No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year and this can be determined by using the formula of z-score.
Given :
The mean is 12,494 miles. The standard deviation of 1290 miles.The following steps can be used in order to determine whether you have to buy a vehicle or not:
Step 1 - The formula of z-score can be used in order to determine whether you have to buy a vehicle or not.
Step 2 - The z-score formula is given below:
[tex]\rm z = \dfrac{x-\mu}{\sigma}[/tex]
Step 3 - Substitute the known terms in the above expression.
[tex]\rm z = \dfrac{6000-12494}{1290}=-5.0341[/tex]
Step 4 - Now, the p-value is given below:
[tex]\rm P(x < 6000)=P(z<-5.0341)[/tex]
Step 5 - Now, using the z table the value of P is:
P(x < 6000) = 0
No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year.
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S is directly proportional to the fifth power of t
[tex]\[ s = kt^5 \][/tex]
This equation represents the model for the statement "s is directly proportional to the fifth power of t".
When two variables [tex]\( s \)[/tex] and [tex]\( t \)[/tex] are directly proportional to each other, it means that as one variable increases, the other variable also increases by a constant factor. Mathematically, we can express this relationship as:
[tex]\[ s = kt^n \][/tex]
Where:
- [tex]\( s \)[/tex] is the dependent variable.
-[tex]\( t \)[/tex] is the independent variable.
- [tex]\( k \)[/tex] is the constant of proportionality.
- [tex]\( n \)[/tex] is the exponent representing the power to which the independent variable is raised.
In this case, the statement says that s is directly proportional to the fifth power of t . So, we have:
[tex]\[ s = kt^5 \][/tex]
This equation represents the model for the statement "s is directly proportional to the fifth power of t".
Complete correct question:
Write a model for the statement
s is directly proportional to the fifth power of t.
Rachel poured 4/5 of a gallon of water into a bucket. Later, she added 3/10 of a gallon more. How much water is in the bucket now?
Answer:
1 1/10 gallons
Step-by-step explanation:
Add 4/5 gallon + 3/10 gallon
Get a common denominator of 10
4/5*2/2 + 3/10
8/10 +3/10
11/10
Change from an improper fraction to a mixed number
10/10 + 1/10
1 1/10 gallons
Answer:
1.1
Step-by-step explanation:
If she added the first 4/5 then she added the 3/10 then you have to add them to figure out how much water is in the bucket.
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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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
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
How many numbers are greater than 45?
There are 54 two-digit numbers greater than 45. This is calculated by finding the range of valid two-digit numbers (46 to 99) or carefully counting possible combinations without including 45.
Explanation:The two-digit numbers greater than 45 are any numbers from 46 to 99. We can find the amount of these numbers by subtracting 45 from 99. So, there are 54 two-digit numbers greater than 45.
Another way to visualize this is by considering the two-digit possibilities. The first digit can range from 4 to 9 (six possibilities), and the second digit can range from 0 to 9 (ten possibilities). However, since 40-45 are not included, we subtract 5 from the total possibilities, resulting in 60 (=6*10) -5 = 55. Therefore, it seems that we have one number too many, but we must not forget that 45 itself is not included, hence the total numbers exceeding 45 are 54 (55-1).
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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.
These are the means and standard deviations for samples of prices from two
different brands of shoes
Brand A
Mean: $50
Standard deviation: $5
Brand B
Mean: $40
Standard deviation: $8
Select the two true statements,
A. Brand A has a higher average price than brand B.
B. Brand A's prices are more spread out than brand B's prices.
C. Brand A has a lower average price than brand B.
D. Brand A's prices are less spread out than brand B's prices,
Answer:
A. Brand A has a higher average price than brand B.
D. Brand A's prices are less spread out than brand B's prices.
Step-by-step explanation:
We are given the means and standard deviations for samples of prices from two different brands of shoes below;
Brand A Brand B
Mean : $50 Mean : $40
Standard deviation : $5 Standard deviation : $8
Now, from the given statements;
Statement A is correct that Brand A has a higher average price than brand B because as given above Mean of Brand A ($50) > Mean of Brand B ($40).
Also, Statement D is correct that Brand A's prices are less spread out than brand B's prices because the Variance of Brand A is less than the variance of Brand B, i.e.;
Variance of Brand A = [tex]5^{2}[/tex] = $25
Variance of Brand B = [tex]8^{2}[/tex] = $64
Clearly, $25 < $64, so statement D is also correct.
Therefore, the two true statements are Statement A and Statement D.
Final answer:
A. Brand A has a higher average price than brand B.
D. Brand A's prices are less spread out than brand B's prices.
Explanation:
The true statements are that Brand A has a higher average price and less variability in prices than Brand B, which is represented by a lower standard deviation for Brand A.
To expand on these points:
Brand A has a mean price of $50 which is higher than Brand B's mean price of $40, confirming that Brand A has a higher average price (Statement A).
Brand A's standard deviation is $5, while Brand B's standard deviation is $8. A standard deviation is a measure of spread or variability in a set of data. The fact that Brand A's standard deviation is lower indicates that its prices are less variable and more closely clustered around the mean, hence less spread out compared to Brand B (Statement D).
A survey is to be conducted to determine the average driving in miles by Minnesota State University, Mankato students. The investigator wants to know how large the sample should be so that he/she can be 92% confident on the estimate and the estimate is within 1.5 miles of the true average. A similar study conducted in past and it was found that the standard deviation of the students’ driving distances was 8.2 miles.
Answer:
[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]
So the answer for this case would be n=92 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =1.5 and we are interested in order to find the value of n, if we solve n from equation (b) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 92% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.04;0;1)", and we got [tex]z_{\alpha/2}=1.75[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]
So the answer for this case would be n=92 rounded up to the nearest integer
The culinary herb cilantro, Coriandrum sativum, is very polarizing; some people love it and others hate it. A genetic component is suspected to be at play. A survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro. A total of 3181 said that they dislike the taste of cilantro.
