The slant height of the cone is 39.7 cm
Explanation:
Given:
Lateral surface area of a cone = 558π cm²
Radius, r = 31 cm
Slant height, l = ?
We know:
[tex]A = \pi r\sqrt{h^2+r^2}[/tex]
Where,
h is the height of the cone
r is the radius
Solving the equation further:
[tex]558\pi = \pi r\sqrt{h^2+r^2} \\\\558 = 31\sqrt{h^2+(31)^2} \\\\(18)^2 = h^2 + 961\\\\324 = h^2+ 961\\\\h = 25.23[/tex]
Lateral height, H = ?
Applying pythagoras theorm,
(H)² = (h)² + (r)²
(H)² = (25.23)² + (31)²
(H)² = 636.55 + 961
(H)² = 1597.55
H = 39.7 cm
Therefore, the slant height of the cone is 39.7 cm
Answer
uestions below.
A researcher measured the shoe size and math ability of a large group of children. She found that having a larger shoe size does not
indicate that a child has more or less math ability. What does her analysis show
There is no correlation between shoe size and math abity.
There is a correlation between shoe size and math ability. There may or may not be causation. Further studies would have to be done to determine
this.
There is a correlation between shoe size and math ability. There is probably also causation. This is because there is likely an increase in math
ability with an increase in shoe size
Answer:
There is no correlation between shoe size and math abity.
Step-by-step explanation:
The researcher's examination showed that there's no correlation between a child's shoe size and math ability. Hence, a larger shoe size doesn't inherently relate to better or worse math skills. The concepts of correlation and causation are critical in such evaluations.
Explanation:The researcher's analysis indicates that there is no correlation between a child's shoe size and their math abilities. In other words, having a larger shoe size does not necessarily mean that a child would be better or worse at mathematics. The subjects of correlation and causation are important in studies like these. Correlation refers to a mutual relationship or connection between two or more things. In this case, there is no evident correlation between shoe size and math ability. On the other hand, causation would mean that one event (a larger shoe size) is the result of the occurrence of the other event (higher math ability), which in this scenario is not the case.
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what unit of measurement do you measure the length of a living room?
Answer:
ft
Step-by-step explanation:
just the most common
area
i would say feet, so it could be like ''the room is 45 feet long'' or something
What is the correct answer to the equation
Answer:
right answer is 8cm
Step-by-step explanation:
if QM=x
so. Om=32+x
ON=64+16=80
(32+x)/x=80/16
32+x=5x
4x=32
x=8
The calculator shows the result that Luiza got after
evaluating the expression 9 (52+ 18) + 42. She checked
her work by rounding all of the values to the nearest ten and
comparing it to the calculator result. Which is true regarding
her estimate and the accuracy of her calculator result?
1.) The estimated result is 560, which suggests the
calculator is correct.
2.)The estimated result is 740, which suggests the
calculator is incorrect.
3.) The estimated result is 840, which suggests the
calculator is incorrect.
4.) The estimated result is 1,100, which suggests the
calculator is incorrect.
Answer:
Answer 2 is correct, 740
Step-by-step explanation:
The rounded equation would be 10 (50+20) + 40. So if you do the equation then it would be 740
Jada sells ground paprika
Her weekly profit (in dollars) as a function of the amount of paprika she sold that week (in kilograms) is
graphed
What is Jada's profit if she sells 60 kilograms of paprika?
Answer:
If Jada sells 60 kilograms of paprika, her profit would be $200.
Step-by-step explanation:
Note: The missing graph is attached below.
From the graph,
Taking two points
(35, 0) (60, 200)[tex]\mathrm{Slope\:between\:two\:points}:\:\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(35,\:0\right),\:\left(x_2,\:y_2\right)=\left(60,\:200\right)[/tex]
[tex]m=\frac{200-0}{60-35}[/tex]
[tex]m=8[/tex]
The equation of line in slope-intercept form is
[tex]y=mx+b[/tex]
Putting (60, 200) and m = 8 in the slope-intercept form
[tex]200=\left(60\right)\left(8\right)+b[/tex]
[tex]\left(60\right)\left(8\right)+b=200[/tex]
[tex]480+b=200[/tex]
[tex]\mathrm{Subtract\:}480\mathrm{\:from\:both\:sides}[/tex]
[tex]480+b-480=200-480[/tex]
[tex]b=-280[/tex]
Thus
[tex]y=mx+b[/tex]
[tex]y=8x+\left(-280\right)[/tex]
[tex]y=8x-280[/tex]
Putting x = 60
[tex]y=8\left(60\right)-280[/tex]
[tex]y=200[/tex]
Therefore, if Jada sells 60 kilograms of paprika, her profit would be $200.
