Answer:
Test statistic = 1.818
Reject H0
Step-by-step explanation:
H0 : μ = 90
H1 : μ > 90
xbar = 94 ; s = 22 ; n = 100
The test statistic : (xbar - μ) ÷ (s/√(n))
Test statistic = (94 - 90) ÷ (22/√100)
Test statistic = 4 ÷ 2.2
T = 1.818
The critical value :
At α = 0.10
Degree of freedom = n - 1 = 100 - 1 = 99
Tcritical(0.10, 99) = 1.290
Decison region :
Reject H0 if Test statistic > |Tcritical |
1.818 > 1.290
We reject H0
Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72
inches and standard deviation 3.17 inches. Compute the probability that a simple random sample of size n=
10 results in a sample mean greater than 40 inches. That is, compute P(mean >40).
Gestation period The length of human pregnancies is approximately normally distributed with mean u = 266
days and standard deviation o = 16 days.
Tagged
Math
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days
or less?
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days
or less?
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of
the mean?
Know
Learn
Booste
V See
Answer:
0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
Gestation periods:
1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.
2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.
3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.
4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.
Step-by-step explanation:
To solve these questions, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.
This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]
Sample of 10:
This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]
Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
This is 1 subtracted by the p-value of Z when X = 40. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997
1 - 0.8997 = 0.1003
0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.
Gestation periods:
[tex]\mu = 266, \sigma = 16[/tex]
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
This is the p-value of Z when X = 260. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{260 - 266}{16}[/tex]
[tex]Z = -0.375[/tex]
[tex]Z = -0.375[/tex] has a p-value of 0.3539.
0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?
Now [tex]n = 20[/tex], so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]
[tex]Z = -1.68[/tex]
[tex]Z = -1.68[/tex] has a p-value of 0.0465.
0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?
Now [tex]n = 50[/tex], so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]
[tex]Z = -2.65[/tex]
[tex]Z = -2.65[/tex] has a p-value of 0.0040.
0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?
Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.
X = 276
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]
[tex]Z = 2.42[/tex]
[tex]Z = 2.42[/tex] has a p-value of 0.9922.
X = 256
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
0.9922 - 0.0078 = 0.9844
0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.
The table shows the proof of the relationship between the slopes of two perpendicular lines. What is the missing statement in step 2?
Answer:
[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex]
Step-by-step explanation:
Given
The attached proof
Required
Complete the missing piece
In (a), we have:
[tex]\triangle ABC \to \triangle CED[/tex]
This implies that, the following sides are similar:
[tex]AB \to CE[/tex]
[tex]AC \to CD[/tex]
[tex]BC \to ED[/tex]
An equation that compares the triangle can be any of:
[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex]
[tex]\frac{AB}{AC} = \frac{CE}{CD}[/tex]
.....
From the options;
[tex]\frac{AB}{BC} = \frac{CE}{ED}[/tex] is true
Joaquin drew the triangle below.
On a coordinate plane, triangle K L J has points (3, 6), (4, 0) and (negative 5, 0).
Which statement must be true about a figure that is congruent to Joaquin’s triangle?
It has two angles on the x-axis.
It has a side that is 9 units long.
It has a side that lies on the x-axis.
It has an obtuse angle.
Answer:
It has a side that is 9 units long.
Step-by-step explanation:
Answer:
B) It has a side that is 9 units long.
Step-by-step explanation:
Since it does not have two angles on the X-axis, a side that lies on the X-axis, or an obtuse angle the reasonable answer would be B as it is true, and all of the others are false.
How many cups of flour are required to make 9 dozen cookies? ( write your answer as a mixed number) Demonstrate your method of choice
Answer:
45/16
Step-by-step explanation:
[tex]1 \frac{1}{4} = 4[/tex]
[tex]x = 9 [/tex]
[tex]x = 1 \frac{1}{4} \times 9 \div 4[/tex]
[tex]x = \frac{5}{4} \times 9 \div 4[/tex]
[tex]x = \frac{45}{16} [/tex]
What is the sum of the 14th square number and the 3rd square number?
Answer:23
Step-by-step explanation:
HELPPPPPPP PLEASEEEEEEE
Answer:
150 dollars. if I am wrong correct me
Answer:
C and D
Step-by-step explanation:
15 to 30 galons at $9.95 to $21.00
the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25
the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630
there are 2 choices that are between 149.25 and 630, C, and D
Translate the sentence into an inequality. The product of w and 2 is less than 23.
Answer:
2w<23
Step-by-step explanation:
The product of w and 2 mean that w multiplied by 2
The graph below is the graph of a function.
10
- 10
10
- 10
True
B. False
Answer:
hgfyjtdjtrxgfyfguktfkgh
Step-by-step explanation:
hgfytrdutrc
Read the following scenario, and then answer the question.
Juan assumes that the temperature of the hot tea cooling on his desk can be modeled with an exponential function like this one: T(t)=179(0.92)t. He bases his assumption on the following: The tea cools about 8% every minute. The tea's current temperature is around 179 degrees Fahrenheit.
Which explanation correctly addresses Juan's assumption?
He is incorrect. The tea will cool linearly since it cools at the same number of degrees every minute.
He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.
He is incorrect. The tea will cool along the curve of a parabola since it cools at an increasing percentage rate every minute.
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Answer:
(b) He is correct. The tea will cool exponentially since it cools at a percentage rate every minute.
Step-by-step explanation:
Newton's Law of Cooling says the change in temperature is proportional to the temperature. This relation gives rise to an exponential function describing the temperature.
In this description, the temperature referred to is the difference between the temperature of the object and the temperature of the environment to/from which heat is being transferred.
Juan is only partially correct. The function is exponential, but the temperature that should be used in his equation is not the temperature of the tea, but the temperature difference between the tea and his desk.
__
The curve is not linear and not parabolic, excluding the other answer choices.
What is the probability that this spinner will stop on blue or white when it is spun?
1/4 is white
1/4 is purple
1/4 is blue
1/4 is black
Answer:
1/2 or 50-50
Step-by-step explanation:
1/4 +1/4 = 1/2 or 50-50
Which of the following is a polynomial?
Answer:
(D.) 3x^2 + 6x
Step-by-step explanation:
the other options aren't complete and some don't even create a parabola.
Triangle A'B'C' is formed using the translation (x + 2 y + 0) and the dilation by a scale factor of 1/2 from the origin. Which equation explains the relationship between
AB and A"B"?
Answer:
[tex]A"B" = \frac{AB}{2}[/tex]
Step-by-step explanation:
Given
[tex]k = \frac{1}{2}[/tex] --- scale factor
Required
Relationship between AB and A"B"
[tex]k = \frac{1}{2}[/tex] implies that the sides of A"B"C" are smaller than ABC
i.e.
[tex]A"B" = k * AB[/tex]
[tex]A"B" = \frac{1}{2} * AB[/tex]
This gives:
[tex]A"B" = \frac{AB}{2}[/tex]
Find the slope of every line that is parallel to the line on the graph ob Enter the correct answer. 6 4 OOO DONE Clear al N ? (-8,0) 10-12 pop -6 ko 8 ४ 2 2 8 do
Step-by-step explanation:
x=-6 y= 0
x0 y= -1
y=mx+b
b= -1
0= -6m -1
-6m= 1
m= -1/6
parallel lines have the same slope
slope = -1/6
solve the system of equations using substitution or graphing.
Step-by-step explanation:
I think substitution would be the easiest since you already have one of the variables solved for.
[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]
(You can just set the equations equal to each other since they both equal y).
Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)
[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]
So, your final points are:
(4,5) and (-1,0)
Answer: A
Step-by-step explanation:
We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.
-x²+4x+5=x+1 [subtract both sides by x]
-x²+3x+5=1 [subtract both sides by 1]
-x²+3x+4=0
Now that we have the equation above, we can factor it to find the roots.
-x²+3x+4=0 [factor out -1]
-1(x²-3x-4)=0 [factor x²-3x-4]
-1(x+1)(x-4)=0
This tells us that x=-1 and x=4.
We can narrow down our answer to A, but let's plug in those values to be sure it is correct.
