We have been given that the typical amount of sleep per night that adults get has a bell-shaped distribution with a mean of 7.5 hours and a standard deviation of 1.3 hours. Suppose last night you slept for 5 hours.
We will use z-score formula to solve our given problem as z-score tells a data point is how many standard deviation from the mean.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in z-score formula, we will get:
[tex]z=\frac{5-7.5}{1.3}[/tex]
[tex]z=\frac{-2.5}{1.3}[/tex]
[tex]z=-1.923076923[/tex]
Upon rounding to two decimal places, we will get:
[tex]z\approx -1.92[/tex]
Therefore, you are [tex]-1.92[/tex] standard deviations from the mean or 1.92 standard deviation below mean.
Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 19 specimens of a particular species, 6 resprouted after fire. Estimate with 96% confidence the proportion of all shrubs of this species that will resprout after fire. Interval: .1884 to
The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.
Here, we have,
To estimate the proportion of all shrubs of this species that will resprout after fire with 96% confidence, we will use the formula for a confidence interval for a proportion.
The formula for the confidence interval for a proportion (p) is given by:
CI = p ± Z * √(p * (1 - p) / n)
where:
CI is the confidence interval
p is the sample proportion (resprouted specimens / total specimens)
Z is the critical Z-score corresponding to the desired confidence level (96% confidence level corresponds to a Z-score of approximately 1.750)
n is the sample size (total number of specimens)
Given information:
Total number of specimens (n) = 19
Number of specimens that resprouted after fire = 6
Now, calculate the sample proportion (p):
p = (number of specimens that resprouted) / (total number of specimens)
p = 6 / 19 ≈ 0.3158 (rounded to four decimal places)
Now, calculate the critical Z-score for a 96% confidence level (use a Z-table or calculator):
Z ≈ 1.750
Now, calculate the margin of error (E):
E = Z * √(p * (1 - p) / n)
E = 1.750 * √(0.3158 * (1 - 0.3158) / 19)
E ≈ 0.1884 (rounded to four decimal places)
Finally, calculate the confidence interval:
CI = p ± E
CI = 0.3158 ± 0.1884
The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.
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jared buts 2.4 pounds of broccoli for $3.24 which equation could jared use to find c, the cost of each pound of broccoli
Answer:
2.4c = 3.24
Step-by-step explanation:
Answer:
it is 4 ounces + 18 ounces
Determine the value of x for the triangle. show work.
Answer:
x=5
Step-by-step explanation:
x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.
Answer:
5
Step-by-step explanation:
Because this is a right triangle, you know that by the Pythagorean theorem:[tex]\sqrt{(x+7)^2+x^2}=x+8[/tex]
Squaring both sides to get rid of the square root:
[tex](x+7)^2+x^2=(x+8)^2[/tex]
Expanding all of the parentheses:
[tex]x^2+14x+49+x^2=x^2+16x+64[/tex]
Combine like terms:
[tex]x^2-2x-15=0[/tex]
Factor:
[tex](x-5)(x+3)=0[/tex]
Since x cannot be negative, it is equal to 5. Hope this helps!
what is the equation to the following sentence?
Seven subtracted from two times a number is 13
Answer:
4x-7>13
add 7
4x>20
divide by 4
x>5
Step-by-step explanation:
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a-1) Find the test statistic. (Round your answer to 4 decimal places.) The test statistic (a-2) At the .01 level of significance, is the true mean greater than 10
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≤ 10
For the alternative hypothesis,
µ > 10
The inequality sign indicates that It is a right tailed.
Since the population standard deviation is not given, the distribution is a student's t.
Since n = 35,
Degrees of freedom, df = n - 1 = 35 - 1 = 34
t = (x - µ)/(s/√n)
Where
x = sample mean = 14.44
µ = population mean = 10
s = samples standard deviation = 4.45
t = (14.44 - 10)/(4.45/√35) = 5.9
We would determine the p value using the t test calculator. It becomes
p < 0.00001
Since alpha, 0.01 > than the p value, then we would reject the null hypothesis. Therefore, At a 1% level of significance, we can conclude that the true mean is greater than 10.
The plans for a home renovation include a new window. The homeowner picked a window shaped like the one shown. Identify the polygon and classify it as regular or irregular.
Answer:
Octagon regular.
Step-by-step explanation:
This shape has 8 sides to it is an octagon. A octagon irregular doesn't have equal sides while this one does. The best way to tell is if it looks like a stop sign which are octagon regular.
Lacy enjoys running around the lake, and Paul enjoys running around the park. Lacy contends that she runs
farther around the lake than Paul runs around the park, and Paul contends the opposite.
To settle their debate, they find satellite images of the lake and the park and juxtapose them on a single
coordinate grid (shown below).
The perimeter of the lake is m
Round the final answer to the nearest meter. Do not round intermediate calculations.
The perimeter of the park is m
Round the final answer to the nearest meter. Do not round intermediate calculations.
Who should win the debate?
Answer:
The perimeter of the lake is 314m. The perimeter of the park is 339 m. Paul should win the debate.
Step-by-step explanation:
a number rounded to the nearest hundred thousand is 400,000 the same number rounded to the nearest ten thousand is 350,000 what could be the number
Answer:350000
Step-by-step explanation:
The number is 350000
350000 rounded to the nearest hundred thousand is 400000
350000 rounded to the nearest ten thousand is 350000
A building is 864 inches (in) tall. How many feet (ft) is this?
Answer:
72 ft.
Step-by-step explanation:
12 inches = 1 foot
Answer:
72 feet
Step-by-step explanation:
math calculator
Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 80 grams of salt in 40 liters of water.
A solution of 2 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 3 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.
The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.
Letting x represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
Let a(t) and b(t) denote the amounts of salt in tanks A and B, respectively.
The volume of liquid in tanks A and B after t minutes are
A: 50 L + (5 L/min + 3 L/min - 8 L/min)t = 50 L
B: 40 L + (7 L/min + 8 L/min - 3 L/min - 12 L/min)t = 40 L
so the amount of solution in the tanks stays constant.
Salt flows into tank A at a rate of
(2 g/L)*(5 L/min) + (b(t)/40 g/L)*(3 L/min) = (10 + 3/40 b(t)) g/min
and out at a rate of
(a(t)/50 g/L)*(8 L/min) = 4/25 a(t) g/min
so the net flow rate is given by the differential equation
[tex]\dfrac{\mathrm da(t)}{\mathrm dt}=10+\dfrac{3b(t)}{40}-\dfrac{4a(t)}{25}[/tex]
We do the same for tank B: salt flows in at a rate of
(3 g/L)*(7 L/min) + (a(t)/50 g/L)*(8 L/min) = (21 + 4/25 a(t)) g/min
and out at a rate of
(b(t)/40 g/L)*(3 L/min + 12 L/min) = 3/8 b(t) g/min
and hence with a net rate of
[tex]\dfrac{\mathrm db(t)}{\mathrm dt}=21+\dfrac{4a(t)}{25}-\dfrac{3b(t)}8[/tex]
Replace a(t) and b(t) with x and y. Then the system is (in matrix form)
[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\end{bmatrix}=\dfrac1{200}\begin{bmatrix}-32&15\\32&-75\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}+\begin{bmatrix}10\\21\end{bmatrix}[/tex]
with initial conditions x(0) = 60 g and y(0) = 80 g.
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. How long will it take the coin to reach the stream?
Answer:
about 5.613 seconds
Step-by-step explanation:
Using the quadratic formula to find the value of t when h = 0, we have ...
at² +bt +c = 0
t = (-b±√(b²-4ac))/(2a)
t = (-72±√(72² -4(-16)(100)))/(2(-16))
t = (-72±√11584)/-32 = (9±√181)/4
Only the positive value of t is of interest.
The coin will hit the stream after (9+√181)/4 seconds ≈ 5.613 seconds.
A surveyor has determined that a mountain is
h = 2340
ft high. From the top of the mountain he measures the angles of depression to two landmarks at the base of the mountain and finds them to be 42° and
c = 42°.
(Observe that these are the same as the angles of elevation from the landmarks as shown in the figure below.) The angle between the lines of sight to the landmarks is 68°. Calculate the distance between the two landmarks. (Round your answer to the nearest integer.)
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters which measurement does 17 meters represent
The answer in length
The length is used to measure the distance between to end points or edges. so 17 meters measurement represent the length.
What is perimeter?Its the sum of length of the sides used to made the given figure.
Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters.
Area is what is on the inside.
The perimeter is the outside of the hole thing.
Hence, the length is used to measure the distance between to end points or edges.
so 17 meters measurement represent the length.
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Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
x > 25
Step-by-step explanation:
x+25> 50
Subtract 25 from each side
x+25-25 >50-25
x > 25
Answer:
x>25
Step-by-step explanation:
x+25>50
1. Subtract 25 from both sides of the equation
x+25>50
-25 -25
x>25
Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52? ..
23% of $52 is $..
An easy way to check your answer is to use the friendly and divide 52 by to get ..
Answer:
Which expression can you use to find 23% of 52? "0.23 x 52"
23% of $52 is $. "11.96"
An easy way to check your answer is to use the friendly 25% and divide 52 by 4 to get 13.
Step-by-step explanation:
just did it good luck everyone
23% of $52 is $11.96.
In order to determine the value of 23% of $52, we would multiply 23% by $52. Multiplication is a basic mathematical operation that entails adding a certain number by itself a certain number of times. The sign used to represent multiplication is ×.
23% x 52
= 0.23 x 52 = $11.96
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What type of probability distribution will most likely be used to analyze the number of blue chocolate chips per bag in the following problem? The quality control manager of a candy plant is inspecting a batch of chocolate chip bags. When the production process is in control, the average number of blue chocolate chips per bag is 6.0. The manager is interested in analyzing the probability that any particular bag being inspected has fewer than 5.0 blue chocolate chips.
binomial distribution
When the production process is in control, the mean number of blue chocolate chips per bag is 6.0. The manager is interested in analyzing the probability that any particular bag being inspected has fewer than 5.0 blue chocolate chips. a) binomial distribution.
