Step-by-step explanation:
1.
the expected sample mean is always the general mean : 168.5 pounds.
2.
the SD of a sample is the general SD / sqrt(sample size).
in our case
the sample SD = 68/sqrt(150) = 5.55217675...
3.
if we are looking for only the probability that any single woman is below 160 pounds, we would use the normal z calculation :
z = (x - mean)/SD = (160 - 168.5)/68 = -8.5/68
but we have here the question about the probability of the mean value of a whole sample of 150 women.
so, we need to adapt the z-calculation by the principle of 2) for the SD of a sample :
z = (x - mean)/(SD × sqrt(sample size)) =
= (160 - 168.5)/(68 × sqrt(150)) = -8.5/(68×sqrt(150)) =
= -0.010206207 ≈ -0.01
that gives us in the z-table the p-value 0.49601
this 0.49601 is the probability that a sample of 150 women has a mean value of below 160 pounds.
4.
similar to 3.
the z value we are looking for
z = (175 - 168.5)/(68 × sqrt(150)) = 6.5/(68 × sqrt(150)) =
= 0.007804747... ≈ 0.01
that gives us the p-value 0.50399.
that would be the probability of a sample mean of 175 or below.
to get above 175 we need to get the other side of the bell-curve :
1 - 0.50399 = 0.49601
so, this case has about the same probability as 3.
5.
as 3), just with the sqrt(200) instead of the sqrt(150).
z = -8.5/(68 × sqrt(200)) = -0.008838835... ≈ 0.01
so, the probability is still about the same as in 3) :
0.49601
6.
as 4) just with sqrt(200).
z = 6.5/(68 × sqrt(200)) = 0.006759109... ≈ 0.01
so, the probability is still about the same as for 4) :
0.49601
The answers are :
1) The expected mean for a sample of 150 women is 168.5 pounds.
2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.
3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.
4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.
5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.
6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.
What is probability ?
Probability is a measure of the likelihood of event to occur. The probability of all the events in a sample space adds up to 1.
1)
We know that the expected mean of a sample is always equal to general mean.
As per the question, mean weight is 168.5 pounds.
This implies :
The expected mean for a sample of 150 women is :
= 168.5 pounds
2)
The standard deviation (SD) of the mean for a sample of 150 women is :
= 68 / (√150)
= 5.55
3)
The probability of 150 women having a sample mean below 160 pounds will be represented by z and will be :
z = ( x - mean) / ( SD × (√sample size))
= (160 - 168.5) / (68 × √150)
= 0.01
If we use the z table then the probability will be :
= 0.49601
4)
Similarly as part 3 :
z = (175 - 168.5) / (68 × √150)
z = 0.01 (approximately)
The probability of 150 women having a sample mean below 175 pounds will be :
= 0.50399
And the probability of 150 women having a sample mean above 175 pounds will be :
= 1 - 0.50399
= 0.49601
5)
Here , we have to find probability of 200 women , so 150 in formula of z in 3rd part will be replaced by 200.
i.e.,
z = (160 - 168.5) / (68 × √200)
z = 0.01 ( approximately)
and probability will be :
= 0.49601
6)
Here , we have to find probability of 200 women , so 150 in formula of z in 4th part will be replaced by 200.
z = (175 - 168.5) / (68 × √200)
z = 0.01
And probability equal to :
= 0.49601
Therefore , the answers are :
1) The expected mean for a sample of 150 women is 168.5 pounds.
2) The standard deviation (SD) of the mean for a sample of 150 women is 5.55.
3) The probability of 150 women having a sample mean below 160 pounds will be 0.49601.
4) The probability of 150 women having a sample mean above 175 pounds will be 0.49601.
5) The probability of 200 women having a sample mean below 160 pounds will be 0.49601.
6) The probability of 200 women having a sample mean above 175 pounds will be 0.49601.
