Answer:
2.5 , 3.5
Step-by-step explanation:
Midpoint = (x1+x2)/2 , (y1+y2)/2
(3+2)/2 , (5+2)/2
5/2 , 7/2
2.5 , 3.5
In Vancouver, British Columbia, the probability of rain during a winter day is 0.42, for a spring day is 0.23, for a summer day is 0.16, and for a fall day is 0.51. Each of these seasons lasts one quarter of the year. If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
Answer:
31.82% probability that this day would be a winter day
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening
In this question:
Event A: Rain
Event B: Winter day
Probability of rain:
0.42 of 0.25(winter), 0.23 of 0.25(spring), 0.16 of 0.25(summer) or 0.51 of 0.25(fall).
So
[tex]P(A) = 0.42*0.25 + 0.23*0.25 + 0.16*0.25 + 0.51*0.25 = 0.33[/tex]
Intersection:
Rain on a winter day, which is 0.42 of 0.25. So
[tex]P(A \cap B) = 0.42*0.25 = 0.105[/tex]
If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
[tex]P(B|A) = \frac{0.105}{0.33} = 0.3182[/tex]
31.82% probability that this day would be a winter day
The standard error of the estimate measures the scatter or dispersion of the observed values around a __________________________________________________________
Answer:
True mean/population mean
Step-by-step explanation:
The standard error in this case gives an estimate on how far the values observed during the course of the experiment ate likely to be from the true mean/population mean.
Assume that cans are filled so that the actual amounts have a mean of 17.00 ounces. A random sample of 36 cans has a mean amount of 17.79 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 17.00 ounces and a standard deviation of 0.08 ounce.
Required:
How many standard deviations is the sample mean from the mean of the distribution of sample?
Answer:
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{s}[/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.
In this question:
[tex]X = 17.79, \mu = 17, s = 0.08[/tex]
How many standard deviations is the sample mean from the mean of the distribution of sample?
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.79 - 17}{0.08}[/tex]
[tex]Z = 9.875[/tex]
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the same. The domain stays the same, but the range changes. The range stays the same, but the domain changes.
Answer:
Domain stays the same while the range changes
Step-by-step explanation:
While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.
=> x- coordinate = Domain
=> y-coordinate = Range
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
What is the domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.
When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.
The Domain represent as x-coordinate and the range as y-coordinate
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
Hence, option C is correct.
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Help me please I dont understand
Answer:
42°
Step-by-step explanation:
This is right triangle and sum of 2 angles is 90°:
y+48°=90°
so y= 90°- 48°= 42°
Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a horizontal or vertical tangent line. g
I suppose the curve is [tex]r(\theta)=e^\theta[/tex].
Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.
[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]
We have
[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]
[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]
[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]
[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]
The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:
[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]
[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]
(where [tex]n[/tex] is any integer)
The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:
[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]
[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]
. Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito. (a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points) (b) 20% of Chipotle burritos weigh more than what weig
Complete Question
Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.
(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)
(b) 20% of Chipotle burritos weigh more than what weight
Answer:
a
[tex]P(X < 445 )= 0.3085[/tex]
b
[tex]k = 458.42[/tex]
Step-by-step explanation:
From question we are told that
The population mean is [tex]\mu = 450 \ g[/tex]
The variance is [tex]var = 100 \ g^2[/tex]
The consider weight is [tex]x = 445 \ g[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{var}[/tex]
substituting values
[tex]\sigma = \sqrt{ 100}[/tex]
[tex]\sigma = 10[/tex]
Given that weight of Chipotle burritos follows a normal distribution the the probability that a Chipotle burrito weighs less than x grams is mathematically represented as
[tex]P(X < x ) = P ( \frac{X - \mu }{\sigma } < \frac{x - \mu }{\sigma } )[/tex]
Where [tex]\frac{X - \mu }{\sigma }[/tex] is equal to z (the standardized values of the random number X )
So
[tex]P(X < x ) = P (Z < \frac{x - \mu }{\sigma } )[/tex]
substituting values
[tex]P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )[/tex]
[tex]P(X < 445 ) = P (Z <-0.5 )[/tex]
Now from the normal distribution table the value for [tex]P (Z <-0.5 )[/tex] is
[tex]P(X < 445 ) = P (Z <-0.5 ) = 0.3085[/tex]
=> [tex]P(X < 445 )= 0.3085[/tex]
Let the probability of the Chipotle burritos weighting more that k be 20% so
[tex]P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - 450}{10 } ) = 0.2[/tex]
From the normal distribution table the value of z for [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex] is
[tex]z = 0.8416[/tex]
=> [tex]\frac{k - 450}{10 } = 0.8416[/tex]
=> [tex]k = 458.42[/tex]
Convert 100 kilometers to meters.
Answer:
100,000 meters
Step-by-step explanation:
There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.
Answer:
it is 100000 kilometers
Step-by-step explanation:
use the metric system and you get 10000 kilometers.
Solve the system by the method of elimination.
Answer:
no solution
Step-by-step explanation:
x-y = 2
-4x +4y = 4
Multiply the first equation by 4
4(x-y) = 2*4
4x -4y = 8
Add this to the second equation
4x -4y = 8
-4x +4y = 4
------------------------
0x + 0y = 12
0 =12 is never true so there is no solution
Answer:
no solutions
Step-by-step explanation:
work is shown
After adding up all your expenses for the month you spent $465.36. your total budget for the month is$529.What percentage are under budget?(Round to the nearest whole percentage).Do not include symbol
Answer:
12%.
Step-by-step explanation:
It is given that, after adding up all your expenses for the month you spent $465.36. your total budget for the month is $529.
Total budget = $529
Total expenditure = $465.36
Under budget = $529 - $465.36 = $63.64
We need to find the percentage of under budget.
[tex]\%=\dfrac{\text{Under budget}}{\text{Total budget}}\times 100[/tex]
[tex]\%=\dfrac{63.64}{529}\times 100[/tex]
[tex]\%=0.12030\times 100[/tex]
[tex]\%=12.030\%[/tex]
[tex]\%\approx 12\%[/tex]
Therefore, the required percentage is 12%.
n a nature conservatory, the ratio of butterflies to total number of flying insects is 36 to 100. There are 450 total flying insects. (a) Create a table for how many butterflies there are for 1, 50, and 100 flying insects. Show your work. (b) How many butterflies are in the conservatory? Show your work.
Answer:
There are 172 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 172
Thus, there are 172 butterflies in the conservatory.
Answer:
There are 162 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 162
Thus, there are 162 butterflies in the conservatory.
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers 3 or odd are 1, 3, 5, and 7.
4 numbers out of 8.
4/8 = 1/2
P(3 or odd) = 1/2
PLEASE HELP ME FOR BRAINLIEST Reduce to simplest form. 6/3+(-1/6)
Answer: 1 5/6, or 11/6, or 1.83333333
Step-by-step explanation:
[tex]\frac{6}{3} + -\frac{1}{6}[/tex]
6/3 is 2.
Thus, the answer is 2 - 1/6 or 1 5/6
Answer:
11/6
Step-by-step explanation:
First, we need to find a common denominator for the 2 fractions.
A common denominator for 3 and 6 is 6.
Let’s get the fraction 6/3 to a denominator of 6.
Multiply by 2/2
6/3 * 2/2
(6*2) / (3*2)
12/6
Now the fractions have common denominators and can be added.
12/6 + (-1/6)
When adding negative fractions, you can simply subtract.
12/6 - 1/6
Subtract across the numerator and leave the denominator as is
11/6
This fraction can be written as: 2 1/6, 11/6, or 1.83333
[URGENT] Suppose A and B are dependent events. If P(A) = 0.4 and P(B A) = 0.8, what is
P(A B)?
Answer:
Option (B)
Step-by-step explanation:
If the probabilities of two events A and B are P(A) and P(B) then the conditional probability of an event that can be derived by the formula,
P(B | A) = [tex]\frac{P(A\cap B)}{P(A)}[/tex]
P(A ∩ B) = P(B|A) × P(A)
P(A ∩ B) = (0.8) × (0.4)
= 0.32
Therefore, Option (B) will be the correct option.
Answer:
Option B is correct.
Step-by-step explanation:
If (x) = 3x - 5 and g(x) = x + 3, find (f - g)(x).
O A. 8 - 2x
O B. 2x-2
O c. 2x-8
O D. 4x-2
Answer:
C
Step-by-step explanation:
(f-g)(x)=(3x-5)-(x+3) = 3x-5-x-3 = 2x-8
Answer:
2x -8
Step-by-step explanation:
f (x) = 3x - 5
g(x) = x + 3,
(f - g)(x) = 3x - 5 - ( x+3)
Distribute the minus sign
= 3x-5 -x-3
Combine like terms
= 2x -8
Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability 0.23 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent. Give your answer to four decimal places. a. What is the probability that both professors get their grants funded
Answer:
14.72% probability that both professors get their grants funded
Step-by-step explanation:
Independent events:
If two events, A and B are independent, the probability of both happening is:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question:
Event A: Professor Jane is funded
Event B: Professor Joe is funded.
Professor Jane has a probability of 0.64 of being funded.
This means that [tex]P(A) = 0.64[/tex]
Professor Joe has probability 0.23 of being funded.
This means that [tex]P(B) = 0.23[/tex]
What is the probability that both professors get their grants funded
[tex]P(A \cap B) = P(A)*P(B) = 0.64*0.23 = 0.1472[/tex]
14.72% probability that both professors get their grants funded
Prompt The cell-phone datafile is available in the Data section below. Once again, here is the research question for this lab. Based on a recent study, roughly 80% of college students in the U.S. own a smartphone. Is the proportion of smartphone owners lower at this university? Respond to each of the following in your initial post. State your hypotheses in symbolic form and in words. (The following should be clear in your answer: the population of interest and the meaning of the proportion p in terms of the variable Cell.) StatCrunch uses a normal model to estimate the P-value probability. Verify that normality conditions are met. Use StatCrunch to conduct the hypothesis test. (directions) Copy and paste the results (the StatCrunch output window) into your initial post. Give your P-value and interpret its meaning as a conditional probability. State a conclusion that answers the research question. Use a significance level of 5%. (Your answer should include the P-value and reference the population and the variable Cell.)
Answer:
Step-by-step explanation: i really would day if 80 % was college students it would be more then enogh
P-value and interpret its meaning as a conditional probability is 206
What is conditional probability?
conditional probability is a degree of the chance of an event taking place, for the reason that another event has already occurred. the particular technique is predicated on occasion B occurring with some kind of courting with every other event A.while conditional probabilities can offer extremely useful information, limited records are often furnished or to hand.
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Use the following data to compute a 98% upper confidence bound for μ1 − μ2:
m = 41
x = 42,700
s1 = 2030
n = 41
y = 36,275
s2 = 1360.
Answer:
[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]
[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]n_1 = 41 , \bar X_1 =42700 , s_1 = 2030[/tex]
[tex]n_2 = 41 , \bar X_2 =36375 , s_2 = 1360[/tex]
And for this case we want a 98% confidence interval. The significance would be:
[tex] \alpha= 1-0.98=0.02[/tex]
The degrees of freedom are:
[tex] df = n_1 +n_2 -2= 41+41 -2= 80[/tex]
And the critical value for this case is:
[tex] t_{\alpha/2}= 2.374[/tex]
And the confidence interval would be given by:
[tex](\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]
And replacing we got:
[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]
[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]
A teacher based in California calculated a particular date in the calendar and named it Square Root Day. Try and find out why the day was named so. Can you find more such days? When was last square root day and when is next square root day
Answer:
may 5 the is squareroot day and it is when the day and the month has the first two digits in the date are the square root of the last two digits. examples 2nd February,2004 3rd March 2009 and the last time we had one was April 4th 2016. The next square root day is May 5th 2025
Matías and José want to distribute 4.5 kilograms of lemons in 3/4 kilogram bags. How many bags will they be able to complete?
