Answer:
P(M > 260.2-cm) = 0.702
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are 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.
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 [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 = 260.5, \sigma = 1.6, n = 8, s = \frac{1.6}{\sqrt{8}} = 0.5657[/tex]
P(M > 260.2-cm)
This is 1 subtracted by the pvalue of Z when X = 260.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260.2 - 260.5}{0.5657}[/tex]
[tex]Z = -0.53[/tex]
[tex]Z = -0.53[/tex] has a pvalue of 0.298.
1 - 0.298 = 0.702
So
P(M > 260.2-cm) = 0.702
Solve for x in the equation x 2 - 4 x - 9 = 29.
Answer:
x= -19
Step-by-step explanation:
2x-4x-9=29
-2x=29+9
x=38/-2
= -19
Answer:
[tex]x=2-\sqrt{42}[/tex] and [tex]x=2+\sqrt{42} \\[/tex]
Step-by-step explanation:
Solve using the quadratic formula, which is [tex]x=\frac{-b + \sqrt{b^{2}-4ac }}{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
I need help! Someone help me please
Answer:
4. 27
Step-by-step explanation:
11-10=1 which is <=16
15-10=5 which is <=16
26-10=16 which is <=16
27-10=17 which isn't <=16
Therefore 27 doesn't satisfy the inequality
Answer:
4. 27
Step-by-step explanation:
w - 10 ≤ 16
w≤16 + 10
w ≤ 26
11 ≤ 26
15≤26
26≤26
26≤ 27 False
Find the area of a circle with radius, r = 9cm.
Give your answer in terms of π .
Answer:
[tex]81\pi[/tex]
Step-by-step explanation:
[tex]Area = \pi * r^{2} \\\pi *9^{2} =81\pi[/tex]
Answer:
81 π
Step-by-step explanation:
formula is radius squared times pi or π so the answer would be 9x9=81 and you said to leave in terms of π so the answer is 81 π.
Find the balance at the end of 4 years if $10000 is deposited at a rate of 1.5% simple interest
Answer:
$9400
Step-by-step explanation:
1.5x4=6%
100-6=94
0.94x10000=9400
What is the area of a rectangle with a base of 23 feet and a height of 6 feet
Answer:
Step-by-step explanation:
Area of rectangle = l × b
= 23 × 6
= 138 feet
hope this helps
plz mark it as brainliest!!!!!!!
A circle with circumference 6 has an arc with a 20 degrees central angle. What is the length of the arc?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
So first calculate what fraction of the circumference the arc is.
[tex]\frac{20}{360}=\frac{1}{18}[/tex]
Now the circumference is 6, so one eighteenth of that is [tex]\frac{1}{3}[/tex]
The total energy need during pregnancy is normally distributed, with a mean of 2600 kcal/day and a standard deviation of 50 kcal/day. Include your Normal curve for all parts! a) [4 pts] If one pregnancy is randomly selected, find the probability that the total energy need is more than 2650 kcal/day. b) [4 pts] The middle 30% of total energy need during pregnancy are between what values? c) [4 pts] What is the probability that a random sample of 20 pregnant women has a mean energy need of more than 2625 kcal/day?
Answer:
a) 0.3085
b) 2574
c) 0.0125
Step-by-step explanation:
mean (μ) = 2600 kcal/day and a standard deviation (σ) = 50 kcal/day
a) The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{x-\mu}{\sigma}=\frac{2650-2600}{50}=1[/tex]
From the normal distribution table, P(x > 2650) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 0.1587
b) A probability of 30% corresponds with a z score of -0.52
[tex]z=\frac{x-\mu}{\sigma}\\-0.52=\frac{x-2600}{50} \\x-2600=-26\\x=2600-26\\x=2574[/tex]
c) For a sampling distribution of sample mean, the standard deviation is [tex]\frac{\sigma}{\sqrt{n} }[/tex]
The z score is given by:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} }}[/tex]
n = 20
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} }}=\frac{2625-2600}{\frac{50}{\sqrt{20} }}=2.24[/tex]
From the normal distribution table, P(x > 2625) = P(z > 2.24) = 1 - P(z < 2.24) = 1 - 0.9875 = 0.0125
The drama club is selling candles for a fundraiser. They spend $100 on the candles and sell them for $4.50 each. How many candles must they sell to make more than $125 profit?
Let x represent the number of candles sold. Which inequality can you use to find x?
