(a) The probability that the individual's pressure will be between 120 and 121.8 mm Hg is 0.1255.
(b) The probability that the sample mean will be between 120 and 121.8 mm Hg is 0.4608.
(c) The probability in part a is so much smaller than the probability in part b since, in part a, the probability is calculated for an individual's pressure whereas, in part b, the probability is calculated for a sample of adults.
How to calculate the z-score?The z-score formula in a normal distribution is given by
z = (X - μ)/σ
Here, the mean (μ), standard deviation (σ), and random variable (X) are used for finding the z-score.
With this z-score, from the normal distribution table, we can find the probability of the required random variable.
Calculation:It is given that,
The mean of the pressure of normal adults is μ = 120 mm of Hg
The standard deviation is σ = 5.6
Consider X is a normally distributed variable.
(a) Then, the probability that the individual's pressure will be between 120 and 121.8 mm Hg is calculated by P(120 < X < 121.8).
Here, the z-scores for the given means are:
z-score for the random variable 120 mm Hg is
z = (X - μ)/σ
⇒ z = (120 - 120)/5.6 = 0
z - score for the random variable 121.8 mm Hg is
z = (X - μ)/σ
⇒ z = (121.8 - 120)/5.6 = 0.32
So, the required probability is
P(120 < X < 121.8) = P(0 < z < 0.32)
⇒ P(z < 3.2) - P(z < 0)
From the normal distribution table, we get P(z < 3.2) = 0.6255 and P(z < 0) = 0.5000.
Then, the probability is
P(z < 3.2) - P(z < 0) = 0.625 - 0.5000 = 0.1255
(b) The sample size n = 30 and the random variables are 120 and 121.8 mm Hg.
Since the distribution is for a sample of adults, the sample mean value is
μₓ = μ = 120 and the sample standard deviation is
σₓ = σ/√n = 5.6/√30 = 1.022
Then, the z-scores for the given random variables are:
z-score for the random variable 120 mm Hg is
z = (X - μₓ)/σₓ = (120 - 120)/1.022 = 0
z-score for the random variable 121.8 mm Hg is
z = (X - μₓ)/σₓ = (121.8 - 120)/1.022 = 1.76
So, the required probability is
P(120 < X < 121.8) = P(0 < z < 1.76)
⇒ P(z < 1.76) - P(z < 0)
From the normal distribution table, we get P(z < 1.76) = 0.9608 and P(z < 0) = 0.5000.
Then, the probability is
P(z < 1.76) - P(z < 0) = 0.9608 - 0.5000 = 0.4608.
(c) The answer to part a is so much smaller than the answer to part b. This is because part a is the distribution for an individual and part b is the distribution for a sample of adults.
So, the sample mean and sample standard deviation will get changed in part b.
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!! Please help
Solve the system using substitution
x + 3y = 3
3y - 2x = 12
What is the slope of the line on this graph?
Enter your answer in the box.
Answer: 6 units
Step-by-step explanation:
There are two ways to do this. You can either choose 2 points on the graph and find the rise/run, or you can plug them in the formula. Let's choose the two points that are dotted. (1,5) and (0,-1)
Let's first do rise/run.
From (0,-1) to (1,5) the rise is 6 units, and the run is 1 unit. So we just divide that. 6/1 which means the slope is 6 units.
We can also use the formula: m = y2 - y1 / x2 - x1
(0,-1) will be our first coordinate and (0,-1) will be our second coordinate. So 0 is x1 and -1 is y1, 1 will be x2 and 5 will be y2. Now we just plug in the numbers
m=5-(-1)/1-0
m=5+1/1-0
m=6/1
m=6 units
So in both ways we get that the slope is 6 units.
Evaluate triple integral_W dx dy dz/(x^2 + y^2 + z^2)^3/2, where W is the solid bounded by the two spheres x^2 + y^2 + z^2 = a^2 and x^2 + y^2 + z^2 = b^2, where 0 < b < a.
