Answer:
[tex]66\pi[/tex] ft²
Step-by-step explanation:
First find the area of the rectangle surrounding the cylinder.
Since the base diameter is 6 feet, the circumference [tex]=\pi d=6\pi[/tex].
Since the height is 8 feet, the area of the rectangle is [tex]6\pi\times8[/tex] or [tex]48\pi[/tex]
Now the area of the base circle [tex]=\pi r^2 = \pi\times\frac{1}{4}d^2=9\pi[/tex]
There are 2 base circles, so [tex]9\pi\times2=18\pi[/tex]
Surface area = [tex]18\pi+48\pi=66\pi[/tex] ft²
Which table represents a linear function?
X
1
2
34
y
3 1/1/2
O
777772
X
1
2
3
4
O
11121314
X1234
y
X1234
7
6
13
21
y
0
6
16
30
Answer:
2
Step-by-step explanation:
The first table represents the linear function.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The first table represents a linear function because the slope remains constant through out the function
Hence, the first table represents the linear function.
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The linear function has the domain (-2, -1, 0, 1, 2). Find the range or output of. h(x) = 2x + 3
If the linear function has the domain (-2, -1, 0, 1, 2). Then the range of the function h(x) = 2x + 3 will be (-1, 1, 3, 5, 7).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given as
h(x) = 2x + 3
The linear function has the domain (-2, -1, 0, 1, 2).
For x = -2
h(-2) = 2 (-2) + 3
h(-2) = -1
For x = -1
h(-1) = 2 (-1) + 3
h(-1) = 1
For x = 0
h(0) = 2 (0) + 3
h(0) = 3
For x = 1
h(1) = 2 (1) + 3
h(1) = 5
For x = 2
h(2) = 2 (2) + 3
h(2) = 7
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what term is defined by the formula b^2 = a^2 + c^2 - 2ac(cosB)
Answer:
It is cosine theorem
Step-by-step explanation:
It is cosine theorem.
Graph the set x-6≤ x < -2} on the number line.
Then, write the set using interval notation.
On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.
Interval Notation: [ -6, -2 ]
What is the interval notation form of the set of inequality?An inequality has an infinitely number of solution, the solution set is easily described using interval notation.
Given the set of inequality { x| -6 ≤ x < - 2}
This can easily be written in the form of interval notation as;
[ -6, -2 ]
On the number line, -2 is not shaded and moving left to show that x is less than -2 but shaded on -6 moving right to show that x is greater than or equals to -6.
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Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second. What does point I represent in this context?
CORRECT (SELECTED)
Chana's distance from the starting line at a time when she is behind Josiah.
Explanation: Point I is on line b, so it does represent Chana's distance at a certain time. Also, point I is below line a, so it represents a distance that is less than Josiah's distance.
The best representation for the point I is that Chana's distance from the starting line at a time when she is behind Josiah.
How to solve for the line BThe point I is the distance of Chana at a particular point in time. This distance is the line a.
At point a, the speed is more so below it, it shows a speed that is less than the distance which Josiah has covered.
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A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
Which of the following histograms is the best representation of the data?
a.
A histogram with frequency on the x-axis and ages on the y-axis. 20 to 24, 2; 25 to 29, 2; 30 to 34, 5; 35 to 39, 4; 40 to 44, 5; 45 to 49, 5; 50 to 54, 1; 55 to 59, 1.
b.
A histogram with frequency on the x-axis and ages on the y-axis. 20 to 24, 4; 25 to 29, 1; 30 to 34, 6; 35 to 39, 2; 40 to 44, 5; 45 to 49, 5; 50 to 54, 3; 55 to 59, 4.
c.
A histogram with ages on the x-axis and frequency on the y-axis. 20 to 24, 2; 25 to 29, 2; 30 to 34, 5; 35 to 39, 4; 40 to 44, 5; 45 to 49, 5; 50 to 54, 1; 55 to 59, 1.
d.
A histogram with ages on the x-axis and frequency on the y-axis. 20 to 24, 4; 25 to 29, 1; 30 to 34, 6; 35 to 39, 2; 40 to 44, 5; 45 to 49, 5; 50 to 54, 3; 55 to 59, 4.
