Answer:
Selling price=rs.600.
Profit of rs=100.
Step-by-step explanation:
C.P=500; profit%=20%
S.P.=100+profit%×C.P/100
S.P=120×500/100
=rs.600
S.P>C.P
Profit S.P-C.P
600-500=100
he gained for rs.100.
Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 56 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.440. Determine if there is sufficient evidence to say that his batting average has improved at the 0.02 level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, we have that:
The value of the test statistic is z = 1.65.The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.As the test involves a comparison of samples, it involves subtraction of normal variables, and for this, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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 [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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Before:
Average of 0.250 in 56 at bats, so:
[tex]p_B = 0.25[/tex]
[tex]s_B = \sqrt{\frac{0.25*0.75}{56}} = 0.0579[/tex]
After:
Average of 0.44 in 25 at bats, so:
[tex]p_A = 0.44[/tex]
[tex]s_A = \sqrt{\frac{0.44*0.56}{25}} = 0.0993[/tex]
Test if there was improvement:
At the null hypothesis, we test if there was no improvement, that is, the subtraction of the proportions is 0:
[tex]H_0: p_A - p_B = 0[/tex]
At the alternative hypothesis, we test if there was improvement, that is, the subtraction of the proportions is positive, so:
[tex]H_1: p_A - p_B > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_B - p_A = 0.44 - 0.25 = 0.19[/tex]
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0579^2 + 0.0993^2} = 0.1149[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.19 - 0}{0.1149}[/tex]
[tex]z = 1.65[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.
Looking at the z-table, z = 1.65 has a p-value of 0.9505.
1 - 0.9505 = 0.0495.
The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.
A similar question is found at https://brainly.com/question/23827843
A research worker gave a scholastic aptitude test to a sample of eighth graders. Then he correlated the aptitude test scores with the chronological ages of the subjects. He found a correlation of - .42. How should this result be interpreted?
Answer: There is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
Step-by-step explanation:
The correlation coefficient tells about the strength and direction of the relation ship between any 2 variables. When the value of correlation coefficient lies between -0.5 to -0.3 or 0.3 to 0.5, then it indicates that there is moderate association between variables.Here , variables → aptitude test scores and chronological ages of the subjects.
Since correlation coefficient (-0.42) lies between -0.5 and -0.3 .
[-0.5< -0.42< -0.3]
That means there is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
The length of the sides of the triangle are in the ratio 3:4:5 and it’s perimeter is 144 cm find its area and height corresponding to the longest side
PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
1)
1/5 of the students earned a C
2)
3% more students earned an A then B
3)
20% of the students earned a D
4)
1/4 of the class earned a B
Answer:
3) 20% of the students earned a D
Step-by-step explanation:
9 students got a D.
5 students got a C.
14 students got a B.
17 students got an A.
Total number of students:
9 + 5 + 14 + 17 = 45
1) 1/5 of the students earned a C
1/5 of 45 = 9
5 students got a C
False
2) 3% more students earned an A then B
3 more students got an A than a B, but not 3%.
False
3) 20% of the students earned a D
20% of 45 = 9
9 students got a D.
True
4) 1/4 of the class earned a B
1/4 of 45 = 11.25
There were 14 B's.
False
Answer: 3) 20% of the students earned a D
Evaluate C 3y − esin(x) dx + 7x + y4 + 1 dy, where C is the circle x2 + y2 = 16. SOLUTION The region D bounded by C is the disk x2 + y2 ≤ 16, so let's change to polar coordinates after applying Green's Theorem: C 3y − esin(x) dx + 7x + y4 + 1 dy
By Green's theorem,
[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]
The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.
We'll verify this by actually computing the integral. Convert to polar coordinates, setting
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]
The interior of the circle is the set
[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]
So we have
[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]
as expected.
Please help! picture above plus, part B: write the quadratic expression in the numerator and the dominator in factored form. Part C: cancel the common factor of the numerator and the denominator to write the expression in simplified form.
Answer:
work is shown and pictured
Answer:
Hi, there!!!
The answer would be 2(2x-1)/x(x-4).
See explanation in picture.
Hope it helps...
Find the value of x.
