Answer:
x=135
Step-by-step explanation:
We know that sin(270) = -1/2
So 2x = 270
x = 135
Please answer this correctly without making mistakes
Answer:
589
Step-by-step explanation:
l x w
19x11
5x31
5x45
589
Answer:
589 is the answer
If 20 drops fall in 76 seconds, how long will 8 drops take?
Answer:
x =30.4 seconds
Step-by-step explanation:
We can use ratios to solve
20 drops 8 drops
--------------- = ----------------
76 seconds x seconds
Using cross products
20x = 8*76
20x =608
Divide each side by 20
20x/20 = 608/20
x =30.4 seconds
Answer:
30.4 secs = 30secs
Step-by-step explanation:
20 drops fall in 76s
Hence 1 drop is 76/20
Therefore 8 drops would be ;
76/20 × 8 = 30.4 secs
Thirty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly three will end up being replaced under warranty
Answer:
26.68% probability that exactly three will end up being replaced under warranty
Step-by-step explanation:
For each telephone under warranty, there are only two possible outcomes. Either they need to be replaced, or they do not need to be replaced. Each telephone is independent of other telephones. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
30% must be replaced with new units
This means that [tex]p = 0.3[/tex]
If a company purchases ten of these telephones, what is the probability that exactly three will end up being replaced under warranty
This is [tex]P(X = 3)[/tex] when [tex]n = 10[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{10,3}.(0.3)^{3}.(0.7)^{7} = 0.2668[/tex]
26.68% probability that exactly three will end up being replaced under warranty
What is the equation of the line that passes through (4, 2) ) and is parallel to 3x - 2y = - 6 ?
Answer:
[tex]y=\frac{3}{2} x-4[/tex]
Step-by-step explanation:
The graph I provided shows it passes thru (4,2) and that it is parallel
Answer:
y = 3/2x -4
Step-by-step explanation:
3x - 2y = - 6
First find the slope by putting it in slope intercept form
Subtract 3x from each side
-2y = -3x-6
Divide by -2
y = -3x/-2 -6/-2
y = 3/2x +3
The slope is 3/2
Parallel lines have the same slope
We have the slope 3/2 and a point (4,2)
y = mx+b where m is the slope and b is the y intercept
y =3/2x+b
Substitute the point into the equation
2 = 3/2(4) +b
2 = 6 +b
Subtract 6
2-6 = 6-6+b
-4 =b
y = 3/2x -4
Car engine needs ______________ to avoid friction.
a) water
b) smooth surface
c) oil
d) air
Answer:
Oil
Step-by-step explanation:
Car engine needs oil to avoid friction.
Answer:
[tex]oil \\ [/tex]
Answer C is correct
Step-by-step explanation:
car engine needs oil to avoid the friction .
hope this helps
brainliest appreciated
good luck! have a nice day!
A thermometer shows a temperature of Negative 20 and three-fourths degrees. A chemist recorded this temperature in her notebook using a decimal. Which number did the chemist write in the notebook?
Answer:
20.75
Step-by-step explanation:
Answer:
C. -20.75
Step-by-step explanation:
In 2014, 2.756 billion dollars of e-cigarettes were sold worldwide. Fill in the table with the 2014 sales amount written in millions of dollars.
Answer:
$2756 million
Step-by-step explanation:
2.756×10⁹ = 2756×10⁶
Sales in 2014 were $2756 million.
_____
Comment on the question
In the US, a billion is 1000 million. In some other parts of the world, a billion is a million million. This sort of question can be ambiguous.
Write the equation of a line that is perpendicular to y= -x - 6 and that passes through the point (-9, -4).
Answer:
y = x + 5
Step-by-step explanation:
Perpendicular slope is opposite inverse so the perpendicular slope to -1x would be 1x
Then find b in y=mx+b
Plug in all the number
y=-9
x=-4
m=1
So, -4=1(-9)+b
1×-9=-9
+9 to both sides
5=b
Therefore,
y=x+5
The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width The perimeter of the rectangle playing field is 432 yards the length of the field is 4 yards less than triple the width. What is the length and width in yards?
Answer:
160 yards
Step-by-step explanation:
P=2l+2w
P=2(3w-8)+2(w)
432=2(3w-8)+2(w)
432=6w-16+2w
432=8w-16
432+16=8w
448=8w
w=448/8
w=56yards
l=3(56)-8
l=168-8=160yards
Captain Jessica has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Michael and his merciless band of thieves.
The Captain has probability \dfrac{1}{2}
2
1
start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability \dfrac{1}{6}
6
1
start fraction, 1, divided by, 6, end fraction.