So I try to help
Step-by-step explanation:
I don't no sorrry
Answer:
the first one!!
Step-by-step explanation:
Which is the same as asking:
To what power must 5 be raised to get 3,125?
Answer: 5^5
Step-by-step explanation:
Since 5x5x5x5x5 = 3,125
(2)/(5) and (1)/(x)common denominator =10 find the value of x
Answer:
[tex]x=5/48[/tex]
Step-by-step explanation:
[tex]2/5 + 1/x =10[/tex]
[tex]1/x=10-2/5[/tex]
[tex]1/x=48/5[/tex]
[tex]48x=5[/tex]
[tex]x=5/48[/tex]
Answer:
[tex]x = \frac{5}{48} [/tex]
Step-by-step explanation:
[tex]\frac{2}{5} + \frac{1}{x} = 10 \\ \frac{1}{x} = 10 - \frac{2}{5} \\ \frac{1}{x} = \frac{50 - 2}{5} \\ \frac{1}{ x } = \frac{48}{5} \\
use \: \: \: \: cross \: \: \: multiply
\\ 5 = 48x \\ \frac{5}{48} = \frac{48x}{48} \\ x = \frac{5}{48} \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
82
R5
6
,92 5
4 8
12
12
0
Answer:
see below
Step-by-step explanation:
The first subtraction has a zero result (blue) from the thousands digit, so we know the dividend has 4 in that place. The 5 in the 1s place of the dividend is brought down to fill the space on the bottom line. 6 goes into that number 0 times, so the final quotient digit is 0.
4,925 = 6×820 +5
or
4,925 ÷ 6 = 820 r5
Write down five numbers with a mode of 6.
Answer:
6 4 5 6 7
Step-by-step explanation:
The mode would be 5. The first 2 letters of MODE are MO, which can be an abbreviation for MOST OFTEN.
What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve
Answer:
[tex]x=1\\x=-1[/tex]
Step-by-step explanation:
[tex]9x^{4} -2x^{2} -7=0\\y=x^{2} \\9y^{2} -2y-7=0\\y=\frac{2\pm\sqrt{(-2)^{2} -4*9(-7)} }{2*9} =\frac{2\pm\sqrt{4+252} }{18} =\frac{2\pm\sqrt{256} }{18}[/tex]
[tex]\sqrt{256} =16[/tex]
[tex]y=\frac{2+16}{18} =\frac{18}{18} =1 \\or \\y=\frac{2-16}{18} =-\frac{14}{18} =-\frac{7}{9}[/tex]
[tex]x^{2} = 1 \\or \\x^{2} =-\frac{7}{9}[/tex]
[tex]x=\pm 1[/tex]
[tex]x^{2} =-\frac{7}{9}[/tex] has no solution since fot all [tex]x[/tex] on the real line, [tex]x^{2} \geq 0[/tex] and [tex]-\frac{7}{9} < 0.[/tex]
An unevenly heated plate has temperature T(x, y) in °C at the point (x, y). If T(2, 1) = 130, and Tx(2, 1) = 16, and Ty(2, 1) = −13, estimate the temperature at the point (2.03, 0.96). (Round your answer to 2 decimal places.)
Answer:
The estimated temperature at the point (2.03, 0.96) is 131
Step-by-step explanation:
In this question, we are to estimate the temperature at the given point using the temperature of the unevenly heated plate.
We proceed as follows;
In the question, we identify that the temperature at the point T(2,1) = 130 degrees celcius
Now, let’s look at how the temperature changes. There is a positive change of 16 units when we move across the x-axis and a negative decrease when we move up the y-axis to a tune of 16 units(negative)
Now, how does the problem wants us to move using the notation of change?
Look at the point (2.03, 0.96), since movement across the x-axis is positive, the motion here in terms of x i.e Δx is 0.03 while the corresponding motion in terms of y(albeit negative) is Δy = -0.04
Mathematically, the change in temperature is proportional to the distance traveled. What this means is that we need to multiply the changes in direction by the corresponding temperature. This is shown below;
ΔTx =Δx*Tx(2,1) => ΔTx = (0.03)*(16) = 0.48
ΔTy = Δy*Ty(2,1) => ΔTy = (-0.04)*(-13) = 0.52
We can now combine the equations above to form a single one as follows; which is an approximation;
ΔT = Δx*Tx(2,1) + Δy*Ty(2,1) => ΔT = (0.03)*(16) + (-0.04)*(-13) = 1
To arrive at the final answer, we add the change in temperature to the staring temperature which is ;
T(2.03,0.96) = T(2,1) + ΔT = 130 + 1= 131
A fair 6-sided die is colored in the following way: The faces of 1 - 3 are colored red. The faces of 4 and 5 are colored blue. The face of 6 is colored green. What is the probability that the face comes up red OR a prime number
Answer:
There are 6 total possibilities, 3 red faces and 3 prime numbers however, 2 and 3 are prime numbers and they are red as well so total successful outcomes = 3 + 3 - 2 = 4. This means that the answer is 4 / 6 or 2 / 3.
