Answer:
6.67% probability that the result is a multiple of 5 and a multiple of 2
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Desired outcomes:
Multiples of 2 AND 5
Between 1 and 15, the multiples of 2 are: 2,4,6,8,10,12,14
Between 1 and 15, the multiples of 5 are: 5,10,15
So only 10 is a multiply of both 2 and 5, so only one desired outcome, which means that [tex]D = 1[/tex]
Total outcomes:
Any number between 1 and 15, there are 15, so [tex]T = 15[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1}{15} = 0.0667[/tex]
6.67% probability that the result is a multiple of 5 and a multiple of 2
Answer:
Step-by-step explanation:
3/5 or 9/15
An automobile manufacturer has given its car a 52.6 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 250 cars, they found a mean MPG of 52.8. Assume the population standard deviation is known to be 1.6. A level of significance of 0.05 will be used. State the null and alternative hypotheses.
Answer:
Null hypothesis:[tex]\mu = 52.6[/tex]
Alternative hypothesis:[tex]\mu \neq 52.6[/tex]
[tex]z=\frac{52.8-52.6}{\frac{1.6}{\sqrt{250}}}=1.976[/tex]
[tex]p_v =2*P(z>1.976)=0.0482[/tex]
Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.
Step-by-step explanation:
Information provided
[tex]\bar X=52.8[/tex] represent the sample mean for the MPG of the cars
[tex]\sigma=1.6[/tex] represent the population standard deviation
[tex]n=250[/tex] sample size of cars
[tex]\mu_o =52.6[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test
Hypothesis
We need to conduct a hypothesis in order to check if the true mean of MPG is different from 52.6 MPG, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 52.6[/tex]
Alternative hypothesis:[tex]\mu \neq 52.6[/tex]
Since we know the population deviation the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Calculate the statistic
Replacing we have this:
[tex]z=\frac{52.8-52.6}{\frac{1.6}{\sqrt{250}}}=1.976[/tex]
Decision
Since is a two tailed test the p value would be:
[tex]p_v =2*P(z>1.976)=0.0482[/tex]
Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.
An environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 55% and 9090% confidence. To gauge the size of the problem, the agency first picks 7070 cars and finds 1414 with faulty emissions systems. How many should be sampled for a full investigation?
Answer:
[tex]n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13[/tex]
And rounded up we have that n=173
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]p[/tex] represent the real population proportion of interest
[tex]\hat p[/tex] represent the estimated proportion for the sample
n is the sample size required (variable of interest)
[tex]z[/tex] represent the critical value for the margin of error
Solution to the problem
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.10[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
We can assume that the estimates proportion is [tex]\hat p=\frac{14}{70}=0.2[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13[/tex]
And rounded up we have that n=173
To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades: 3.9 in a 5 credit Math course 2.1 in a 3 credit Music course 2.9 in a 4 credit Chemistry course 3.4 in a 4 credit Journalism course What is the student's GPA for that term
Answer:
The student GPA is 3.1875
Step-by-step explanation:
First we calculate the grade point by multiplying the grade with the weight;
= (3.9 * 5) + (2.1 * 3) + (2.9 * 4) + (3.4 * 4)
= 19.5 + 6.3 + 11.6 + 13.6
= 51
Total weight = 5+3+4+4=16
GPA = 51/16=3.1875
To calculate the student's GPA, we multiply each course grade by its credit hours, sum those totals to get the quality points, and then divide by the total number of credits. In this case, the student's GPA is 3.1875.
To calculate a student's Grade Point Average (GPA) for a term, each course grade is multiplied by the course's credit hours to get the total quality points for that course. Then, the sum of all quality points is divided by the total number of credit hours taken.
Step-by-Step GPA Calculation
For each course, multiply the grade by the number of credits:
(3.9 × 5) + (2.1 × 3) + (2.9 × 4) + (3.4 ×4).
Sum the results of these multiplications to get the total quality points.
Sum the total number of credits: 5 + 3 + 4 + 4.
Divide the total quality points by the total number of credits.
Let's do the math:
(3.9 × 5) = 19.5
(2.1 × 3) = 6.3
(2.9 × 4) = 11.6
(3.4 × 4) = 13.6
Total quality points = 19.5 + 6.3 + 11.6 + 13.6 = 51
Total credits = 5 + 3 + 4 + 4 = 16
The student's GPA for the term is the total quality points divided by the total credits:
GPA = 51 / 16 = 3.1875.
