Answer:
V = pi x radius x 2 x height OR pi x diameter x height
Hope that helps!
Answer:
the formula for the volume of a cylinder is V=πr²h
Complete the following proof.
Prove: In an equilateral triangle the three medians are equal.
+a
e-(.*)-(
2a
P=
- (0 + 2ª + )-( ₂² )-(.)
?
2
0+
2-(+)-()
|− a)² + (
R-
C(a. b)
PC
=
(2a, 0)
√3 (with side - 2a)
QA-
- √(₁-2)* ·-(- -)
J(J
9a² 8²
a² (√3)²
B
(Height of equalateral A = b)
X
RB
a²3
√3
(²-²)² + (- - -)*
-J* · ·
()*(3
√√3
The median of an equilateral triangle are equal has been proved.
How to proof the triangle?The medians are given as AD, BE, and CF.
Let AB = AC = BC = x unit.
In triangles, BFC and CEB, we've
BF = CE.
ABC = ACB since they're both 60°
BC = BC
By SAS congruence,
BFC = CEB = BE = CF.
Similarly, we've AB = BE
Therefore, AD = BE = CF
median of an equilateral triangle are equal has been proved.
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Suppose that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease. Suppose also that the incidence of the disease is 1%. If a person tests positive for the disease, what is the chance that they have the disease
If the test gives positive results for 95% of those having disease and correctly gives negative results for 90% of those who don't have disease and the incidence of the disease is 1% then the chance of having disease is 0.0105.
Given that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease.
We have to calculate the chance of having disease.
Probability that test is correct in determining the disease when person is suffering from it is 0.95.
Probability that test is not correct in determining the disease when person is suffering from it is 1-0.95=0.05.
Probability that test is correct in determining that the person is not suffering from disease when person is not suffering from it is 0.90.
Probability that test is not correct in determining that the person is not suffering from disease when person is not suffering from it is 1-0.9=0.10.
The chance of having disease is equal to incidence of disease multiplied by probabilities that the test has corectly determined disease when personis suffering from it and when test is not able to determine the disease when person is suffering from it.
Chance=0.01*0.95+0.01*0.10
=0.0095+0.001
=0.0105.
Hence the chance of having disease is 0.0105.
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A desk is on sale for $595, which is 32% less than the regular price. What is the regular price?
Answer:
875
Step-by-step explanation:
1-0.32=0.68 so its 0.68 of its original price.
x*0.68=595 x is the original price
x=595/0.68
x=875
Find the hourly rate of pay for each of the following jobs: a) Tamara owns a salon and earns R1050 for 6 hours and 15 minutes of work.
Answer:
₹168 per hour
Step-by-step explanation:
The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.
HoursWe know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...
(15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h
Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.
Hourly rateThe pay per hour is found by dividing pay by hours.
₹1050/(6.25 h) = ₹168/h
Tamara's hourly rate of pay is ₹168 per hour.
Manju and Arif are playing a game in which one of them thinks of a number from the grid shown
below and the other has to guess it using some clues that are given. Manju thinks of a number
and gives the following clues:
It is a multiple of 3.
It is even.
It is in the third row.
What is Manju's number?
The number from the grid that fulfills all the given clues is; 12
How to find the multiple of a number?
The grid is shown in the attached image.
Now, we are told that Manju and Arif are thinking of a number on the grid and the clues are;
It is a multiple of 3.
It is even.
It is in the third row.
Now, looking at the third row, we see the numbers as;
11, 12, 13, 14, 15
Now, the only number that fulfills all the given clues is 12.
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A score that is three standard deviations above the mean would have a z score of
a. -3
b. 3
c. 0
d. 1
The value of z-score for a score that is three standard deviations above the mean is 3.
In this question,
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
Let x be the score
let μ be the mean and
let σ be the standard deviations
Now, x = μ + 3σ
The formula of z-score is
[tex]z_{score} = \frac{x-\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{ 3\sigma }{\sigma}[/tex]
⇒ [tex]z_{score} = 3[/tex]
Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.
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This figure represents a design found in a glass panel. ABCD is a rectangle with
midpoints X, Y, Z, and W. Emily states that the quadrilateral formed by the segments
that join the midpoints of the sides is a rhombus. Do you agree with her? Explain why
or why not.
Answer: Yes
Step-by-step explanation:
Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.
Fyodor and his three sons, Ivan, Dmitri and Alyosha, are standing exactly on the corners of a rectangular room. Fyodor is $3$ meters from Dmitri and $5$ meters from Ivan. What is the minimum possible distance that Fyodor could be from Alyosha, in meters
The minimum possible distance that Fyodor could be from Alyosha is 4 meters.