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]1 \: 2\:3[/tex] are red
[tex]5[/tex] is prime.
Total of [tex]4[/tex] possibilities out of [tex]6[/tex]
[tex]\frac{4}{6}[/tex]
I will mark you as BRANLIEST and I will give you 55 points if you answer correctly.
~Solve each system of equations using elimination. SHOW YOUR WORK
1) -4x+3y=-5
4x-5y=3
2) 2x+3y=36
10x-6y=12
Answer:
1. x = 2 y = 1
2. x = 17 y = 29/3
Step-by-step explanation:
1. Use elimination
-4x+3y=-5
4x-5y=3
x's cancel, so add them
-2y = -2
y = 1
substitute
4x -5(1) = 3
4x - 5 = 3
4x = 8
x = 2
2. Use elimination
2x+3y=36
10x-6y=12
Multiply top equasion by 5
10x+30y = 360
10x-6y = 12
x's cancel so subract
36y = 348
y = 29/3
Substitute
2x+3(2/3)=36
2x+2 = 36
2x = 34
x = 17
What is the simplified expression for 5 a b + 9 a b minus a b?
Answer:
[tex]=13ab[/tex]
Step-by-step explanation:
[tex]5ab+9ab-ab\\\mathrm{Add\:similar\:elements:}\:5ab+9ab-ab=13ab\\=13ab[/tex]
Solve for x and y
5x + 3y = 7
y=4
Answer:
-1
Step-by-step explanation:
plug in y, subtract 12 from seven, divide -5 by 5
The values of x and y are -1 and 4 respectively.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given are a system of linear equations.
5x + 3y = 7
y = 4
We already have the value of y as 4.
Substituting that value of y = 4 in the first equation 5x + 3y = 7, we get,
5x + (3 × 4) = 7
5x + 12 = 7
Subtracting both sides by 12, we get,
5x + 12 - 12 = 7 - 12
5x = -5
Dividing both sides by 5, we get,
5x / 5 = -5 / 5
x = -1
Hence the value of x is -1 and the value of y is 4.
To learn more about Linear Equations, click on the link :
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what is the range of the exponential function shown below? f(x)=9*2^x
Answer:
(0, ∞)
Step-by-step explanation:
An exponential function has a horizontal asymptote at y=0. Its vertical extent is toward infinity.
The range is ...
0 < f(x) < ∞
en un parque hay una zona de columpios y una pista de patinaje que ocupa en total 5 quintos del espacio .si los columpios ocupan 2 septimos del parque . que fraccion del parque ocupa la pista de patinaje
Answer:
The rink occupies 69% of the whole park, approximately, which is equivalent to 280/408.Step-by-step explanation:
To solve this problem, we need to find the number which express the whole park.
Notice that the park is divided in two sections, one occupies 5/8 of the total, and the other occupies 2/7 of the total. So, the sum would be
[tex]\frac{5}{8}+\frac{2}{7}=\frac{35+16}{56} =\frac{51}{56}[/tex]
Now we have the total space there, we need to divide 5/8 by 51/56, so
[tex]\frac{5}{8} \div \frac{51}{56}=\frac{5}{8} \times \frac{56}{51}=\frac{280}{408} \approx 0.69[/tex]
Therefore, the rink occupies 69% of the whole park, approximately, which is equivalent to 280/408.
Round 90.2844097979 to 3 decimals
Answer:
only allow 3 decimals
90.284 is the answer we removed all others except for 3
A sample of 500 nursing applications included 60
from men. Find the 90% confielence interval
for the
true proportion of men who applied to the nursing
program.
Answer:
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 500
sample proportion
[tex]p = \frac{x}{n} = \frac{60}{500} = 0.12[/tex]
Level of significance ∝= 0.90 or 0.10
90% confidence interval for the true proportion of men who applied to the nursing program.