There is a 99% chance that the true difference in RDI levels between mean and women is contained in the interval already computed.
a. True
b. False
Answer:
a. True
Question 13 of the attached image;
Step-by-step explanation:
Confidence interval, in statistics can be defined as the probability that a population parameter will fall between two set values( upper and lower bound) for a certain proportion of times. Therefore, there's 99% chance that the true difference in RDI levels between men and women is contained within the 99% Confidence interval shown in the previous questions.
The statement is a matter of statistical inference and would be true if the interval was correctly computed using appropriate methods. While the 99% confidence level suggests we are highly confident the true value lies within the interval, it is not a direct measure of probability.
Explanation:The statement 'There is a 99% chance that the true difference in RDI levels between men and women is contained in the interval already computed' is an assertion relating to statistical inference, specifically, confidence intervals. If this interval was correctly computed using appropriate statistical methods, then it would be true that we are 99% confident that the true difference in RDI levels between mean and women is within this interval. However, it's worth noting that a 99% confidence interval does not necessarily mean there is a 99% probability that the value lies within the interval, it rather suggests that if we were to repeat this study 100 times, we would expect the true mean difference to be within the computed confidence interval 99 times.
Learn more about confidence intervals here:https://brainly.com/question/34700241
#SPJ12
John O’Malley worked 40 regular hours and 10 overtime hours this week. His regular rate of pay is $8.50. For overtime pay, he earns 1.5 times his regular pay. What is John’s gross pay for this week?
You times 40 by $8:50 to get what he earned for the 40 hours. This will get you $340. To get the overtime pay, it's 1.5 times $8.50. This will get you $12.75, so times it by 10 to get the overtime pay. You end up with $127.50. You add both pays together (340 + 127.5) to get $467.50.
what can you say about the two given equations of a line below ?
y= 2x+4
y= -1/2x+4
Answer:
y=2x+4
y=-1/2x+4
linear quations
both have the same y intercept (=4).
y=2x+4 is positive straight line, slope = 2
y=-1/2x+4 is negative straight line, slope=-1/2
Step-by-step explanation:
a band played encore at 7 of its last 12 shows. what is the experimental probability that the band will play an encore at its next show?
The experimental probability that the band will play an encore at its next show is 7/12 or approximately 0.5833.
Explanation:To find the experimental probability that the band will play an encore at its next show, we need to divide the number of times the band played an encore by the total number of shows. In this case, the band played an encore at 7 out of 12 shows. To calculate the experimental probability, divide 7 by 12. So, the experimental probability that the band will play an encore at its next show is 7/12 or approximately 0.5833.
Four students were discussing how to find the unit rate for a proportional relationship. Which method is valid?
V
"Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the
"Look at the graph of the relationship. Count the number of units up and the number of units to the right onen
arrive at the next point on the graph. Write these two numbers as a fraction."
"Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the
"Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit ra
difference in the corresponding x-values."
0 M2
Answer:
Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.
Step-by-step explanation:
The unit rate is the change in y for a 1-unit change in x. Since the graph of a proportion will go through the origin, it is appropriate to look at the y-value for x = 1 (one unit from the origin).
___
The ratio of units up to units to the right is also the unit rate when the fraction is reduced to lowest terms. It is a "unit" rate when the denominator of the fraction is 1 unit.
Answer:
A
Step-by-step explanation:
The mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points. What is the probability that a student will score more than 1700 points?
Answer:
Probability that a student will score more than 1700 points is 0.50.
Step-by-step explanation:
We are given that the mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points.
Let X = Scores results on a test
So, X ~ N([tex]\mu=1700,\sigma^{2} =75^{2}[/tex])
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X -\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean score = 1700 points
[tex]\sigma[/tex] = standard deviation = 75 points
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, the probability that a student will score more than 1700 points is given by = P(X > 1700 points)
P(X > 1700) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{1700-1700}{75}[/tex] ) = P(Z > 0) = 1 - P(Z [tex]\leq[/tex] 0)
= 1 - 0.50 = 0.50
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0 in the z table which has an area of 0.50.
Hence, the probability that a student will score more than 1700 points is 50%.
The number of cupcakes sold by a local bakery in April can be represented by the function p(x)=24x+48, where x represents the number of days the bakery was open that month..