Given Information and Deduction
It is given that Fyodor is 3 meters in distance away from Dmitri and 5 meters from Ivan.
Now, since we know that the longest side of a right angle triangle formed by the dividing the rectangular room into two parts using a diagonal is the hypotenuse. Thus, if we want to find the minimum possible distance between Fyodor and Alyosha, we will have to assume that Ivan is standing diagonally opposite to Fyodor, as shown in the figure below.
Calculating the Minimum Distance
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Here, the hypotenuse is the distance between Fyodor and Ivan.
Perpendicular and the base are the distances between Fyodor and Dmitri, and Fyodor and Alyosha respectively.
⇒ base = √(hypotenuse)² -(perpendicular)²
⇒ base = √(5)²-(3)²
⇒ base = √(25-9)
⇒ base = √16
⇒ base = 4 meters
Therefore, the minimum possible distance between Fyodor and Alyosha is 4 meters.
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7. The table below shows the soft drinks preferences of people in two age groups.
Sprite
Lemonade
20
30
50
Under 21 years of age
Between 21 and 40
Totals
25
35
60
If one of the 110 subjects is randomly selected, find the probability that:
a) A person prefers to drink sprite
b) A person is between 21 and 40 years old.
c) A person drinks lemonade given they are between 21 and 40.
d) A person drinks Sprite given they are under 21 years of age.
Totals
45
65
110
The calculated probabilities are
0.54550.59090.46150.5556a. The probability of the people that prefer sprite isProbability = 60/110
= 0.5455
B. The probability that a person is between 21 and 40probability = 65/110
= 0.5909
C. Probability of drinking lemonade given that age is between 21 and 40Probability = 30/65
= 0.4615
d. Probability of sprite when under 2125/45
= 0.5556
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Suppose you are asked to compare two functions, A and B. Function A written in slope-intercepts form, y= -3x + 4. Function B is graphed on the coordinate plane and has a greater rate of change but lower y-intercept than function A. Describe what is true about the graph of function B.
Answer:
Use the slope and one of the points to solve for the y-intercept (b). One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Step-by-step explanation:
Pleassee help!!!
will give brainliest!!
The amplitude is 6 and vertical translation is 2. Therefore Option C is correct
For the transformation of y=f(x) to f(x)+k, for k>0, f(x) is moved k upwards and for transformation of f(x) to f(ax) it depends upon the value of a If |a|>1 then f(ax) is f(x) squashed horizontally by a factor of a and If 0<|a|<1 then f(x) is stretched horizontally by a factor of a.
So by the graph it is clearly visible that amplitude of the graph is 6 as the distance from the centre line (or the still position) to the top of a crest or to the bottom of a trough is 6 and the vertical translation is 2 as distance moved by the graph upwards is 2.
Thus the amplitude is 6 and vertical translation is 2.
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The point M(-6, -4) is translated 2 units right. What are the coordinates of the resulting point, M'?
Answer:
(-4,-4)
Step-by-step explanation:
If the point is moved 2 units to the rights then we add 2 to the x value: -6+2 = -4
(-4,-4)
For what value of mc009-1 is the function one-to-one?
(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)
2
5
11
13
Using the concept of an one-to-one function, it will be one-to-one for c = 13.
What is an one-to-one function?A function is said to be one-to-one if each output is mapped to only one input.
In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.
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The three sides of a right triangle have integral lengths which form an arithmetic sequence. How many numbers between 1 and 2020 inclusive can be the side of the hypotenuse
There are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence. This can be obtained by forming the arithmetic sequence, equating by Pythagoras theorem and finding numbers divisible by the integral.
Find the value of hypotenuse?Let the arithmetic sequence be (a - d), a, (a+d)
Using Pythagoras theorem,
(a - d)² + a² = (a+d)²
a² -2ad + d² + a² = a² + 2ad + d²
2a² - 2ad + d² = a² + 2ad + d²
2a² - a² + d² - d² = 2ad + 2ad
a² = 4ad
a = 4d
Thus hypotenuse will be (a + d) = 4d + d = 5d
How many numbers between 1 and 2020 inclusive can be the side of the hypotenuse?Since the value of hypotenuse is 5d, the total numbers divisible by 5 between 1 and 2020 will be the number of possible sides of the hypotenuse.
There are 2020 numbers between 1 and 2020 inclusive
The numbers divisible by 5 = 2020/5 = 404
Hence there are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence.
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Find the sum.
