The volume of cone is gotten by dividing the volume of cylinder by 3.
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
The volume of a solid figure is the amount of space it occupies in three dimension.
The volume of a cylinder = π * radius² * height
The volume of a cone = (1/3) * π * radius² * height
Hence:
If the cone and cylinder have the same radius and height:
Volume of cone = (1/3) * volume of cylinder.
The volume of cone is one-third volume of cylinder.
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The life (in hours) of a randomly chosen led light produced by a manufacturer is normally distributed with mean 1100 and standard deviation 70. Find the number of sample if the probability that the mean life is less than 1120 hours is 0.92
The sample size if the probability that the mean life is less than 1120 hours is 0.92 is given as follows:
n = 24.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 1100, \sigma = 70, s = \frac{70}{\sqrt{n}}[/tex]
The p-value of Z when X = 1120 is of 0.92, hence Z = 1.405, and the sample size is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.405 = \frac{1120 - 1100}{\frac{70}{\sqrt{n}}}[/tex]
[tex]20\sqrt{n} = 70 \times 1.405[/tex]
[tex]n = \left(\frac{70 \times 1.405}{20}\right)^2[/tex]
n = 24.
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ANSWER ASAP PLS!
The area of the parallelogram below is ____ square meters
Answer:
Below
Step-by-step explanation:
Area is base ( which is 6 m) times the height ( which is 8m)
6 x 8 = 48 m^2
which of the shapes below is an enlargement of shape x by a scale factor of 2
Answer:
E
Step-by-step explanation:
just looking for the ration if scale factor is 2
multiply it and fimd the ans
A) What is the value of x?
B) What is the value of y?
C) What is the best classification for the triangle?
Answer: x = 14; y = 74; Isosceles and Acute
Step-by-step explanation: 3(x+7) = 3x + 21
Isosceles triangles have congruent base angles making 63 = 3x +21
Solve for x.
All angles of a triangle add up to 180 making y = 180 - 63 - 63.
Isosceles because two sides are congruent. And acute because all angles are under 90.
Max’s custom lacrosse stringing experienced fixed costs of $750 and variable costs of $15 for each lacrosse stick that was restrung. Write an equation that can be used to determine the total cost when x sticks are restrung. Then determine the total cost of restringing 32 lacrosse sticks.
The equation representing the total cost is 15x + 750 and the total cost of restringing 32 lacrosse sticks would be $1230.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let, The number of lacrosse sticks be 'x' and the total cost is C(x).
Therefore, The equation representing the context is,
C(x) = 25x + 750.
The total cost of restringing 32 lacrosse sticks would be,
C(32) = 15×32 + 750.
C(32) = 480 + 750.
C(32) = 1230.
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Solve the following proportion:
6/8=8/a
Step-by-step explanation:
Cross multiply to solve for "a":
6 * a = 8 * 8
Simplify the right side:
6 * a = 64
Divide both sides by 6 to isolate "a":
a = 64 / 6
Simplify:
a = 10.67
classafy the numbers some numbers are more than 1 box numbers are 54,72,84,90,96 sections are divisible by 5 and 9 divisible by 6 and 9 divisable by 2 and 6
2/23 divided by 3 1/2
Answer:
4/161
Step-by-step explanation:
2×2
____
23×7
=4
161
=4
161
1/x+5 + 3/x+4 = -1/x^2+9x+20
Please solve this for me I keep getting -5 as the answer but the answer is no solution.
someone explain.
Thank you
Answer: no solution
Step-by-step explanation:
Find the surface area of the sphere. Use 3.14 for pi.
A. 1519.8 yd2
B. 276.3 yd2
C. 6079.0 yd2
D. 552.6 yd2
The surface area of the sphere is 1519.8 yd².
What are 3D shapes?Three-dimensional shapes or solids are the names given to 3D shapes in geometry. Three separate dimensions, such as length, width, and height, are used to describe 3D shapes. The lack of thickness or depth in 2D shapes is the only distinction between them and 3D ones.