Answer:
the answer is 35 kilograms
Step-by-step explanation:
got it from khan academy
What parts of the American System are still in effect today
Answer:
Many of the policy tools used by these earlier American systems are obsolete today. But the idea is not. Now, as in the nineteenth and twentieth centuries, national economic development rests on a mutually reinforcing triad of policies to encourage American industry, national infrastructure, and adequate finance.
The principles of economic nationalism, financial stability, and infrastructure development remain influential in modern economic policy.
The American System, also known as the National System or Henry Clay's American System, was an economic plan devised by American statesman Henry Clay in the early 19th century. The plan aimed to promote economic growth and national unity by focusing on three key areas:
Tariff Protection: Clay advocated for high tariffs on imported goods to protect American industries from foreign competition. This policy is still reflected in modern trade agreements, where tariffs are used to balance trade and protect domestic industries.
National Bank: Clay supported the establishment of a strong national bank to regulate the money supply, stabilize the economy, and facilitate commerce. While the specific form of the Second Bank of the United States, which Clay supported, is no longer in existence, the concept of a central bank remains central to modern economic policy.
Internal Improvements: Clay believed in investing in infrastructure projects such as roads, canals, and railroads to improve transportation and connect different regions of the country. This concept is still relevant today, as governments continue to invest in infrastructure to support economic growth and mobility.
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If a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?
100 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)
95 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)
(100 minus 5) (StartFraction 1 Over 500 EndFraction) = E (X)
(100) (StartFraction 1 Over 500 EndFraction) = E (X)
Answer:
B
Step-by-step explanation:
It's the right answer
The expected value of the given scenario is -$4.80
What is probability?The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.
The expected value refers to the value for a person who decides to purchase one ticket.
And that value is the sum of the values of the different possible scenarios.
There are two scenarios, wining and losing.
Note that we need to subtract the cost of the ticket (i.e. $5) from the return.
Winning :-
Probability 1 out of 500 chances
Return expected: ($100 - $5) *1/500 = $95 * 1/500 = $0.19
Losing :-
Probability 499 out of 500 chances
Return expected: (0 - $5)*499/500 = -$4.99
The expected value is the sum of the two returns: $0.19 - $4.99 = -$4.80 (it is negative).
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Khan academy use Pythagorean theorem to find isosceles triangle size length
Answer:
I know
Step-by-step explanation:
The length of each equal side of the isosceles triangle Pythagorean theorem is equal to the square root of half the square of the length of the base.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
To find the length of an isosceles triangle, we need to consider the two equal sides as the legs of a right-angled triangle, and the remaining side as the hypotenuse.
Let's denote the length of the equal sides as "a" and the length of the remaining side (the base) as "b".
According to the Pythagorean theorem, we have:
[tex]a^2 + a^2 = b^2[/tex]
Simplifying this equation, we get:
[tex]2a^2 = b^2[/tex]
To find the length of the equal sides, we can solve for "a" by taking the square root of both sides:
[tex]a = \sqrt{b^2 / 2}[/tex]
Therefore, the length of each equal side of the isosceles triangle Pythagorean theorem is equal to the square root of half the square of the length of the base.
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Rita wants to know the average weight of each apple in
an 8-pound bag of apples. She purchased 5 bags and
found the average apple weight. Using her results, an
apple from an 8-pound bag of apples should weigh
between:
O
O lbs and 0.9 lb.
1.0 lb and 1.2 lbs.
0.8 lb and 1.2 lbs.
O 0.8 lb and 0.9 lb.
Answer:
c
Step-by-step explanation:
because all your doing is picking the smallest and the biggest number and i just got it right .
Answer:C
Step-by-step explanation: 0.8 lb and 1.2 lb
Answer the question
Answer:
on my screen the picture is blocked just comment on my answer and i will do it for you
Step-by-step explanation:
Which of the following is the best thing to do as a first step in using substitution to solve the system of equations?
(3x + y=-3
2x-3y = -13
A. Solve the top equation for x.
B. Solve the top equation for y.
C. Solve the bottom equation for x.
D. Solve the bottom equation for y.
Classify each pair of angles listed below as adjacent or vertical.
Given:
Intersecting lines DA and CE.
To find:
Each pair of adjacent angles and vertical angles.
Solution:
Adjacent angles are in the same straight line.