Please select the best answer from the choices provided
A
B
C
D
A histogram with frequency on the x-axis and ages on the y-axis is shown below. Then the correct option is A.
What is a histogram?A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.
A large construction company wants to review the ages of its sales representatives.
A sampling of the ages of 25 sales reps are given:
50, 42, 32, 35, 41, 44, 24, 46, 31, 47, 36, 32, 30, 44, 22, 47, 31, 56, 28, 37, 49, 28, 42, 38, 45.
Then the histogram with frequency table is given as
Range Frequency
20 to 24 2
25 to 29 2
30 to 34 5
35 to 39 4
40 to 44 5
45 to 49 5
50 to 54 1
55 to 59 1
Then the correct option is A.
The histogram is given below.
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Please help!!! Select the quadratic equation that has no real solution.
Answer:
2x² + 6x + 20
Step-by-step explanation:
See the picture
What is the distance between the points (3, 6) and (4, 2)?
Select the best answer from the choices provided.
A. √113
B. √65
C. √50
D. √17
Answer:
Step-by-step explanation:
Givens
x2 = 4
x1 = 3
y2 = 2
y1 = 6
Formula
distance = sqrt( (x2 - x1)^2 + (y2 - y1)^2) )
Solution
distance = sqrt( (4 - 3)^2 + (2 - 6)^2 )
distance = sqrt( 1^2 + 4^2)
distance = sqrt (17)
Answer
D
What is the distance between the points (3, 6) and (4, 2)?
Select the best answer from the choices provided.
Answer is: ∅ D. √17
Formula:
Distance (d) Square roots (sqrt) ( x 2 - x 1 )² + ( y2 - y1 )²
d = sqrt ( 4 - 3 )² + ( 2 - 6 )²
d = sqrt ( 1² + 4² )
d = sqrt ( 17 ) 1^2 + 4^2 = 17
CarryOnLearning <(￣︶￣)>
What is an equation of the line that passes
through the point (5,
-2) and is parallel
to the line 2x
- 5y = 35?
the results of a poll indicate that between 33% and 37% of the population of a town visit the library at least once a year. what is the polls margin of error?
The margin of error is ±2%
What is Margin error?A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
Let x be margin of error and y be the percentages of the population.
So,
y-x =33%
y +x = 37%
Solving above equations
2y= 70
y= 35%
and x= 2%
Hence, the margin of error is ±2%.
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What is 10 1/2 divded by 2 1/4?
Answer:
4.66666666667
Step-by-step explanation:
Answer:
Step-by-step explanation:10 1/2÷ 2 1/4
solution:
=20/2 ÷ 8/4
= 10 ÷
=5
In an olimpiad , each of the 25 questions is worth 3 marks. So every correct answer is awarded 3 marks. But for every incorrect answer 1 mark is subtracted. lesley scored 55 marks out of a possible 75. how many problems did leley get correct.
An equation is formed of two equal expressions. The number of questions that Lesley answered correctly is 20.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of correct questions answered be x, while the number of questions incorrectly answered be y.
The total number of questions can be written as,
x + y = 25
Solving the equation for y,
y = 25 - x
The total marks can be written as,
3x - 1y = 55
Substitute the value of y,
3x - 25 + x = 55
4x = 80
x = 20
Hence, the number of questions that Lesley answered correctly is 20.
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Solve for x in the diagram below.
Answer:
35 degrees
Step-by-step explanation:
Given all 3 angles add up 180(Sum of angles in a straight line)
[tex]2x + 30 + 40 + 40 = 180 \\ 2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ x = 35deg[/tex]
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Solve for x in the diagram below.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Notice that all 3 of those angles together make a linear pair, or a [tex]\bf{180^\circ}[/tex] angle.
This is the key to solving this problem, because the sum of these angles is 180 degrees.
[tex]\bf{2x+30+40+40=180}[/tex] | arrange the like terms
[tex]\bf{2x+30=180-40-40}[/tex] | arrange the like terms
[tex]\bf{2x+30=100}[/tex] | subtract 30
[tex]\bf{2x=70}[/tex] | divide by 2
[tex]\bf{x=35}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=m\angle x=35^\circ}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics \not1\theta l}}[/tex]
Find the equation of the line through the points (3,-4) and (0,2) answer in slope intercept form
Answer:
y= -2x+2.
Step-by-step explanation:
1) according to the condition interception is '2' (point (0;2));
2) slope is: (2+4)/(0-3)= -2;
3) finally the required equation is: y=-2x+2.
P.S. the suggested option is not the only one.
If it cost $6 to fill a gas tank in 1970, how much would it have cost to fill the same tank in 2010?
Step-by-step explanation:
Well since it cost 6$ and the price was 0.36 you can calculate how many gallons you needed to fill up your tank which is calculated by dividing the price to fill the gas tank by the price per gallon
6/0.36 = 16.667 gallons
Now multiply the amount of gallons you need to fill your gas tank by the price in 2010
16.667 * 2.84 = 47.36
You could also just look at the price as a percentage relative to 1970 prices and see that the price increased by 788.9% and the find what 788.9% is of 6$. Which can be done by dividing 788.9 by 100 to convert it into decimal form which gives you 7.889 and then multiply that by the original price of 6$ to fill your gallon to get 47.33 which is slightly different although this is likely due to rounding.
Maria is going to purchase celery and onions for a new black bean soup recipe. The recipe calls for 1.5 times as many pounds of onions as celery. If she has $8.10, what is the most pounds of celery she can buy if celery costs $1.80 per pound and onions cost $1.50 per pound?
The maximum pounds of celery she can buy is 3.25 pounds.
What are the linear equations that represent the question?1.5c = o equation 1
1.50o + 1.80c = 8.10 equation 2
Where:
o = pounds of onions
c = pounds of celery
How many pounds of celery can she buy?
Substitute for o in equation 2 using equation 1
1.50(1.50) + 1.80c = 8.10
2.25 + 1.80c = 8.10
1.80 = 8.10 - 2.25
1.80c = 5.85
c = 5.85 / 1.80
c = 3.25 pounds
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Convert 3 tons, 569 pounds into pounds
Answer:
6,569 pounds
Step-by-step explanation:
Ton= 2,000 pounds each
Therefore, 3 x 2,000 (pounds) = 6,000(pounds). You can use a shortcut by multiplying 3 x 2 and adding the three zeros at the end. 6,000 pounds + 569 pounds will result in 6, 569 pounds.
For the pair of
functions, f and g, determine the domain of f + g.
f(x) = 4x + 19, g(x) = 12x + 14
Answer: (-∞,∞)
Step-by-step explanation:
f(x)=4x+19
g(x)=12x+14
f + g= 4x +19 + 12x + 14 = 16x + 33
Domain of 16x + 33 = (-∞,∞)
1. Given
G(n) = 4n-5
H(n) = 2n + 1
Find G(H(8))
Answer:
first H(8)= 2×8+1=16+1=17
and G(17)= 4×17-5=68-5=63
On a coordinate plane, a line goes through points (negative 2, negative 2) and (4, 2).The graphed line can be expressed by which equation?
Answer:
y=⅔m-8 or 3y=2m-8
Step-by-step explanation:
put both equations in the form y=mx+c and solve simultaneously. when done, you will recive values for m and c. replace those values into y=mx+c
what is the surface area of the walls of a hall measuring length 14m,width9m and height 4m?
Answer:
184 m²
Step-by-step explanation:
lateral area of a prism = perimeter of base × height
A = 2(14 m + 9m) × 4 m
A = 184 m²
find the expression that represents the length of the hypotenuse of a right triangle whose legs measure 2x2-y2 and 2xy
The expression for hypotenuse is √4x^4 + y^4.
What is Pythagoras theorem?A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.
Given:
one leg = 2x²- y²
another leg = 2xy
H² = (2x²- y²)² + (2xy)²
H² = 4x^4 + y^4 - 4x²y² + 4x²y²
H²= 4x^4 + y^4
H= √4x^4 + y^4
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factor: 128 + 2d^3
cubes lol
The factorization if the given expression 128 + 2d³ is 2(64 + d³).
Factorization128 + 2d³
There are two parameters in the expression;
128 2d³The common factors between 128 and 2d³ is 2
So,
128 + 2d³
= 2(64 + d³)
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The mean on a Advanced Algebra test was 86 with a standard deviation of 4.5. If the test scores are normal distributed, find the interval about the mean that contains 68% of the scores. Use the empirical rule.