The number of cookies sold by the same bakery in April can be represented by the function q(x)=51+32x, where x represents the number of days the bakery was open that month
Which function, r(x), represents the total number of cupcakes and cookies sold by the bakery during the month of April?
1) r(x)=80x+75
2) r(x)=56x+99
3) r(x)=75x+80
4) r(x)=8x+3
Answer:
r(x) = 56x + 99
Step-by-step explanation:
You need to add the two equations together:
r(x) = (24x+48) + (51+32x)
r(x) = 24x + 32x + 48 + 51
r(x) = 56x + 99
Answer:
2) r(x)=56x+99Step-by-step explanation:
Took the test
Larry has 9 gallons of paint. He uses 10 quarts to paint his kitchen and 3 gallons to paint his living room. How many pints will be left?
Answer: 28
Step-by-step explanation:
Answer:
28 pints
Step-by-step explanation:
There are 4 quarts in a gallon
There are 2 pints in a quart
We know 10 guarts = 10/4 = 2 .5 gallons = 2 gallons 2 guarts
Subtracting the 10 quarts in the kitchen
9 gallons - 2 gallons 2 quarts
Changing 1 gallon to 4 quarts
8 gallons 4 quarts - 2 gallons 2 quarts = 6 gallons 2 quarts
Then he used 3 gallons in the living room
6 gallons 2 quarts - 3 gallons = 3 gallons 2 quarts
Changing gallons to quarts
3*4 = 12 12 quarts + 2 quarts = 14 quarts
Now we need to change to pints
14 quarts * 2 pints = 28 pints
Which inequality describes the graph?
The final inequality that defines the shaded region on the graph is y ≥ -2 + 2x. Here option A is correct.
Given Linear Equation:
The general form of a linear equation is y = mx + c, where c is the y-intercept (the value of y when x = 0). Given that the point (0, -2) lies on the line, c = -2. The equation is then y = mx - 2.
Equation: y = mx - 2
Using Another Point on the Line:
The point (2, 2) is also on the line. Substitute x = 2 and y = 2 into the equation:
2m - 2 = 2
Solve for m:
2m = 4
m = 2
Now we know m = 2, so the equation becomes:
y = 2x - 2
Inequality for Shaded Region:
The inequality sign ≥ suggests that the shaded region is above the line. Therefore, the inequality for the shaded region is:
y ≥ 2x - 2
Rewriting the Inequality:
To match the given form y ≥ -2 + 2x, rearrange terms:
y ≥ -2 + 2x. Here option A is correct.
Complete question:
Which inequality describes the graph?
Simon claims that Plant B will be taller than Plant A in 6 weeks because it has the greater initial value. Is he correct?
The answer is: No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.
Answer:
The answer is C.
Step-by-step explanation:
Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
Answer:
In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR
Step-by-step explanation:
Probability of a teacher being certified in Cardio-Pulmonary Resuscitation (CPR).
36 of 80
So
[tex]p = \frac{36}{80} = 0.45[/tex]
In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?
45% of the days
0.45*180 = 81
In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR
To calculate the number of days a teacher certified in CPR will be on bus duty, use the ratio of certified teachers (9/20) multiplied by the total number of school days (180), resulting in an expectation of 81 days.
Explanation:The student is asking to calculate the number of days one can expect a teacher certified in CPR to be on bus duty at a local intermediate school. Given that 36 out of 80 teachers are certified in CPR, the ratio of certified to non-certified teachers is 36/80, which can be simplified to 9/20. To find out how many days a teacher on bus duty will likely be certified in CPR, we apply this ratio to the total number of school days, which is 180.
Step-by-Step CalculationFirst, simplify the ratio of CPR certified teachers to the total number of teachers: [tex]36/80 = 9/20.[/tex]Next, multiply this ratio by the total number of school days to find the expected number of days: [tex]9/20 * 180 = 81.[/tex]Thus, one can expect that the teacher on bus duty will likely be certified in CPR for 81 days out of the 180 days of school.Learn more about CPR Certification Probability here:https://brainly.com/question/32753638
#SPJ3
At one school, the average amount of time tenth-graders spend watching television each week is 21.6 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal performs a significance test using α= 0.05 to determine whether the average amount of time spent watching television per week has decreased. The hypotheses are:
H0: µ = 21.6 hours
Ha: µ < 21.6 hours
If the P-value 0.04 and a decision error is made, what type of error is it? Explain.
a) Type II error. We conclude that the average amount of time spent watching television each week is 21.6 hours when it is in fact less.
b) Type I error. We conclude that the average amount of time spent watching television each week is 21.6 hours when it is in fact less.
c) Type II error. We conclude that the average amount of time spent watching television each week is less than 21.6 hours when it is in fact not.
d) Type I error. We conclude that the average amount of time spent watching television each week is less than 21.6 hours when it is in fact not.