-(-1)²+4(-1)+5=(-1)+1 [exponent]
-1+4(-1)+5=-1+1 [multiply]
-1-4+5=-1+1 [add and subtract from left to right]
0=0
-------------------------------------------------------------------------------------------
-(4)²+4(4)+5=(4)+1 [exponent]
-16+4(4)+5=4+1 [multiply]
-16+16+5=4+1 [add and subtract from left to right]
5=5
Therefore, we can conclude that A is the correct answer.
The measure of each interior angle of reglar convex polygon is 150 How many sides it does have
Step-by-step explanation:
Since an interior angle is 150 degrees, its adjacent exterior angle is 30 degrees. Exterior angles of any polygon always add up to 360 degrees. With the polygon being regular, we can just divide 360 by 30 to get 12 sides.
Celia was a contestant on Jeopardy. At the
beginning of the round her score was -40.
Celia's score at the end of the round was -
35. How many points did Celia score (or
lose) during the round?
Answer:
75
Step-by-step explanation:
She is in the negatives right now so add 40 to get Celicia points equal to 0. Then add an extra 35 points (which is what she ended with). Overall, she gained 75 points to end with 35.
solve the system of equation — 3х + бу = 9
5х + 7y = -49
Answer:
y = 64/3
x = -119/3
Step-by-step explanation:
3х + 6у = 9 => 5*3x+5*6у = 9*5 => 15x+30у=45 (1)
5х + 7y = -49 => 3*5x + 3*7y = -49*3 => 15x+21y=-147 (2)
(1)-(2) => 9y = 192 => y = 64/3
x = -119/3
HELP ASAP?
the two answers not showing on screen are
C:y<6x-3
D:y<6-3
Answer:
A is that answer
A) y<2x-3
Using the following image, solve for x
Answer:
x= -3
Step-by-step explanation:
2x+14= 8
2x= -6
x = -3
Answer:
-3
Step-by-step explanation:
According to the question,
[tex]\longrightarrow[/tex] CE = CD + DE
[tex]\longrightarrow[/tex] 8 = (x + 10) + (x + 4)
[tex]\longrightarrow[/tex] 8 = x + 10 + x + 4
[tex]\longrightarrow[/tex] 8 = 2x + 14
[tex]\longrightarrow[/tex] 8 ― 14 = 2x
[tex]\longrightarrow[/tex] ―6 = 2x
[tex]\longrightarrow[/tex] ―6 ÷ 2 = x
[tex]\longrightarrow[/tex] –3 = x
Therefore, the value of x is ― 3.
What is the range of the table of values
Answer:
Range: { 0,3,5,7,9}
Step-by-step explanation:
The range is the values that y takes
Range: { 0,3,5,7,9}
Now we have to find,
The range of the table of values,
→ Range = ?
Then the range will be the numbers that is in the Y column.
→ Range = ?
→ Range = (value that Y takes)
→ Range = 0,3,5,7,9
Therefore, the range is 0,3,5,7,9.
An important factor in selling a residential property is the number of times real estate agents show a home. A sample of 15 homes recently sold in the Buffalo, New York, area revealed the mean number of times a home was shown was 24 and the standard deviation of the sample was 5 people.
a. What is the margin of error for a 98% confidence interval? (Round your answer to 3 decimal places.)
b. What is the 98% confidence interval for the population mean? (Use Student's t Distribution Table.) (Round your answers to 2 decimal places.)
Answer:
a) The margin of error for a 98% confidence interval is of 3.388 people.
b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the hypergeometric distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.
Question b:
The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people
The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.
The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
Can someone help me out here? Not sure how to solve this problem or where to start either?
Answer:
19.3 miles per gallon
Step-by-step explanation:
First, subtract 54,042.8-53,737.7. The answer is 305.1
Then, find the unit rate. 305.1/15.8
You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.
That's your answer!
Help me find the domain and range please!
Answer:
Domain: (-∞, 1]
Range: (-∞, 3]
Step-by-step explanation:
The function starts at point (1, 3) and goes to the left and down forever.