What type of lines are shown?
Answer:
the angle is acute angle
Answer:
The type of angle shown is an acute angle
Step-by-step explanation:
there are 4 main types of angles. this is an acute angle as it is less than 90°.
Types of angles:
The 4 main types of angles are: acute, obtuse, right angles, reflex angles.
Acute angles- Acute angles are angles less than 90°.
Obtuse Angles-Obtuse angles are angles greater than 90° but less than 180°.
Right Angles- Right angles are angles of 90°.
Reflex Angles- Reflex angles are angles greater than 180° but less than 360°.
a candlemaker prices one set of scented candles at $10
y=10x
x= how many candles
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
Izan can use the slope formula to show that the slope of KL and MN are equal.
If the fish tanks dimension are 60 by 15 by 34 and its is completely empty, what volume of water is needed to fill three fourths of the aquarium? Please help
Answer:
22,950 units³
Step-by-step explanation:
All you have to do is:
[tex]\frac{3}{4} *60*15*34=\\45*15*34=\\675*34=\\\\22,950[/tex]
Matt says 3/3 is equivalent to 1 is he correct?
Answer: Yes
Step-by-step explanation:
It isn't an
1 an improper fraction
Less than the denominator
Therefore, three thirds or 3/3 is one whole fraction
Rly hope I helped!
☆꧁Ashlin꧂☆
Answer:yes he his correct
Step-by-step explanation:
3/3=1
Hello I need help not sure if I got it incorrectly
The first row of the table shows (x,y) = (-4,2). If we add in (-4,1), then we will re-use x = -4 a second time. The input x = -4 leads to multiple outputs of 2 and 1 at the same time. Visually the two points stack on each other to form a vertical line, therefore failing the vertical line test.
The second answer choice (1,-4) looks like your teacher might be trying to trick you or place out a trick/trap answer due to how similar it looks. This point can be added and the function is still valid because x = 1 hasn't been used yet in the table.
Which expression can be used to find the area of the rectangle shown on the coordinate plane 6×7 7×7 8×7 8×8
Answer:that’s a lot of numbers.
Step-by-step explanation:
What is the measure of its remote interior angle?
Answer:<1=126° <2=54°
Step-by-step explanation:
sum of angles in a =180°
<2+90+36=180
<2+126=180
Collect like terms
<2=180-126
<2=54°
<2 and <1 are supplementary angles therefore their sum is equal to 180
<2 + <1=180
54 + <1=180
Collect like terms
<1=180-54
<1=126
The average hourly wage for a high school student in Illinois is $8.25 per hour with a standard deviation of $.25. Assume hourly wages vary normally.
A) Determine the margin of error for this scenario.
B) For the previous question you just answered, construct a 95% confidence interval for the hourly wage for a high school student.
C) For the 95% confidence interval you just constructed, does an hourly wage of $9.15 fall within that acceptable range?
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: hourly wage of a high school student
X~N(μ;σ²)
X[bar]= $8.25
σ= $0.25
For a 95% CI for the average hourly wage for 1 high school student:
For this exercise you have to consider the sample size n=1
a) The margin of error of the CI is calculated as:
d= [tex]Z_{1-\alpha /2}[/tex] * σ
1-α: 0.95 ⇒ α:0.05
1-α/2:0.975
[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
d= 1.96 * 0.25= 0.49
b)
The formula for the interval is
X[bar] ± [tex]Z_{1-\alpha /2}[/tex] * σ
[8.25 ± 0.49]
[7.76; 8.74]
With a 95% you'd expect the interval $[7.76; 8.74] to include the average hourly wage of one high school student in Illinois.
c)
Te calculated interval is $ [7.76; 8.74] the value $9.15 does nor fall within that acceptable range.
I hope this helps!
!!!!!!!!!!!!!!!!HELP
Answer:
You have to use this equation: [tex]a^{2} + b^{2} -c^{2}[/tex]
Step-by-step explanation:
C is the hypotenuse but you need another one so you got to do
[tex]x^{2} +8^{2} =17^{2}[/tex]
now you have to find [tex]x^{2}[/tex] which is
[tex]x^{2} = 17^{2} - 8^{2}[/tex]
[tex]x^{2} = 289 - 64[/tex]
[tex]x^{2} = 225[/tex]
[tex]x = \sqrt{255}[/tex]
[tex]x = 15[/tex]
F=440(2)h/12 where h is 6
Answer:440
Step-by-step explanation:
F=440(2)h/12 h=6
F=440 x 2 x 6/12
F=(440 x 2 x 6) ➗ 12
F=5280 ➗ 12
F=440
f(x) = 5 cos (2x)
Graph
Answer:
Here is the graph amplitude is 5.
Step-by-step explanation:
change 5 out of 19 to a percentage
Answer:
26.3%
Step-by-step explanation:
5 is divided by 19
That answer is then multiplied by 100.
You may round your answer to the nearest whole number.
In ΔPQR, the measure of ∠R=90°, RP = 9.9 feet, and QR = 3.2 feet. Find the measure of ∠P to the nearest tenth of a degree.
Answer:
17.9
Step-by-step explanation:
