Answer:
Mark will use 153 no of trays to accomplish his task.
Final answer:
Mark can use 9 trays to distribute 153 hot dogs and 171 hamburgers evenly by finding the Greatest Common Divisor (GCD) of the two numbers, which is 9.
Explanation:
Mark has 153 hot dogs and 171 hamburgers and wants to distribute them evenly across the greatest number of trays. To do this, Mark needs to find the Greatest Common Divisor (GCD) of the two numbers, which is the largest number that can evenly divide both 153 hot dogs and 171 hamburgers. The GCD of 153 and 171 is 9.
Step 1: List the factors of 153 (1, 3, 9, 17, 51, 153) and 171 (1, 3, 9, 19, 57, 171).Step 2: Identify the largest factor that appears in both lists, which is 9.Step 3: Divide the number of hot dogs and hamburgers by the GCD to find the number of items per tray. For hot dogs: 153 / 9 = 17 hot dogs per tray. For hamburgers: 171 / 9 = 19 hamburgers per tray.Therefore, Mark can use 9 trays, with 17 hot dogs and 19 hamburgers on each tray, to distribute them evenly.
Researchers are interested in whether having an older sibling provides people a model for stable relationships in adolescence. They gather random samples of people with either older siblings or not and measure the number of relationships they have as teenagers. For individuals with no older siblings (N=16), they find an average of 5 relationships (s=1.4) For individuals with older siblings (N=20), they find an average of 3.5 relationships (s=0.8). Test the null hypothesis that the number of adolescent relationships is equal between those with an older sibling and those without (alpha=0.05).
Answer:
Step-by-step explanation:
So, we do not have enough evidence to conclude that the number of adolescent relationships is equal between those with an older sibling and those without.
check the attached file for explanation and solution
Drains A and B are used to empty a swimming pool. Drain A alone can empty the pool in 4.75 hours. How long will it take drain B alone to empty the pool if it takes 2.6 hours when both drains are turned on?
B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and it takes 2.6 hours when both drains are turned on.
Step-by-step explanation:
The given is,
A alone can empty the pool in 4.75 hours.
It takes 2.6 hours when both drains are turned on.
Step:1
One hour work drains A and B =
One hour work of drain A + One hour work of Drain B.........(1)
One hour work of Drain A = [tex]\frac{1}{4.75}[/tex]
One hour of ( A + B ) = [tex]\frac{1}{2.6}[/tex]
Equation (1) becomes,
One hour work of B = One hour work of ( A + B )
- One hour work of A
Substitute the values,
One hour work of B = [tex]\frac{1}{2.6} - \frac{1}{4.75}[/tex]
= [tex]\frac{4.75-2.6}{(4.75)(2.6)}[/tex]
= [tex]\frac{2.15}{12.35}[/tex]
= [tex]\frac{1}{5.744}[/tex]
One hour work of B = [tex]\frac{1}{5.744}[/tex]
B alone can empty the pool in 5.744 hours
Result:
B alone can empty the pool in 5.744 hours, if A alone can empty the pool in 4.75 hours and it takes 2.6 hours when both drains are turned on.
Tomos is a skier he completed a ski race in 2 min 6 seconds the race was 525 m in length. tomos assumes that his average speed is the same for each race. using this assumption, work out how long tomos should take to complete an 800 m race give your answer in minutes and seconds
By calculating the average speed of Tomos in the 525-meter race, we can estimate that he would take about 3 minutes 12 seconds to complete an 800-meter race if he maintains the same average speed.
Explanation:To solve this problem, we first need to figure out Tomos's average speed in the 525-meter ski race that he completed in 2 minutes and 6 seconds. We convert the time to seconds for ease of calculation. So, 2 minutes 6 seconds equals 126 seconds. Now, we calculate his average speed by dividing the length of the race by the time he took to complete it:
Average speed = Distance / Time
Average speed = 525m / 126s
Average speed = 4.17 m/s
Now to calculate how long Tomos should take to complete an 800 m race, we rearrange the formula to solve for time. Time = Distance / Average Speed:
Time = 800m / 4.17 m/s
Time = 191.84 seconds
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Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
(a) Construct and interpret a 90% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
Answer:
[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]
[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]
And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57
Step-by-step explanation:
Data provided
[tex]\bar X=9797[/tex] represent the sample mean for the steps
[tex]\mu[/tex] population mean
s=2313 represent the sample standard deviation
n=61 represent the sample size
Solution
The confidence interval for the true population mean is given by :
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
Since we need to find the critical value [tex]t_{\alpha/2}[/tex] we need to calculate first the degrees of freedom, given by:
[tex]df=n-1=61-1=60[/tex]
The Confidence is 0.90 or 90%, the value for the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that [tex]t_{\alpha/2}=1.67[/tex]
Now we have everything in order to replace into formula (1):
[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]
[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]
And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57
90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps.