Pair of adjacent angles:
(1) ∠EBD and ∠DBC
(2) ∠DBC and ∠CBA
(3) ∠CBA and ∠ABE
(4) ∠ABE and ∠EBD
Vertical angles are opposite angles in the same vertex.
Pair of vertical angles:
(1) ∠EBD and ∠CBA
(2) ∠DBC and ∠EBA
A sprinkler head is equidistant from flower garden A and a small shrub B. The sprinkler waters in a
circular pattern. If the length of minor arc AB is 12 feet and the radius of the circle is 10 feet, find the
measure of the central angle subtended by minor arc AB, to the nearest degree.
Answer:
[tex]69^{\circ}[/tex]
Step-by-step explanation:
We are given that
Length of minor arc AB=12 feet
Radius of circle=r=10 feet
Let x be the measure of central angle subtended by minor arc AB.
We know that
Length of an arc=[tex]\frac{Central\;angle}{360}\times 2\pi r[/tex]
Where [tex]\pi=3.14[/tex]
Using the formula
[tex]12=\frac{x}{360}\times 2\times 3.14\times 10[/tex]
[tex]x=\frac{12\times 360}{2\times 3.14\times 10}[/tex]
[tex]x=69^{\circ}[/tex]
A pair of designer sneakers were purchased for $150. Since they were purchased, their price has increased by 20%. After the increase what would the new ammount for the sneakers?
Answer:
the new price is... i think 180
Step-by-step explanation:
For which equation is x = 4.5 a solution?
a
-2x - 4 = 13
b
4x - 3 = 12
c
2x - 2.5 = 6.5
d
2x + 0.5 = 11
How many Starbucks do you think there were in the US in 20152 Make a quick estimate and write it in the box below
Answer:
0
Step-by-step explanation:
Some president will make Russia mad enough to start a nuclear war and the entire planet will be destroyed, let alone Starbucks.
tommy likes to run up and down and "up" escalator. Going up, he can cover 30 steps in 6 seconds. Going down, it takes him 15 seconds to cover 30 steps. Find Tommy's rate (in steps per second) if the escalator stopped moving.
Answer:
3 steps per second.
Step-by-step explanation:
Find the Unit Rates of each going up and down:
--> 30/6 unit rate is 5 steps per second.
--> 30/15 unit rate is 2 steps per second.
Now subtract them to get the amount if the elevator wasn't moving:
--> 5-2= 3.
Final answer:
To find Tommy's rate (in steps per second) if the escalator stopped moving, calculate his speed going up and going down, then subtract the speed going down from the speed going up.
Explanation:
To find Tommy's rate (in steps per second) if the escalator stopped moving, we need to calculate his speed when going up and when going down.
When going up, Tommy covers 30 steps in 6 seconds. So his speed going up is 30 steps / 6 seconds = 5 steps per second.
When going down, Tommy covers 30 steps in 15 seconds. So his speed going down is 30 steps / 15 seconds = 2 steps per second.
If the escalator stopped moving, Tommy's rate would be the difference between his speed going up and his speed going down. So his rate would be 5 steps per second - 2 steps per second = 3 steps per second.
If three unbiased coins are tossed, then what is the probability of getting one or more heads is
The odds would be 7/8 that at least one would be a heads.
Step-by-step explanation:To find your answer, see each coin flip as unrelated to the last one.
For the first coin flip, you can either get heads or tails. So, there's only 2 possible outcomes.
Flip 1 (Outcome 1): H or T
Flip 1 (Outcome 2): H or T
But when it comes to the second flip, now each outcome has two possible "sub-outcomes" of their own. So there's now four total outcomes.
Flip 2 (Outcome 1) : H, H
Flip 2 (Outcome 2) : H, T
Flip 2 (Outcome 3) : T, H
Flip 2 (Outcome 4) : T, T
On the third flip, there would now be 8 outcomes. As each "sub-outcome" has own of their own.
Flip 3 (Outcome 1) : H, H, H
Flip 3 (Outcome 2) : H, H, T
Flip 3 (Outcome 3) : H, T, H
Flip 3 (Outcome 4 : H, T, T
Flip 3 (Outcome 5) : T, H, H
Flip 3 (Outcome 6) : T, H, T
Flip 3 (Outcome 7) : T, T, H
Flip 3 (Outcome 8): T, T, T
So all but one of the eight outcomes have at least one heads drawn. Due to this, the odds of an heads happening would be 7/8 within all of the possible outcomes.