Given a sphere
diameter = 22 yards
radius = d/2 = 22/2
radius = 11 yards
the surface area of the sphere = 4πr²
S = 4πr²
S = 4(3.14)11²
S = 1519.76 yd²
S = 1519.8 yd²
Hence option A is correct
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7. Which of the following graphs would represent the solution set for y ≤ 5?
There are 84 students in the Beachwood Middle School chorus. The number of girls in the chorus is 15 more than twice the number of boys.
Answer:
Expression for number of girls:
2b + 15
Equation for number of boys and girls:
b + (2b + 15) = 84
Number of boys
23
Number of girls
61
Step-by-step explanation:
b = number of boys
g = number of girls
b + g = 84
g = 2b+15
b + (2b + 15) = 84
3b + 15 = 84
3b = 69
b = 23
b + g = 84
23 + g = 84
g = 61
please solve me in this maths question ya
Step-by-step explanation:
well, you have it further up :
P(A) = 17x = 17 × 1/32 = 17/32 = 0.53125
1. A biconditional statement says, "A polygon is a square if and only if the polygon has
four equal sides and four right angles." Write the hypothesis and condusion.
2. A statement says, "If the measure of 4] equals the measure of K, the angles are congruent." Write the converse, inverse, and contrapositive of this statement.
3. What is the original statement if the converse of the original statement is "If a number is divisible by two, then it is an even number"? What is the inverse of the original statement?
4. Write the biconditional statement if the hypothesis is "This month is November," and the conclusion is "Next month is December."
5. A right triangle is a triangle that contains a right angle. Write the biconditional statement for the statement above. Also write the converse of the statement. Is the converse a true statement? Explain.
Answer:Hypothesis: A polygon has four equal sides and four right angles.
Conclusion: The polygon is a square.
Converse: If the angles are congruent, then the measure of 4] equals the measure of K.
Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.
Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.
Original statement: If a number is even, then it is divisible by two.
Inverse: If a number is not divisible by two, then it is not even.
Biconditional statement: This month is November if and only if next month is December.
Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.
Converse: If a triangle contains a right angle, then it is a right triangle.
The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).
Step-by-step explanation:
Hypothesis: A polygon has four equal sides and four right angles.
Conclusion: The polygon is a square.
Converse: If the angles are congruent, then the measure of 4] equals the measure of K.
Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.
Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.
Original statement: If a number is even, then it is divisible by two.
Inverse: If a number is not divisible by two, then it is not even.
Biconditional statement: This month is November if and only if next month is December.
Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.
Converse: If a triangle contains a right angle, then it is a right triangle.
The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).
suppose theta is an angle in standard position whose terminal side lies in quadrant 3 . if sin theta = -4/5 find the values of the remaining five functions
Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.
What does trigonometry actually mean?Relationships between cubic splines and trigonometry When the professions of mathematicians were united, it is thought that the field was founded during the third millennium BC. Precise mathematical methods can be used to solve a wide range of geometric issues or to determine the outcomes of calculations that use them. The study of the six fundamental trigonometric operations is known as trigonometry.
Here,
Given :
There are in 3 quadrant :
=> Sinθ = -4/5
=> Cosθ = √1 - Sin²θ
=> Cosθ = √1 - 16/25
=> Cosθ = 3/5
=>Tan θ = -4/5 / 3/5
=> Tan θ = -4/3
=>Cot θ = -3/4
and
Cosec θ = -5/4
Sec θ = 5/3
Therefore , the solution of the given problem of trigonometry comes out to be the five functions value are written above Cosθ = 3/5.
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Solve the compound inequality 2u-5>7 or -3u≤-6
Answer:
u ≥ 2
Step-by-step explanation:
2u-5>7 :
Add 5 to both sides:
2u = 7 + 5
2u > 12
Divide by 2:
u > 6
-3u ≤ -6
Multiply both sides by -1, inequality reverses
-3u(-1) ≥ -6(-1)
3u ≥ 6
Divide by 3:
u ≥ 2
Since u > 6 is a subset of u ≥ 2, the interval for both inequalities is
u ≥ 2
Please help pic is below
The point (1, 1/2) lie on the equation y(x² + 1) = 1.