Answer:
Option choice D
Step-by-step explanation:
It wont be that big of an error.
Brainliest?
Which region represents the solution to the given system of inequalities?
-0.5x+y23
15x+y=-1
-5 4 -3 -2 -1
FLY?
Answer:
3
Step-by-step explanation:
The region representing the solution to a system of inequalities is where the shading of all individual inequalities overlap on a graph. In this case, the provided inequalities should be graphed individually, and the overlapping shaded area is the solution.
Explanation:The region that represents the solution to a system of inequalities is the area in a graph where all the inequality solutions overlap. In the given inequalities:
-0.5x + y > 3 15x + y = -1
First, graph each inequality individually on the coordinate plane using a method that makes sense (linear inequality graphing for this case). The region that is shaded by both inequalities, or resides in the overlap of the shading of the individual inequalities, represents the solution to the system of inequalities.
Do recall that when dealing with 'greater than' or 'less than' signs, we use dashed lines to represent the boundary where inequality is not equal to the boundary. If the sign was 'greater than or equal to' or 'less than or equal to', we would use solid lines.
Learn more about Systems of Inequalities here:https://brainly.com/question/6908880
#SPJ2
1. A homozygous dominant female is represented by a(n):
unfilled circle
Answer: The correct answer is an UNFILLED CIRCLE
Step-by-step explanation: An organism can be homozygous dominant, if it carries two copies of the same dominant allele, or homozygous recessive, if it carries two copies of the same recessive allele.
A homozygous dominant is represented by an UNFILLED CIRCLE.
Pauline is going to buy grey parrots ($300 each) and blue lovebirds ($20 each) for the store. She wants 10 birds total. She has $1040 to spend. How many of each type of bird should she order?
Answer:
You have every right to be angry, but that doesn't give you the right to be mean.
He drank life before spitting it out.
My Mum tries to be cool by saying that she likes all the same things that I do.
Step-by-step explanation:
Pauline can purchase 3 grey parrots and 7 blue lovebirds with her budget of $1040 to fulfill the requirement of buying a total of 10 birds.
To figure out how many of each bird Pauline can buy, we can setup and solve a system of equations:
Let the number of grey parrots be represented by p and the number of blue lovebirds be represented by l.The first equation comes from the total number of birds: p + l = 10.The second equation comes from the total amount of money Pauline can spend: 300p + 20l = 1040.Solving these equations simultaneously gives us the combination of grey parrots and blue lovebirds Pauline can afford.Solving the system:
Multiply the first equation by 20 to make it easier to eliminate l: 20p + 20l = 200.Subtract this new equation from the second equation to solve for p: 300p - 20p = 280p; 1040 - 200 = 840. Therefore, 280p = 840.Divide both sides by 280 to find p: p = 3.Substitute p = 3 into the first equation to solve for l: 3 + l = 10, so l = 7.Therefore, Pauline should purchase 3 grey parrots and 7 blue lovebirds.
Angel has 8 DVD movies on a shelf, 2 dramas,5 sicence fiction movies, and 1 comedy. Two movies will be selected at random. Determine the probabilty of each situatuin below.
A) The probablity of selecting at least one drama movie without replacement
B)The probability of selecting at least one drama movie with replacement
Answer:
A) Pd = 13/28
B) Pd = 7/16
Step-by-step explanation:
Given;
Drama = 2
Comedy = 1
Science fiction = 5
Total = 8
a) The probability of selectingat least one drama movie Pd;
Pd = 1 - Pd'
Without replacement;
Probability of not selecting a drama movie Pd' is;
Pd' = 6/8 × 5/7 = 15/28
Pd = 1 - 15/28
Pd = 13/28
b) with replacement;
Probability of not selecting a drama movie Pd' is;
Pd' = 6/8 × 6/8 = 9/16
Pd = 1 - 9/16
Pd = 7/16
Which inequality is represented by this graph?
The box plot shows the number of years during which 12 teams have participated in a rugby tournament:
At least how many schools have participated for 6 years or more?
2 schools
3 schools
4 schools
6 schools
Answer:
3 schools did
Step-by-step explanation:
A research study investigated the adhesion of various biofilms to solid surfaces for possible use in environmental technologies. Suppose that for the bacterial strain Acinetobacter, five measurements gave readings of 2.69, 5.76, 2.67, 1.62, and 4.12 dyne-cm2. Assume that the standard deviation is known to be 0.66 dyne-cm2 Find a 95% two-sided confidence interval for the mean adhesion.
Answer:
[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]
[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]
We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2 is between (2.793; 3.951)
Step-by-step explanation:
Data provided
2.69, 5.76, 2.67, 1.62, and 4.12
We can calculate the sample mean with this formula:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
And replacing we got:
[tex]\bar X=3.372[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=0.66[/tex] represent the population standard deviation
n=5 represent the sample size
Confidence interval :
The two sided confidence interval for the true mean is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
We have the confidence level given of 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]
Replacing into the formula for the interval we have this:
[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]
[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]
We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2 is between (2.793; 3.951)
Final answer:
The 95% confidence interval for the mean adhesion of the bacterial strain Acinetobacter, based on the given measurements and standard deviation, is [2.795, 3.949] dyne-cm².
Explanation:
The question asks us to find a 95% confidence interval for the mean adhesion of the bacterial strain Acinetobacter based on five given measurements and a known standard deviation. To calculate the confidence interval, we can use the formula for the confidence interval of the mean when the standard deviation is known:
mean ± Z*(standard deviation/√n),
where Z is the Z-value corresponding to the desired level of confidence from the standard normal distribution, and n is the sample size.
First, we need to calculate the mean of the given measurements:
Mean = (2.69 + 5.76 + 2.67 + 1.62 + 4.12) / 5 = 16.86 / 5 = 3.372 dyne-cm²Since we are looking for a 95% confidence interval and the standard deviation (σ) is 0.66 dyne-cm² with a sample size (n) of 5, our formula becomes:
3.372 ± (Z * 0.66 / √5)
To find the appropriate Z-value, we look at the standard normal distribution table for a two-sided 95% confidence interval, which gives us a Z-value of approximately 1.96.
Plugging this Z-value into the formula, we can calculate the confidence interval:
3.372 ± (1.96 * 0.66 / √5) = 3.372 ± 0.577
Therefore, the 95% confidence interval for the mean adhesion is [2.795, 3.949] dyne-cm².
A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. According to the model, how many fish of the new species were released initially?
Answer:
7 fishes
Step-by-step explanation:
Given the growth of the population of fish which is modeled by the exponential function:
[tex]P(t)=7 \cdot b^t[/tex]
Where:
t=time in weeks after release
b=growth rate of the fish
At t=0
[tex]P(0)=7 \cdot b^0\\P_0=7 \cdot 1 \\P_0=7[/tex]
The initial number, [tex]P_0[/tex] of fish which was released into the lake is 7.
A wooden plaque is in the shape of an ellipse with height 26 centimeters and width 16 centimeters. Find an equation for the ellipse and use it to find the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point. (Round your answer to the nearest hundredth if necessary.)
Answer:
14.19
Step-by-step explanation:
The equation of the ellipse with height = 26 cm and width = 16 cm is - [tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex] and the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point is 9.81cm
We have a wooden plaque in the shape of an ellipse with height 26 centimeters and width 16 centimeters.
We have to find equation for the ellipse and use it to find the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point.
What is general form of Equation of Ellipse?The general form of the equation of ellipse is -
[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } =1[/tex]
Where -
a is the length of semi major axis.
b is the length of semi minor axis.