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(3x) (4x) =
A. – x
B. 7x
C. 12x
D. 12x²
E. none of these
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textbf{Equation: }[/tex]
[tex]\large\textsf{(3x)(4x)}[/tex]
[tex]\large\textbf{Solving:}[/tex]
[tex]\large\textsf{(3x)(4x)}[/tex]
[tex]\large\textsf{= 3x} * \large\textsf{4x}[/tex]
[tex]\large\textbf{Combine the like terms:}[/tex]
[tex]\large\textsf{(3x * 4x)}[/tex]
[tex]\large\textsf{= 3x * 4x}[/tex]
[tex]\large\textsf{= 12x}^2[/tex]
[tex]\large\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{Option\ D. 12\mathsf{x}^2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
ILL GIVE BRAINLIEST
4. Multiply the following signed numbers:
a. (-42x)(+2x) =
b. (+8x)(-4x)(-3x) =
c. (+7)(-4)(-4) =
d. (+10)(-2)(-2)(+4) =
Explanation:(x)(x)=x^2 and(x)(x)(x)=x^3
Fatima purchased a new mattress when it was on sale. The sale price was 20% less than the regular price. If the sale price was $358, what was the original price? (Round your answer to the nearest dollar).
well, the regular price is really "x", which oddly enough is 100%, but we also know that $358 is really the discounted price by 20%, namely 100% - 20% = 80%, so we know that 358 is really just 80% of "x", so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 358& 80 \end{array} \implies \cfrac{x}{358}~~=~~\cfrac{100}{80} \\\\\\ \cfrac{x}{358}=\cfrac{5}{4}\implies 4x=1790\implies x=\cfrac{1790}{4}\implies x\approx 448[/tex]
divide 360 in the ratio 1:7
Answer:
45:315
Step-by-step explanation:
Add up the ratio to get the total ratio.
1+7=8
Divide the 360 by the total ratio.
360÷8=45
The number 45 tells you how many times to multiply both sets of the ratio to get a total of 360.
1×45=45
7×45=315
so,
45:315
Hope this helped. Comment below if you need more assistance! :)
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat?
Answer:
40 apples
Step-by-step explanation:
x = (4·2)/(1/5) = 8/(1/5) = (8/1):(1/5) = (8/1)·(5/1) = 40/1 = 40 apples
It takes 10 apples to make a gram of fat. Multiply the 10 apples by 4 grams of fat to find that it takes 40 apples to make 4 grams of fat.
Find the missing segment in the image below
Answer:
42
Step-by-step explanation:
similar triangles
24/x = (24+8)/x+14
that looks complicated so we do
8/24 = 14/x
or
24/8 = x/14
3 = x/14
x = 3*14
x = 42
we test it with the first equation
24/42 = 32/56
simplify
4/7 = 4/7
true so 42 is correct
You have moved into a new house and your friends have come over to help paint the walls. Everyone paints at the same rate of 1.5 hours/wall.
QUESTION: If there are six people painting on Saturday, how many walls could you get painted in 3 hours?
walls
Answer:
12 walls
Step-by-step explanation:
Let's take everyone paints a different wall and there are no overlaps.
Given information from the question:
1.5 hours = 1 wall
1 hour =
[tex] \frac{1}{1.5} \\ = \frac{2}{3} walls[/tex]
per person.
From the information above, we can deduce:
6 people =
[tex] \frac{2}{3} \times 6 \\ = \frac{12}{3} \\ = 4 \: walls[/tex]
Since we know 6 people can paint 4 walls in an hour,
3 hours =
[tex]3 \times 4 \\ = 12 \: walls[/tex]
A one to one function is given. Write an equation for the inverse function
M(x)=4x^3-3
Step-by-step explanation:
M(x) = 4x^3 - 3
let M(x) = Y
Y = 4x^3 - 3...swap places of x & y.
X = 4y^3 - 3
look for x in terms of y.
4y^3 = x + 3
Y^3 = x + 3 / 4...put both sides under cube root.
y = ( x + 3 / 4 )^1/3
What’s the slope of the following graph?
A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 4x. The container must contain 8cm3. The top and the bottom will cost $3.90 per square centimeter, while the four sides will cost $4.90 per square centimeter.
What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.
The most efficient measurements of the box should be 4cm long, 1cm wide and 2cm high so that its cost is $129.2
How to calculate the measures of the rectangular box?To calculate the measurements of the rectangular box we must take into account the following condition:
Bottom and top measure x by 4x.According to the above, we can establish that the most appropriate measurement for the bottom and top should be 1cm (width) × 4cm (length). Additionally we can establish that the height of the box would be 2cm.
How to find the volume of this box?To find the volume of the box we must use the following formula:
height × width × length = volume.2cm × 1cm × 4cm = 8cm³What are the areas of this box?The areas of this box are:
Bottom and top: 1cm × 4cm = 4cm²Sides: 1cm × 2cm = 2cm²Front and rear: 2cm × 4cm² = 8cm²What is the price of this box?The total price of this box is as follows:
Top and bottom:
4cm² × $3.90 = $15.6$15.6 × 2 = $31.2Sides:
2cm² × $4.90 = $9.80$9.80 × 2 = $19.68cm² × $4.90 = $39.2$39.2 × 2 = $78.4$78.4 + $19.6 + $31.2 = $129.2Learn more about boxes in: https://brainly.com/question/23952628
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What is the behavior of the graph y=−x6−6x5+50x3+45x2−108x−108 at each of its zeros
The behavior of the graph with the equation y=x66x5+50x3+45x2108x108 at each of its zeros will be as follows: two of them will resemble a quadratic function, while one of them will resemble a linear function.
This is further explained below.
What is a graph?Generally, a diagram that illustrates the relationship between variable quantities, usually consisting of two variables, with each variable being measured along one of a pair of axes that are intersected at right angles.
In conclusion, At each of its zeroes, the graph y=x66x5+50x3+45x2108x108 will exhibit one linear behavior and two behaviors that resemble quadratic functions.
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I need help! DUE IN 2 HOURS WILL MARK BRAINLIEST!!!
The exponential model for the data is: [tex]y = 693(1.5)^x[/tex]
When the cost is of $6000, the weight is of approximately 5.3 carats.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.From the table, the rate of change is given by:
b = 4980/3210 = 3210/2140 = 2140/1430 = 1.5.
When x = 1, y = 1040, hence the initial value is found as follows:
1.5a = 1040.
a = 1040/1.5
a = 693.
So the model is:
[tex]y = 693(1.5)^x[/tex]
When the cost is of $6000, the weight is found as follows:
[tex]693(1.5)^x = 6000[/tex]
[tex](1.5)^x = \frac{6000}{693}[/tex]
[tex]1.5^x = 8.658[/tex]
[tex]\log{1.5^x} = \log{8.658}[/tex]
x log(1.5) = log(8.658)
x = log(8.658)/log(1.5)
x = 5.3
When the cost is of $6000, the weight is of approximately 5.3 carats.
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Identify the discrete data.
A. the length of a caterpillar during a week
B. the number of dogs you take for a walk each day
C. the wind speed during a particular day
D. the temperature of the water in the local river during the day
Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting.
Therefore, the correct answer is option B. the number of dogs you take for a walk each day.
What is discrete data?Discrete data exists as a numerical kind of data that contains total, concrete numbers with clear and fixed data values specified by counting. Discrete data exists a count that involves integers only a limited number of values exists possible. This kind of data cannot be subdivided into distinct parts. Discrete data contains discrete variables that exist in finite, numeric, countable, and non-negative integers.
Therefore, the correct answer is option B. the number of dogs you take for a walk each day.
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The Bureau of Alcohol, Tobacco, and Firearms (BATF) has been concerned about lead levels in California wines. In a previous testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. How many wine specimens should be tested if the BATF wishes to estimate the true mean lead level for California wines to within 10 parts per billion with 95% confidence? (Round your answer up to the nearest whole number.)
The number of specimens should be tested is 1352.
According to the statement
we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.
so,
Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.
For an uniform distribution of bounds a and b, the standard deviation is given by:
σ = [tex]\sqrt{\frac{(b-a^{2})}{12} }[/tex]
and put the values a= 50 and b= 700 then the
standard deviation is 187.64
And here the critical value become 1.6 then
We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.
Then n is 1352.
So, The number of specimens should be tested is 1352.
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Juan and Ari went to the farmers market to buy fruit. Juan’s bag of apples that he bought weighed StartFraction 31 over 7 EndFraction pounds. Ari’s bag of oranges that he bought weighed StartFraction 19 over 3 EndFraction pounds. Using compatible fractions, estimate how much heavier Ari’s bag is compared to Juan’s bag.
Answer:
approximately 2 lb
Step-by-step explanation:
Juan: 31/7
Ari: 19/3
Juan's fraction is close to 32/8 = 4
Ari's fraction is close to 18/3 = 6
6 - 4 = 2
Answer: approximately 2 lb
A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g. How many of each weight is needed?
Answer:
See below
Step-by-step explanation:
237/50 = 4 R 37
37/20 = 1 R 17
17 / 10 = 1 R 7
7 / 1 = 7 R 0
4 50gm's 1 20gm 1 10gm and 7 1g wts
The required number of weights used in chemical balance to weigh 237g is 4,1,1,7 respectively.
What is mathematical expression?
A mathematical expression expression in mathematical is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Here, it is given that :
A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g.
Now, let us find the number of weights for each weight type :
For 50g weight the maximum number of weights needed will be 4 that is :
50g x 4 = 200g
Now, for 20g weight the maximum number of weights needed will be 1 that is :
20g x 1 = 20g
Now, for 10g weight the maximum number of weights needed will be 1 that is :
10g x 1 = 10g
Now, for 1g weight the maximum number of weights needed will be 7 that is :
1g x 7 = 7g
Adding all the weights we get :
200g + 20g + 10g + 7g = 237g;
which is the required weight and the number of weights used is 4,1,1,7 respectively.
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Find the measure of angles a and b
Find the standard form of the equation whose graph is the line through (1, -2) and (-5, 6).
The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.
According to the question,
The standard form of the equation whose graph is the line through (1, -2) and (-5, 6). Now first to find slope of the equation using below formula,
Slope of the equation (m)= (change in y axis) / (change in x axis)
= (6- (-2))/(-5 - 1)
= 8/-6
=-(4/3)
Slope of the equation (m) = -4/3. whose graph is the line through (1, -2) and (-5, 6).Formula to find Standard form of the equation is y = mx + c.
-2 = -(4/3) 1 + c
c = -2 +(4/3)
c = -2/3
The standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2. y = -(4/3)x -(2/3).
⇒ 3y = -4x -2.
Hence, the standard form of the equation whose graph is the line through (1, -2) and (-5, 6) is 3y = -4x -2.
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what is a1 of the arithmetic sequence for which a3=126 and a64= 3,725
If the third term of the aritmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
Given the third term of the aritmetic sequence is 126 and sixty fourth term is 3725.
We are required to find the first term of the arithmetic sequence.
Arithmetic sequence is a series in which all the terms have equal difference.
Nth term of an AP=a+(n-1)d
[tex]A_{3}[/tex]=a+(3-1)d
126=a+2d--------1
[tex]A_{64}[/tex]=a+(64-1)d
3725=a+63d------2
Subtract second equation from first equation.
a+2d-a-63d=126-3725
-61d=-3599
d=59
Put the value of d in 1 to get the value of a.
a+2d=126
a+2*59=126
a+118=126
a=126-118
a=8
[tex]A_{1}[/tex]=a+(1-1)d
=8+0*59
=8
Hence if the third term of the arithmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
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Please please answer
Answer:
thanks for your support of the personal information on the direction of economics class
A binomial experiment is given. Decide whether you can use the normal distribution to approximate the binomial distribution. If you can, find the mean and standard
deviation. If you cannot, explain why.
A survey of adults found that 66% have used a multivitamin in the past 12 months. You randomly select 40 adults and ask them if they have used a multivitamin in the
past 12 months.
Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
OA. No, because np < 5.
B. No, because nq <5.
OC. Yes, the mean is_______
(Round to two decimal places as needed.)
and the standard deviation is _____
Yes, the mean is 26.4 and the standard deviation is 3
How to find the mean in binomial experiment?We are given;
n = 40, p = 66% = 0.66, and q = 1 – 0.66 = 0.34
If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;
Mean; µ = np
Standard deviation; σ = √npq
where;
n is the sample size.
p is the population proportion.
q = 1 – p.
Calculating np and nq gives;
np = (40)(0.66) = 26.4
nq = (40)(0.34) = 13.6
Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.
Thus, µ = np
µ = 40(0.66) = 26.4
Standard deviation;
σ = √(40 * 0.66 * 0.34)
σ = 3
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A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 92.5% for the medical students admitted through special programs. Round your answers to 4 decimal places. If 12 of the students from the special programs are randomly selected, find the probability that at least 11 of them graduated.
The probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.
Given that graduation rate is 95.2%.
We are required to find the probability that out of 12 selected candidates atleast 11 should be graduated.