[tex](p - Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} } , p + Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](p - Z_{0.05 } \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.05 } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.12 - 1.645 \sqrt{\frac{0.12(1-0.12)}{500} } , 0.12 + 1.645 \sqrt{\frac{0.12(1-0.12)}{500} })[/tex]
On calculation , we get
( 0.12 - 0.02326 , 0.12 + 0.02326)
(0.09674 ,0.14326)
Final answer:-
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
If the nurse to patient ratio in a long term care unit is 3:15, how many nurses would you expect to see in a unit with 25 patients?
Answer:
5
Step-by-step explanation:
Divide both sides by 3 to get
1:5
Multiply by 5
To get 5:25
5 nurses for 25 patients
Answer:
5
Step-by-step explanation:
3 x 5 = 15
n x 5 = 25
n = 5
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
64
Step-by-step explanation:
If the mean is 15, the sum of 5 numbers is:
5*15 = 75Minimum value for the first four numbers would be:
1, 2, 3, 4Then the fifth number is:
75 - (1+2+3+4) = 75 - 10 = 65So the maximum difference is:
65 - 1 = 64The luxury Swiss Chalet hotel general manager (GM) reported to her owner that the hotel's Occupancy Index for the calendar year 2019 was 1.25. Based upon only this information alone, what MUST be correct?
Answer:
the Swiss Chalet had higher occupancy than its competitive set in 2019
Step-by-step explanation:
Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain.
Please help
Answer:
(7, -11)
Step-by-step explanation:
If the point is shifted 3 to the right and 2 down, you just have to add 3 to the x-coordinate and subtract 2 from the y-coordinate. 4+ 3 = 7 and -9 - 2 is -11. So, the new point will be (7, -11).
Answer:
(7, -11)
Step-by-step explanation:
The point is translated three units to the right, and 2 units down.
[tex](4,-9)=>(4+3,-9-2)=>(7,-11)[/tex]
Point " ' " should be (7,-11)
Jana ran 7 days last week. She ran the same number of miles every day, and she ran 28 miles in all. What is Janas rate?
Answer:
Janas rate is of 4 miles per day.
Step-by-step explanation:
Her rate is the number of miles she ran per day.
We can solve this using a rule of three.
In 7 days, she ran 28 miles. How many miles she ran a day, that is, in one day?
1 day - x miles
7 days - 28 miles
[tex]7x = 28[/tex]
[tex]x = \frac{28}{7}[/tex]
[tex]x = 4[/tex]
Janas rate is of 4 miles per day.
Exactly one pair of opposite sides is parallel
Answer:
Yeah btw is this a question?
The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2617 and standard deviation 586. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X N,(_____ , ____)
b. Find the probability that the customer consumes less than 2409 calories. ______
c. What proportion of the customers consume over 2764 calories? __________
d, The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? __________ calories. (Round to the nearest calorie)
Answer:
a) N(2617, 586)
b) 0.3613 = 36.13% probability that the customer consumes less than 2409 calories.
c) 0.4013 = 40.13% of the customers consume over 2764 calories
d) 3981 calories.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 2617, \sigma = 586[/tex]
a. What is the distribution of X?
Here we first place the mean, then the standard deviation.
N(2617, 586)
b. Find the probability that the customer consumes less than 2409 calories.
This is the pvalue of Z when X = 2409. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2409 - 2617}{586}[/tex]
[tex]Z = -0.355[/tex]
[tex]Z = -0.355[/tex] has a pvalue of 0.3613
0.3613 = 36.13% probability that the customer consumes less than 2409 calories.
c. What proportion of the customers consume over 2764 calories?
This is 1 subtracted by the pvalue of Z when X = 2764. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2764 - 2617}{586}[/tex]
[tex]Z = 0.25[/tex]
[tex]Z = 0.25[/tex] has a pvalue of 0.5987
1 - 0.5987 = 0.4013
0.4013 = 40.13% of the customers consume over 2764 calories
d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?
Top 1%, so the 100-1 = 99th percentile.
The 99th percentile is the value of X when Z has a pvalue of 0.99. So it is X when Z = 2.327. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 2617}{586}[/tex]
[tex]X - 2617 = 2.327*586[/tex]
[tex]X = 3980.6[/tex]
Rounding to the nearest calorie, 3981 calories.
A 12cmx2cm rectangle sits inside a circle with a radius of 8cm. What isnthe area of the shaded region of the circle
Answer:
The answer would 177.06 centimeters