To construct a 90% confidence interval for the mean number of steps taken on a typical workday for people working in New York City who wear activity trackers, you can use the following formula:
Confidence Interval = X ± Z * (σ/√n)
Where:
X is the sample mean (9,797 steps).
Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645, but you can use a Z-table or calculator to get the exact value).
σ is the population standard deviation (2,313 steps).
n is the sample size (61).
Now, let's plug in the values and calculate the confidence interval:
Z for a 90% confidence level is approximately 1.645.
Confidence Interval = 9,797 ± 1.645 * (2,313/√61)
Confidence Interval = 9,797 ± 1.645 * (299.98)
Confidence Interval ≈ 9,797 ± 494.06
Now, calculate the lower and upper bounds of the confidence interval
Lower Bound = 9,797 - 494.06 ≈ 9,302.94
Upper Bound = 9,797 + 494.06 ≈ 10,291.06
Interpretation:
We are 90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps. This means that if we were to take many random samples and calculate a 90% confidence interval for each sample, we would expect about 90% of those intervals to contain the true population mean.
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The graph shows sales as a function of time.
Answer:
You can use the graph of a trigonometry function to show sales amounts over a given period of time. Here’s an example: Even though people in many parts of the world play soccer year-round, certain times of the year show an increase in the sales of outdoor soccer shoes.
Step-by-step explanation:
Let F = sin ( 8 x + 5 z ) i − 8 y e x z k . F=sin(8x+5z)i−8yexzk. Calculate div ( F ) div(F) and curl ( F ) . and curl(F). (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answer:
Required results are [tex]\nabla .\vec{F}[/tex]=8\cos(8x+5z)-8ye^x[/tex] and [tex]\nabla\times \vec{F}=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]
Step-by-step explanation:
Given vector function is,
[tex]\vec{F}=\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k}[/tex]
To find [tex]\nabla .\vec{F}[/tex] and [tex]\nabla \times \vec{F}[/tex] .
[tex]\nabla .\vec{F}[/tex]
[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]
[tex]=\frac{\partial}{\partial x}(\sin(8x+5z))-\frac{\partial}{\partial z}(8ye^xz)[/tex]
[tex]=8\cos(8x+5z)-8ye^x[/tex]
And,
[tex]\nabla \times \vec{F}[/tex]
[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})\times(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]
[tex]\end{Vmatrix}[/tex]
[tex]=\uvec{i}\Big[\frac{\partial}{\partial y}(-8ye^xz)\Big]-\uvec{j}\Big[\frac{\partial}{\partial x}(-8ye^xz)-\frac{\partial}{\partial z}(\sin(8x+5z))\Big]+\uvec{k}\Big[-\frac{\partial}{\partial y}(-\sin(8x+5z))\Big][/tex]
[tex]=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]
Hence the result.
Can someone help me?
(-9).(-9).(-9).(-9).(-9)
Answer:
This would be -9 to the 5th power. (-9^5)
Step-by-step explanation:
-9 to the 5th power when put in a calculator equals -59,049.
The exponent is how many times the number is multiplied by itself.
Answer:
-59049
Step-by-step explanation:
(-9).(-9).(-9).(-9).(-9)
=81.(-9).(-9).(-9)
= -729.(-9).(-9)
= 6561.(-9)
= -59049
Graphing Quadratic Equations, if you have a graph, how do you find zeros?
Answer:
look for the x-intercepts
Step-by-step explanation:
A "zero" is a value of x where the function value is zero. On a graph, that point is where the graph meets the x-axis. Every x-intercept is a zero of the function.