Answer:
6 bags
Step-by-step explanation:
3/4 = .75
4.5/.75 = 6 =
6 BAGS
The number of people who voted in the most recent local election was up from the last local election by about 24%. Therefore the number of people who voted in this election was how many times the number who voted in the last election
Answer:
The number of people who voted in this election was 1.24 times the number who voted in the last election
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
In this question:
Up by about 24%, so we want the multiplier for a increase of 24%.
So
1 + (24/100) = 1 + 0.24 = 1.24
The number of people who voted in this election was 1.24 times the number who voted in the last election
The time it took for a man to walk from his house to the park and back was 2 hours. The distance from his house to the park is 7 miles. The rate at which he walked to the park was twice the rate at which he walked back. What is the man's rate (in mph) walking back to his house?
Answer:
5.25 mph
Step-by-step explanation:
Let r represent the rate at which the man walked back from the park. Then 2r is the rate at which he walked to the park. His total travel time is ...
time = distance/speed
total time = time to the park + time from the park
2 = 7/(2r) +7/r
2 = (7 +14)/(2r) . . . combine terms
r = 21/(2·2) = 5.25 . . . miles per hour
The man's rate walking back from the park is 5.25 miles per hour.
The area of a square is increasing at the constant rate of 16sq.ft./min. When the perimeter of the square is 36ft, how fast is the perimeter of the square increasing?
Answer:
The perimeter of square is increasing by 3.76ft/min and then by 3.4 ft/min.
Step-by-step explanation:
Given that area of square is increasing at a rate of 16 sq ft/min.
Given that final perimeter is 36ft
Perimeter of a square = 4 [tex]\times[/tex] side = 36
So, side, a' = 9 ft
We know that area of a square is given by the formula:
[tex]A = side^2 = a^2[/tex] (If we let side = a units)
Change in area =
[tex]a'^2 - a^2\\\Rightarrow 9^2 - a^2 = 16\\\Rightarrow 81 - 16 = a^2\\\Rightarrow a = 8.06\ ft[/tex]
So, side got changed from 8.06ft to 9 ft.
So, perimeter when side was 8.06 ft:
[tex]4 \times 8.06 = 32.24\ ft[/tex]
Hence, increase in the perimeter when perimeter is 36 ft is = 36 - 32.24 = 3.76 ft
For finding Next increase:
area gets changed from 81 sq ft to 81+16 = 97 sq ft
So, new side = [tex]\sqrt{97}[/tex] ft = 9.85 ft
Next increase in perimeter = 4 (New side - Old side)
= 4 (9.85 - 9)
= 3.4 ft/min
A low calorie dinner has 480 calories in an 9 ounce serving. What is the unit rate in simplest form?
Answer: 53.333333, 53 1/3
Step-by-step explanation:
The unit rate in this question means how many calories for one ounce. Thus, you can simply divide 480 by 9 to get 53.3333333
Answer:
53.33 caloriesStep-by-step explanation:
Calories in a low calorie dinner = 480 calories
Serving at one time = 9 ounce
then,
Unit rate = Amount of calories in one serving
So,
Amount of calorie in 9 serving = 480
Amount of calorie in 1 serving = 480/9
In simple form : 160/3
= 53.33 calories
Hope this helps...
Good luck on your assignment..
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
Required:
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
Answer:
a) 0.65 mpg
b) Between 24.99 mpg and 28.01 mpg.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
s = 0.65 mpg
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
From the: 50 - (98/2) = 1st percentile
To the: 50 + (98/2) = 99th percentile
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = -2.327*0.65[/tex]
[tex]X = 24.99[/tex]
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = 2.327*0.65[/tex]
[tex]X = 28.01[/tex]
Between 24.99 mpg and 28.01 mpg.
Find all solutions of the equation in the interval , 02π. =4cosx+−sin2x4 Write your answer in radians in terms of π. If there is more than one solution, separate them with commas.
Answer:
The answer is "2nπ".
Step-by-step explanation:
Given:
[tex]4 \cos x= -\sin^2x+4.......(1)[/tex]
We know:
[tex]\Rightarrow \sin^2 x+\cos^2 x=1\\\\\Rightarrow \sin^2 x= 1 -\cos^2 x\\[/tex]
put the value of [tex]\sin^2 x[/tex] value in the above equation:
[tex]\Rightarrow 4 \cos x= - (1-\cos^2 x)+4\\\\\Rightarrow 4 \cos x= - 1+\cos^2 x+4\\\\\Rightarrow 4 \cos x= \cos^2 x+3\\\\\Rightarrow \cos^2 x-4 \cos x+3=0\\\\[/tex]
Let [tex]\cos x= A[/tex]
[tex]\Rightarrow A^2-4A+3=0 \\ \Rightarrow A^2-(3A+A)+3=0 \\\Rightarrow A^2-3A-A+3=0\\\Rightarrow A(A-3)-1(A-3)=0\\\Rightarrow (A-3)(A-1)=0 \\[/tex]
[tex]\Rightarrow A- 3=0 \ \ \ \ \ \ \ \ \ \ \ \Rightarrow A -1 =0 \\\\[/tex]
[tex]\Rightarrow A= 3\ \ \ \ \ \ \ \ \ \ \ \Rightarrow A =1 \\\\\Rightarrow \cos x = 3\ \ \ \ \ \ \ \Rightarrow \cos x =1\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow \cos x =\cos 0\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow x = 0\\\\[/tex]
The value of x is [tex]2n\pi\ \ \ _{where} \ \ \ \ \ \ \ n=1, 2, 3......[/tex]
[tex]\boxed{\bold{x=2 n \pi}}[/tex]
798/8×41 rounded to one significant figure
Answer:
2.5
Step-by-step explanation:
the other persons answer is wrong
The number after rounding to the one significant figure is 4000.
What is significant figure?
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number
According to the given question we have an expression.
[tex]\frac{798}{8} (41)[/tex]
When we evaluate this expression we get
[tex]\frac{798}{8} (41)[/tex]
[tex]=99.75(41)[/tex]
[tex]= 4089.75[/tex]
Here, the first significant figure is 4 and the second one is 0 which is less than 5.
Hence, the number after rounding to the one significant figure is 4000.
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In a basketball shooting competition there are ten balls from 1-10. The number of points earned is based on the number on the ball (I.e shoots a 7 gets 7 points), if a person misses 2 shots what number is not possible
52
44
41
38
35
The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part
Look at picture please
Answer:
BCD
Step-by-step explanation:
Is that hegarty maths? Just curious. Anyway acute means a angle below 90
Answer:
∠C
Step-by-step explanation:
Angle A is incorrect because it is 90° and acute angles are LESS than 90°.
Angle B is incorrect because it is more than 90° which makes it obtuse.
Angle D is incorrect because it is more than 90° which makes it obtuse.
Angle C is correct because it is less than 90°.
When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the _______. a.remainder b.divisor c.dividend d.quotient
Answer:
The answer is not "REMAINDER" it's "Quotient"
Step-by-step explanation:
Cancelling identical factors in the numerator and the denominator will give the quotient.
When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that when dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.
A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is also known as the integer portion of a division, a fraction, or a ratio.
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