Answer:
C(x)=16600+63x
R(x)=160x
Break-even Point, x=172
Step-by-step explanation:
Let x be the number of Toilets Produced.
Fixed cost = $16,600
Variable costs = $63 per toilet.
Total Cost, C(x)=16600+63x
The company expects to sell the toilets for $160.
Selling Price Per Toilet=160
Total Revenue for x Toilets, R(x)=160x
Next, we determine the break-even point.
The break-even point is the point where the Cost of Production equals Revenue generated.
i.e. C(x)=R(x)
16600+63x=160x
16600=160x-63x
16600=97x
x=171.13
The company needs to sell at least 172 Toilets to break even.
To formulate the functions C(x) and R(x) for the total cost and revenue of producing and selling x toilets, we can use the given information about fixed costs, variable costs, and selling price. By setting the total cost equal to the total revenue, we can find the number of toilets needed to break even, which is approximately 171.
Explanation:To formulate the function C(x) for the total cost of producing x new toilets, we need to consider the fixed cost and the variable cost. The fixed cost is $16,600, which remains constant regardless of the number of toilets produced. The variable cost is $63 per toilet, so we multiply it by x to account for the number of toilets produced. Therefore, the function C(x) can be expressed as:
C(x) = 16,600 + 63x
The function R(x) for the total revenue generated from the sales of x toilets can be found by multiplying the selling price of each toilet by the number of toilets sold. Since each toilet is sold for $160, the function is:
R(x) = 160x
To find the number of toilets needed to break even, we need to determine the value of x when the total cost is equal to the total revenue. In other words, we set C(x) = R(x) and solve for x:
16,600 + 63x = 160x
Subtracting 63x from both sides:
16,600 = 97x
Dividing both sides by 97:
x = 170.10
Therefore, the company needs to sell approximately 171 toilets to break even.
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help need full solution i &ii
Step-by-step explanation:
[tex]1)\:v = 2 {e}^{3t} + 5 {e}^{ - 3t} \\ differentiating \: w.r.t.t \: on \: both \: sides \\ acceleration =\\ \frac{dv}{dt} = \frac{1}{dt} (2 {e}^{3t} + 5 {e}^{ - 3t} ) \\ = 2 \times \frac{1}{dt} {e}^{3t} + 5 \times \frac{1}{dt} {e}^{ - 3t} \\ \\ = 2 \times {e}^{3t} \times 3 + 5 \times {e}^{ - 3t} \times ( - 3) \\ = 6{e}^{3t} - 15{e}^{ - 3t} \\ \therefore \frac{dv}{dt} = 6{e}^{3t} - 15{e}^{ - 3t} \\ \therefore \bigg(\frac{dv}{dt} \bigg) _{t=1} = 6 {e}^{3 \times 1} - 15 {e}^ { - 3 \times 1} \\ \bigg(\frac{dv}{dt} \bigg) _{t=1} = 6 {e}^{3} - 15 {e}^ { - 3 } \\ acceleration = \\ \purple{ \boxed{ \bold{\bigg(\frac{dv}{dt} \bigg) _{t=1} = \bigg(\frac{6 {e}^{6} - 15}{ {e}^{3} } \bigg) \: m {s}^{ - 2} }}} \\ \\ 2) \: let \:s \: be \: the \: total \: distance \: travelled \\ \therefore \: s = v \times t \\ \therefore \: s= (2 {e}^{3t} + 5 {e}^{ - 3t}) \times t \\ \therefore \: (s)_{t=2} = (2 {e}^{3 \times 2} + 5 {e}^{ - 3 \times 2}) \times 2 \\ \therefore \: (s)_{t=2} = (2 {e}^{6} + 5 {e}^{ - 6}) \times 2 \\ \therefore \: (s)_{t=2} = 4 {e}^{6} + 10{e}^{ - 6} \\ \red{ \boxed{ \bold{\therefore \: (s)_{t=2} = \bigg(\frac{4 {e}^{12} + 10}{{e}^{ 6}} \: \bigg)m}}}\\ [/tex]
The number of cars running a red light in a day, at a given intersection, possesses a distribution with a mean of 2.4 cars and a standard deviation of 4. The number of cars running the red light was observed on 100 randomly chosen days and the mean number of cars calculated. Describe the sampling distribution of the sample mean.