In the question given to us -
height of ellipse = length of major axis = 2a =26
width of ellipse = length of minor axis = 2b = 16
Therefore -
a = 13 cm
and
b = 8 cm
Substituting the values in the equation of ellipse, we get -
[tex]\frac{x^{2} }{(13)^{2} } +\frac{y^{2} }{(8)^{2} } =1[/tex]
[tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex]
Now, at y = 6 cm above the center -
[tex]\frac{x^{2} }{169 } = 1 - \frac{36 }{64} }\\\\\frac{x^{2} }{169 } = 0.57\\x^{2} = 169\times0.57\\x = 9.81 cm[/tex]
Hence, the equation of the ellipse with height = 26 cm and width = 16 cm is - [tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex] and the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point is 9.81cm
To solve more questions on Ellipse, visit the link below -
https://brainly.com/question/2660421
#SPJ2
The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 30. A pollster draws a sample of 90 people to interview. a. What is the probability that the sample mean income is less than 38?
Answer:
[tex]P(\bar X <38)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 38 we got:
[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]
So then we want to find this probability:
[tex] P(z<-1.265)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex] P(z<-1.265)=0.103[/tex]
Step-by-step explanation:
For this case we define the random variable X as the annual income for people at certain city. And we know the following properties:
[tex] E(X) = 42, Sd(X) =42[/tex]
They select a sample size of n = 90>30. So then we can assume that the central limit can be applied.
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
We want to calculate this probability:
[tex]P(\bar X <38)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for 38 we got:
[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]
So then we want to find this probability:
[tex] P(z<-1.265)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex] P(z<-1.265)=0.103[/tex]
A marketing research company is estimating the average total compensation of party clowns. Data were randomly collected from 48 party clowns and the 90% confidence interval for the mean was calculated to be ($9394, $9926). Explain what the phrase "90% confident" means.
a. 90% of the sample means from similar samples fall within the interval. In repeated sampling.
b. 90% of the intervals constructed would contain p.
c. Notes 90% of the similarly constructed intervals would contain the value of the sample mean.
d. 90% of the population values will fall within the interval.
Answer:
"90% confidence" means there is a probabilty of 90% that the population mean (average compensation for the population of party clowns) lies within the confidence interval.
Step-by-step explanation:
The confidence interval is a range of values in which, according to the level of confidence that is calculated, is likely to include a parameter of the population. In this case, this parameter is the population mean compensation of party clowns.
The level of confidence is 90%, so there is 90% of confidence (or probability) that the population mean compensation for party clowns lie within $9394 and $9926.
None of the options below is correct.
Jackson purchases a new car for $48,000. The car’s value can be modeled by the following exponential function:y=48000(0.76)^t where y represents the cars value and t represents time in years . What is the decay rate expressed as a percentage?
Answer:
The decay rate expressed as a percentage is of 24%.
Step-by-step explanation:
The equation for the value of the car has the following format:
[tex]y(t) = y0(1-r)^{t}[/tex]
In which y(t) is the value of the car after t years, y0 is the initial value and r is the decay rate, as a decimal.
In this problem:
y=48000(0.76)^t
So
Comparing to the general formula:
1 - r = 0.76
r = 1 - 0.76
r = 0.24
To convert from decimal to percentage, we multiply by 100
The decay rate expressed as a percentage is of 24%.
8 more than the product of 12 and 4
Answer:
56
Step-by-step explanation:
The product of 2 numbers is what you get multiplying them together:
12x4 = 48
Now we need 8 more of that product so:
48 + 8 = 56
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Answer:
yes
Step-by-step explanation:
no
maybe
perhaps
done
NEED HELP ASAP How many solutions does an equation have and how many solutions does an inequality have?
Answer:
If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.
Step-by-step explanation:
Final answer:
Equations can have differing numbers of solutions: linear equations typically have one, while quadratic equations usually have two, but may have one or none depending on their discriminant. Inequalities often have a range of solutions, representing values that satisfy the inequality condition.
Explanation:
The number of solutions an equation has can vary depending on the type of equation. Linear equations typically have one solution, representing where the line intersects the x-axis on a graph. Equations that involve an unknown squared, also known as quadratic equations, generally have two solutions; these solutions represent the x-intercepts or the points where the parabola crosses the x-axis. However, there are cases where a quadratic equation might have one or no real solutions depending on its discriminant (b2 - 4ac).
Inequalities are different from equations. They often have a range of solutions rather than exact values, because they represent values that are less than (<), less than or equal to (≤), greater than (>), or greater than or equal to (≥) a certain number, rather than being exactly equal to it. A simple linear inequality, for instance, has a set of all possible solutions that make the inequality true, which can be illustrated as a region on a number line or in coordinate space.