10+12+14+...+78
Answer:
1540
Step-by-step explanation:
This is an arithmetic progression.
a = first term = 10
Common difference = d = second term - first term
= 12 - 10
d = 2
Last term = l = 78
First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d
78 = 10 + (n -1) * 2
78 -10 = (n -1)*2
68 = (n -1) *2
68 ÷2 = n -1
34 = n - 1
34 + 1 = n
n = 35
There are 35 terms.
[tex]\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}}[/tex][tex]\sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}[/tex]
[tex]\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540[/tex]
Step-by-step explanation:
This is an arithmetic progression.
a = first term = 10
Common difference = d = second term - first term
= 12 - 10
d = 2
Last term = l = 78
First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d
78 = 10 + (n -1) * 2
78 -10 = (n -1)*2
68 = (n -1) *2
68 ÷2 = n -1
34 = n - 1
34 + 1 = n
n = 35
There are 35 terms.
\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}} \sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}
Sum =
2
n
(a+l)
\begin{gathered}\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540\end{gathered}
=
2
35
(10+78)
=
2
35
∗88
=35∗44
=1540
What is the solution for the compound 5/2+x>1/3 or x+2 < -29/6
Answer:
x < -41/6 or x > -13/6.
Step-by-step explanation:
5/2+x>1/3
x > 1/3 - 5/2
x > 2/6 - 15/6
x > -13/6
x+2 < -29/6
x < -29/6 - 2
x < -41/6
The answer is x < -41/6 or x > -13/6.
Answer:
x > -13/6 or x < -41/6
Step-by-step explanation:
5/2+x>1/3 or x+2 < -29/6
x > 1/3 - 5/2 or x < -29/6 - 2
x > 2/6 - 15/6 or x < -29/6 - 12/6
x > -13/6 or x < -41/6
match the graph with jts inequality
help helphelphelp help
Answer:
y<x
Step-by-step explanation:
Alright so you do know that the y=x has got the equal amount for both y and x right and it also is a bisector for the first and third area, that's that
the graph is show the same thing but with some blue area and the area show x values which less than y values sooo you answer is y<x
Tony is given _9 10 hour to mow a lawn. he only uses _ 2 3 of the given time to mow the lawn. how much time is left
[tex]\frac{7}{30}[/tex] units of time is left.
What is a fraction?A fraction is a component of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of pieces of a specific size, such as one-half, eight-fifths, and three-quarters.To find how much time is left:
Given - Tony is given [tex]\frac{9}{10}[/tex] hour to mow a lawn. he only uses [tex]\frac{2}{3}[/tex] the given time to mow the lawn.
Simplify subtract [tex]\frac{9}{10}[/tex] by [tex]\frac{2}{3}[/tex] as follows:
[tex]\frac{9}{10}-\frac{2}{3} =\frac{27-20}{30} =\frac{7}{30}[/tex]
Therefore, [tex]\frac{7}{30}[/tex] units of time is left.
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what are the differences between cos(x) and cos^-1(x)
cos^-1(x) represents the inverse of cos(x).
The number of jobs for nurses is expected to increase by 711,900 between 2010 and 2020. during the same decade, the number of jobs for physicians is expected to increase by 168,300. find the ratio of the increase in jobs for physicians to the increase in jobs for nurses.
The Ratio would be 43:100.
Lets simplify the problem,
Expected increase of nurses = 711900
Expected increase of physicians = 168300
Ratio = Expected increase of nurses / Expected increase of physicians
Ratio = 711900 / 168300
= 43/100
Ratio = 43:100
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What are the plotting points?
Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V
-3|0+2|+4=-2
-3|1 +2|+4= -5
-3|2+2|+4= -8
-3|-1+2|+4=1
+3|-2+2|+4=1
Step-by-step explanation:
Someone help me with a step by step explanation to simplifying
100x(5 - 3p)
ty
Answer:
500x - 300xp.
Step-by-step explanation:
100x(5 - 3p)
First distribute the 100x over the parentheses:
= 100x*5 - 100x * 3p
Now simplify:
= 500x - 300xp.
The cost of 11 identical mobile phones is 91,300rs/-. what is the cost of 1 mobile phone?
The answer is 8300.
Divide 91300 by 11 you will get the answer.
Problem-solving is the act of defining trouble; figuring out the cause of the problem; figuring out, prioritizing, and choosing alternatives for an answer; and enforcing a solution.
Problem-fixing starts with identifying the difficulty. For instance, a teacher might want to discern the way to improve student performance on a writing talent test. To do that, the trainer will assess the writing checks looking for areas of development.
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Four different sets of objects contain 4,5,6, and 8 objects respectively. how many unique combinations can be formed by picking one object from each set?
A. 23
B. 141
C.960
D. 529
The number of unique combinations that can be formed by picking one object from each set is =960. That is option C.
Calculation of unique combinations of a number setNumber combination is a mathematical technique that shows the number of possible arrangements in a collection of items.
The first set of objects = 4. There are a total of 4 possibilities.
The second set of objects = 5. There are a total of 5 possibilities
Therefore from first and second set, the total number of possibilities = 4×5 = 20
For the whole set, the total possibilities;
= 4×5×6×8
= 960
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210÷[5+16÷2{6−18÷(7+2)}]−15
Answer:
[tex]-\frac{345}{37}[/tex]
Step-by-step explanation:
Just follow the order of operations
210÷[5+16÷2{6−18÷(7+2)}]−15
= 210÷[5+16÷2{6−18÷9}]−15 (calculate 7+2)
= 210÷[5+16÷2{6−2}]−15 (calculate 18÷9)
= 210÷[5+16÷2{4}]−15 (calculate 6-4)
= 210÷[5+16÷2×4]−15
= 210÷[5+8×4]−15 (calculate 16÷2)
= 210÷[5+32]−15 (calculate 8×4)
= 210÷[37]−15 (calculate 5+32)
= 210÷37−15
= 210÷37−(15×37)÷37 (put on the same denominator)
= 210÷37−555÷37 (calculate 15×37)
= (210−555)÷37
=-345÷37 (calculate 210-555)
Julian wants to ride his bicycle 20.6 miles this week. He has already ridden 8 miles. If he rides for 3 more days, write and solve an equation which can be used to determine xx, the average number of miles he would have to ride each day to meet his goal.
Answer:
Step-by-step explanation:
Our equation will be 3x+8=20.6
3x=12.6
x=4.2
Which geometric series results in a sum of -69, 905?
O A.
SOB.
O C.
O D.
10
k=0
(-4)*
- }(4) *
Σ-1(5)
k=0
Σ 1 (-5)*
k=0
The geometric series which result in a sum of -69,905 is: D. [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
The standard form of a geometric series.Mathematically, the standard form of a geometric series can be represented by the following expression:
[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]
Where:
a₁ is the first term of a geometric series.r is the common ratio.Also, the sum of a geometric series is given by:
[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]
For option A, we have:
r = -5, n = 8, a₁ = 1/4 = 0.25
[tex]S=\frac{0.25(1-(-5)^8)}{1-(-5)}[/tex]
S = -24,414.
For option B, we have:
r = 5, n = 12, a₁ = -1/4 = -0.25
[tex]S=\frac{-0.25(1- 5)^{12})}{1-5}[/tex]
S = -15,258789.
For option C, we have:
r = -4, n = 11, a₁ = 1/5 = 0.2
[tex]S=\frac{0.2(1-(-4)^{11})}{1-(-4)}[/tex]
S = -279,620.
For option D, we have:
r = 4, n = 10, a₁ = -1/5 = -0.2
[tex]S=\frac{-0.2(1-4^{10})}{1-4}[/tex]
S = -69,905.
In conclusion, the geometric series which result in a sum of -69,905 is [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
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WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
last choice
Step-by-step explanation:
The domain is the set of x values: from -3 to 3.
The range is the set of y values: from 1 to 10.
Answer: last choice
PLEASE HELP IM SUPER STUCK
Answer:
27 cm³
Step-by-step explanation:
To find the volume, multiply the length, the width, and the depth together.
3*3*3=27
The volume of the cube is 27 cm³
Hope this helps!
In the exponential function f(x) = 3^-x 2, what is the end behavior of f(x) as x goes to [infinity]?
For an exponential function [tex]f(x) = 3^{-x}2[/tex] as x goes to infinity, f(x) goes to zero.
We have been given an exponential function [tex]f(x) = 3^{-x}2[/tex]
We need to check the end behavior of f(x) as x goes to infinity.
Consider,
[tex]\lim_{x \to \infty} f(x)\\\\= \lim_{x \to \infty} 3^{-x}2\\\\=2\times \lim_{x \to \infty} 3^{-x}\\\\=2\times 3^{-\infty}\\\\=2\times 0\\\\=0[/tex]
This means, x [tex]\rightarrow[/tex] infinity, f(x) goes to 0
As x goes to infinity, f(x) goes to zero.
Therefore, for an exponential function [tex]f(x) = 3^{-x}2[/tex] as x goes to infinity, f(x) goes to zero.
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