Answer:
The sampling distribution of the sample mean is:
[tex]\bar X\sim N(\mu_{\bar x}=2.4,\ \sigma_{\bar x}=0.40)[/tex]
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the distribution of sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
Let X = number of cars running a red light in a day, at a given intersection.
The information provided is:
[tex]E(X)=\mu=2.4\\SD(X)=\sigma=4\\n=100[/tex]
The sample selected is quite large, i.e. n = 100 > 30.
The Central limit theorem can be used to approximate the sampling distribution of the sample mean number of cars running a red light in a day, by the Normal distribution.
The mean of the sampling distribution of the sample mean is:
[tex]\mu_{\bar x}=\mu=2.4[/tex]
The standard deviation of the sampling distribution of the sample mean is:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{4}{\sqrt{100}}=0.40[/tex]
The sampling distribution of the sample mean is:
[tex]\bar X\sim N(\mu_{\bar x}=2.4,\ \sigma_{\bar x}=0.40)[/tex]
Final answer:
The sampling distribution of the sample mean is approximately normally distributed, with a mean of 2.4 cars and a standard deviation of 0.4 cars.
Explanation:
The sampling distribution of the sample mean can be described as follows:
The sampling distribution of the sample mean is approximately normally distributed.The mean of the sampling distribution of the sample mean is equal to the mean of the population, which is 2.4 cars in this case.The standard deviation of the sampling distribution of the sample mean, also known as the standard error, is equal to the standard deviation of the population divided by the square root of the sample size. In this case, the standard deviation of the sampling distribution of the sample mean is 4 / sqrt(100) = 0.4 cars.6. A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 568 consumers who recognize the Dull Computer Company name? Find the mean and standard deviation to answer this question. Must show work and explain why or why not.
Given Information:
Population = n = 800
Probability = p = 68% = 0.68
Answer:
We can say with 68% confidence that 568 lies in the range of (518, 570) therefore, it would not be unusual to get 568 consumers who recognize the Dull Computer Company name.
Step-by-step explanation:
Let us first find out the mean and standard deviation.
mean = μ = np
μ = 800*0.68
μ = 544
standard deviation = σ = √np(1-p)
σ = √800*0.68(1-0.68)
σ = 13.2
we know that 68% of data fall within 2 standard deviations from the mean
μ ± 2σ = 544-2*13.2, 544+2*13.2
μ ± 2σ = 544-26.4 , 544+26.4
μ ± 2σ = 517.6, 570.4
μ ± 2σ = 518, 570
We can say with 68% confidence that 568 lies in the range of (518, 570) therefore, it would not be unusual to get 568 consumers who recognize the Dull Computer Company name.
A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens and pencils were purchased if there were 80 more pencils than pens?
Answer:
200 pencils and 120 pens
Step-by-step explanation:
Let the number of pencils be x while pens be y.
Considering the cost of whole purchase then, we get the equation
0.5x+y=220
Considering the number of items bought, then the equation is
x-y=80
Adding the two equations then we have
1.5x=300
x=300/1.5=200
Consideeing that x-y=80 and x is 200 then
200-y=80
y=200-80=120
Therefore, the pencils were 200 and pens 120 pieces
A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 6% margin of error at a 90% confidence level, what size of sample is needed? Be sure to round accordingly.
A sample size of 188 would be needed to achieve a 6% margin of error at a 90% confidence level.
Used the formula for sample size calculation:
[tex]n = \dfrac{z^2 \times p (1 - p)}{E^2}[/tex]
Where: n = sample size.
Z = Z-score corresponding to the desired confidence level.
p = estimated proportion of the population that supports the candidate.
E = desired margin of error.
Here we have to give that,
90% confidence level corresponds to a Z-score of approximately 1.645.