__
If there are no x-intercepts, then there are no real zeros. The roots (zeros) will be complex.
which expressions are equivalent to 7•7•7•7•7•7
Answer:7^6
Step-by-step explanation:
Answer:
7^6
Step-by-step explanation:
Hannah is is a keen archer one day she shoots five arrows each arrow scores and eight what is her total score
Answer:
40
Step-by-step explanation:
8*5
I need some help pls
Answer:
160°
Step-by-step explanation:
∠C and ∠D are both inscribed angles of arc AB. Therefore, they are equal.
5w + 20 = 7w − 4
24 = 2w
w = 12
Therefore, ∠C = ∠D = 80°.
Inscribed angles are half the central angle, so mAB = 2 × 80° = 160°.
1. Heather rode her horse 2 kilometers down the mountain side trail. Hailey rode 1900 meters on her horse on the same trail. Who rode the farthest and how much farther did they ride in kilometers?
Answer:
Heather rode the farthest
She rode 0.1km farther than Hailey.
Step-by-step explanation:
This is a conversion of units question.
Heather rode her horse 2 kilometers.
Hailey rode 1900 meters on her horse.
Each km has 1000 meters.
So 1900 meters = 1900/1000 = 1.9 km
This means that Hailey rode for 1.9 km.
Heather rode the farthest(2km is greather than 1.9km)
2 - 1.9 = 0.1km
She rode 0.1km farther than Hailey.
The fuel tanks on some ships are spheres of which only the top halves are above deck. If one of these tanks is 96 ft in diameter, how many gallons of fuel does it hold? Use
1 ft3 ≈ 7.5 gal
Answer:
720
Step-by-step explanation:
96 * 7.5
Choose the correct graph of the following condition.
Answer:
the correct graph is pictured below
Step-by-step explanation:
the graph is below
3. For the school Band, Marcia decides to order t-shirts for all of the participants. It will
cost $4 per shirt for the medium size and $5 per shirt for the large size. Marcia orders
a total of 70 T-shirts and spends $320. Determine the two linear equations to
represent the information. [4A) **Hint: One equation is for amount of t-shirts and the second is
for money. YOU DO NOT NEED TO SOLVE,
Let x represent number of medium size shirts
Let y represent total large size shirts
Answer:
4x+5y = 320
x+y = 70
Step-by-step explanation:
We need one equation for the total number of shirts, and one for the total cost.
Total number = 70
So that means medium shirts + large shirts = 70
So our first equation is x+y = 70
Total cost = $320
So that means $4 times medium shirts + $5 times large shirts = 320
So our second equation is 4x+5y = 320
The length of a rectangular garden is 7 feet longer than its width. If the garden’s perimeter is 178 feet what is the area of the garden in square feet.
Answer:1968ft^2
Step-by-step explanation:
Perimeter(p)=178feet
P=2L+2w
178=2L+2w
178=2(L+w)
L+w=178 ➗ 2
L+w=89.............(1)
W+7=L
L-w=7...................(11)
L+w=89... ..........(1)
L-w=7...................(11)
Subtract (11) from (1)
2w=89-7
2w=82
w=82 ➗ 2
w=41 width=41feet
Substitute w=41 in (11)
L-w=7
L-41=7
L=7+41
L=48feet
Area= length x width
Area=48 x 41
Area=1968ft^2
The area of the garden is 1968 square feet by setting up and solving equations based on the information about the garden's length, width, and perimeter.
Explanation:The problem is asking for the area of a rectangular garden where the length is 7 feet longer than its width. We also know the perimeter of the garden is 178 feet. Normally in a rectangle, the formula for the perimeter is P = 2(length + width).
Since the length is 7 feet longer, let's denote the width as 'w' and therefore the length as 'w+7'. Substituting in the perimeter formula we get: 178 = 2(w + w + 7).
By simplifying and solving the equation we find that the width, w = 41 feet. Therefore, the length is w+7 = 48 feet.
Lastly, the area of a rectangle is calculated as length * width, so substituting the values we found we get the area = 48 feet * 41 feet = 1968 square feet.
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The number of guppies that a fish tank can safely hold depends on its volume.A fish tank should have a volume of 576 cubic inches to safely hold 3 guppies.how many guppies can a fish tank that is 24 inches long, 12 inches wide, and 16 inches highly safely hold?