A. 6
B. 3
C. 5
D. 2
[tex]\\ \sf\longmapsto \dfrac{AK}{DK}=\dfrac{CK}{BK}[/tex]
[tex]\\ \sf\longmapsto \dfrac{14}{12}=\dfrac{4x+1}{3x+3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{7}{6}=\dfrac{4x+1}{3x+3}[/tex]
[tex]\\ \sf\longmapsto 7(3x+3)=6(4x+1)[/tex]
[tex]\\ \sf\longmapsto 21x+21=24x+6[/tex]
[tex]\\ \sf\longmapsto 24x-21x=21-6[/tex]
[tex]\\ \sf\longmapsto 3x=15[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{15}{3}[/tex]
[tex]\\ \sf\longmapsto x=5[/tex]
Find the slope of the line containing the points (2, 7) and (-5, -4).
the answer is 11/7.you can see the image
Answer:
[tex]\boxed {\boxed {\sf \frac{11}{7}}}[/tex]
Step-by-step explanation:
The slope describes the direction and steepness of a line. The formula is:
[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are the points the line contains. For this problem, the line contains the points (2,7) and (-5, -4). Therefore:
x₁= 2 y₁ = 7 x₂ = -5 y₂ = -4Substitute these values into the formula.
[tex]m= \frac{ -4 -7}{-5-2}[/tex]
Solve the numerator (-4 -7 = -11).
[tex]m= \frac{ -11}{-5-2}[/tex]
Solve the denominator (-5-2 = -7).
[tex]m= \frac{ -11}{-7}[/tex]
Simplify the fraction. The 2 negative signs cancel each other out.
[tex]m= \frac{11}{7}[/tex]
The slope of the line is 11/7
An IQ test is designed so that the mean is 100 and the standard deviation is for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with % confidence that the sample mean is within IQ points of the true mean. Assume that and determine the required sample size.
Complete Question
An IQ test is designed so that the mean is 100 and the standard deviation is 24 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the simple mean is with in 3 IQ points of the true mean. Assume that standard deviation = 24 and determine the required sample size using technology. Determine if this is a reasonable sample size for a real world calculation.
The required sample size ______ (round up to the nearest integer.
Answer:
The sample size is [tex]n = 246[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 100[/tex]
The standard deviation is [tex]\sigma = 24[/tex]
The margin of error is [tex]E = 3[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The sample size is evaluated as
[tex]n = [ \frac{ Z_{\frac{\alpha }{2} } * \sigma }{E }]^2[/tex]
=> [tex]n = [ \frac{ 1.96 * 24 }{3 }]^2[/tex]
=> [tex]n = 246[/tex]
to check if this n is applicable in real world then we calculate E and compare it with the given E
apter 3 If a driver uses of a tank of gas every day, what fraction of a tank will he use in a) 3 days? b) 1 week? 21
You need to re copy and paste it, I can’t see the full possible answers/question.
Plz answer last question and im lost!
Answer:
[tex]\pi[/tex] radian
Step-by-step explanation:
We know that angle for a full circle is 2[tex]\pi[/tex]
In the given figure shape is semicircle
hence,
angle for semicircle will be half of angle of full circle
thus, angle for given figure = half of angle for a full circle = 1/2 * 2[tex]\pi[/tex] = [tex]\pi[/tex]
Thus, answer is [tex]\pi[/tex] radian
alternatively, we also know that angle for a straight line is 180 degrees
and 180 degrees is same as [tex]\pi[/tex] radian.
A sound technician analyzes the audio feedback by placing a microphone at certain distances from a speaker. If the microphone is connected to the speaker, then the microphone senses 606060 decibels (\text{dB})(dB)left parenthesis, start text, d, B, end text, right parenthesis at a distance of 000 meters (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis from the speaker with the decibel level decreasing by half of itself for every additional meter from the speaker. If the microphone is not connected to the speaker, then the microphone senses 30 \, \text{dB}30dB30, start text, d, B, end text at a distance of 0 \, \text{m}0m0, start text, m, end text from the speaker with the decibel level decreasing by 888 for every additional meter from the speaker. Three meters from the speaker, what is the difference between the decibel level when it is connected to the speaker versus when it is not connected to the speaker?