That is, z = 1.645
p = 0.5
E = 0.06
Substituting the given values into the formula, we get:
[tex]n = \dfrac{z^2 \times p (1 - p)}{E^2}[/tex]
[tex]n = \dfrac{(1.645)^2 \times 0.5(1 - 0.5)}{0.06^2}[/tex]
[tex]n = \dfrac{0.6765}{0.0036}[/tex]
[tex]n =187.9[/tex]
Rounded to whole numbers,
[tex]n = 188[/tex]
Therefore, the size of the sample would be 188.
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In order to achieve a 6% margin of error and a 90% confidence level in a poll, the correct sample size must be determined using the error bound formula. A larger and representative sample will minimize the margin of error and improve the poll's precision and accuracy. A number of key factors, like identification of the target population and select a random sample, should be considered while conducting a poll.
Explanation:The subject matter dealt with here involves conducting a poll to gauge public opinion, with a desired accuracy defined by a 6% margin of error and a 90% confidence level. This is primarily related to Statistics, a branch of Mathematics.
To determine an appropriate sample size for a given margin of error and confidence level, the error bound formula is utilized. Although the actual formula could appear complex for some, many online calculators can complete the task. The 90% confidence level means that if we were to take multiple sets of samples, roughly 90% of the calculated confidence intervals would contain the true population mean or proportion.
Furthermore, sample size influences the margin of error; a larger sample reduces the margin of error and makes the poll result more precise and accurate. As a rule of thumb, the sample should be random and representative of the population in question to ensure the accuracy and reliability of poll results.
Take note that many criteria must be met to conduct a valid and scientifically accurate poll, some of which include: identifying the desired population of respondents, ensuring the sample is both random and representative of the wider population, and interviewing a sufficient number of citizens to achieve a reasonable sample size.
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3) A state policeman has a theory that people who drive red cars are more likely to drive too fast. On his day off, he borrows one of the department’s radar guns, parks his car in a rest area, and measures the proportion of red cars and non-red cars that are driving too fast (he decided ahead of time to define "driving too fast" as exceeding the speed limit by more than 5 miles per hour). To produce a random sample, he rolls a die and only includes a car in his sample if he rolls a 5 or a 6. He finds that 18 out of 28 red cars are driving too fast and 75 of 205 other cars are driving too fast. Is this convincing evidence that people who drive red cars are more likely to drive too fast, as the policeman has defined it?
Answer:
Yes, it is convincing evidence to conclude that the proportion of red cars that drive too fast on this
highway is greater than the proportion of non-red cars that drive too fast.
Step-by-step explanation:
From the, we wish to first test;
H0; P_r - P_o = 0
And; H0; P_r - P_o > 0
Where; P_r and P_o are the proportion of red cars and other cars, respectively, who are driving too fast.
We will use a significance level of a = 0.05.
Thus;
The procedure is a two-sample z-test for the difference of proportions.
For, Random Conditions: The policemen chose cars randomly by rolling a die.
10%: We can safely assume that the number of cars driving past the rest area is essentially infinite, so the 10% restriction does not apply.
Large counts: The number of successes and failures in the two groups are 18, 10, 75, and 130—all of which are at least 10.
So, P_r = 18/28 = 0.64
P_o = 75/205 = 0.37
P_c = (18 + 75)/(28 + 205) = 0.4
Thus:
z = [(0.64 - 0.37) - 0]/√[[(0.4 x 0.6)/28] + [(0.4 x 0.6)/205]]
z = 2.73
From the one tailed z-score calculator online, I got P value = 0.003167
Thus, the P-value of 0.0032 is less than a = 0.05, so we reject H0. We
have sufficient evidence to conclude that the proportion of red cars that drive too fast on this
highway is greater than the proportion of non-red cars that drive too fast.
Does the sum of 1/5 + 1/5 equals 2/5 make sense in situations
Answer:
It equals 2/5.
Step-by-step explanation:
Basically you ignore the 5 because it stays the same. All you have to add are the numerators. 1+1=2. So it would be 2/5.