solve -2 | 3x - 6 | + 5 = 1
Answer:
x = [tex]\frac{4}{3}[/tex], x = [tex]\frac{8}{3}[/tex]
Step-by-step explanation:
Given
- 2 | 3x - 6 | + 5 = 1 ( subtract 5 from both sides )
- 2 | 3x - 6 | = - 4 ( divide both sides by - 2 )
| 3x - 6 | = 2
The absolute value function always returns a positive solution, however, the expression inside can be positive or negative, that is
3x - 6 = 2 ( add 6 to both sides )
3x = 8 ( divide both sides by 3 )
x = [tex]\frac{8}{3}[/tex]
OR
- (3x - 6) = 2, that is
- 3x + 6 = 2 ( subtract 6 from both sides )
- 3x = - 4 ( divide both sides by - 3 )
x = [tex]\frac{4}{3}[/tex]
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = [tex]\frac{8}{3}[/tex] : - 2| 8 - 6 | + 5 = - 2| 2| + 5 = -2(2) + 5 = - 4 + 5 = 1 = right side
x = [tex]\frac{4}{3}[/tex] : - 2 | 4 - 6| + 5 = - 2| - 2| + 5 = - 2(2) + 5 = - 4 + 5 = 1 = right side
Thus the solutions are x = [tex]\frac{4}{3}[/tex] and x = [tex]\frac{8}{3}[/tex]
Answer:
x = 1⅓, 2⅔
Step-by-step explanation:
-2 | 3x - 6 | + 5 = 1
-2 | 3x - 6 | = 1 - 5
-2 | 3x - 6 | = -4
| 3x - 6 | = 2
3x - 6 = 2
3x = 8
x = 8/3 = 2⅔
3x - 6 = -2
3x = 4
x = 4/3 = 1⅓
V+6/2=-8. For each step, choose the reason that best justifies it.
Answer:
V=-11
Step-by-step explanation:
V + 6/2 = -8
You simplify the 6/2 PEMDAS
V + 3 = -8
You subtract 3 from both sides PEMDAS/isolate the variable/combine like terms
V = -11
Simplify the expression (3x^3 y^-2)^-4
what is 6x^2+60x+150=0?
6x²+60x+150=0
36x+60x= -150
96x= -150
x= -1.56
Answer: x= -5twice
Step-by-step explanation:
6x2+60x+150=0
Quadratic equation
But firstly,divide all by 6
6x2/6+60x/6+150/6=0
X2+10x+25=0
Variable of 25 that will give 10 is 5&5
Substitute
X2+5x+5x+25=0
X(x+5)+5(x+5)=0
(X+5)(x+5)=0
X+5=0
X= -5 twice
The function f(x)f(x) is a quartic function and the zeros of f(x)f(x) are -6−6, -5−5, -2−2 and 11. Assume the leading coefficient of f(x)f(x) is 11. Write the equation of the quartic polynomial in standard form.
[tex]\boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}[/tex]
Explanation:A quartic function is a function given by the the following equation in standard form:
[tex]f(x)=a_{4}x^4+a_{3}x^3+a_{2}x^2+a_{1}x+a_{0} \\ \\ \\ Where: \\ \\ a_{4},a_{3},a_{2},a_{1},a_{0} \ \text{are constant} \\ \\ \text{and} \ a_{4} \ \text{is the leading coefficient}[/tex]
From the statement we must assume the leading coefficient of f(x) is 11, so:
[tex]a_{4}=11[/tex]
The zeros are:
[tex]x=-6 \\ \\ x=-5 \\ \\ x=-2 \\ \\ x=11[/tex]
So, we can write:
[tex]f(x)=11(x-(-6))(x-(-5))(x-(-2))(x-11) \\ \\ \\ So: \\ \\ \mathrm{Rule}:-\left(-a\right)=a \\ \\ \\ Then: \\ \\ f(x)=11\left(x+6\right)\left(x+5\right)\left(x+2\right)\left(x-11\right)[/tex]
[tex]Expand:\left(x+6\right)\left(x+5\right):\ x^2+11x+30: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^2+11x+30\right)\left(x+2\right)\left(x-11\right) \\ \\ \\ Expand:\left(x^2+11x+30\right)\left(x+2\right):\ x^3+13x^2+52x+60: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^3+13x^2+52x+60\right)\left(x-11\right)[/tex]
[tex]Expand: \left(x^3+13x^2+52x+60\right)\left(x-11\right):\ x^4+2x^3-91x^2-512x-660 \\ (Distributive \ property)[/tex]
Finally:
[tex]f(x) = 11(x^4 + 2x^3 - 91x^2 - 512x - 660) \\ \\ \boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}[/tex]
The radius of the base of a metallic rod is 2 centimeters, and its height is 15 centimeters. What is the volume of this cylinder?