Domain: (-∞, 1]
Range: (-∞, 3]
Answer:
Domain: [tex](-\infty, 1][/tex]
Range: [tex](-\infty, 3][/tex]
Step-by-step explanation:
The domain of a function represents the range of x-values that are part of the function, read left to right. We can see that the function goes forever to the left and stops at [tex]x=1[/tex] when we read left to right. Therefore, the domain of this function is [tex]\boxed{(-\infty, 1]}[/tex].
The point at [tex]x=1[/tex] is a filled-in solid dot so it is included as part of the function. Use square brackets to denote inclusive.
The range of a function represents all y-values that are part of the function, read bottom to top. The function continues down forever and stops at [tex]y=3[/tex] when read bottom to top. Therefore, the range of this function is [tex]\boxed{(-\infty, 3]}[/tex]. Similar to the domain, we use a square bracket on the right to indicate that [tex]y=3[/tex] is included in the function. If the dot was not filled-in, then we would use a parenthesis to indicate that [tex]y=3[/tex] would not be part of the function.
Please help. I'm stuck on this problem
Answer:
Step-by-step explanation:
[tex]h(t)=-16t^2+96t\\\\h(t)=-t(16t-96)[/tex]
[tex]96=2^5*3\\\\16=2^4\\\\h(t)=-t(2^5*3*t-2^4)=-2^4t(2^1*3*t-1)\\\\h(t)=-16t(6t-1)[/tex]
the b) part is easy do it!
Wrap your foot by plastic cover. B. Directions: Read the sentences carefully. Write TRUE if the statement is True and FALSE if not. 16. Rain and dull clouds, windy blue skies, cold snow, and sticky heat are very different conditions, yet they are all weather. 17. A weather instrument is any type of measurement device that gives information about the weather. 18. Weather is the mix of events that happen each day in our atmosphere. 19. Weather is different in different parts of the world and changes over minutes, hours, days and weeks. 20. The four letters EW, SW, NE, SN represent the four directions: East West, South West, North East, and South North.
Answer:
16. false
17. True
18. True
19. True
20. false
Step-by-step explanation:
16. all terms are expressions of weather - except for cold snow. "snowfall" would be the weather condition. "snow" itself is the accumulated mass of snowflakes on the ground.
17. that is simply true. there is nothing really to explain.
18. the same as 17. that is the definition of weather.
19. yes, that is part of the explanation of the difference between weather and climate.
20. South North is NOT a direction. it kind of contradicts itself. and what is between South and North ? East and West. so, even from that perspective it is not clear.
overall, what kind of math question is that ? that is more for geography, Earth science, or meteorology or something like this.
A roll of carpet that contains 250 yd of carpet will cover how many rooms if each room requires 7 3/4 yards of carpet?
Answer: 32 room
Step-by-step explanation:
[tex]7\frac{3}{4} =\frac{4(7)+3}{4} =\frac{28+3}{4} =\frac{31}{4}=7.75[/tex]
If 1 room = 7.75 yd of carpet ⇒ x rooms = 250 yd of carpet
Use proportions & cross-multiply to solve:
[tex]\frac{1}{7.75} =\frac{x}{250}\\7.75x=250\\x=\frac{250}{7.75} =32.258[/tex]
So 250 yd of carpet can cover about 32 rooms.
Which could be the function graphed below?
[tex]f(x)=\sqrt{x} -2[/tex] is the correct option
Explain the steps to find x- and y- intercepts of an equation of the form Ax + By = C
Step-by-step explanation:
For an equation of form Ax + By = C, we are given A, B, and C.
The x intercept is when the line/equation is on the x axis, or when y=0.
Therefore, if we plug y=0 into the equation Ax+By=C, and anything multiplied by 0 is equal to 0, we can say that
Ax + 0 = C
Ax = C
divide both sides by A
x = C/A
Therefore, the x intercept is equal to C/A
Similarly, for the y intercept, or when the line is on the y axis (or when x=0), we have
A*0 + By = C
By = C
divide both sides by B
y= C/B at the y intercept
Which function represents the graph below?
Answer:
The answer is the third one below
someone please help!!<3
Question 4 of 10
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f - g)(x).
A. 3 - 3x
B. 7x-3
O C. 7x-1
D. 3x - 3
Answer:
the answer is c
Step-by-step explanation:
the answer is c