A scenario:
2 pizzas cut into 5th's. Everyone ate 4 in each and kept one slice. When you add those 2 together you would be 2 slices.
2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled Middleton. There is 1 dot above 1, 4 dots above 2, 5 dots above 3, 4 dots above 4, 4 dots above 5, 1 dot above 6, 0 dots above 7, 0 dots above 8, 1 dot above 9, 0 dots above 10. Plot 2 is titled Westwood. There are 0 dots above 0, 0 dots above 1, 4 dots above 2, 5 dots above 3, 4 dots above 4, 4 dots above 5, 3 dots above 6, and 0 dots above 7, 8, 9, and 10.
The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
Check all that apply.
Both have the same number of data points.
Both means are between 3 and 4.
Both have the same median.
Both have the same range.
Westwood has less variability than Middleton.
Answer:
It is A,B,and E.
I just did the question and it was right
The true statements about the dot plots are (A) Both have the same number of data points, (B) Both means are between 3 and 4. and (C) Westwood has less variability than Middleton.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Given are two plots, Middleton and Westwood.
Data points in plot 1 are 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 9
Total number of data points in plot 1 or Middleton = 20
Data points in plot 2 are 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6
Total number of data points in plot 2 or Westwood = 20
So, both have the same number of data points.
Mean of Middleton = Sum of the data points / Total number of data points
= [1 + (4×2) + (5×3) + (4×4) + (4×5) + 6 + 9] / 20
= 75/20
= 3.75
Similarly,
Mean of Westwood = 77/20 = 3.85
So both means are between 3 and 4.
Median is the exact middle element when arranged in increasing or decreasing order.
Exact middle point is the average of 10th and 11th element.
Median of Middleton = (3 + 4)/2 = 3.5
Median of Westwood = (4 + 4)/2 = 4
Both have different medians.
Range of the data set is the difference of maximum point and minimum point.
Range of Middleton = 9 - 1 = 8
Range of Westwood = 6 - 2 = 4
Both have different ranges.
Range is a measure of variation.
Range of Westwood is less than range of Middleton.
So, Westwood has less variability than Middleton.
Hence the true statements are A, B and C.
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How many 5 digit codes are possible if the first digit cannot be 0 and digits can be repeated?
Answer:
Step-by-step explanation:
Zip codes with 5 digits (all five digits can be repeated): 10^5=100,000 if first digit is 0, its no longer 5-digit right? Zip codes with no digit being repeated: 10*9*8*7*6=30,240 if first digit is 0, its no longer 5-digit right? Zip codes with at least one digit being repeated: 90000-27216 = 62784 ?N
A chord is 16 units from the center of a circle. The radius of the circle is 20 units. What is the length of the chord?
How is the measure of a central angle and the corresponding chord related to the measure of the arc intercepted by the chord?
Answer:
Length of the chord: 24 units
Angles are equal
Step-by-step explanation:
Drop a Perpendicular from the centre onto the chord. It will divide the chord into two equal parts, d units each
d² + 16² = r²
d² = 20² - 16²
d² = 144
d = 12
Chord = 2d = 24 units
Measure of central angle and the corresponding chord related to the measure of the arc intercepted by the chord are the same, they're equal
Answer:
The entire chord length is 12*2 = 24
The degree measure of a minor arc is equal to the measure of the central angle that intercepts it.
Step-by-step explanation:
We can make a right triangle to solve for 1/2 of the chord length. The hypotenuse is 20 and one of the legs is 16
a^2+b^2 = c^2
16^2 + b^2 = 20^2
256 +b^2 = 400
Subtract 256 from each side
b^2 = 400-256
b^2 =144
Take the square root of each side
b = 12
That means 1/2 of the chord length is 12
The entire chord length is 12*2 = 24
Which point do The graphs F and G have in common
Answer:
1,0
Step-by-step explanation:
Answer:
1,0
Step-by-step explanation:
The "cold start ignition time" of an automobile engine is being investigated by a gasoline manufacturer. The following times, in seconds, were obtained for a test vehicle. 0.17, 1.94, 2.62, 2.35, 3.05, 3.15, 2.53, 4.81 and 1.92 Write answers as decimal values (i.e. 0.12) and round to two decimal places (if necessary)
Answer:
1. Sample Mean = 2.50
2. Sample Variance = 1.35
3. Standard Deviation = 1.16
Step-by-step explanation:
Note: As this question is not complete, similar can be found on internet where following are asked to calculate and here I will calculate these as well.