What is an ordered pair?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
Pair in Order = (x, y)
x is the abscissa, the distance measure of a point from the primary axis x
y is the ordinate, the distance measure of a point from the secondary axis y
Given, A function y(x² + 1) = 1.
y = 1/(x² + 1).
When x = 1, y = 1/2.
When x = - 1, y = 1/2.
So, The points that lie on the equation y(x² + 1) = 1 is (1, 1/2).
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River says that KM is the
bisector of
error in River's reasoning.
The error in River's analysis is that it is known if LM and MJ are perpendicular to KL and KJ.
What is error analysis?
Error analysis is a technique used to track out errors in learner language, ascertain whether they are systematic, and (if possible) provide an explanation for why they occurred.
It is given that -
Line segment KM is the bisector of ∠LKJ.
Also, line segment LM = MJ.
According to the angle bisector theorem if a line is a bisector of an angle then the corresponding sides of the angle should be perpendicular to the third side which is getting bisected.
Although it is given that LM = MJ, but it is not known that if LM and MJ are perpendicular to the sides of ∠LKJ.
Therefore, River cannot conclude that KM is the bisector of ∠LKJ.
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Which three lengths could be the lengths
of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm
B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm
D. 21 cm, 7 cm, 6 cm
Answer:
A. 12 cm, 5 cm, 17 cm
Step-by-step explanation:
For any three given lengths to be the sides of a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each of the options:
A. 12 cm, 5 cm, 17 cm: 5 + 12 = 17, which is greater than 17, so this is a valid triangle.
B. 10 cm, 15 cm, 24 cm: 10 + 15 = 25, which is greater than 24, so this is a valid triangle.
C. 9 cm, 22 cm, 11 cm: 9 + 11 = 20, which is not greater than 22, so this is not a valid triangle.
D. 21 cm, 7 cm, 6 cm: 7 + 6 = 13, which is not greater than 21, so this is not a valid triangle.
Therefore, the three lengths that could be the sides of a triangle are A (12 cm, 5 cm, 17 cm) and B (10 cm, 15 cm, 24 cm).
If you buy a phone for $500 and its value decreases by 50% each year, what is it worth
at the end of 2 years?
O $10
$0
O $125
$250
11 + 5x < 26 word problem
Answer: x<3
Step-by-step explanation:
Bring the 11 to the other side of the equation, and subtract.
5x<15.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{11 + 5x < 26}[/tex]
[tex]\mathsf{5x + 11 < 26}[/tex]
[tex]\large\textbf{Subtract 11 to both sides:}[/tex]
[tex]\mathsf{5x + 11 - 11 < 26 - 11}[/tex]
[tex]\large\textbf{Simplify it}[/tex]
[tex]\mathsf{5x < 26 - 11}[/tex]
[tex]\mathsf{5x < 15}[/tex]
[tex]\large\textbf{Divide 5 to both sides}[/tex]
[tex]\mathsf{\dfrac{5x}{5} < \dfrac{15}{5}}[/tex]
[tex]\large\textbf{Simplify it}[/tex]
[tex]\mathsf{x < \dfrac{15}{5}}[/tex]
[tex]\mathsf{x < 3}[/tex]
[tex]\large\textbf{You have an \boxed{\rm{\bf o p e n e d}} circle shaded to the left}[/tex]
[tex]\huge\boxed{\mathsf{x < 3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
An article which costs 17.50 is sold at a loss of 20%.what is the selling price.
True or False?
A triangular prism contains two parallel hexagonal faces.
False
True
SUBANE
0:03/0:03
The statement that A triangular prism contains two parallel hexagonal faces is False
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
A triangular prism contains two parallel hexagonal faces.
As a general rule, the parallel faces in a triangular prism are triangles
This is so because a triangular prism is a 3-dimensional object with a triangular base and three rectangular sides.
The two parallel faces of a triangular prism are congruent triangles, not hexagons.