At three meters, the difference in the decibel level if and if not connected to the speaker is 1.5 dB
The reason for arriving at the above value is as follows:
The known parameters:
The audio sensed by the microphone when connected to the speaker are;
0 meters = 60 decibels
The level of the decibel decrease by half for each additional meter;
Therefore, when the microphone is connected to the speaker, we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&60\\1&&30\\2&&15\\3&&7.5\end{array}\right][/tex]
If the microphone is not connected to the speaker, we have;
0 meters = 30 decibels
The level of the decibel decreasing by 8 dB for every additional meter from the speaker, therefore, when the microphone is not connected to the speaker we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&30\\1&&22\\2&&14\\3&&6\end{array}\right][/tex]
At three meters from the speaker, the difference in the decibel level when it is connected and when it is not connected to the speaker is therefore;
Decibel level at 3 meters when connected, s₁ = 7.5 dB
Decibel level at 3 meters when not connected, s₂ = 6 dB
The difference in the decibel level = s₂ - s₁ = 7.5 dB - 6 dB = 1.5 dB
The difference in the decibel level when connected to the speaker and when not connected to the speaker is 1.5 dB
Learn more about sound level here:
https://brainly.com/question/11047787
PLEASE HELP!!!!!!
Look at the triangle ABC.
A (4.5)
5
4
3
2
1
C (4.1)
B (2.1)
1 2 3
4 5
--5 -4 -3 -2 -1 0
-1
-2
-3
-4
-5
What is the length of the side AB of the triangle?
2
20
38
=========================================
Explanation:
Count out the spaces, or use subtraction, to find the horizontal side BC is 2 units long. Similarly, you'll find the vertical side AC is 4 units long.
Use the pythagorean theorem to find the length of segment AB.
a^2 + b^2 = c^2
2^2 + 4^2 = c^2
4 + 16 = c^2
20 = c^2
c^2 = 20
c = sqrt(20)
We stop here since it matches with choice B.
-----------------
Optionally, we can simplify like so
sqrt(20) = sqrt(4*5)
sqrt(20) = sqrt(4)*sqrt(5)
sqrt(20) = 2*sqrt(5)
Answer:
The answer is [tex]\sqrt{20}[/tex].
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]2^{2} + 4^{2} = c^{2} \\4+16 = c^{2} \\\sqrt{20} = c[/tex]
We want to model the daily movement of a particular stock (say Amazon, ticker = AMZN) using a homogeneous markov-chain. Suppose at the close of the market each day, the stock can end up higher or lower than the previous day’s close. Assume that if the stock closes higher on a day, the probability that it closes higher the next day is .65. If the stock closes lower on a day, the probability that it closes higher the next day is .45.
(a) What is the 1-step transition matrix? (Let 1 = higher, 2 = lower)
(b) On Monday, the stock closed higher. What is the probability that it will close higher on Thursday (three days later)
Answer:
See the explanation and attached images for the answers.
Step-by-step explanation:
a) 1-step transition matrix:
See the attached image for transition matrix.
Let the matrix be M
if the stock closes higher on a day, the probability that it closes higher the next day is 0.65.
If the stock closes lower on a day, the probability that it closes higher the next day is 0.45
if the stock closes higher on a day, the probability that it closes lower the next day is 1 - 0.65 = 0.35
if the stock closes lower on a day, the probability that it closes lower the next day is 1 - 0.45 =0.55
b)
To compute probability for 3 days later multiply matrix M (from part a) thrice i.e. M*M *M
[tex]M^{3} = \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.65 * 0.65 + 0.35 * 0.45 &0.65 * 0.35 + 0.35 * 0.55 \\0.45 * 0.65 + 0.55 * 0.45 &0.45 * 0.35 + 0.55 * 0.55 \end{array}\right] * \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.58&0.42\\0.54&0.46\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc} 0.58 * 0.65 + 0.42 x 0.45&0.58 * 0.35 + 0.42 * 0.55 \\0.54 * 0.65 + 0.46 * 0.45 &0.54 * 0.35 + 0.46 * 0.55 \end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.566&0.434\\0.558&0.442\end{array}\right][/tex]
The probability that it will close higher on Thursday is 0.566. See the transmission matrix of M³ for higher-higher. This can be interpreted as:
if the stock closed higher on Monday, the probability that it closes higher the on Thursday (three days later) is 0.566
write all the prime numbers between 10 and 30.
A restaurant offers two types of pizza
dough: sourdough and whole wheat.
The chefs can make three types of
pizza crust: thin, thick, or deep dish.
What is the probability that the next
customer will order a whole wheat
pizza with thick crust?
Answer:
1/6 or 16.6%
Step-by-step explanation:
There are 6 possible combinations, one of which being whole wheat with thick crust. Therefore there is a 1/6 chance.
What is the answer to 123*456/789?
answer is 71.08745247
in mix form or in short form it is =
71/23/263
In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal places.)
a. x=5
b. x <= 5
c. x>=6
Answer:
[tex]\mathbf{P(X=5) =0.0888}[/tex]
P(x ≤ 5 ) = 0.9707
P ( x ≥ 6) = 0.0293
Step-by-step explanation:
The probability of a binomial mass distribution can be expressed with the formula:
[tex]\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]
[tex]\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]
where;
n = 8 and π = 0.36
For x = 5
The probability [tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}[/tex]
[tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}[/tex]
[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}[/tex]
[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}[/tex]
[tex]\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}[/tex]
[tex]\mathtt{P(X=5) =0.0887645}[/tex]
[tex]\mathbf{P(X=5) =0.0888}[/tex] to 4 decimal places
b. x ≤ 5
The probability of P ( x ≤ 5)[tex]\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})[/tex]
[tex]{P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +[/tex][tex]\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )[/tex]
P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888
P(x ≤ 5 ) = 0.9707
c. x ≥ 6
The probability of P ( x ≥ 6) = 1 - P( x ≤ 5 )
P ( x ≥ 6) = 1 - 0.9707
P ( x ≥ 6) = 0.0293
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Answer:
32.8 miles
Step-by-step explanation:
Amy is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below. Amy has 48 miles remaining after 31 minutes of driving. How many miles will be remaining after 47 minutes of driving?
Answer: The general equation of a line is given as y = mx + c, where m is the slope of the line and c is the intercept on the y axis. Given that the slope is -0.95, substituting in the general equation :
y = -0.95x + c
Amy has 48 miles remaining after 31 minutes of driving, to find c, we substitute y = 48 and x = 31. Therefore:
48 = -0.95(31) + c
c = 48 + 0.95(31)
c = 48 + 29.45
c = 77.45
The equation of the line is
y = -0.95x + 77.45
After 47 minutes of driving, the miles remaining can be gotten by substituting x = 47 and finding y.
y = -0.95(47) + 77.45
y = -44.65 + 77.45
y = 32.8 miles
Find a pair of polar coordinates for the point with rectangular coordinates (5, –5).
Answer:
(5*sqrt(2), 5pi/4)
Step-by-step explanation:
In Polar coordinates, tan(theta)=y/x and r=sqrt(x^2+y^2)
tan(theta)=-5/5=-1. Theta=5pi/4
r=sqrt(5^2+5^2)=5*sqrt(2)
Hence the Polar coordinate is (5*sqrt(2), 5pi/4)
The polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].
What is polar coordinate system?The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
How to convert rectangular coordinates to polar coordinates?To convert rectangular coordinate (x, y) to polar coordinate(r, θ) by using some formula
tanθ = y/x and [tex]r =\sqrt{x^{2} +y^{2} }[/tex]
According to the given question
We have
A rectangular coordinate (5, -5).
⇒ x = 5 and y = -5
Therefore,
[tex]r=\sqrt{(5)^{2} +(-5)^{2} } =\sqrt{25+25} =\sqrt{50} =5\sqrt{2}[/tex]
and
tanθ = [tex]\frac{-5}{5} =-1[/tex]
⇒ θ = [tex]tan^{-1} (-1)[/tex] = [tex]-\frac{\pi }{4}[/tex]
Therefore, the polar coordinate is [tex](5\sqrt{2},\frac{-\pi }{4} )[/tex].
Learn more about polar coordinates here:
https://brainly.com/question/1269731
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The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.
Required:
a. Determine the 26th percentile for the number of chocolate chips in a bag.
b. Determine the number of chocolate chps in a bag that make up the middle 96% of bags.
Answer:
(a) The 26th percentile for the number of chocolate chips in a bag is 1185
(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504
Step-by-step explanation:
From the question, we have the following values:
μ =1262 and σ =118
(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.
P( Z<-0.65 )=0.2578 which is approximately 0.26
So for 26th percentile z-score will be -0.65.
Mathematically;
z-score = (x-mean)/SD
-0.65 = (x-1262)/118
-76.7 = x -1262
x = 1262-76.7 = 1185.3
This value is approximately 1,185
(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.
From z-table, we can find the closest probability;
P(-2.05<z<2.05) = 0.96
So we have two x values to get from the individual z-scores
-2.05 = (x-1262)/118
x = 1020(approximately)
For 2.05, we have
2.05 = (x-1262)/118
x = 1262 + 2.05(118) = 1504 (approximately)
A jet travels 500 kilometers in 40 minutes with a tail wind. Returning, the jet takes 50 minutes to cover the same distance. What is the rate of the plan and the speed of the wind?