If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?
Answer:
[tex]\dfrac{1}{12}[/tex]
Step-by-step explanation:
Probability of the captain hitting the pirate ship [tex]=\dfrac{1}{2}[/tex]
Probability of the pirate hitting the captain's ship [tex]=\dfrac{1}{6}[/tex]
If both fire cannons at the same time, the probability that both the pirate and the captain hit each other's ship
=P(Captain Hits AND Pirate Hits)
=P(Captain Hits) X P(Pirate Hits)
[tex]=\dfrac{1}{2} X \dfrac{1}{6}\\\\=\dfrac{1}{12}[/tex]
A study of the effect of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained:
Smokers: 69.3 56.0 22.1 47.6 53.2 48.1 52.7 34.4 60.2 43.8 23.2 13.8
Non-Smokers: 28.6 25.1 26.4 34.9 28.8 28.4 38.5 30.2 30.6 31.8 41.6 21.1 36.0 37.9 13.9
Which group having greater value of relative dispersion and why?
Answer:
The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.
CV smokers: 0.387
CV non-smokers: 0.234
Step-by-step explanation:
We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).
Then, first we calculate the mean and standard deviation for the smokers data:
Mean: 43.7
Standard deviation: 286.5
[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]
The mean and standard deviation for the non-smokers is:
Mean: 30.3
Standard deviation: 50.9
[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]
Now, we can calculate the coefficient of variation:
CV smokers:
[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]
CV non-smokers:
[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]
a cog company produces 20 cogs a day, 4 of which are defective. Find the probability of selecting 4 cogs from the 20 produced where all are defective?
Answer:
1/4845
Step-by-step explanation:
The probability of selecting a defective cog first is
1/5
The second cog is
3/19
The third cog is
1/9
And the fourth cog is
1/17
Multiplying these together we get
1/5 * 3/19* 1/9 * 1/17 = 1/4845
The probability of selecting 4 cogs from the 20 produced where all are defective is approximately 0.000206.
What is probability?Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.
The probability of selecting 4 defective cogs from the 20 produced can be calculated as follows:
P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20)
The number of ways to select 4 defective cogs can be found by selecting 4 defective cogs out of the 4 defective cogs produced, and 0 non-defective cogs out of the remaining 20-4=16 non-defective cogs. This can be expressed mathematically as:
Number of ways to select 4 defective cogs = (4 choose 4) * (16 choose 0) = 1
The total number of ways to select 4 cogs from 20 can be found by selecting 4 cogs out of the 20 produced. This can be expressed mathematically as:
Total number of ways to select 4 cogs from 20 = (20 choose 4) = 4845
Therefore, the probability of selecting 4 defective cogs from the 20 produced is:
P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20) = 1/4845
Thus, the probability of selecting defective cogs is approximately 0.000206.
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The people at the party ate 16 chocolate chip cookies and 26 sugar cookies. What percent of the cookies were sugar cookies?
Answer:
61%
Step-by-step explanation:
16/26 x 100 = 61.538461
You have to round it up if the question tells you to round it up.
hope it helps! :)
Answer:
62%
Step-by-step explanation:
42 x 62% = 26.04
I am sorry if you get this wrong. I really hope this helps.
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained. 0.10 0.13 0.16 0.15 0.14 0.08 0.15 (a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars. (b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a),
The question is incomplete. Here is the complete qeustion.
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.10 0.13 0.16 0.15 0.14 0.008 0.15
(a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars.
(b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a), can we safely conclude that this requirement is being met?
Answer: (a) 0.089 ≤ μ ≤ 0.171
(b) No
Step-by-step explanation:
(a) To determine the confidence interval, first calculate the mean (X) and standard deviation (s) of the sample
X = [tex]\frac{0.1+0.13+0.16+0.15+0.14+0.08+0.15}{7}[/tex]
X = 0.13
s = [tex]\sqrt{\frac{(0.1-0.13)^{2} + (0.13 - 0.13)^{2} + ... + (0.15 - 0.13)^{2}}{7-1} }[/tex]
s = 0.029
The degrees of freedom is
N - 1 = 7 - 1 = 6
And since the confidence is of 99%:
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
The t-test statistics for [tex]t_{6,0.005}[/tex] is 3.707
(Value found in the t-distribution table)
Now, calculate Error:
E = [tex]t_{6,0.005}[/tex] . [tex]\frac{s}{\sqrt{N} }[/tex]
E = 3.707. [tex]\frac{0.029}{\sqrt{7} }[/tex]
E = 0.041
The interval will be:
0.13 - 0.041 ≤ μ ≤ 0.13+0.041
0.089 ≤ μ ≤ 0.171
(b) No, because according to the interval, the nitrode-oxide emissions range from 0.089 to 0.171, which is greater than required by EPA.