1. Sample Mean.
2. Sample Variance.
3. Sample Standard Deviation.
So, for sample mean to calculate from the given data points. We need to apply to following formula to calculate sample mean.
Sample Mean = (X1 + X2 + .... + XN) divided by Total number of data points.
Sample Mean = (0.17 + 1.94 + 2.62 + 2.35 + 3.05 + 3.15 + 2.53 + 4.81 + 1.92) divided by (9).
Sample Mean = 2.50
Likewise, from the answer of sample mean we can calculate sample variance by following steps.
Solution:
1. Subtract the obtained mean from each of the data point given.
(0.17 - 2.50) = -2.33
(1.94 - 2.50) = -0.56
(2.62 - 2.50) = 0.12
(2.35 - 2.50) = -0.15
(3.05 - 2.50) = 0.55
(3.15 - 2.50) = 0.65
(2.53 - 2.50) = 0.03
(4.81 - 2.50) = 2.31
(1.92 - 2.50) = -0.58
2. Square each of the differences obtained in step 1.
[tex]-2.33^{2}[/tex] = 5.43
[tex]-0.56^{2}[/tex] = 0.31
[tex]0.12^{2}[/tex] = 0.01
[tex]-0.15^{2}[/tex] = 0.02
[tex]0.55^{2}[/tex] = 0.30
[tex]0.65^{2}[/tex] = 0.42
[tex]0.03^{2}[/tex] = 0.01
[tex]2.31^{2}[/tex] = 5.34
[tex]-0.58^{2}[/tex] = 0.34
3. Sum all of these squares.
(5.43 + 0.31 + 0.01 + 0.02 + 0.30 + 0.42 + 0.01 + 5.34 + 0.34) = 12.18
4. Divide 12.18 by (n-1), where n = 9.
Sample Variance = 12.18/9 = 1.35
Now, by using sample variance, we can calculate standard deviation with easy simple steps.
So, in order to find standard deviation, we just need to take the square root of sample variance that we have already calculated above.
Standard Deviation = [tex]\sqrt{1.35}[/tex] = 1.16
Good Luck!
Suppose you are going to conduct a two tail test concerning the population mean. Suppose that you do not know what the population standard deviation is and that you have a sample of 55 observations. If you are going to conduct this test at the .01 level of significance what is the critical value?
Answer:
The critical value of t at 0.01 level of significance is 2.66.
Step-by-step explanation:
The hypothesis for the two-tailed population mean can be defined as:
H₀: μ = μ₀ vs. H₀: μ ≠ μ₀
It is provided that the population standard deviation is not known.
Since there is no information about the population standard deviation, we will use a t-test for single mean.
The test statistic is defined as follows:
[tex]t_{cal.}=\frac{\bar x-\mu}{s/\sqrt{n}}\sim t_{\alpha/2, (n-1)}[/tex]
The information given is:
n = 55
α = 0.01
Compute the critical value of t as follows:
[tex]t_{\alpha/2, (n-1)}= t_{0.01/2, (55-1)}=t_{0.005, 54}=2.66[/tex]
*Use a t-table for the value.
If the desired degrees of freedom are not provided consider he next highest degree of freedom.
Thus, the critical value of t at 0.01 level of significance is 2.66.
3 to the power of 5 and (3) to the power of 5
Answer:
243
Step-by-step explanation:
3x3=9
9x3=27
27x3=81
81x3=243
The plot shows the temperatures (in ºF) for a group of children who visited a doctor’s office.
A plot shows the temperature of children at a doctor's office. 1 child had a temperature of 96 degrees; 2, 97 degrees; 5, 98 degrees; 2, 99 degrees; 1, 100 degrees.
What conclusions can be drawn from the data set? Check all that apply.
Answer:
the answer is 1,3,4,5
Step-by-step explanation:
Erin spent $15.30 on ingredients for cookies she's making for the school bake sale. How many cookies must she sell at $0.35 apiece to make a profit
Answer:
She would have to sell 44 cookies or more.
Step-by-step explanation:
Answer:
She would have to sell 44 cookies or more
Step
Write an equation in slope-intercept form of the line with the given parametric equations.
x = 8t+3
y = 9t+ 3
The equation in slope-intercept from is [tex]y = \frac{9}{8}x - \frac{3}{8}[/tex].
Step-by-step explanation:
Given that,
x = 8t+3
y = 9t+ 3
Now, getting the value of t on both side to compare the equations.
[tex]x = 8t+3[/tex]
[tex]x -3 = 8t[/tex]
[tex]t = \frac{x-3}{8}[/tex]
also
[tex]y = 9t+ 3[/tex]
[tex]t= \frac{y-3}{9}[/tex]
Now, by comparing the values of t, we get
[tex]\frac{x-3}{8} = \frac{y-3}{9}[/tex]
[tex]9x - 27 = 8y -24[/tex]
[tex]9x - 3 = 8y[/tex]
[tex]y = \frac{9}{8}x - \frac{3}{8}[/tex]
Hence, the equation in slope-intercept from is [tex]y = \frac{9}{8}x - \frac{3}{8}[/tex].
Which of the following is the equation of a line that passes through (-2, -1) and (-4, -3)?
Answer:
y = x+1
Step-by-step explanation:
You should use the point-slope form of y-y1 = m(x-x1) to solve this.
First you use the slope formula to find your slope. (y2-y1)/(x2-x1)
(-1 - -3)/(-2 - -4) = 2/2 = 1
With the slope of 1 found, just plug a point into the point-slope form.
y-(-1) = (1)(x-(-2)) ->
y+1 = x+2 ->
y = x+1
y=x+1 is the equation of a line that passes through (-2, -1) and (-4, -3)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The slope of line passing through (-2, -1) and (-4, -3)
m = -3+1/-4+2
=-2/-2= 1
Now let us find y intercept
-1=1(-2)+b
-1=-2+b
b=1
Hence, y=x+1 is the equation of a line that passes through (-2, -1) and (-4, -3)
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Please help me! I need this to complete my math hw
Answer:
1
Step-by-step explanation:
You "complete the square" by adding the square of half the x-term coefficient. Here, that is ...
((-2)/2)² = 1 . . . . value added to complete the square
If you want to keep 0 on the right, you must also subtract this value:
x² -2x -36 = 0
x² -2x +1 -36 -1 = 0 . . . . . . add and subtract 1 on the left
(x -1)² -37 = 0 . . . . . . . . . . . written as a square
An ant arrives at the snail’s starting position at time minutes and follows the snail’s path. During the interval minutes, the ant travels in the same direction as the snail with a constant acceleration of 2 inches per minute per minute. The ant catches up to the snail at time minutes. The ant’s velocity at time is B inches per minute. Find the value of B.
QUESTION BEGINNING
Given a snail is traveling along a straight path. The snail’s velocity can be modeled by [tex]v(t)=1.4ln(1+t^2)[/tex] inches per minute for 0 ≤ t ≤ 15 minutes.
Answer:
B=22.35 Inches per minutes
Step-by-step explanation:
If the snail's velocity is [tex]v(t)=1.4ln(1+t^2)[/tex] per minute, its displacement for 0 ≤ t ≤ 15 minutes is given by the integral:
[tex]\int v(t) dt=\int (1.4ln(1+t^2))dt=76.04307[/tex]
The constant acceleration of the ant is 2 Inches per minute.