The Triple Intergral of the given expression is [tex]4 \pi \times ln (\frac{a}{b})[/tex]
[tex]\int\limits \int\limits \int\limits_w \frac{dx dy dz}{(x^2 + y^2 + z^2)^{\frac{3}{2}}}[/tex]
[tex]\text{Where } x^2 + y^2 + z^2 = a^2 \text{ and } x^2 + y^2 + z^2 = b^2, 0 < b < a[/tex]
Changing to Spherical Coordinates
[tex]b \leq \rho \leq a, 0 \leq \theta \leq 2 \pi, 0 \leq \phi \leq \pi[/tex]
[tex]\therefore x^2 + y^2 + z^2 = \rho^2; dx dy dz = \rho^2 sin \phi .d\phi .d\theta. d\rho[/tex]
[tex]\implies \int\limits^a_b \int\limits^{2\pi}_{0} \int\limits^{\pi}_{0} \frac{1}{\rho^3} \rho^2 sin \phi .d\phi .d\theta. d\rho[/tex]
[tex]=\int\limits^a_b {\frac{1}{\rho}} \, d\rho \int\limits^0_{2\pi} d\theta \int\limits^{\pi}_0 \sin{\phi} \, d\phi[/tex]
[tex]= [ln \rho]^{a}_{b} [\theta]^{2\pi}_{0} [-\cos \phi]^{\pi}_{0}[/tex]
[tex]= [\ln a - \ln b] \times [2\pi] \times [- \cos \pi - (-\cos 0)][/tex]
[tex]= 2\pi \times 2 \times (\ln a - \ln b)[/tex]
[tex]= 4 \pi \, \ln{\frac{a}{b}}[/tex]
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I honestly don’t know what this means or how to do it can some one tell me?
Answer:
No solution.
Step-by-step explanation:
The question is asking how many solutions this has. For example:
1+2=x
x would be 3 and can only be 3, so this would have only one solution
Another example:
x>1
This is stating that x is greater than 1, which can be 2,3,4,5,etc. It goes infinitely long, which means It has infinite solutions.
One example of an equation having no solutions is:
x>3
x<1
This is stating that x is greater than 3, and that it's less than 1, which is impossible, aka no solution.
Process in image.
18. A new college entrance exam scores designed so that for a reference population they are
distributed normally, with mean 650 and standard deviation 125. Based on this
information:
a. What percentage of students in the reference population scored above 775?
b. Between what two scores did the middle 95%of the reference population score?
c. Out of every 1,000 people in the reference population, approximately how many
scored below 525?
a. The percentage of students in the reference population scored above 775 is of: 16%.
b. The middle 95% of scores were between 400 and 900.
c. Approximately 160 students scored below 525.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation in this problem are given as follows:
[tex]\mu = 650, \sigma = 125[/tex]
Then the proportion of students who scored above 775 is one subtracted by the p-value of Z when X = 775, hence:
Z = (775 - 650)/125
Z = 1.
Z = 1 has a p-value of 0.84.
1 - 0.84 = 0.16, hence the percentage is of:
0.16 x 100% = 16%.
By the Empirical Rule, the middle 95% of scores are within 2 standard deviations of the mean, hence:
650 - 2 x 125 = 400.650 + 2 x 125 = 900.The proportion of students who scored below 525 is the p-value of Z when X = 525, hence:
Z = (525 - 650)/125
Z = -1.
Z = -1 has a p-value of 0.16.
Then the amount out of 1000 students is of:
0.16 x 1000 = 160 students.
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2. A skydiver jumps from a plane from an altitude of 8000 ft. An observer on the ground measures the skydiver’s altitude at time t = 0 to be 7500 ft. The linear graph shows the skydiver’s altitude at various times during her descent.
(a) Identify the y-intercept. How does the y-intercept relate to the skydiver’s position relative to the ground? Explain.
(b) Determine the slope of the line. According to the slope, is the skydiver ascending or descending and what is the rate of ascent or descent? Explain.
(c) Identify the x-intercept. What does the x-intercept mean in this context? Explain.
(d) Write an equation for the line.
Answer:
A function is shown. ƒ (x) = 2x − 9
-
What is the value of ƒ (−4) ?
Answer: To find the value of ƒ (−4), we substitute −4 for x in the function ƒ(x) = 2x − 9:
ƒ(−4) = 2(−4) − 9
Performing the multiplication and addition, we get:
ƒ(−4) = −8 − 9
Thus, the value of ƒ(−4) is equal to −17.
Answer: ƒ (−4) = -17
Step-by-step explanation:
To find the value of ƒ (−4) we will substitute all values of x for -4 in the original function and simplify.
ƒ (−4) = 2x - 9
ƒ (−4) = 2(-4) - 9
ƒ (−4) = -17
A movie theater has a seating capacity of 283. The theater charges $5 for children, $7 for students, and $12 of adults. There are half as many adults as there are children. If the total ticket sales was $2,042, How many children, students, and adults attended?
children attended.
students attended.
adults attended.
Use an open number line to find each difference:
93-36
Answer:
57
Step-by-step explanation: mental math.
3.5.PS-15
Question Help
Reasoning Kareem cannot decide which of two washing machines to buy. The selling price of each is $480. The first is
marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each washing
machine. Use pencil and paper. Explain why Kareem should buy the first washing machine rather than the second if the
machines are the same except for the selling price.
The sale price of the first washing machine is $
(Round to the nearest dollar as needed.)
Answer:
$240the sale price on the first machine is lowerStep-by-step explanation:
Two washing machines are offered at $480, with one marked down 50% and the other marked down 30% and another 20% off. You want to know why the first machine has a better price, and what that price is.
First machineThe price after a 50% markdown is ...
$480 × (1 -50%) = $480 × 0.50 = $240 . . . first machine sale price
Second machineThe price after a 30% markdown is ...
$480 × (1 -30%) = $480 × 0.70
After the additional 20% markdown, the price is ...
($480×0.70) × (1 -20%) = $480 × 0.70 × 0.80
= $480 × 0.56 ≈ $269
Better dealThe first machine is a better deal, because The 50% markdown is off the original price.
The 30% markdown on the second machine is off the original price, but the additional 20% is off the reduced price. Hence the total markdown is not as great as on the first machine.
based on the spss output what cna you concllude about the relationship between degree attainment and age dbrn for men
There is sufficient statistical evidence at 5% level of significance that there is relationship between degree attainment and AGEKDBRN for women.
What is ANOVA model for men?
To ascertain whether there are any statistically significant differences between the means of three or more independent (unrelated) groups, the one-way analysis of variance (ANOVA) is used.
An n-way ANOVA allows a researcher to employ more than two independent variables (with n being the number of independent variables you have). For instance, any disparities in IQ scores can be investigated concurrently by country, gender, age group, ethnicity, etc.
Relationship between degree attainment and AGEKDBRN for women
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a customer lunch cost $9.82 after tax if the customer wants to leave an 18% tip what will the total cost be
Answer:
$11.5876 (please give brainiest)
Step-by-step explanation:
9.82x1.18=11.5876
which statement describes the end behavior of the function ? f(x)= x2-4/x2-9
5. I bought (3) boxes of cereal that were on clearance for 20% off. My total bill was $6. What was. the original price of one box of the cereal?
Answer:
2 dollars 50 cents
Step-by-step explanation:
3 boxes = 6 dollars
1 box = 2 dollars
100 - 20 = 80
2 dollars = 80 percent
50 cents = 20 percent
2 dollars 50 cents = 100 percent
Rewrite sin(x - 5π/4) in terms of sin(x) and cos(x)
SOMEONE PLEASE HELP ME ANSWER THIS QUESTION ASAP
Answer:
593
Step-by-step explanation:
sana makatulong hindi ko sure
Ziva bought 6 ⅘ balls of thread for a sweater, but she only ended up using 8 6/12 balls. What fraction of the thread did Ziva use?
Is this how we solve it?
8 6/12 by - 6 4/5 = A
Hope this helps
i think that's how we are supposed to do the problem can someone do a walk through for me with variables so i can find it on my own i just need help. I was trying to find a tutor cause I'm confused. But is that how were supposed to do it cause tutor.com isn't working.
Most likely we have to simplify and then subtract it? I hope that's how you solve it!
nvm i think i got it
A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (-6, 5) What is the vertex of the function defined as g(x)=f(-x)-2
The vertex of a parabola is the point on the graph where the parabola reaches its highest or lowest point. In the case of a quadratic function, the vertex is always of the form (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
The function g(x) = f(-x) - 2 can be obtained from the function f(x) by replacing all instances of x with -x and then subtracting 2 from the result. This transformation will flip the parabola over the y-axis and shift it down by 2 units.
The vertex of the parabola resulting from the function g(x) will be the point where the parabola reaches its highest or lowest point after this transformation. Since the parabola is flipped over the y-axis and shifted down by 2 units, the vertex of the resulting parabola will have the same x-coordinate as the original vertex (-6) and a y-coordinate that is 2 units lower than the original y-coordinate (5 - 2 = 3).
Therefore, the vertex of the function g(x) = f(-x) - 2 is (-6, 3).
welcome to this website
I hope this helps
Find the equation of the linear function represented by the table below in
slope-intercept form.
X
-2
1
4
7
y
6
-6
-18
-30
Answer:
Step-by-step explanation:
the answer c which is 3,280
Tennis balls with a diameter of 2.6 inches are sold in cans of three.
The can is a cylinder. What is the volume of the space NOT occupied
by the tennis balls? (Assume the tennis balls touch the can on all
sides, top and bottom.) Round to the nearest tenth and show all steps
and reasoning.
How can you tell if a formula represents Length, an Area, or Volume? What do you look for in
the formula?
Explain how you could get a formula for the volume of the
16 cm
solid.
Find the diagonal of the box, AD, using the Pythagorean
Theorem twice - 1. To find BD and 2. To find AD.
AB = 12 in
BC= 18 in
CD = 4 in
Show all steps for findin the diagonal of the box above using the formula instead of the
Pythagorean Theorem twice.
0
9
Diagonal of a box of
dimensions a, b, c
a2 + b2+c2 = d2
The volume of the solid is combined of a cone, cylinder, and hemisphere is
329.7 cubic cm.
What are the formulas for the volume of a cone, cylinder, and half of a sphere?The volume of a cone is (1/3)πr²h.
The volume of a cylinder is πr²h.
The volume of half a sphere or a hemisphere is (1/3)πr³.
The given figure has a volume combined of a cone, cylinder, and hemisphere.
∴ The volume of the solid is = (1/3)π(3)²×5 + π(3)²×(8) + (2/3)π(3)³ cubic cm.
= (47.1 + 226.08 + 56.52) cubic cm.
= 329.7 cubic cm.
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What’s the answer to this question
Answer: 1+1=7
Step-by-step explanation: wheres the question
1/4 + X - 1/3=2/3+3+1/4
Answer: x=4
Step-by-step explanation:
Answer:
Step-by-step explanation:
x = 4
Estimate. Then tell if your estimate is an overestimate or underestimate
The numbers that will be estimated based on the information will be 550 + 298 which gives an estimation of 850. This is an overestimation.
What is an estimation?You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation.
The estimate is erroneous if only factors with even numbers are taken into account. The estimate is understated if only factors are rounded down.
In this case, 550 + 298: 298 is nearly 300 so an estimate is:
= 550+300
= 850
This is an overestimation.
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Complete question
Solve an estimation of your choice. Then tell if your estimate is an overestimate or underestimate
3) A restaurant requires customers to pay a 15% tip for the server. Your family spends
$65 on the meal.
a) How much money do you need to pay the server?
Answer: You would leave $9.75 for the tip.
Step-by-step explanation:
15% of 65 is 9.75, so when you add 15% to 65 you get 74.75. In total you would be paying $74.75 but you would leave a $9.75 tip for the server.
a study found that 15% of teenagers get the recommended 8 to 10 hours of sleep each school night. a guidance counselor at a large high school takes a random sample of 80 students and asks them if they get 8 to 10 hours of sleep each night of the school week. of the 80 students, 15 state they get 8 to 10 hours of sleep each school night. The P-value for the test of the hypotheses, H.;p=0.15 and H.:p#0.15, is 0.35. What is the correct interpretation of this value? 1115% of teenagers get 8 to 10 hours of sleep each school night, there is a 35% probability that the sample proportion would be 0.19 or more different by chance alone, Assuming 15% of teenagers get the recommended 8 to 10 hours of sleep each school night, there is a 35% chance that the sample proportion would be 0.19 by chance alone, If 15% of teenagers get the recommended 8 to 10 hours of sleep each school night, then 35% of the teenagers in this sample got the recommended amount of sleep by chance alone, Assuming 15% of teenagers get the recommended 8 to 10 hours of sleep each school night, there is a 35% chance that the true proportion of teenagers getting the recommended sleep is 0.15 by chance alone,
Previous question
The correct interpretation of the p-value of the hypothesis is given as follows:
If 15% of teenagers get 8 to 10 hours of sleep each school night, there is a 35% probability that the sample proportion would be 0.19 or more different by chance alone.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is of 15%, that is:
H0: p = 0.15.