Answer:
24 guppies
Step-by-step explanation:
Assuming a linear relationship, the volume required per guppy is given by:
[tex]g=\frac{576\ in^3}{3\ guppies}\\ g= 192\ in^3/guppy[/tex]
The volume of the fish tank is given by the product of its length, by its width and its height:
[tex]V = 24*12*16\\V=4,608\ in^3[/tex]
The number of guppies that this tank can safely hold is:
[tex]n=\frac{V}{g}=\frac{4,608}{192} \\n=24\ guppies[/tex]
The tank can safely hold 24 guppies.
The number 0.05891 can be expressed using scientific notation as
Answer:
5.892×10^-2
Step-by-step explanation:
Scientific notation has one digit to the left of the decimal point. To write the number in scientific notation, it can work to start by writing the number with that as one of the factors:
0.05891 = 5.891 × 0.01
= 5.891 × 1/10^2
= 5.891 × 10^-2
__
You can also enter this number into your calculator and change the display mode to SCI.
_____
It helps to understand the decimal place-value number system in terms of the power of 10 that multiplies each number place.
A survey of 1000 air travelers1 found that prefer a window seat. The sample size is large enough to use the normal distribution, and a bootstrap distribution shows that the standard error is . Use a normal distribution to find a 90% confidence interval for the proportion of air travelers who prefer a window seat. Round your answers to three decimal places.
Answer:
90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)
Step-by-step explanation:
We have the following data:
Sample size = n = 1000
Proportion of travelers who prefer window seat = p = 60%
Standard Error = SE = 0.015
We need to construct a 90% confidence interval for the proportion of travelers who prefer window seat. Therefore, we will use One-sample z test about population proportion for constructing the confidence interval. The formula to calculate the confidence interval is:
[tex](p-z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}}, p+z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}})[/tex]
Since, standard error is calculated as:
[tex]SE=\sqrt{\frac{p(1-p)}{n} }[/tex]
Re-writing the formula of confidence interval:
[tex](p-z_{\frac{\alpha}{2}} \times SE, p+z_{\frac{\alpha}{2}} \times SE)[/tex]
Here, [tex]z_{\frac{\alpha}{2}}[/tex] is the critical value for 90% confidence interval. From the z-table this value comes out to be 1.645.
Substituting all the values in the formula gives us:
[tex](0.6 - 1.645 \times 0.015, 0.6 + 1.645 \times 0.015)\\\\ = (0.575, 0.625)[/tex]
Therefore, the 90% confidence interval for the true proportion of air travelers who prefer the window seat is (0.575, 0.625)
Someone please help.
Answer:
...
Step-by-step explanation:
...
A population of rabbits oscillates 19 above and below average during the year, hitting the lowest value in january. the average population starts at 650 rabbits and increases by 160 each year. find an equation for the population p in terms of the months since january t
The equation we've developed to represent the rabbit population over time, where 't' is the number of months since January, is P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650. This equation covers the oscillations in the population and the steady yearly increase.
Explanation:The subject matter falls under the discipline of Mathematics, particularly in the topics involving functions. We can create a sinusoidal (sine or cosine) function to represent the oscillation of the population of rabbits.
Given that the population fluctuates 19 above and below the average, and the average increases by 160 each year, this suggests a sinusoidal period of 12 months (a year) with a vertical shift (midline) that increases linearly.
Considering t as the number of months since January, the equation for the population P in terms of the months since January t would be:
P(t) = 19sin((2π/12)t - π/2) + (160t/12) + 650
The 19 is the amplitude, (2π/12)t - π/2 represents the sinusoidal oscillation adjusted to start at the minimum in January, (160t/12) is the yearly change in population that increases per month, and 650 is the average population at the start.
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To find the population equation in terms of months since January considering oscillations and growth, use the formula p(t) = 650 + 160t + 19sin(2πt/12).
Population Equation: The equation for the population p in terms of the months since January t can be written as p(t) = 650 + 160t + 19sin(2πt/12). This equation takes into account the initial population of 650 rabbits, an increase of 160 rabbits per year, and the oscillation of 19 above and below the average population.