The velocity of the ant therefore, twill be:
[tex]\int 2 dt=2t+K, $where K is a constant of integration$[/tex]
For the interval, 12≤t≤15, the displacement of the ant is:
[tex]\int_{12}^{15}(2t+K) dt=81+3K[/tex]
Since the snails displacement and that of the ant are equal in 12≤t≤15.
81+3K=76.04307
3K=76.04307-81
3K=-4.95693
K=-1.65231
At t=12, the velocity of the ant is therefore:
2t+K=2(12)-1.65231=22.348 Inches per minutes
B=22.348 Inches per minutes
Final answer:
The question examines a scenario involving an ant accelerating to catch up with a snail, focusing on determining the ant's velocity at the catch-up point. Utilizing the principle of kinematics and acceleration, the answer lies in relating the acceleration to the final velocity, dependent on the time variable, which underscores the direct relationship between acceleration and velocity increase.
Explanation:
The question essentially deals with kinematics, specifically with the scenario of an ant accelerating from rest to catch up with a snail. Given the ant accelerates at 2 inches per minute per minute, and eventually matches velocities with the snail, the goal is to find the ant's velocity (B inches per minute) at the moment it catches up.
Firstly, we know the acceleration (a) is 2 inches/minute2. From kinematic equations, specifically v = u + at, where 'u' is the initial velocity (0 in this case since the ant starts from rest), 'a' is acceleration, and 't' is time, we can plug in our values. The time variable 't' here represents the duration from when the ant starts until it catches up with the snail, which is not explicitly given but is critical in understanding the rate of acceleration's contribution to velocity.
For the purpose of solving this problem, without explicit time or distances, we focus on the principle that the ant's final velocity (B) is a product of its acceleration over a given period: B = 0 + (2)t. Thus, the value of 'B' entirely depends on the time 't', demonstrating a direct correlation between acceleration duration and velocity increase.
Please help
Prove that the median to the hypotenuse of a right triangle is half the hypotenuse.
To compare lengths, use the _____ Formula.
Answer:
it is the midpoint formula because that is the only equation of that is being divided by 2. The formula is X1 +X2 divied by 2 then it is Y1 + Y2 dived by two which gives you half of something like a line
Step-by-step explanation:
Answer:
mid point
Step-by-step explanation:
Which choices are equivalent to the quotient below? Check All That Apply.
Answer:
A, E
Step-by-step explanation:
brainliest please
The diagram shows the number of dollars each child has in a family. How can you redistribute the money so that each child has the same amount? Check all that apply.
A balance diagram going from 1 to 9. 2 circles are above 4 and 2 circles are above 8.
Each child who has $8 must give away $4.
Each child who has $8 must give away $2.
Each child who has $4 must be given $4.
Each child who has $4 must be given $2.
When fairly balanced, each child has $6.
When fairly balanced, each child has $7.
Answer:
2,4,5
Step-by-step explanation:
Answer:2,4,and5
Step-by-step explanation:Common sense
A sample of 900900 computer chips revealed that 49%49% of the chips do not fail in the first 10001000 hours of their use. The company's promotional literature states that 52%52% of the chips do not fail in the first 10001000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. Determine the decision rule for rejecting the null hypothesis, H0H0, at the 0.020.02 level.
Answer:
The proportion of chips that do not fail in the first 1000 hours of their use is 52%.
Step-by-step explanation:
The claim made by the company is that 52% of the chips do not fail in the first 1000 hours of their use.
A quality control manager wants to test the claim.
A one-proportion z-test can be used to determine whether the proportion of chips do not fail in the first 1000 hours of their use is 52% or not.
The hypothesis can be defined as:
H₀: The proportion of chips do not fail in the first 1000 hours of their use is 52%, i.e. p = 0.52.
Hₐ: The proportion of chips do not fail in the first 1000 hours of their use is different from 52%, i.e. p ≠ 0.52.
The information provided is:
[tex]\hat p=0.49\\n=900\\\alpha =0.02[/tex]
The test statistic value is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.49-0.52}{\sqrt{\frac{0.52(1-0.52)}{900}}}=-1.80[/tex]
The test statistic value is -1.80.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=2\times P(Z<-1.80)\\=2\times 0.03593\\=0.07186[/tex]
*Use a z-table.
