Answer:
[tex]\frac{\pi }{4}[/tex]
Step-by-step explanation:
[tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{2} }{2}[/tex] ) = [tex]\frac{\pi }{4}[/tex]
Calculate the volume of a cylinder with height 14cm and diameter 10cm. Give your answer rounded to 3 SF.
Un significant figured Volume=1099.56
3 sf = 1100.00
a table is 60 cm in diameter. A tablecloth hangs 65cm all around. how much lace trim is needed to edge the cloth
The circumference of a circle is the total length of the boundary of the circle. So that the length of lace trim required is 597.1429 cm.
The diameter of the table is 60 cm, which has 65 cm tablecloth hanging on its sides. The diameter of the cloth required would be the length from one side to the other side. So that the total diameter of the tablecloth is:
= 60 cm + 2*65 cm
= 60 cm + 130 cm
= 190 cm
The diameter of the tablecloth required is 190 cm.
Thus to determine the circumference of the tablecloth, we have;
C = 2[tex]\pi[/tex]r
= [tex]\pi[/tex]D
where D is the diameter of the tablecloth.
C = [tex]\frac{22}{7}[/tex] x 190
= 597.1429
C = 597.1429 cm
Therefore, the length of lace trim required for the edge of the tablecloth is 597.1429 cm.
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The Intelligence Test Scale in a school is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution: a) What number represents the 65th percentile (what number separates the lower 65% of the distribution)? b) What number represents the 90th percentile? c) What is the probability of getting a raw score between 28 and 38? d) What is the probability of getting a raw score between 41 and 44?.
Using the normal distribution, it is found that:
a) The 65th percentile is of 37.31.
b) The 90th percentile is of 42.68.
c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 35, hence [tex]\mu = 35[/tex]The standard deviation is of 6, hence [tex]\sigma = 6[/tex]Question a:
The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.385 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 0.385(6)[/tex]
[tex]X = 37.31[/tex]
The 65th percentile is of 37.31.
Question b:
The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 35}{6}[/tex]
[tex]X - 35 = 1.28(6)[/tex]
[tex]X = 42.68[/tex]
The 90th percentile is of 42.68.
Question c:
The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:
X = 38:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38 - 35}{6}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 35}{6}[/tex]
[tex]Z = -1.17[/tex]
[tex]Z = -1.17[/tex] has a p-value of 0.121.
0.6915 - 0.121 = 0.5705.
There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.
Question d:
The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:
X = 44:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{44 - 35}{6}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 41:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{41 - 35}{6}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
0.9332 - 0.8413 = 0.0919
There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.
A similar problem is given at https://brainly.com/question/24663213
What is the probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, i = 2, 3,. , 12?.
Answer:
0, 1/18, and 1/36
Step-by-step explanation:
For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.
For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.
For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.
The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.
We have,
The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."
Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.
Let's go through the cases:
i = 2 (only possible sum with two dice):
In this case, both dice must show a 1.
The probability of this happening on a fair 6-sided die is
(1/6) * (1/6) = 1/36.
i = 3: The combinations are (1, 2) and (2, 1).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 4:
The combinations are (1, 3), (2, 2), and (3, 1).
The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.
i = 5:
The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).
The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.
i = 6:
The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).
The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.
i = 7:
The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.
i = 8:
The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).
The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.
i = 9:
The combinations are (3, 6), (4, 5), and (5, 4).
The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.
i = 10:
The combinations are (4, 6) and (6, 4).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 11:
The combinations are (5, 6) and (6, 5).
The probability of either happening is 2 * (1/6) * (1/6) = 1/18.
i = 12:
The combination is (6, 6).
The probability of this happening is (1/6) * (1/6) = 1/36.
Now, sum up the probabilities for each case:
(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)
This simplifies to:
69/36 = 23/12
Thus,
The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.
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Which function could be used to represent the sequence 8, 20, 50,
125, 312.5...., given that a, = 8?
(1) a, = 4,- 1 ta
(3) 4, = 4, + 1.5(, -1)
(2) a. = 2.5(
4-1) (4) 4 = (a), -1)
Answer: a = 2.5 (an-1)
Step-by-step explanation: trust me;)
The function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].
What is geometric progression?sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is as a geometric sequence of numbers.
Formula for nth term of geometric progression[tex]a_{n} =ar^{n-1}[/tex]
Where,
[tex]a_{n}[/tex] is the nth term of the sequence or geometric progression
n is the total number of terms
r is the common ratio
and a is the first term
According to the given question
We have
A geometric progression
8, 20, 50, 125, 312.5
Now the common ratio for the above progression is given by
[tex]r = \frac{20}{8} = 2.5[/tex]
And the first term is
a = 8
Therefore, the function which is used to represent the above sequence is given by
[tex]a_{n} = 8(2.5)^{n-1}[/tex]
Hence, the function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].
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2. Order the numbers from least to greatest -0.5, -.025, 0.05,-2,5
Answer:
-2, -0.5, -.025, 0.05, 5
How many solutions does this equation have. 3x + 99 = 3 (x + 33)
Answer:
Infinitely many solutions
Step-by-step explanation:
3x + 99 = 3 (x+33)
distribute 3 to x and 33
3 * x = 3x
3 * 33 = 99
3x + 99 = 3x + 99
If the expressions on both sides of the equal sign are the same, then solving for them would result in 0 = 0 meaning that the equation has infinitely many solutions
show me step by step : 0.18x1.5
Answer:
0.27
Step-by-step explanation:
0.1 8
x 0.50
-----------
000
900
x 1800
-----------
2700 = 0.27
What is the quotient?
126 divided by 7
A. 18
B.16
C. 19
D. 17
Answer:
A
Step-by-step explanation:
I know that 20 times 7 is 140 and if I take away 2 sevens that leaves 126. So 126 \div 7 = 18
Answer:
A. 18
Step-by-step explanation:
I took a photo of my work I didn't know how I could type that here
Tell me if I'm wrong :)
If 2/3 of a number is 10, then what is 0.15 times of that number?
a) 225 b) 825 c) 22.5 d) 2.25
step by step explanation needed
Answer:
d) 2.25Step-by-step explanation:
Let the number is x.
2/3 of a number is 10:
2/3x = 10x = 3*10/2 = 150.15 times of the number is:
15*0.15 = 2.25Correct choice is d
What is the value of y when the value of x is 1?
if the value of x is 1 then the y value is 6
y = x - 15 when x is 2.65
Answer:
y = -12.35
Step-by-step explanation:
Plug in 2.65 for x giving you y = 2.65 - 15
read sddddddddd
dxfcgvhbjnkml,
Answer:
1/5
Step-by-step explanation:
rise = 2 ft
run = 10 ft
slope = rise/run = 2/10 = 1/5
Answer: 1/5
Answer:
1/5
Step-by-step explanation:
The slope is the rise over the run
Y / x
2/10
1/5
Hard cover book lenght in cm
Answer:
f
Step-by-step explanation:
One evening, 2/3 of Mrs. Thorne’s students watched a reality television show. Of Mrs. Lombardo’s students, 4/5 watched the same reality show: Which teacher has more students watch the reality show?
Answer:
They both had the same amount of students watch the reality show.
Step-by-step explanation:
To find the number of students who watched the reality show in each teacher's class, just multiply the fraction by the total number of students per teacher.
For Mrs. Thorne's:
36 * (2/3) = 24 students
For Mrs. Lombardo's:
30 * (4/5) = 24 students
24 = 24 so they had an equal amount of students from each class watch the reality show.
Find the equation of the line that passes through (-3,1) and is parallel to y = 1 − 2 x . Leave your answer in the form y = m x + c
Answer:
y = - 3x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x + y - 1 = 0 ( subtract 3x - 1 from both sides )
y = - 3x + 1 ← in slope- intercept form
with slope m = - 3
Parallel lines have equal slopes, thus
y = - 3x + c ← is the partial equation
To find c substitute (1, 4) into the partial equation
4 = - 3 + c ⇒ c = 4 + 3 = 7
y = - 3x + 7 ← equation of line in form y = mx + c
PLZ HELP DUE SOOOONNNN (solve for z).
Answer:
[tex]{\huge{\green{\mathsf{z\:=\sqrt{\frac{4x}{3y}}}}}[/tex]
Step-by-step explanation:
Given the algebraic equation, [tex]{\huge{\green{\mathsf{x\:=\frac{3yz^2}{4}}}}[/tex], and that we must solve for z :
The first step is to multiply both sides by 4 to eliminate the fraction on the right-hand side of the equation:
[tex]{\huge{\green{\mathsf{x\:=\frac{3yz^2}{4}}}}[/tex]
[tex]{\huge{\green{\mathsf{(4)\:x\:=\frac{3yz^2}{4}(4)}}}[/tex]
4x = 3yz²
Next, divide both sides by 3y:
[tex]{\huge{\green{\mathsf{\frac{4x}{3y}\:=\frac{3yz^2}{3y}}}}[/tex]
[tex]{\huge{\green{\mathsf{\frac{4x}{3y}\:=z^2}}}[/tex]
Lastly, take the square root of both sides to isolate the variable, z :
[tex]{\huge{\green{\mathsf{\sqrt{\frac{4x}{3y}}\:=\sqrt{z^2}}}}[/tex]
[tex]{\huge{\green{\mathsf{z\:=\sqrt{\frac{4x}{3y}}}}}[/tex]
Therefore, the equation for z is: [tex]{\huge{\green{\mathsf{z\:=\sqrt{\frac{4x}{3y}}}}}[/tex]
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
find the area of the parallelogram with the given information:
Answer:
There is a area of triangle and there is two trapezium so 8×17=136
Streams, rivers, ponds, lakes, and wetlands are all kinds of ecosystems.
Answer:
True
Step-by-step explanation:
They can sustain themselves
Answer:
Natural freshwater ecosystems represent the terrestrial phases of the global hydrological cycle and include rivers, streams, lakes, ponds, wetlands, as well as groundwaters.
SOMEONE PLEASE HELP I will give you brainliest it’s due in 11:59 pm TODAY!! Please
If £2000 is placed into a bank account that pays 3% compound interest per year,
how much will be in the account after 2 years?
Help please please help me
Answer:
Hi! I hope this answer helps you.
In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.
any vertical line in the plane can intersect the graph of a function at most once.
HOW TO DO THIS
take your pencil and place it on your paper vertically (up and down direction)
move the pencil across the paper to the right
if the pencil crosses more than two points on the line it is not a function
the first problem would be a function
the second problem would be a function
the third problem would not be a function
hope this helps !!!!
find the value of x and y
from geometry
urgently
One number is twice another number. The sum of their reciprocals is 6. What are the numbers?
Answer:
8 and 2
Step-by-step explanation:
Answer:
1/4 and 1/2
Step-by-step explanation:
One number is twice another number.
x and 2x
The sum of their reciprocals is 6
[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{2x}[/tex] = 6
Use common denominator of 2x
[tex]\frac{2}{2x}[/tex] + [tex]\frac{1}{2x}[/tex] = 6
[tex]\frac{3}{2x}[/tex] = 6
multiply botn sides by 2x
3 = 12x
Divide both sides by 12
1/4 = x
x = 1/4
2x = 1/2
The numbers are
1/4 and 1/2
How do you make a circle graph without any extra space?
Answer:
draw a circle, and draw the degrees
Step-by-step explanation:
What are the coefficient terms and Constants of 10x + 5 + 3x + 1
Answer:
The Coefficients in this expression are 10 and 3, while the constants are 5 and 1.
Step-by-step explanation:
Coefficients = The number that is in front of the variable.
Constant = Any number without a variable.
(Variables are the letters that you may find in an equation or function.)
Hope this helps you :)
Answer:
The coefficient are 10 and 3
The constants are 5 and 1
Step-by-step explanation:
A coefficient is the number in front of any known term.
A constant is a number by itself.
So the coefficient are 10 and 3
The constants are 5 and 1
what is the LCM of 900 and 30000
Answer: 90,000
To find the LCM (Least Common Multiple) of a number, list the multiples of each number.
Multiples of 900
Since they're a lot, we will extend it to the short version.
900, 2700, 9900, 37800, 85500, 90000
Multiples of 30000
30000, 60000, 90000, 120000, 150000
Looking at both multiples, the least common multiple is 90000, as it is listed in both 900 and 30000.
Hence, 90,000 is the answer.
The athletic department raised $14,533 to buy new football uniforms if each uniform costs $258 how many uniforms can they buy
Answer:
56 uniformsStep-by-step explanation:
Available amount = $14533Cost of each uniform = $258Number of uniforms can be bought:
14533/258 = 56 (rounded down)Amount to be spent:
56*258 = 14448Remaining amount:
14533 - 14448 = 851 is the additive identity of any real number True or False
Answer:
False
Step-by-step explanation:
It is False. 1 is the identity element for multiplication, because if you multiply any number by 1, the number doesn’t change. Identity elements are specific to each operation (addition, multiplication, etc.). So while 1 is the identity element for multiplication, it is NOT the identity element for addition.
my bibi’sister need a answer she don't know the answer, she need your help
13. 12008.
14. 59286.
15. 21459.
16. 80478.
17. 130567.
18. 11100.
19. Seventy-two thousand, one hundred eighty.
20. Eighty thousand, seven hundred eighty-six.
Hope This Helps...:)