Probability is basically the chance of happening an event among all the events possible. It cannot be negative. It lies between 0 and 1.
Probability=Number of items/ Total items.
Probability that atleast 11 will be graduated out of 12 selected candidates is as under:
It will be a binomial distribution.
So,
P(X>=11)=[tex]12C_{11}(0.925)^{11} (0.075)^{1} +12C_{12}(0.925)^{12} (0.075)^{0}[/tex]
=12*0.4241*0.075+1*0.3923
=0.3816+0.3923
=0.7739
Hence the probability that at least 11 of them graduated is 0.7739 if graduation rate is 92.5%.
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Find equations of the following. y = x^2 − z^2, (6, 32, 2) (a) the tangent plane (b) the normal line
The equation for the tangent plane is 12x - y + 4z - 56 = 0 and the equation for normal line is (x - 6)/12 = (32 - y) = (z - 2)/4
Finding the Equations for Tangent Plane and Normal Line:
The given function is,
f(x, y, z) = x² - y - z² = 0
∂f/ ∂x = 2x
∂f/ ∂y = -1
∂f/ ∂z = 2z
At given point (6, 32, 2),
∂f/ ∂x = 12
∂f/ ∂y = -1
∂f/ ∂z = 4
(a) The equation of tangent plane is given as follows,
(∂f/ ∂x)(x-x₁) + (∂f/ ∂y)(y-y₁) + (∂f/ ∂z)(z-z₁) = 0
12(x - 6) - 1(y - 32) + 4(z - 4) = 0
12x - 72 - y + 32 + 4z - 16 = 0
The required tangent plane is,
12x - y + 4z - 56 = 0
(b) The equation for normal line is given as,
(x-x₁) / (∂f/ ∂x) = (y-y₁) / (y-y₁) = (z-z₁) / (∂f/ ∂z)
(x - 6)/12 = (y - 32)/(-1) = (z - 2)/4
Thus, the required equation of normal line is,
(x - 6)/12 = (32 - y) = (z - 2)/4
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how many decimal places does 22.22105 have
Answer:
5
Step-by-step explanation:
where there is the decimal point,you count the numbers after the decimal point
Absolute value of sqrt(5) - 2.2
0.03607
Step-by-step explanation:Absolute value is the distance of a number from zero. Since distance is always positive, the absolute value is the same number but positive.
Please note, for this problem I have rounded to 5 decimal points because the answer is irrational.
Subtracting
There are 2 different ways to approach this problem. You can either estimate the square root of 5 or plug this question straight into a calculator.
First, we can estimate [tex]\sqrt{5}[/tex] and round to 5 decimal places.
[tex]\sqrt{5}[/tex] ≈ 2.23607Then, take this value and subtract.
2.23607 - 2.2 = 0.03607Absolute Value
Now that we have solved the subtraction problem we have to find the absolute value. As stated above, the easiest way to find absolute value is to simply make the number positive. Since the answer is already positive, this is the final answer.
|0.03607| = 0.03607Number lineWhich of these numbers represents the difference between -3 and -2
The number which represents the difference between the numbers given -3 and -2 as in the task content is; 1.
Which number represents the difference between -3 and -2 in the task content?It follows from the task content that the difference between the given numbers -3 and -2 is to be determined by means of the number line.
On this note, since, it follows that the difference between two numbers in the number line is given by the absolute value of their arithmetic difference.
It follows that the number which is required in this scenario is; |-3-(-2)| = |-1| = 1.
This follows from the fact that the absolute value big any number is that number with a positive polarity.
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Help me asappp w this question
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
The straight angles are angles that form a straight line, and their measure = 180°
In the given figure, the Straight angles is :
GEB[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct choice is D√2n +6=6
n =
Answer?
Answer:
your question is not correct i can not find the answer
Find a formula for the nth term
of the arithmetic sequence.
First term 9
Common difference -2
Answer:
arithmetic sequence formula: first term + (n - 1)common difference
9 + (n - 1)-2
9 + -2n + 2
= -2n + 11
What number should come next in the sequence? 0.8, 0.35, -0.1, -0.55, ... FASTTTTT
Answer:
-1
Step-by-step explanation:
0.35 - 0.8 = -0.45
-0.1 - 0.35 = -0.45
-0.55 - 0.45 = -1