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The triangles are similar what is the value of x
Answer: 16
Step-by-step explanation:
To get from 3 to 12, you multiply by 4
To get from 5 to 20, you multiply by 4
So you just multiply 4 by 4 to get x
Answer:
x = 16
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] = 4 ( multiply both sides by 4 to clear the fraction )
x = 16
Sean’s baby brother sleeps about
13 hours a day. If he takes
2 two-hour naps, how long does
he sleep at night?
Answer:
He sleeps about 9 hours at night.
Step-by-step explanation:
If Sean's baby brother sleeps 13 hours a day, and takes 2 two-hour naps during the day, he sleeps 2 * 2 = 4 hours during the day.
SOOO, he sleeps 13 - 4 = 9 hours at night.
What is the explicit rule for the nth term of the geometric sequence?
3, 18, 108, 648, 3,888, …
an = 3(6n)
an = 3(6n + 1)
an = 6(3n – 1)
an = 3(6n – 1)
The explicit rule for the nth term of the geometric sequence: 3, 18, 108, 648, 3,888, … is aₙ = 3( 6ⁿ⁻¹ )
What is the explicit rule for the nth term of the geometric sequence?The geometric sequence is expressed as aₙ = a₁ × rⁿ⁻¹
Given the set of numbers in the question;
3, 18, 108, 648, 3,888, …
The first term a₁ = 3
Next, we determine the common ratio r.
Divide a term by the previous term gives the common ratio.
Common ratio r = 18/3
Common ratio r = 6
Now, plug in the values of first and common ratio into the above formula to determine the nth term.
aₙ = a₁ × rⁿ⁻¹
aₙ = 3 × 6ⁿ⁻¹
aₙ = 3( 6ⁿ⁻¹ )
Therefore, the nth term of the sequence is aₙ = 3( 6ⁿ⁻¹ ).
Option D) aₙ = 3( 6ⁿ⁻¹ ) is the correct answer.
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In the figure below, there are three right trangles. Complete the following. (Please answer quickly if possible!)
The similarity statement is competed as follows
triangle LMJ is similar to triangle LMK is similar to LKJThe proportion is completed as below
KL / KJ = ML / KLLJ / MJ = KJ / LJWhat are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
KL / KJ and ML / KL
LJ / MJ and KJ / LJ
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A spinner with 10 equally sized slices has 2 yellow slices, 4 red slices, and 4 blue slices. The dial is spun and stops on a slice at
random. What is the probability that the dial stops on a yellow or red slice?
Write your answer as a fraction in simplest form.
Answer: 3/5
The total number of slices is 10, and the number of yellow or red slices is 2 yellow slices + 4 red slices = 6 slices.
So, the probability of the dial stopping on a yellow or red slice is 6 slices / 10 total slices = 3/5.
This is the final answer, and it is already in its simplest form.
If a tile pattern has an equation `y=-2x+10`, what does the number `-2` tell us about the tile pattern?
The value -2 is the rate of change of the linear equation.
What does the number -2 tell us about the pattern?A general linear equation is:
y = a*x + b
Where a is the rate of change and b is the y-intercept.
The rate of change tells us how the variable y changes when the variable x changes.
In this case we have:
y=-2x+10
So the "-2" is the rate of change, it tells us that each time that x increases 1 unit, the value of y decreases by 2 units.
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Which function represents the following graph?
8
6
-8-6-4-2
N
-2-
-4
-6
do
y=√x-3+3
y=√x+3+3
y-√√x-3 +3
2
4
6 8
00
X
The function that is represented by the graph is y = ∛(x + 3) + 3.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The general form of a cube root function is -
y = a∛(x - h) + k and the parent graph is y = ∛x.
So the parent function is found.
The coordinate point for the parent function is -
(-1,-1) , (0,0) and (1,1).
In the graph it can be seen that the coordinate points are -
(-4,2), (-3,3) and (-2,4)
So the graph is first moved 3 units up and then moved three units left.
So, the coordinated become - (x + (-3) , y + 3)
So, the function that represents the graph is -
y = ∛(x + 3) + 3
Therefore, the function is y = ∛(x + 3) + 3.
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