A) 60π cm³
B) 50π cm³
C) 27π cm³
D) 36π cm³
Answer:
A) 60π cm³
Step-by-step explanation:
Given:
The radius of the base of a metallic rod is 2 centimetres, and its height is 15 centimetres.
Question asked:
What is the volume of this cylinder?
Solution:
As we know''
[tex]Volume\ of\ cylinder=\pi r^{2} h[/tex]
[tex]=\pi \times2\times2\times15\\ \\ =60\pi[/tex]
Therefore, the volume of this cylinder will be [tex]60\pi\ cm^{3}[/tex]
Answer:
The correct option is option (A)
The volume of the metallic rod is 60π cm³.
Step-by-step explanation:
Cylinder:
It is three dimension shape.The lateral surface area is 2πrh, r= radius, h= heightTotal surface area = 2πrh+2πr²,Volume = πr²h.The radius of the base of metallic rod is 2 cm and its height is 15 cm.
Here r= 2 cm, h= 15 cm, [tex]\pi =\frac{22}7[/tex]
The volume of metallic rod is
=πr²h
=π(2 cm)² (15 cm)
=π(4)(15) cm³
=60π cm³
If a circle with a diameter of 57.75 m is inscribed in a square, what is the probability that a point picked at random in the
square is in the shaded region? Round the answer to the nearest thousandth.
A. 0.005
B. 0.027
C 0.215
D. 0.785
Answer:
The answer is C
Step-by-step explanation:
8 books cost \$19.60$19.60dollar sign, 19, point, 60.
Which equation would help determine the cost of 101010 books?
Final answer:
The cost of 10 books can be found by dividing the total cost for 8 books ($19.60) by 8 to get the cost per book ($2.45), and then multiplying that by 10 to get the total cost ($24.50).
Explanation:
To determine the cost of 10 books if 8 books cost $19.60, we need to establish the price per book and then multiply that by 10. First, let's calculate the cost per book by dividing the total cost by the number of books:
Cost per book = Total cost ÷ Number of books = $19.60 ÷ 8 books = $2.45 per book
Now, using the cost per book, we can find the total cost for 10 books:
Total cost for 10 books = Cost per book × 10 = $2.45 × 10 = $24.50
Therefore, the equation that would help determine the cost of 10 books is:
Cost = $2.45 × Number of books
In this case, for 10 books, the cost would be:
Cost = $2.45 × 10
?/6=1/2 Will get Brainliest
Answer:
3/6
Step-by-step explanation:
Answer:
3/6=1/2
Step-by-step explanation:
Cross multiply
x/6=1/2
2x=6
Divide by 2 on both sides
x=3
So, 3/6=1/2
Hope this helps! :)
what is -5% as a decimal
-0.5
Answer: -0.5
Step-by-step explanation:
Answer:-0.05
Step-by-step explanation:
How much grain can this container hold? Express your
answer in terms of it. It’s a cylinder
4 in.
11 in.
176pie in.3
88pie in.3
44pie in.3
484pie in.3
Answer:
[tex]176\pi in.^3[/tex]
Step-by-step explanation:
The figure of the problem is missing: find it in attachment.
In this problem, the container has a shape of a cylinder.
The volume of a cylinder is given by the formula:
[tex]V=\pi r^2 h[/tex]
where
V is the volume
r is the radius of the base of the cylinder
h is its height
For the container in this problem, we have:
r = 4 in. is the radius of the base
h = 11 in. is the height of the container
Substituting into the formula, we can find the volume of the container, and so the volume of grain that it can contain:
[tex]V=\pi (4)^2 (11)=176\pi in.^3[/tex]
The given cylinder container can hold 44π cubic inches of grain. This is calculated using the formula for the volume of a cylinder which is πr²h.
Explanation:To compute the amount of grain a cylindrical container can hold, you would have to calculate the cylinder's volume. The formula for the volume of a cylinder is πr²h, where r represents the radius, and h represents the height.
In this case, the diameter is 4 inches, so the radius (r) would be 2 inches. The height (h) of the cylinder is 11 inches. So, substituting these values into the formula gives us:
Volume = π(2²) x 11 = 44π cubic inches
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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15. n an 1 5 2 −10 3 20
Answer:
The answer to this would be 662.
Step-by-step explanation:
Sigma notation calls for the sum of the terms in the sequence.
Answer:
15
∑ 5(-2)^n-1
n =4
Step-by-step explanation:
15 and n = 4 should be on top (15) and below (n = 4) of the ∑
hope this helps :]