(a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro
(b) Estimate with 95% confidence (and interpret) a lower confidence bound for the proportion of all Amer- ican adults of European ancestry who dislike the taste of cilantro
Answer:
The 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro
( 0.2552 , 0.2709)
b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is 0.2552
Step-by-step explanation:
Explanation:-
Given data a survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro.
large sample size 'n' = 12087 American adults
in survey A total of 3181 said that they dislike the taste of cilantro.
so The sample proportion 'p' = [tex]\frac{3181}{12087} = 0.2631[/tex]
a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European ancestry who dislike the taste of cilantro.
[tex](p - 1.96 \sqrt{\frac{pq}{n} } ,p + 1.96\sqrt{\frac{pq}{n} } )[/tex]
[tex](0.2631 - 1.96 \sqrt{\frac{0.2631 X 0.7369}{12087} } ,0.2631 + 1.96\sqrt{\frac{0.2631 X 0.7369 }{12087} } )[/tex]
(0.2631 - 0.00784 , 0.2631 + 0.00784 )
( 0.2552 , 0.2709)
b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is 0.2552
We are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%, and at least 25.5% dislike the taste.
Explanation:This question is related to confidence intervals in statistics. To compute a confidence interval for a population proportion, we mainly need the sample proportion and the size of the sample. Here, the proportion is the number of respondents that dislike cilantro (3181) divided by the total number of respondents (12087).
Thus, the sample proportion (value of p) is 3181/12087 = 0.263 or 26.3%.
The formula for a confidence interval is:
CI = p +/- Z * sqrt[ (p(1-p)) / n ],
where Z is the Z-score (for 95% confidence, Z = 1.96), p is the sample proportion, and n is the sample size.
Applying the values, we get:
CI = 0.263 +/- 1.96 * sqrt[ (0.263)(1 - 0.263) / 12087 ]
After calculation, the 95% confidence interval is about (0.255, 0.271). This means we are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%.
For the lower bound, we can take the lower limit of our confidence interval, which is 0.255 or 25.5%. This means we are 95% confident that at least 25.5% of all American adults of European ancestry dislike the taste of cilantro.
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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.
What are the zeroes of the function y=3(x-a)(x+b) in terms of a and b?
Answer:
a, -b
Step-by-step explanation:
When x is a, the function becomes
[tex]f(a)=3(a-a)(a+b)[/tex]
as you see, a-a is 0, and as your whole function is multiplied by this, it makes it 0.
[tex]f(-b)=3(-b-a)(-b+b)[/tex]
As you see -b+b is 0, and once again, this would make the whole function 0.
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
please answer tyty :)
Answer:
3
Step-by-step explanation:
0 indicates no relationship. must be full number.
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].
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:
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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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).
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.
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]
Help me answer please.
Answer:
see explanation
Step-by-step explanation:
(a)
For the graph to display direct proportion it must pass through the origin.
The graph shown does not pass through the origin thus does not represent direct proportion.
(b)
Given that q is directly proportional to r then the equation relating them is
q = kr ← k is the constant of proportion
To find k use the condition q = 76 when r = 20, thus
76 = 20k ( divide both sides by 20 )
3.8 = k
q = 3.8r ← equation of proportion
When r = 45, then
q = 3.8 × 45 = 171
Which choices are equivalent to the quotient below? Check All That Apply.
Answer:
A, E
Step-by-step explanation:
brainliest please
Compare to the graph f(x)=x^2 the graph of g(x)=(x-2)+3 is the result of translating f(x)
1.2 units up 3 units to the right
2. 2 units down and 3 units up
3. 2 units right and 3 units up
4 2 units left and 3 units right
Answer:
i believe it is 4 but i'm not so sure
Step-by-step explanation:
:)
The graph of g(x)=(x-2)^2+3 compared to the graph of f(x)=x^2 is translated 2 units to the right and 3 units upwards.
Explanation:To understand the transformation of graphs in mathematical terms, consider the initial function f(x) = x^2. The transition to the new function g(x)=(x-2)^2+3 is a result of a shift or translation of the graph. This transformation behaves as per the following rule: g(x) = f(x-h)+k where 'h' units is the horizontal displacement and 'k' units is the vertical displacement.
In the function g(x), x shifts two units to the right (as indicated by (x-2)) and three units upward (as indicated by +3).
So, the correct answer is 2 units right and 3 units up.
Learn more about graph transformation here:https://brainly.com/question/19040905
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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 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
An SRS of 2,500 individuals was taken from a city with population 1 million, to estimate the percentage of city residents with a graduate degree. 555 people in the sample had a graduate degree. The proportion of individuals in the city with a graduate degree is estimated as 23%. Say the true percentage of individuals in the city who have a graduate degree is 22%. In this case, the standard error of the sample proportion is closest to:
Answer:
The standard error of the sample proportion is closest to 1%
Step-by-step explanation:
Standard error of the sample proportion is given as
σₓ = √[p(1-p)/n]
where
p = sample proportion = estimated to be 23% = 0.23
n = Sample size = 2500
σₓ = √[p(1-p)/n]
σₓ = √[0.23×0.77/2500]
σₓ = 0.0084166502 = 0.00842
σₓ = 0.00842 = 0.842%
Hence, it is easy to see that the standard error of the sample proportion is closest to 1%.
Hope this Helps!!!
Coin Toss Results H = Heads T = Tails T H T H T H T T T T H T H T T Find the experimental probability of tossing heads.
Answer:
1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
took a test and its correct.
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
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:
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%.
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: