5x = 185
x = 37
Now,
the measure of angle,
ZB = 3x + 15
ZB = 3 * 37 + 15
ZB = 126°
Thus, the required measure of the angle EB is 126°.
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[tex]5xx^{2} -9x-10[/tex]
Answer:
Step-by-step explanation:
5
2
−9x−10
Calculate 5 to the power of 2 and get 25.
25−9x−10
1
Calculate 10 to the power of 1 and get 10.
25−9x−10
Subtract 10 from 25 to get 15.
15−9x
Kym is renovating the first floor of her house. She bought 750 square feet of laminate flooring and 525 square
feet of carpet and paid $2717.25. She went back to the store and bought an additional 100 square feet of
laminate flooring and 75 square feet of carpet and paid $374.75. Find the cost per square foot of each type of
flooring. equation
Using simultaneous equations in two variables we get that the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.
Equations in algebra that involve two or more variables simultaneously, such as x and y, are referred to as simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously. There are countless possible solutions to just these equations.
A set of finite equations for which common solutions are sought makes up a system of equations, often known as an equation system.
Let the cost per sq feet of laminate be x and the cost per sq feet of carpet be y.
Now it is given that the cost of 750 sq feet of laminate and 525 square foot of carpet is $2717.25
∴ 750x+525y=2717.25
Again the cost of 100 sq feet of laminate and 75 square foot of carpet is $374.75
∴ 100x + 75 y = 374.15
Now we solve the pair of simultaneous equations to find the value of x and y:
Multiplying the second equation by 7 and subtracting from the first we get:
750x + 525y = 2717.25
600x + 575 y = 2619.05
150x = 98.20
or, x = 0.654...
Substituting this value in the first equation we get:
y= 4.115...
Therefore the solution of the simultaneous equation is:
x = $ 0.65 and y = $ 4.12
Therefore the cost of laminate is $ 0.65 per sq. feet and the cost of carpet is $ 4.12 per sq. feet.
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Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
f(x)-2 g(x)
The values for f(x)-2 g(x) = -2x² + 8x - 1
What are the domain of the function f(x)-2 g(x)?Given : f(x)=2 x+5
g(x)=x²-3 x+2
Solution:
2g(x)=2x²-6x+4
f(x)-2 g(x) = 2 x+5 - (2x²-6x+4)
f(x)-2 g(x) = 2 x+5 - 2x² + 6x - 4
f(x)-2 g(x) = -2x² + 8x - 1
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PLEASE I REALLY NEED HELP !!!
79°
73°
Find the value of the missing angle x.
||
२००
Answer:
152 =x
Step-by-step explanation:
180 - 152= 28
180-28= 152
PLS HELP!
A group of friends wants to go to the amusements part, they have no more than $235 to spend on parking and admission, Parking is $17.50 and tickets cost over $36.25 per person, including tax. Use the drop down menu below to write an inequality representing p, the number of people who can go to the amusement park.
Which inequality ≥ or ≤
then what is Answer
p (Inequality) _____
Answer: The answer is <
Step-by-step explanation:
Really can explain sorry
3.
Evaluate
O-16
16
O-4
O 1
32
-
1
2-2x-3y5
for x = 2 and y = -4.
Answer:
58
Step-by-step explanation:
2-2x-3y5
2-2(2)-3(-4)5
-2+60
58
Based on the stemplot, which of the following is a correct comparison of the eastern and western states’ expenditures?
Going by the stemplot, a correct comparison to make between eastern and western states’ expenditures is The eastern states have, on average, a higher per-pupil expenditure than the western states.
How to read a stemplot?Reading a stemplot requires looking at the stem first which is the number in the middle. Then combine this with the leaf to find the actual number. For instance, a stem of 7 and a leaf of 6 in the attached photo is $76,000.
From the attached photo, we see that the Eastern states have more numbers of per-pupil expenditure which means that on average, they have a higher per-pupil expenditure than the western states.
Options for this question are:
The western states exhibit more variability in their expenditures than the eastern states. The eastern states have, on average, a higher per-pupil expenditure than the western states. The distribution of per-pupil expenditures in the eastern states is more symmetric than the distribution of the western states. The distribution of the western states' per-pupil expenditure is skewed left, while the distribution of the eastern states' per-pupil expenditure is skewed right. Valid conclusions comparing the distributions cannot be made, since there is a different number of states in each group.Find out more on stemplots at https://brainly.com/question/22400218
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show that theorem 2.6, the additive law of probability, holds for conditional probabilities. that is, if a, b, and c are events such that p(c) > 0, prove that p(a ∪ b|c)
P(AUB|C)=P(A|C) + P(B|C) - P(AnB|C) is the correct answer.