The p-value = 0.07186 > α = 0.02.
The null hypothesis was failed to be rejected at 2% level of significance.
Conclusion:
The proportion of chips that do not fail in the first 1000 hours of their use is 52%.
Ximena spent 72 of the day
shopping at the mall. She spent
74 of this time trying on jeans.
What fraction of the day did
Charlotte spend trying on jeans?
Answer:
Step-by-step explanation:
1/8
1/2 multiply 1/4
Consider the following sets of matrices: M2(R) is the set of all 2 x 2 real matrices; GL2(R) is the subset of M2(R) with non-zero determinant: SL2(R) is the subset of GL2(R) with determinant 1. We know that multiplication is a binary operation on M2(R); show that it is an induced operation on the other 2 sets (You may freely use known facts from Math 3A for this).
Answer:
Step-by-step explanation:
REcall the following definition of induced operation.
Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.
So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.
For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).
Case SL2(R):
Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So
[tex]\text{det(AB)} = \text{det}(A)\text{det}(B)\neq 0[/tex].
So AB is also in SL2(R).
Case GL2(R):
Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So
[tex]\text{det(AB)} = \text{det}(A)\text{det}(B)=1\cdot 1 = 1[/tex].
So AB is also in GL2(R).
With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).
What is the value for x 2x+3=x-4
Answer:
x = -7
Step-by-step explanation:
2x + 3 = x - 4
→ Minus x from both sides to isolate -4
x + 3 = -4
→ Minus 3 from both sides to isolate x and henceforth find the value of x
x = -7
Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion? Group of answer choices We can select a higher confidence level and increase the sample size. We can select a higher confidence level and decrease the sample size. We can select a lower confidence level and increase the sample size. We can select a lower confidence level and decrease the sample size.
Answer:
We can select a lower confidence level and increase the sample size.
Step-by-step explanation:
The precision of the confidence interval depends on the margin of error ME = Zcritical * Sqrt[(p(1-p)/n]
In this Zcritical value is in the numerator. Z critical decreases as Confidence level decreases. (Zc for 99% = 2.576, Zc for 95% is 1.96, Zc for 90% = 1.645). Therefore decreasing the Confidence level decreases ME.
Also we see that sample size n is in the denominator. So the ME decreases as sample size increases.
Therefore, We can select a lower confidence level and increase the sample size.
The best option that could be used to produce higher precision in our estimates of the population proportion is;
Option C; We can select a lower confidence level and increase the sample size.
Formula for confidence interval is given as;
CI = p^ ± z√(p^(1 - p^)/n)
Where;
p^ is the sample proportion
z is the critical value at given confidence level
n is the sample size
Now, the margin of error from the CI formula is:
MOE = z√(p^(1 - p^)/n)
Now, the lesser the margin of error, the narrower the confidence interval and thus the more precise is the estimate of the population proportion.
Now, looking at the formula for MOE, two things that could change aside the proportion is;
z and n.
Now, the possible values of z are;
At CL of 99%; z = 2.576
At CL of 95%; z = 1.96
At CL of 90%; z = 1.645
We can see that the higher the confidence level, the higher the critical value and Invariably the higher the MOE.
Thus, to have a narrow CI, we need to use a lower value of CL and increase the sample size.
Read more at; https://brainly.com/question/14225622
Select all the expression that
Answer:
2nd, 4th and last one are correct answers
Step-by-step explanation:
[tex] {16}^{ \frac{5}{2} } \\ = ( {4}^{2} )^{ \frac{5}{2} } \\ = {4}^{{2} \times \frac{5}{2} } \\ = {4}^{5} \\ [/tex]
Options: 2nd, 4th and last one are correct answers
implify the product. 2p(–3p2 + 4p – 5)
Answer:
=2p(-2p-5)
Step-by-step explanation:
2p(–3p2 + 4p – 5)
=2p(4p-6p-5)
=2p(-2p-5)