Find the area of the following square.
Write your answer in simplest form.
Be sure to include the correct unit in your answer.
4 1/2m
Answer:
[tex]20.25 \: m^2[/tex]
Step-by-step explanation:
Use the formula for the area of a square.
[tex]A=s^2[/tex]
Where [tex]s=4.5[/tex]
[tex]s^2\\(4.5)^2\\20.25[/tex]
The area of the square is 20.25 square meters as per the concept of the square.
To find the area of a square, we need to square the length of one of its sides. In this case, the side length is given as 4 1/2 meters.
First, we need to convert the mixed number 4 1/2 into an improper fraction. We can rewrite it as 9/2.
Next, we square the side length:
[tex]\frac{9}{2}^2 = \frac{81}{4}[/tex].
To simplify the fraction, we can divide the numerator by the denominator:
81 ÷ 4 = 20 remainders 1.
Therefore, the area of the square is 20 1/4 square meters.
However, we can simplify the mixed number further. Since 4 can be divided by 4 and 1 can be divided by 4, we have:
20 1/4
= 20 + 1/4
= 20 + 1/4
= 20 + 0.25
= 20.25.
Therefore, the area of the square is 20.25 square meters.
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If f(x) = 4–1 and g(x) = 8x, which expression is equivalent to (g-1)(3)?
O 8-3-(4 + 3)
08-3-(4-32
813)-4432
O 6(3) 4-32
Answer:
Option (3)
Step-by-step explanation:
Given functions are f(x) = 4 - x² and g(x) = 6x
We gave to find the expression for (g - f)(3).
(g - f)(x) = g(x) - f(x)
= 6x - (4 - x²)
= 6x - 4 + x²
By substituting x = 3 in this expression,
(g - f)(x) = 6(3) - 4 + (3)²
Therefore, option (3) will be the answer.
Use the quadratic formula to find both solutions to the quadratic equation given below. 2x^2+3x-5=0
Answer:
[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where a = 2 , b= 3, c= -5, replacing we have this:
[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]
And simplifying we got:
[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]
And the two solutions are:
[tex] x_1 = \frac{-3+7}{4}= 1[/tex]
[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]
And the correct options are:
B and C
Step-by-step explanation:
We have the following equation given:
[tex] 2x^2 +3x -5=0[/tex]
And if we use the quadratic formula given by:
[tex] x =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where a = 2 , b= 3, c= -5, replacing we have this:
[tex]x =\frac{-3 \pm \sqrt{(-3)^2 -4(2)(-5)}}{2*2}[/tex]
And simplifying we got:
[tex] x = \frac{-3 \pm \sqrt{49}}{4}[/tex]
And the two solutions are:
[tex] x_1 = \frac{-3+7}{4}= 1[/tex]
[tex] x_2 = \frac{-3-7}{4}= -\frac{5}{2}[/tex]
And the correct options are:
B and C
Answer:
B and C
Step-by-step explanation:
Let x = 8.99999 . (a) Is x < 9 or is x = 9? x < 9 It is neither; x > 9 x = 9 x < 9 and x = 9 It cannot be determined. (b) Sum a geometric series to find the value of x. x = (c) How many decimal representations does the number 9 have? decimal representations (d) Which numbers have more than one decimal representation? the integers the rational numbers except for 0 all rational numbers that have a terminating decimal representation except for 0 all integers except for 0 all real numbers
Answer: idk
Step-by-step explanation:
idk
c. Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 4 feet. What is the area of the shade?
Answer:
A=12 feet²
Step-by-step explanation:
1/2*base*height=area
(1/2)*4*6=12
What is the distance from point N to line LM in the figure below?
Answer:
The correct answer would be F. 7.8
Step-by-step explanation:
the line is more or less a reflection of segment ON
so they are more or less the same.
I hope this helped you!
There are 1760 yards in one mile about how many miles will a runner have to run
Answer:
3
I used to be an olimpic runner and I ran the 400 all the time and I did cross country
Which cosine function has maximum of 0.5, a minimum of -0.5, and a period of 2(pi)/3
Answer:
The answer is "[tex]\bold{y=0.5 \cos 3 \theta}[/tex]"
Step-by-step explanation:
The choices were missing the question so the answer to this question can be defined as follows:
The answer is [tex]y= 0.5 \cos 3\theta[/tex] because:
[tex]\Rightarrow -1 \leq \cos 3 \theta \leq 1\\\\\Rightarrow -0.5 \leq \cos 3 \theta \leq 0.5\\[/tex]
So, the maximum value is = 0.5 and the minimum value is = -0.5 of [tex]\frac{2\pi}{3}[/tex].
Answer:
D. y= 0.5 cos 3 theta
Step-by-step explanation:
Factorize (3x-2y)2 + 3(3x-2y)-10
Answer:
[tex]5(3x-2y-2)[/tex] i think. i am sorry if i am wrong
Step-by-step explanation:
If P(-2, 1) is rotated 90°, its image is
A state end-of-grade exam in American History is a multiple-choice test that has 50 questions with 4 answer choices for each question. A student must get at least 25 correct to pass the test, and the questions are very difficult. Question 1. If a student guesses on every question, what is the probability the student will pass
Answer:
0.004% probability the student will pass
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 50, p = \frac{1}{4} = 0.25[/tex]
So
[tex]\mu = E(X) = np = 50*0.25 = 12.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.25*0.75} = 3.06[/tex]
If a student guesses on every question, what is the probability the student will pass
Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 12.5}{3.06}[/tex]
[tex]Z = 3.92[/tex]
[tex]Z = 3.92[/tex] has a pvalue of 0.99996
1 - 0.99996 = 0.00004
0.004% probability the student will pass
John averages 58 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose John's words per minute on a minute on a typing test. Then X~N(58,11)
Answer:
The z score when x =72 is:
[tex] z = \frac{72-58}{11}= 1.273[/tex]
The mean is 58
This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.
Step-by-step explanation:
Assuming the following info for the question: Suppose John's words per minute on a typing test are normally distributed. Let X -the number of words per minute on a typing test. Then X N(58, 11) If necessary, round to three decimal places.
Provide your answer below rds per minute in a typing test on Sunday. The z score when x =72 is
For this case we know that the variable of interest is modelled with the normal distribution:
[tex]X \sim N (\mu= 58, \sigma=11)[/tex]
And the z score is given by:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z = \frac{72-58}{11}= 1.273[/tex]
The mean is 58
This z-score tells you that x= 72 is 1.273 standard deviations to the right of the mearn.
George is given two circles 0 and circles X as shown if he wants to prove that two circles are similar what would be the correct second step in his proof
Answer: Option A.
Step-by-step explanation:
Here we have two equations for the circumference, one for each circle:
C = 2*pi*r
C' = 2*pi*r'
now, if we take the quotient of those two equations, the left side must still be equal to the left side, this means that:
C/C' = 2*pi*r/(2*pi*r') = r/r'
So we have the relation:
C/C' = r/r'
And this is obtained for the division property of equality.
IF A = B, then as both numbers are equal, if we divide both sides by the same thing, then the equality must remain true.
Then the correct option is A.
TIMED PLEASE HELP When f = 2 and g = 8, n = 4. If n varies jointly with f and g, what is the constant of variation?
1/4
1/2
4
64
The Answer is 1/4
Step-by-step explanation:
The required constant of variation for given data is k = 1/4
The correct option is (a)
What is constant of variation?In a direct variation, the product of two variables; in an inverse variation, the ratio of two variables, is called constant of variation
Formula:
k = [tex]\frac{n}{fg}[/tex]
How calculate constant of variation?Here we have given that n = 4, f = 2 and g = 8
Substitute the given values into above formula
k = [tex]\frac{4}{2(8)} =\frac{1}{4}[/tex]
The required constant of variation is 1/4
Therefore the correct option is (a)
This is the conclusion to the answer.
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I need HELP PLEASE HELP ME
Answer:
Graph 2
Step-by-step explanation:
You can see that all the shaded numbers are above negative 25 in that graph. Hope this helped!
The population of bats in a large cave is 7000 and is growing exponentially at 14% per year. Write a function to represent the population of bats after
tt
t years, where the monthly rate of change can be found from a constant in the function.
Answer:
y=7000+14^t
Step-by-step explanation:
This equation shows that the original population of bats was 7000 and grows exponentially at a rate of 14% per year.
I put the graph below so you can see it.
In this exercise we have to identify how to write an exponential function from the data informed in the text, in this way we find that:
[tex]y=7000+14^t[/tex]
From the information given in the statement we find that:
The original population of bats was 7000Rate of 14% per year.Then writing this function as:
[tex]y=7000+14^t[/tex]
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