Answer:
Denver got 72 inches of snow over three days.
Step-by-step explanation:
Since it has snowed consistently for 3 days, accumulating an inch of snow per hour, over that number of days at least 72 inches of snow would have accumulated.
This is so because, since each day has 24 hours, in the event of a 3-day snowfall, it would have lasted 72 hours. Thus, while every hour a new inch of snow would accumulate, at the end of the storm the city of Denver would have accumulated 72 inches of snow (1 x 24 x 3 = 72).
A male student of the author has a measured pulse rate of 52 beats per
minute. According to a National Center for Health Statistics data set, males have a mean
pulse rate of 67.3 beats per minute and a standard deviation of 10.3 beats per minute.
Determine whether the student's pulse rate is significantly low or high by calculating the
z score. Consider usual pulse rates to be within 2 standard deviations of the mean.
Justify your answer.
Answer:
[tex]z=-1.49[/tex]
Step-by-step explanation:
[tex]\text{Standard Score, z} =\dfrac{X-\mu}{\sigma} $ where:\\\\Mean Pulse rate, \mu =67.3$ beats per minute\\Standard Deviation, \sigma = 10.3$ beats per minute.\\[/tex]
For a male student who has a measured pulse rate of 52 beats per minute.
Raw Score, X =52 beats per minute.
Therefore:
[tex]\text{Standard Score, z} =\dfrac{52-67.3}{10.3}\\z=-1.49[/tex]
Since the usual pulse rates are within 2 standard deviations of the mean, a z-score of -1.49 tells us that the selected student's pulse rate is within the usual pulse rates.
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. The test scores of 40 students are listed below. Construct a boxplot for the data set.
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
Answer:
Minimum = 25
First quartile = 58
Second quartile = 72
Third quartile = 80
Maximum = 98
Step-by-step explanation:
Find the vertex of the graphed function.
f(x) = |x-4| +3
AY
00
6
4
2
Y
4
The vertex is at
Answer:
The x-coordinate is the solution to x - 4 = 0, which is x = 4 and the y-coordinate is 3 so the answer is (4, 3).
What is the distance between (8, -3) and (4, - 7)?
Answer:
[tex]distance=\sqrt{32}[/tex] , which agrees with answer "c" in your list of possible options
Step-by-step explanation:
Use the formula for distance between two points [tex](x_1,y_1)[/tex], and [tex](x_2,y_2)[/tex] on the plane:
[tex]distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance= \sqrt{(4-8)^2+(-7-(-3))^2} \\distance= \sqrt{(-4)^2+(-4)^2} \\distance=\sqrt{16+16}\\distance=\sqrt{32}[/tex]
The FDA regulates that fresh Albacore tuna fish that is consumed is allowed to contain 0.82 ppm of mercury or less. A laboratory is estimating the amount of mercury in tuna fish for a new company and needs to have a margin of error within 0.023 ppm of mercury with 97% confidence. Assume the population standard deviation is 0.143 ppm of mercury. What sample size is needed? Round up to the nearest integer, do not include any decimals. Answer:
Answer:
[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]
So the answer for this case would be n=183 rounded up to the nearest integer
Step-by-step explanation:
Information provided
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma = 0.143[/tex] represent the population standard deviation
n represent the sample size
[tex] ME = 0.023[/tex] the margin of error desired
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 =0.023 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The confidence level is 97% or 0.97 and the significance would be [tex]\alpha=1-0.97=0.03[/tex] and [tex]\alpha/2 = 0.015[/tex] then the critical value would be: [tex]z_{\alpha/2}=2.17[/tex], replacing into formula (5) we got:
[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]
So the answer for this case would be n=183 rounded up to the nearest integer
Any help would be great
Hey there! :)
Answer:
[tex]-25m^{6}n^{9}[/tex]
Step-by-step explanation:
The product rule means that when multiplying variables with exponents, the exponents must be added together. Therefore:
[tex](-5m^{5}n^{6})(5mn^{3}) =[/tex]
[tex]-25m^{5+1}n^{6+3} =[/tex]
Simplify:
[tex]-25m^{6}n^{9}[/tex]
This is your answer!
The demand for the video games provided by Mid-Tech Video Games Inc. has exploded in the last several years. Hence, the owner needs to hire several new technical people to keep up with the demand. Mid-Tech gives each applicant a special test that Dr. McGraw, the designer of the test, believes is closely related to the ability to create video games. For the general population, the mean on this test is 100. Below are the scores on this first test for the applicants. 95 105 120 81 90 115 99 100 130 10 The owner is interested in the overall quality of the job applicants based on this test. Compute the mean and the median scores for the 10 applicants. What would you report to the owner
Answer:
Mean: 94.5.
Median: 99.5
Standard deviation: 33.1
We can tell the owner that the applicants don't have a score significantly below from 100.
Step-by-step explanation:
First, we analize the sample and calculate the statistics (mean, median and standard deviation).
Mean of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(95+105+120+81+90+115+99+100+130+10)\\\\\\M=\dfrac{945}{10}\\\\\\M=94.5\\\\\\[/tex]
The median, as the sample size is an even number, can be calculated as the average between the fifth and sixth value, sort by value:
[tex]\text{Median}=\dfrac{99+100}{2}=99.5[/tex]
The standard deviation is:
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((95-94.5)^2+(105-94.5)^2+(120-94.5)^2+. . . +(10-94.5)^2)}\\\\\\s=\sqrt{\dfrac{9834.5}{9}}\\\\\\s=\sqrt{1092.7}=33.1\\\\\\[/tex]
To tell if this sample has a value significantly lower than the expected score of 100, we should make a hypothesis test.
The claim is that the mean score is significantly lower than 100.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=94.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.1.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{33.1}{\sqrt{10}}=10.467[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{94.5-100}{10.467}=\dfrac{-5.5}{10.467}=-0.53[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
This test is a left-tailed test, with 9 degrees of freedom and t=-0.53, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.53)=0.306[/tex]
As the P-value (0.306) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean score is significantly lower than 100.
Butler Trucking Company has developed a regression equation to predict the delivery time for its drivers (y). The model is based on the miles traveled (x 1), the number of deliveries (x 2) and whether or not the travel will occur during rush hours (x 3 - 1 if during rush hour and 0 if not during rush hour). The regression equation that they use is y
Answer:
The answer is Y = 6.3973.
Note: Kindly find an attached document of the complete question to this solution
Sources: The complete question was researched from Quizlet site.
Step-by-step explanation:
Solution
Given that:
The regression equation is given below:
Y = - 0.3302 + 0.0672 x₁ + 0.6735 x₂ + 0.9980 x₃
Now,
When x₂ = 5, x₁ = 50, x₃ = 0
Y = - 0.3302 + 0.0672 * 50 +0.6735 * 5
Y= - 0.3302 + 3.36 + 3.3675
Y = 6.3973
Therefore the time (hour) it will take for the driver to make five deliveries on a 50 mile journey not during rush hour is 6.3973.
Factor completely 6x to the second power - 36xy + 12x
Answer:
6x(x - 6y +2)
Step-by-step explanation:
Step 1: Write out expression
6x² - 36xy + 12x
Step 2: Factor out x
x(6x - 36y + 12)
Step 3: Factor out 6
6x(x - 6y + 2)
That is the most we can do. We can only take GCF to factor. Since we don't have an y² term we do not have binomial factors.
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound- shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph
Answer:
15.74% of the player's serves were between 115 mph and 145 mph
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 100, \sigma = 15[/tex]
What percentage of the player's serves were between 115 mph and 145 mph
This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.
X = 145
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{145 - 100}{15}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
X = 115
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.9987 - 0.8413 = 0.1574
15.74% of the player's serves were between 115 mph and 145 mph
You're pretty sure that your candidate for class president has about 6565% of the votes in the entire school. But you're worried that only 100100 students will show up to vote. How often will the underdog (the one with 3535% support) win? To find out, you
Answer:
You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.
a. describe-how-you-will-simulate a component.
b. describe-how-you-will-simulate a trial.
c. describe-the-response-variable
Step-by-step explanation:
Part A:
A component is one voter's voting. An outcome is a vote in favor of our candidate.
Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.
Part B:
A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.
And counted how many people voted for each candidate. Whoever gets the majority of the votes wins the trial.
Part C:
The response variable is whether the underdog wins or not.
To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.
In general, shopping online is supposed to be more convenient than going to stores. However, according to a recent Harris Interactive poll, 87% of people have experienced problems with an online transaction (The Wall Street Journal, October 2, 2007). Forty-two percent of people who experienced a problem abandoned the transaction or switched to a competitor′s website. Fifty-three percent of people who experienced problems contacted customer-service representatives.
a. What percentage of people did not experience problems with an online transaction?
b. What percentage of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website?
c. What percentage of people experienced problems with an online transaction and contacted customer-service representatives?
Answer:
a) 13% of people did not experience problems with an online transaction.
b) 36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website
c) 46.11% of people experienced problems with an online transaction and contacted customer-service representatives.
Step-by-step explanation:
a. What percentage of people did not experience problems with an online transaction?
87% of people have experienced problems with an online transaction. So 100 - 87 = 13% of people did not experience problems with an online transaction.
b. What percentage of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website?
87% of people have experienced problems with an online transaction. Forty-two percent of people who experienced a problem abandoned the transaction or switched to a competitor′s website.
Then:
0.87*0.42 = 0.3654
36.54% of people experienced problems with an online transaction and abandoned the transaction or switched to a competitor′s website.
c. What percentage of people experienced problems with an online transaction and contacted customer-service representatives?
87% of people have experienced problems with an online transaction. Fifty-three percent of people who experienced problems contacted customer-service representatives.
Then:
0.87*0.53 = 0.4611
46.11% of people experienced problems with an online transaction and contacted customer-service representatives.
Where is my phone? I seem to have lost my phone. I know where I last saw it but it has been moved since then and I need help to locate it. It started at the following coordinates A (14, -12); B (14, -19); C (10, -19); D (10, -14); E (13, -14); F (13, -12). My Mom told me she translated it 6 units to the left Then my little brother said he had reflected it over the Y-axis My friend many found it and translated it 9 units up Dad said he tripped over it and reflected it over the X-axis My sister then rotated it 900 clockwise Uncle Jose translated it 5 units left and 4 units down Cousin Michelle then said she rotated it 900 clockwise Finally my dog picked it up and translated it 5 units down and 10 units to the right Where is my phone? Using the scenario on this page do the following. Graph the preimage using the given points. Label points (A, B, C, ...) Transform the objects using the information provided. Show each transformation and label. (A', B', C', ...) Determine the final location. Write a 2 to 3 sentence explain on how you found the phone location.
Answer:
see attached
Step-by-step explanation:
The attachments show the initial (brown) and final (blue) positions of the phone. The spreadsheet shows all the intermediate locations and the formulas used to determine them.
The two reflections cancel the total of 180° of CW rotation, so the net result is simply a translation. That translation is up by 9 units.
__
Translation up adds to the y-coefficient; translation right adds to the x-coefficient. Down or left use negative values.
90° CW does this: (x, y) ⇒ (y, -x)
Reflection across y does this: (x, y) ⇒ (-x, y)
Reflection across x does this: (x, y) ⇒ (x, -y)
Margo borrows $1700, agreeing to pay it back with 4% annual interest after 6 months. How much interest
will she pay?
Round your answer to the nearest cent, if necessary.
Answer:
$1733.67
Step-by-step explanation:
Simple interest rate formula: A = P(1 + r)^t
Simply plug in your known variables
A = 1700(1 + 0.04)^0.5
A = 1733.67
Remember that t is time in years.
there are only red counters and blue counters in a bag. Jim takes at random a counter from a bag. the probability that the counter is red is 0.45 Jim puts the counter back into the bag. Molly takes at random a counter from the bag. She puts the counter back in the bag. What is the probability that Jim and Molly take counters of different colours? Give your answer as a decimal
Answer:
0.495 probability that Jim and Molly take counters of different colours
Step-by-step explanation:
For each trial, there are only two possible outcomes. Either a blue counter is picked, or a red counter is picked. The counter is put back in the bag after it is taken, which means that we can use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that the counter is red is 0.45
This means that [tex]p = 0.45[/tex]
Jim taken a counter, then Molly:
Two trials, so [tex]n = 2[/tex]
What is the probability that Jim and Molly take counters of different colours?
One red and one blue. So this is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{2,1}.(0.45)^{1}.(0.55)^{1} = 0.495[/tex]
0.495 probability that Jim and Molly take counters of different colours
What is the value of (4-2): – 3 x 4?
-20
-4
4
20
Answer:
4
Step-by-step explanation:
2.
√3x + 7 + √x + 1 =2
Answer:
x = -1
Step-by-step explanation:
The usual approach to these is to square the radicals until they are gone.
[tex]\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}[/tex]
Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.
The solution is x = -1.
_____
Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.
A student said that the y-intercept of the function y = 3 · 4x is 4. What is their mistake? What is the actual y-intercept?
Answer:
The y intercept is 0Step-by-step explanation:
the equation of a line is given as
[tex]y= mx+c[/tex]
where
m= is the slope
c= is the y intercept
their mistake is that they did not recall that if the "c" is not shown, it is assumed to be zero (0)
N
Write the rate as a unit rate
729 riders in 9 subway cars
А
The unit rate is
This
(Simplify your answ
riders/car
Answer:
Unit rate = 81 riders/ car.
Step-by-step explanation:
Given
729 riders in 9 cars
we have to find unit rate in terms of riders per car
let the the riders per car (i.e rate) be x.
If there are 9 cars then
total no. of riders in 9 cars = no. of cars * riders per car = 9*x = 9x
given that 729 riders in 9 cars
then
9x = 729
=> x = 729/9 = 81
Thus, riders per car = x = 81.
Unit rate is 81 riders per car.
The following questions pertain to the properties of the STANDARD NORMAL distribution. (a) True or False: The distribution is bell-shaped and symmetric. True False (b) True or False: The mean of the distribution is 0. True False (c) True or False The probability to the left of the mean is 0. True False (d) True or False The standard deviation of the distribution is 1. True False
Answer:
a. The distribution is bell-shaped and symmetric: True.
b. The distribution is bell-shaped and symmetric: True.
c. The probability to the left of the mean is 0: False.
d. The standard deviation of the distribution is 1: True.
Step-by-step explanation:
The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].
It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.
We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where [tex] \\ x[/tex] is the raw score that we want to standardize.
Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:
(a) True or False: The distribution is bell-shaped and symmetric
Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.
(b) True or False: The mean of the distribution is 0.
Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
If [tex] \\ x = \mu[/tex]
[tex] \\ z = \frac{\mu - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{0}{\sigma}[/tex]
[tex] \\ z = 0[/tex]
Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.
(c) True or False: The probability to the left of the mean is 0.
Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].
(d) True or False: The standard deviation of the distribution is 1.
Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.
In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].
In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.
Answer:
A: true
B: true
C: false
D: true
6 identical toys weigh 1.8kg how much would 4 weigh
Answer:
1.2kg
Step-by-step explanation:
6 identical toys weigh 1.8kg.
1 toy would weigh:
1.8/6 = 0.3
0.3 kg.
Multiply 0.3 with 4 to find how much 4 identical toys would weigh.
0.3 × 4 = 1.2
4 identical toys would weigh 1.2kg
Answer:
[tex]1.2kg[/tex]
Step-by-step explanation:
6 identical toys weigh = 1.8kg
Let's find the weight of 1 toy ,
[tex]1.8 \div 6 = 0.3[/tex]
Now, lets find the weigh of 6 toys,
[tex]0.3 \times 4 = 1.2kg[/tex]
Justin spent $23 on fruit at grocery store. He spent a total of $25 at the store. What percentage of the total did he spend on fruit?
Step-by-step explanation:
In my opinion maybe he has spent 98%
Please answer this correctly
Answer:
The number of employees classified into groups as shown below:
1 - 10: 3 6 (2companies)
11-20: 16 (1 company)
21-30: 25, 26, 27 (3 companies)
31-40: 34, 35, 35, 35, 36 (5 companies)
41-50: 41, 43, 48, 48 (4 companies)
Hope this helps!
Answer:
11-20 is 1
31-40 is 5
Step-by-step explanation:
Just count the amount
Hope that helps :D
Simplify the expression by combining like terms
15 + 12x – 5.2 + 4y - 7
9.8 +12x+y-7
2.8+12x+4y
The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 < T < 36 , where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T ( t ) = 8 t + 1.7 , where t is the time in hours. Find the composite function N ( T ( t ) ) : N ( T ( t ) ) = Find the time when the bacteria count reaches 8019. Time Needed = hours
Answer:
[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]
Time for bacteria count reaching 8019: t = 2.543 hours
Step-by-step explanation:
To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:
[tex]N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40[/tex]
[tex]N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40[/tex]
[tex]N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1[/tex]
[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]
Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:
[tex]8019 = 1408t^2 - 385.6t - 105.52[/tex]
[tex]1408t^2 - 385.6t - 8124.52 = 0[/tex]
Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.
The weights of steers in a herd are distributed normally. The variance is 10,000 and the mean steer weight is 1400lbs. Find the probability that the weight of a randomly selected steer is between 1539 and 1580lbs. Round your answer to four decimal places.
Answer:
[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]
And we can find this probability using the normal standard table with this difference:
[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(1539,1580)[/tex]
Where [tex]\mu=1400[/tex] and [tex]\sigma=\sqrt{10000}= 100[/tex]
We are interested on this probability
[tex]P(1539<X<1580)[/tex]
And we can solve the problem using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]
And we can find this probability using the normal standard table with this difference:
[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 1 2 , 1 3 , 1 3 , 1 4 , 1 4 , 1 5 , 1 5 , 1 6 , ...
Answer:
if the sequence is:
12, 13, 13, 14, 14 etc, and each term keeps growing up, the sequence obviusly diverges.
Now, if the sequence is
1/2, 1/3, 1/3, 1/4, 1/4, 1/5 , 1/5
so the terms after the first one repeat, we could group the terms with the same denominator and get:
1/2, 2/3, 2/4, 2/5..... etc.
So the terms after the first one are aₙ = 2/n.
Now, a criteria to see if a sequence converges if seing if:
[tex]\lim_{n \to \infty} a_n = 0[/tex]
and here we have;
[tex]\lim_{n \to \infty} 2/n[/tex]
that obviusly tends to zero, so we can conclude that this sequence converges.
then the limit is:
There exist a n' such that for any n > n' then IL -aₙI < ε
where L is the limit
I2/n - 0I = I2/nI < ε
then this is true if n > 2/ε = n'
I NEED HELP ASAP PLEASE!!! I REALLY NEED HELP!
Answer:
D.
Step-by-step explanation:
One slope is positive and one negative, so one line should go up and one down. B or D.
y = 1/2 x - 1 line goes up and y-int. = - 1. Answer D.
y = - 1/2 x + 3 line goes up and y-int. = 3. Answer D.
Pls help marking Brainliest! (x-1)(x-1)=?
Answer:
Brainleist!Step-by-step explanation:
x^2-2x+1thats the answer...
just: Expand the polynomial using the FOIL method.
Answer:
(x-1)(x-1)=(x-1)² because it's the same thing multiplied by itself
Using FOIL method:
(x-1)(x-1)=
x²-x-x+1=
x²-2x+1
Please show work for number 3 and 4!
Answer:
Three: x = 400
Four : 9
Step-by-step explanation:
Three
a = 10*√2
2a = √(2x) Square both sides.
4a^2 = 2x Divide both sides by 2
2a^2 = x Put a = 10√2 into a^2
2(10√2)^2 = x Square a
2(100*2) = x Multiply the result by 2.
2(200) = x
x = 400
Four
x^(a^2) / x ^(b^2) = x^36
Substitute a + b = 4 in for b.
x^(a^2) / x^(4 - a)^2 = x^36
Subtract powers
x^(a^2 - (4 - a)^2 = x^36
x^(a^2 - (16 - 8a + a^2) = x^36
Gather like terms
x^(8a - 16) = x^36
The powers are now equal
8a - 16 = 36
Add 16 to both sides
8a = 36 + 16
8a = 52
Divide by 8
a = 6.5
Solve for b
a + b = 4
6.5 + b = 4
b = 4 - 6.5
b = - 2.5
a - b = 6.5 - (- 2.5) = 9