Using the Empirical Rule, the interval that contains 68% of the scores is [81.5, 90.5].
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.68% of the scores are within 1 standard deviation of the mean, hence the bounds of the interval are:
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Most of Mauna Kea, a volcano on Hawaii, lies below sea level. If this volcano begins at 5998 meters below sea level and then rises 10,203 meters, find the height of the volcano above sea level.
Final answer:
Height of volcano above sea level is 4205m.
Step-by-step explanation:
Step 1
Height of volcano below sea level: 5998m
Step 2
Total height of volcano below and above sea level:
10203m
Step 3
Subtract height of volcano below sea level from total height of volcano to get height of volcano above sea level:
10203 - 5998
Step 4
Subtract the terms:
10203 - 5998 = 4205
The terminal side of angle θ intersects the unit circle in the first quadrant at (16/19,y). What are the exact values of sinθ and cosθ?
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The terminal side of an angle is the angle at the standard position. The terminal side of an angle θ drawn in angle standard position is the side which isn't the initial side.
Given that the point of intersection of the terminal side of θ an the unit circle is:
(16/19,y)
The exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
The given parameters is represented by:
(16/19,y)
This means that :
(cosθ ,sinθ )=(16/19,y)
Using the following trigonometric identity:
cos²θ +sinθ =1
We have:
(16/19)²+y²=1
Expand fraction:
(256/361)+y²=1
Collect like terms:
y²=1-(256/361)
Take LCM:
y²=(361-256)/361
y²=105/361
Take square roots
y=(√105)/19
Substitute value for y in
(cosθ ,sinθ )=(16/19,y)
By comparison:
cosθ =16/19
sinθ =(√105)/19
So the exact value of sin θ and cos θ is: sinθ =(√105)/19 and cosθ =16/19
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Ten members of Balin’s soccer team ran warm ups for practice. Each member ran the same distance. Their combined distance was StartFraction 5 Over 6 EndFraction of a mile. To find the distance that each member ran, Balin wrote the expression below.
StartFraction 5 Over 6 EndFraction divided by 10
Which expression is equivalent to Balin’s expression?
The expression that is equivalent to Balin's expression is 5/6 x 1/10.
What is the equivalent expression?Division is the mathematical operation that is used to determine the quotient of a number.
In order to determine the distance ran by each member, divide the total distance ran by the total number of people.
5/6 ÷ 10
5/6 x 1/10
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The expression is equivalent to Balin’s expression is StartFraction 5 Over 6 EndFraction divided by 10
Division of fractionCombined distance = 5/6 mileNumber of Balin’s soccer team = 10Distance each member ran = Combined distance ÷ Number of Balin’s soccer team
= 5/6 ÷ 10
= 5/6 × 1/10
= 5/60
= 1/12 mile
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Question Write an equation of the line that passes through (1, −2) and is parallel to the line y=7x+7. An equation of the parallel line is y= .
Answer:
Step-by-step explanation:
7 = (y+2)/(x-1)
Parallel lines have equal slopes.
You can "massage" the form into any form you need.
A garden table and a bench cost 735 combined. The garden table costs 35 more than the bench. What is the cost of the bench?
Answer:
350
Step-by-step explanation:
Let,
x = bench
x + 35 = garden table
EQUATION:
(x) + (x + 35) = 735
2x = 735 - 35
2x = 700
x = 350
SUBSTITUTE:
bench costs 350 and garden table costs 385
Hello!
Based on the info we have we can form 2 equations :
(Keep in mind x is the cost of the garden table and y is that of the bench)
x + y = 735x = y + 35Now substitute x in the first equation.
⇒ y + 35 + y = 735
⇒ 2y = 700
⇒ y = 350
∴ The cost of the bench is [tex]\fbox {350}[/tex]
2 factored expressions equivalent to -20x-30
The two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression
What are Expressions ?Expressions are the mathematical statement consisting of variables , constants and mathematical operators .
The expression given is
-20x -30
-2(10x +15)
-20x -30
-5x ( x+6)
Therefore these two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression.
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