A company receives shipments of a component used in the manufacture of a high-end acoustic speaker system. When the components arrive, the company selects a random sample from the shipment and subjects the selected components to a rigorous set of tests to determine if the components in the shipments conform to their specifications. From a recent large shipment, a random sample of 250 of the components was tested, and 24 units failed one or more of the tests.
a) What is the point estimate of the proportion of components in the shipment that fail to meet the company's specifications?
b) What is the standard error of the estimated proportion?
c) At the 98% level of confidence, what is the margin of error in this estimate?
d) What is the 95% confidence interval estimate for the true proportion of components, p, that fail to meet the specifications?
e) If the company wanted to test the null and alternative hypotheses: H_0: p = 0.10 against H_a: p notequalto 0.10 at the alpha = 0.05 level of significance, what conclusion would they draw?
Step-by-step explanation:
a) 24 / 250 = 0.096
b) Standard error for a proportion is:
σ = √(pq/n)
σ = √(0.096 × 0.904 / 250)
σ = 0.0186
c) At 98% confidence, the critical value is 2.326. The margin of error is therefore:
2.326 × 0.0186 = 0.0433
d) At 95% confidence, the critical value is 1.960. The margin of error is therefore:
1.960 × 0.0186 = 0.0365
So the confidence interval is:
(0.0960 − 0.0365, 0.0960 + 0.0365)
(0.0595, 0.1325)
e) 0.10 is within the 95% confidence interval, so the null hypothesis would not be rejected.
Final answer:
a) The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is 9.6%. b) The standard error of the estimated proportion is 1.9%. c) The margin of error at the 98% confidence level is 4.4%. d) The 95% confidence interval estimate for the true proportion is approximately 5.9% to 13.3%. e) The null hypothesis that the proportion is 0.10 is rejected if the z-test statistic falls outside the range (-1.96, 1.96).
Explanation:
a) Point estimate:
The point estimate of the proportion of components in the shipment that fail to meet the company's specifications is the number of failed components divided by the total number of components tested. In this case, the point estimate is 24/250 = 0.096, or 9.6%.
b) Standard error:
The standard error of the estimated proportion is calculated using the formula SE = sqrt((phat * (1 - phat)) / n), where phat is the point estimate and n is the sample size. In this case, the standard error is sqrt((0.096 * (1 - 0.096)) / 250) = 0.019, or 1.9%.
c) Margin of error:
The margin of error is determined by multiplying the standard error by the appropriate critical value from the standard normal distribution. For a 98% confidence level, the critical value is approximately 2.33. Therefore, the margin of error is 2.33 * 0.019 = 0.044, or 4.4%.
d) Confidence interval:
The 95% confidence interval estimate for the true proportion of components that fail to meet the specifications is given by the formula phat +/- z * SE, where phat is the point estimate, z is the appropriate critical value from the standard normal distribution (for 95% confidence, z is approximately 1.96), and SE is the standard error. Therefore, the confidence interval is 0.096 +/- 1.96 * 0.019, or approximately 0.059 to 0.133.
e) Hypothesis test:
To test the null hypothesis H_0: p = 0.10 against the alternative hypothesis H_a: p != 0.10, we can use a two-tailed z-test. The test statistic is calculated as (phat - p_0) / sqrt((p_0 * (1 - p_0)) / n), where p_0 is the null hypothesis value (0.10), phat is the point estimate, and n is the sample size. The critical value for a significance level of 0.05 is approximately 1.96 from the standard normal distribution. If the test statistic is outside the range (-1.96, 1.96), we reject the null hypothesis. In this case, if the test statistic falls outside the range (-1.96, 1.96), we would reject the null hypothesis and conclude that the true proportion of components that fail to meet the specifications is not 0.10.
Candy. Someone hands you a box of a dozen chocolate-covered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla.
a) If there really were 6 vanilla and 6 peanut butter candies in the box, what is the probability that you would have picked three vanillas in a row?
b) Do you think there really might have been 6 of each? Explain.
c) Would you continue to believe that half are vanilla if the fourth one you try is also vanilla? Explain.
Answer:
a) P=0.091
b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but it is still possible that there are 6 of each taste.
c) The probability of picking 4 vainilla in a row, if there are half of each taste, is P=0.030.