Answer:
675 km/hr and 75 km/hr
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*(40/60)=500 and (x-y)*(50/60)=500. Solving it, we get x=675 and y=75
Which part of an I-statement involves a description of your needs or feelings?
Answer:
the answer is c
Step-by-step explanation:
Find y using the Angle Sum Theorem
Step-by-step explanation:
Hey, there!!
Look this figure, simply we find that;
In triangle ABC,
angle CBD is an exterior angle of a triangle.
and its measure is 90°
Then,
angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.
or, 90°= y + 48°
Shifting, 48° in left side,
90°-48°= y
Therefore, the value of y is 42°.
Hope it helps...
The sum of 5 consecutive odd integers is 425. Find the integers.
Answer:
Hello,
Step-by-step explanation:
This a method knowing nothing.
1+3+5+7+9=25
425-25=400
400/5=80
Numbers are 80+1,80+,80+5,80+7,80+9 whose sum is 425.
What is the length of the hypothenuse of the triangle?
Answer:
26ft
Step-by-step explanation:
10^2 +24^2 =AB^2
AB=26
Answer: 26 ft
Step-by-step explanation:
a^2+b^2=c^2
10^2+24^2 = c^2
100+576=c^2
Sqrt 676 = c
C = 26
Nghiệm riêng của phương trình
y′′−y′=x2+x
có dạng
Answer:
i don't understand the question
A radio telescope has a parabolic surface, as shown below. A parabola opening up with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 9 meters and its width from left to right is 12 meters. If the telescope is 9 m deep and 12 m wide, how far is the focus from the vertex?
The telescope shape and the characteristic equations of the telescope parameters are the same as parabolic equations
The distance between the focus and the vertex, of the parabola is 3.375 meters
The process for obtain the above values is as follows:
The known parameters of the parabola are;
The location of the vertex of the parabola= The origin = (0, 0)
The height of the parabola = 9 meters
The width of the parabola = 12 meters
The unknown parameter;
The distance between the focus and the vertex
Method:
Finding the coordinate of the focus from the general equations of the the parameters of a parabola
The equation of the parabola in standard form is y = a·(x - h)² + k
From which we have;
(x - h)² = 4·p·(y - k)
The coordinates of the focus, f = (h, k + p)
Where;
(h, k) = The coordinates of the vertex of the parabola = (0, 0)
∴ a = 1/(4·p)
From the question, we have the following two points on the parabola,
given that the parabola is 12 meters wide at 9 meters above the origin and
it is symmetric about the y-axis;
Points on the parabola = (9, 6), and (9, -6)
Plugging in the values of the vertex, (h, k) and the two known points, in the equation, y = a·(x - h)² + k, we get;
6 = a·(9 - 0)² + 0 = 81·a
a = 6/81 = 2/27
p = 1/(4·a)
∴ p = 1/(4 × 2/27) = 27/8
The coordinate of the focus, f = (h, k + p)
∴ f = (0, 0 + 27/8) = (0, 27/8)
The coordinate of the focus f = (0, 27/8)
Given the vertex and the focus of the parabola have the same x-values of 0, we have;
The distance between the focus and the vertex, d = the difference in their y-values;
∴ d = 27/8 - 0 = 27/8 = 3.375
The distance between the focus and the vertex, d = 3.375 meters
Learn more about parabola here;
https://brainly.com/question/22404310
3x²+12x-15=0 factrozation method quadratic equations
Answer:
x = -5 or x = 1
Step-by-step explanation:
[tex] 3{x}^{2} + 12x - 15 = 0 \\ {x}^{2} + 4x - 5 = 0 \\ (x + 5)(x - 1) = 0 \\ x = - 5 \: or \: x = 1[/tex]
hope this makes sense:)
Salema's score on a test was 80%. If the test was worth a total of 60 points, how many points did Salema earn?
Answer:
48
Step-by-step explanation:
Do 60*.80
60 represent the total points the test was worth
.80 represents the % number
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
100% = 60
80% = 48
The points Salema earned are 48 points.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Salema's score = 80%
Total score in the test = 60 points
Salema's score.
= 80% of 60 points
= 80/100 x 60
= 48
Thus,
The points Salema earned are 48 points.
Learn more about percentages here:
https://brainly.com/question/11403063
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