At the alternative hypothesis, it is tested if the proportion is different of 15%, that is:
H1: p ≠ 0.15.
We have a two-tailed test, as we are testing if the proportion is different of a value, meaning that the p-value gives the probability of the sample proportion differing by 0.15 at least by the proportion that it differed.
The p-value of this test is given as follows:
0.35.
Hence the first option is correct.
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Prob-1A random sample of 21 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.12 mm and sample standard deviation is S = 0.14 mm. Construct a 95% two-sided confidence interval for the mean glass thickness.
For the typical glass thickness of 3.12 mm, the 95% two-sided confidence interval will be (3.067,3.173).
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.
Here,
mean x=3.12 mm
Standard deviation s=0.14 mm
number of sample n=21
two-sided confidence interval,
=x±tₐ÷₂(s/√n)
a=1-0.95
a=0.05
t₀.₀₅,₂₀=1.725
=3.12±1.725*(0.14/√21)
=3.12±1.725*(0.14/4.58)
=3.12±1.725*0.0306
=3.12±0.053
=(3.067,3.173)
The 95% two-sided confidence interval for the mean glass thickness of 3.12 mm will be (3.067,3.173).
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The satellite Space Explorer flies 82800 miles in 18 hours. Find the rate of change.
In linear equation, 4,600 mph is the rate of change.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The satellite Space Explorer flies 82800 miles.
time = 18 hours
= 82800/18
= 4,600 mph.
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Casho is deciding between two different movie streaming sites to subscribe to. Plan A
costs $22 per month plus $2 per movie watched. Plan B costs $13 per month plus $3
per movie watched. Let A represent the monthly cost of Plan A if Casho watches a
per month, and let B represent the monthly cost of Plan B if Casho watches a movies
per month. Write an equation for each situation, in terms of a, and determine the
number of monthly movies watched, x, that would make the two plans have an equal
monthly cost.
For x=9 movies, the costs of A and B are equal and the equation in terms of A is A=22+2x.
What is meant by an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables.
For plan A, cost is $22 and $2 per movie then, for x movies
A=22+2x
For plan B, cost $13 and $3 per movie then, for x movies
B=13+3x
The costs of A and B equal then,
22+2x=13+3x
x=9
For x=9 movies, the costs of A and B are equal and the equation in terns of A is A=22+2x.
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Write each of the following expressions in the form Axmyn, where A is a real number and m and n are integers. 2x^2∙3yx^2
The simplified exponential expression for this problem is given as follows:
6x^4y.
How to simplify the expression?The exponential expression in this problem is defined as follows:
2x² multiplied by 3yx².
The first step to simplify the expression is multiply the numeric coefficients, as follows:
2 x 3 = 6.
Then:
2x² multiplied by 3yx² = 6x²yx².
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
x²x² = x^(2 + 2) = x^4.
Thus the simplified exponential expression is presented as follows:
6x^4y.
As the variable y is elevated to exponent y and not multiplied, while there were two exponential terms with the variable x, which is why it was multiplied.
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In a mixture of concrete, the ratio of sand to cement is 1:4. How many bags of cement are needed to mix with 100 bags of sand?
bags of cement
The ratio of sand to cement is 1:4, which means that for every 4 units of cement, there are 1 unit of sand. If we let x represent the number of bags of cement, then the number of bags of sand is 4x.
We are given that there are 100 bags of sand, so we can set up the equation:
4x = 100
x = 100 / 4
x = 25
Therefore, 25 bags of cement are needed to mix with 100 bags of sand.
Hope this helps
Help me with this question pleaseeee
Answer:
option b .....is answer