From distributive law we have,
P((AUB)nC)=P(AnC) + P(BnC)-P(AnBnC)
Dividing both sides by P(C)
P((AUB)nC)/P(C)=P(AnC)/P(C) + P(BnC)/P(C) - P(AnBnC)/P(C)
P(AUB|C)=P(A|C) + P(B|C) - P(AnB|C)
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Solve this linear quadratic system
y = 3x + 4
y + x² = 0
Answer:
x = -1, y = 1
Step-by-step explanation:
Solve the following system:
{y = 3 x + 4 | (equation 1)
y = x + 2 | (equation 2)
Express the system in standard form:
{-(3 x) + y = 4 | (equation 1)
-x + y = 2 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{-(3 x) + y = 4 | (equation 1)
0 x + (2 y)/3 = 2/3 | (equation 2)
Multiply equation 2 by 3/2:
{-(3 x) + y = 4 | (equation 1)
0 x + y = 1 | (equation 2)
Subtract equation 2 from equation 1:
{-(3 x) + 0 y = 3 | (equation 1)
0 x + y = 1 | (equation 2)
Divide equation 1 by -3:
{x + 0 y = -1 | (equation 1)
0 x + y = 1 | (equation 2)
Collect results:
Answer: {x = -1, y = 1
For each annual rate of change, find the corresponding growth or decay factor. +0.1%
The growth factor for the annual rate of change +0.1 % is 1.001.
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.
Now, we have the annual rate of change as:
r = + 0.1% = + 0.1 / 100 = + 0.001
From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.
So, let B = 1 + r
B = 1 + r
B = 1 + (+0.001)
B = 1.001
Now, the value of B is greater than 1 therefore, the corresponding growth factor is 1.001.
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please help !! choose the right answer i’ll mark the brainliest
What’s 181 x 42 step by step
answer: 7,602
explanation: 2×3×7×181
Answer:7602
Step-by-step explanation:First line up the numbers vertically and match the places from the right like this.
181
942
* ____
Now multiply the first number with the 1 st digit in 2 nd
number to get intermediate results. That is Multiply 181 with 2. Write the result 362 at the end leaving 0 spaces to the right like this.
181
42
*_____
362
Now multiply the first number with the 2nd digit in 2nd
number to get intermediate results. That is Multiply 181 with 4. Write the result 724 at the end leaving 1 spaces to the right like this.
181
42
*______
362
724
______-
Now add the intermediate results to get final answer.
181
42
*_____
362
724
______
7602
During the 2006 Olympics a gymnastics receives the following scores: 8.9, 9.2, 9.15, 9.03. What is the gymnasts average score?
The gymnasts average score is 9.07
What is the gymnasts average score?The scores are given as
8.9, 9.2, 9.15, 9.03
The gymnasts average score is calculated using'
Average = Sum/Count
So, we have
Average = (8.9 + 9.2 + 9.15 + 9.03)/4
Evaluate
Average = 9.07
Hence, the gymnasts average score is 9.07
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What is each expression written as a single logarithm?
a. log₄ 5 x+log₄3 x
If the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].
Given that the expression is log₄ 5x+log₄3x.
We have to express the expression in single logarithm.
Product property of logarithm says that the logarithm of a product is equal to a sum of logarithms. Because logs are exponents which we have to multiply like bases, we can add the exponents.
The expression is log₄ 5x+log₄3x.
log₄ 5x+log₄3x=[tex]log_{4} 15x^{2}[/tex] (We are not required to change the base)
Hence if the expression is log₄ 5x+log₄3x, then the expression in single logarithm form looks like [tex]log_{4} 15x^{2}[/tex].
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Mark and Gary had a basketball game Saturday. Mark had three times as many rebounds as Gary. If together they had 28 rebounds, how many rebounds did Mark have?
Answer: 19
Step-by-step explanation:
The number below is not correctly written in scientific notation.
0.0038 × 105
What is the new exponent for the power of 10 after rewriting the number correctly in scientific notation?
3.8 × 10?
Write the new exponent value in the blank below.
Answer: use a picture math thing
Step-by-step explanation:0.0038 x 105=0.399 so move the decimal point over 1 then it should look like 0.038 x 10.5=0.399 then repeat.
4. Four of the twelve members of the panel were late for
the meeting. What fraction of the members were on
time?
A. 12
B.
4
C. 1
3
D.
2
3
Answer:
3/4 of the members.
Step-by-step explanation:
4/12 simplifies to 3/4
Draw a scatter plot and find the line of best fit for each set of data. (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14)
The scatter plot is shown in attached images and the line of best fit for the data set is y=1.9821x+2.1937.
The given data set is (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14).
Plot the points on a coordinate plane.
Calculate the means of the x -values and the y -values.
[tex]\begin{aligned}\bar{X}&=\frac{0+1+2+3+4+5+6}{7}\\ &=\frac{21}{7} \text{ or } 3\\ \bar{Y}&=\frac{2+4+6.5+8.5+10+12+14}{7}\\ &=\frac{57}{7}\text{ or }8.14\end[/tex]
Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get
[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=28[/tex]
and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=55.5[/tex]
Calculate the slope.
[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{55.5}{28}\\ &=1.9821\end[/tex]
Calculate the y -intercept.
Use the formula to compute the y -intercept.
[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=8.14-(1.9821\times3)\\ &=8.14-5.9463\\ &=2.1937\end[/tex]
Use the slope and y -intercept to form the equation of the line of best fit.
The slope of the line is 1.9821 and the y -intercept is 2.1937 .
Therefore, the equation is y=1.9821x+2.1937 .
Draw the line on the scatter plot.
Hence, the scatter plot is shown in attached image and the line of best fit for given data set (0,2),(1,4),(2,6.5),(3,8.5),(4,10),(5,12),(6,14) is y=1.9821x+2.1937.
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Please Help, Consider the following sets in the universal set U, which is the set of all elements of the three given sets below. List the elements of the sets being described.
B = {d, o, I, e} I = {p, i, n, a, y} J = {p, i, n, o, y}
The solutions are;
1. U = {a, d, e, i, l, n, o, p, y}
2. E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = { }
4. J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, o, y}
6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = {a, i, n, p, y}
8. I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = {d, e, l}
What is Union of the set?
Union of two or more set is the set containing all the elements of the given set.
Here, U is the universal set, which is the set of all elements of the three given sets.
And, Three sets are;
⇒ E = {d, o, I, e}, I = {p, i, n, a, y}, J = {p, i, n, o, y}
Now, We find the universal set as;
1. U = {{a, d, e, i, l, n, o, p, y}
2. And, E ∪ I = {d, o, I, e} ∪ {p, i, n, a, y}
= {a, d, e, i, l, n, o, p, y}
Hence, E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = {d, o, I, e} ∩ {p, i, n, a, y}
Since, It cannot contain any common elements.
So, Intersection of E and I is null set.
Hence, E ∩ I = { }
4. Since, J' = U - J
J' = {a, d, e, i, l, n, o, p, y} - {p, i, n, o, y}
J' = {a, d, e, l}
Hence, J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, y} ∪ {p, i, n, o, y}
= {p, i, n, a, o, y}
Hence, I ∪ J = {p, i, n, a, o, y}
6. ( J ∩ I ) ∪ E = ({p, i, n, o, y} ∩ {p, i, n, a, y}) ∪ {d, o, I, e}
= {p, i, n, y} ∪ {d, o, I, e}
= {d, o, l, e, p, i, n, y}
Hence, ( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = U - E
= {a, d, e, i, l, n, o, p, y} - {d, o, I, e}
= {a, i, n, p, y}
Hence, E' = {a, i, n, p, y}
8. I' ∪ J = (U - I) ∪ J
= ( {a, d, e, i, l, n, o, p, y} - {p, i, n, a, y}) ∪ {p, i, n, o, y}
= {d, e, l, o} ∪ {p, i, n, o, y}
= {d, e, l, o, p, i, n, y}
Hence, I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = ( {d, o, I, e} ∩ {p, i, n, a, y}) ∩ ({p, i, n, a, y} ∪ {p, i, n, o, y})
= { } ∩ {p, i, n, a, o, y}
= { }
Hence, (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = U - (J ∪ I)
= {a, d, e, i, l, n, o, p, y} - ({p, i, n, a, y} ∪ {p, i, n, o, y})
= {a, d, e, i, l, n, o, p, y} - {p, i, n, a, o, y}
= {d, e, l}
Hence, (J ∪ I)' = {d, e, l}
So, The solutions are;
1. U = {a, d, e, i, l, n, o, p, y}
2. E ∪ I = {a, d, e, i, l, n, o, p, y}
3. E ∩ I = { }
4. J' = {a, d, e, l}
5. I ∪ J = {p, i, n, a, o, y}
6.( J ∩ I ) ∪ E = {d, o, l, e, p, i, n, y}
7. E' = {a, i, n, p, y}
8. I' ∪ J = {d, e, l, o, p, i, n, y}
9. (E ∩ I) ∩ (I ∪ J) = { }
10. (J ∪ I)' = {d, e, l}
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The number of calories in an order of waffle fries is 20 more than the number of calories in 6 apples. If the waffle fries have 590 calories, what is the number of calories in 1 apple
1 apple contains a number of times calories = 95
Arithmetic function:In contrast to functions defined for other values, an arithmetic function is any mathematical function defined for integers (..., 3, 2, 1, 0, 1, 2, 3,...) and relies on the qualities of the integer itself as a number (real numbers, complex numbers, or even other functions)
According to the given data:Based on the given conditions, formulate: 20+6 * x = 590
Rearrange unknown terms to the left side of the equation: 6x = 590 - 20
Calculate the sum or difference:6x = 570
Divide both sides of the equation by the coefficient of variable: x = 570/6
Cross out the common factor: x = 95
get the result: x = 95
1 apple contains a number of times calories = 95.
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3(w-2)=9 please
answer
Answer:
w=5
Step-by-step explanation:
3(w-2)=9
3w-6=9
w=5
Answer:
w = 5
Step-by-step explanation:
The equation is 3(w - 2) = 9
1st : Distribute 3 to w and -2
Should equal 3w and -6
2nd : Add 6 on both sides
Should equal 3w = 15
3rd : Divide 3 on both sides
Should equal w = 5
Hope this helps!
--Blu
F(2x) graph and domain and range
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( -∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
The range is the set of all valid y values. Use the graph to find the range.
Interval Notation:
( -∞ , ∞ )
Set-Builder Notation:
{ y | y ∈ R }
Determine the domain and range.
Domain: ( −∞ , ∞ ), { x | x ∈ R }
Range: ( −∞ , ∞ ), { y | y ∈ R }
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44. The Loveland town council wants to build a bandstand. Architects were asked to submit plans. In the plan shown, the floor has the shape of a regular octagon. a) What is the area of the floor of the bandstand in this plan? 20 ft b) What would the dimensions be of a square bandstand with the same area as the octagon above? c) Which one has the largest perimeter?
Area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
floor has the shape of a regular octagon
Area of a regular octagon = 2a²(1+[tex]\sqrt{2}[/tex])
a = length of the side of the octagon
here a = 20 ft
Area = 2a²(1+[tex]\sqrt{2}[/tex]) = 2(20)(20)(1+[tex]\sqrt{2}[/tex])
= 800(1+1.414)
= 800(2.414)
= 1931.2 ft²
square bandstand with the same area as the octagon
Area of square = b²
b = length of the side of the square
1931.2 = b²
b = 43.94 ft
Perimeter of regular octagon = 8a
= 8(20)
= 160ft
Perimeter of Square = 4b
= 4(43.94)
= 175.78ft
area of the floor of the bandstand in regular octagon is 1931.2 ft²
dimensions of a square bandstand with the same area as the octagon is 43.94 ft
square bandstand has largest perimeter.
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There were four hundred fifty-seven employees working in an office building. fifty-two of them left to go have lunch. 204 cars are still in the parking lot. how many emplyees are left in the building
A 14 ounce energy drink contains 10 1/2 teaspoons of sugar. How much sugar is in one ounce of the drink
Answer:
1.33
Step-by-step explanation:
14÷10 1/2= 1.33
Erica went shopping for new clothes for school. She bought a pair of jeans for $35.99 and several shirts for $11.33 each. If x
represents the number of shirts she bought, which of the following equations should be used to find y, the total cost of Erica's
shopping trip?
Answer:
Simplify
x
=
35.99
dollar
11.33
dollar
.
x
=
3.1765225
Step-by-step explanation:
simplify completely 5√28+√63
The expression is completely simplified to give 13√7
What are surds?Surds are defined as square root values that cannot be further decreases to integers or whole numbers.
Another name for surds are irrational numbers.
Given the surd forms;
5√28 + √63
Now, let's find the factors of the value 28 with perfect squares.
√28 = √4 × 7
The factors of 63 with perfect squares
√63 = √9 × 7
Now, let's substitute the values
5√4 × 7 + √9 × 7
Find the perfect squares
5 × 2√7 + 3√7
Multiply through
10√7 + 3√7
Since the values have common roots, add the coefficient and keep the root the same.
We have;
13√7
Thus, the expression is completely simplified to give 13√7
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