This is a very improbable case, so if this happens we would have reasons to think that there are more than half vainilla candies in the box.
Step-by-step explanation:
We can model this problem with the variable x: number of picked vainilla in a row, following a hypergeometric distribution:
[tex]P(x=k)=\dfrac{\binom{K}{k}\cdot \binom{N-K}{n-k}}{\binom{N}{n}}[/tex]
being:
N is the population size (12 candies),
K is the number of success states in the population (6 vainilla candies),
n is the number of draws (3 in point a, 4 in point c),
k is the number of observed successes (3 in point a, 4 in point c),
a) We can calculate this as:
[tex]P(x=3)=\dfrac{\binom{6}{3}\cdot \binom{12-6}{3-3}}{\binom{12}{3}}=\dfrac{\binom{6}{3}\cdot \binom{6}{0}}{\binom{12}{3}}=\dfrac{20\cdot 1}{220}=0.091[/tex]
b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but is possible.
c) In the case k=4, we have:
[tex]P(x=3)=\dfrac{\binom{6}{4}\cdot \binom{6}{0}}{\binom{12}{4}}=\dfrac{15\cdot 1}{495}=0.030[/tex]
This is a very improbable case, so we would have reasons to think that there are more than half vainilla candies in the box.
Using the hypergeometric distribution, it is found that:
a) 0.0909 = 9.09% probability that you would have picked three vanillas in a row.b) The probability is above 5%, hence it is not an unusual event and gives no evidence that there might not have been 6 of each.c) The probability is below 5%, hence it is an unusual event and there is enough evidence to believe that there might not have been 6 of each.The candies are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.Item a:
There is a total of 12 candies, hence [tex]N = 12[/tex].6 of those candies are vanillas, hence [tex]k = 6[/tex].3 candies are chosen, hence [tex]n = 3[/tex].The probability that you would have picked three vanillas in a row is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,12,3,6) = \frac{C_{6,3}C_{6,0}}{C_{12,3}} = 0.0909[/tex]
0.0909 = 9.09% probability that you would have picked three vanillas in a row.
Item b:
The probability is above 5%, hence it is not an unusual event and gives no evidence that there might not have been 6 of each.
Item c:
Now n = 4, and the probability is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,12,4,6) = \frac{C_{6,4}C_{6,0}}{C_{12,4}} = 0.0303[/tex]
The probability is below 5%, hence it is an unusual event and there is enough evidence to believe that there might not have been 6 of each.
To learn more about the hypergeometric distribution, you can take a look at https://brainly.com/question/4818951
The study report gives a scatterplot for a random sample of penguins. The dive duration is measured in minutes and depth (x value) is in meters. The depths are all positive numbers. The dives varied from 40 meters to 300 meters in depth. The report then says, "The regression equation for this bird is y|x = 2.59 + 0.0126x.
(a) What is the y-intercept of the regression line? (Use 2 decimal places)
(b) What is the correct interpretation of the y-intercept?
Answer:
a) y-intercept = 2.59
b) Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.
Step-by-step explanation:
(a) What is the y-intercept of the regression line? (Use 2 decimal places)
The given regression equation is
y = 2.59 + 0.0126x
The standard form of the regression equation is given by
y = a + bx
Where a is the y-intercept of the regression line and b is the slope of the regression line.
Comparing the given equation with the standard form,
y-intercept = 2.59
(b) What is the correct interpretation of the y-intercept?
The y-intercept is the value we get when x = 0
y = 2.59 + 0.0126(0)
y = 2.59 + 0
y = 2.59 minutes
Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.
what is one thousand five hundred divided by five equal
Answer: 300
We know that 5×3=15. Since we are trying to get 1500 we Multiply 300×5 and get 1500.
How do we know?
As you can see if you cross out 2 of the 0 in 300 you have 3×5. When you multiply it you get 15.Also if you cross out 1 of the 0 in 300 you have 30×5. When you multiply that you get 150.As you see when you still multiply either of those problems you have 15 in it. So we should know 300×5=1500.
Note: We can also multiply 500×3 and get 1500. You still get the same answer but just switched numbers.
Answer:
[tex]300[/tex]
Step-by-step explanation:
[tex] \frac{1500}{5} = 300[/tex]
It's very easy to find if you use a calculator.
To know whether that the answer is correct or wrong you can do like this.
[tex]300 \times 5 = 1500[/tex]
hope this helps
thanks.
3х2 = 147
Solve by undoing
Answer: +/- 7
Step-by-step explanation:
3x² = 147
To solve for x divide through by three first.
3x² = 147
x² = 49, now we take the square root of both side by trying to apply laws of indices.
√x² = √49
The square root will neutralize the effect of the square because
√a = a¹/² so (x²)¹/², and (x²)¹/² =
x²×¹/² = x, therefore the solution is
x = +/- 7.
Which statement represents the expression 11 (30 + 7)?
Answer:
330+77= 407
Step-by-step explanation:
*Danganronpa flashbacks*
If you drive 27.54 km to school and then 21.86 km to your
friends, how far do you drive?
Answer:
49.4 km
Step-by-step explanation:
you add 27.54 plus 21.86 so 49.4 km total between school and to your friends house
You drive a total distance of 49.4 kilometers when you travel 27.54 kilometers to school and then 21.86 kilometers to your friend's house.
When you drive 27.54 km to school and then 21.86 km to your friend's place, you are covering a total distance of 49.4 kilometers. To calculate this, you simply add the two distances together:
Distance to school: 27.54 km
Distance to friend's place: 21.86 km
Total distance = 27.54 km + 21.86 km = 49.4 km
So, you drive a total of 49.4 kilometers when you travel to both school and your friend's house. This cumulative distance is the sum of the individual distances you cover for each leg of your journey. It's important to keep track of such distances, especially if you want to estimate fuel consumption, plan your commute, or calculate travel time accurately. In this case, you've covered 49.4 kilometers in total, which is the combined distance for your trip.
for more such questions on distance
https://brainly.com/question/30395212
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Smoking levels: According to the Centers for Disease Control and Prevention, the proportion of U.S. adults age 25 or older who smoke is .22. A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree or higher education level. What is the alternative hypothesis in this case? Group of answer choices a.The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than .22. b.The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is .22. c.The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is not .22. d.There is a relationship between level of education level and smoking habits.
Answer:
The correct option is (a).
Step-by-step explanation:
According to the Centers for Disease Control and Prevention, 0.22 or 22% of US adults of 25 years or older smoke.
But a researcher suspects that this percentage is lower if the US adults of 25 years or older have a bachelor's degree or higher education level.
So, the researcher needs to test whether the proportion of US adults of 25 years or older who smoke is less in case the adults have bachelor's degree or higher.
To test his suspicion the researcher can use a one-proportion z-test.
The hypothesis of the test can be defined as:
H₀: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is 0.22, i.e. p = 0.22.
Hₐ: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is less than 0.22, i.e. p < 0.22.
Thus, the correct option is (a).
Final answer:
The alternative hypothesis for the scenario where a researcher suspects a lower smoking rate among U.S. adults with higher education is that the proportion of smokers in this group is less than .22.
Explanation:
The alternative hypothesis in this research scenario is that the proportion of U.S. adults age 25 or older who have a bachelor's degree or higher education level and smoke is lower than .22. The alternative hypothesis translates the researcher's suspicion into a testable statement and is essential for conducting a hypothesis test. The correct alternative hypothesis based on the research question would be: 'The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than .22.'
In the figure below, the radius of circle P is 10 units. The arc length of ABC is 16 pi. What is the arc measure of AC, in degrees?
Answer:
25
Step-by-step explanation:
Answer:
72 degrees
Step-by-step explanation:
We need to know the total circumference in order to determine the arc measure for ABC before we figure out AC
Circumference =2πr → =2π(10) → =20π
We know the length of ABC
so we set up a proportion to figure out its arc measure.
arc length/ circumference = arc measure/ degrees in a circle
16π/ 20π = arc measure/ 360 degrees
arc measure= 360 x 16π/ 20π =228 degrees
The arc measure of ABC is 228 degrees
If we combine the major arc ABC, and the minor arc AC we have the entire circle.
288 degrees +m AC= 360
m AC= 72 degrees
The measure of AC is 72 degrees
(i got the explanation off of Klan Academy when i answered the question)