Answer:
In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".
Step-by-step explanation:
This is just something to keep in mind
Answer:
-2
Step-by-step explanation:
Well, lt me hope the expression is complete amd correct.
Let's go on with the information you submitted.
y² + 7y + 4
When y= -6.
Let's substitute the value, y= -6 in the expression. We'll have to be careful with the signs.
y² + 7y + 4
-6² + 7(-6) + 4
36 - 42 + 4
40 - 42 =
-2
part of a $3,600 bonus was invested at 9% annual simple interest. The rest was invested at %8 annual simple interest. The total interest at the end of one year was $312. How much was invested in the %9 account?
Answer:
$2400
Step-by-step explanation:
Let x represent the amount invested at 9%. (3600-x) will be the amount invested at 8%. The total interest earned is then ...
312 = 0.09x +0.08(3600 -x)
24 = .01x . . . . subtract 288, simplify
2400 = x . . . . divide by .01
$2400 was invested in the 9% account.
I NEED HELP DUE IN 2 MINS!!
Answer:Triangle A
Step-by-step explanation: It has one right angle.
Answer:
THE ANSWERS A
Step-by-step explanation:
OMG GOOD LUCK!!! BECAUSE IT HAS THE AREA LAYED OUT HAVE A BLESSED DAY!!!
Meta-analysis involves:
a. averaging all the test statistics from every possible study on a given topic.
b. finding all studies published on a topic, calculating the effect size for each of those studies, and averaging the effect sizes together to find the average size of the effect across all studies.
c. finding all studies published on a topic, contacting the authors of the studies to request their original data, and then analyzing all the obtained data in one large analysis of variance.
d. attempting to recreate the experimental conditions of every published study on a given topic.
Answer: b. finding all studies published on a topic, calculating the effect size for each of those studies, and averaging the effect sizes together to find the average size of the effect across all studies.
Step-by-step explanation:
Callie evaluated the expression 0.42 times 4.73 using the steps shown below. 0.42 times 4.73 = 1.26. 1.26 + 29.40 + 168.00 = 198.66 Which best explains Callie’s error? Callie incorrectly placed the decimal. Callie multiplied incorrectly. Callie added incorrectly. Callie incorrectly used placeholder zeros.
Answer:
The correct option is;
Callie multiplied incorrectly
Step-by-step explanation:
Here we have 0.42 × 4.73 = 1.9866 then
1.9866 + 29.4 + 168 = 199.3866
Therefore, from the question, we had 0.42 × 4.73 = 1.26 which is incorrect, meaning that Callie multiplied incorrectly
Apparently, Callie multiplied as follows;
0.42 × 3 = 1.26 but what was in the question was
0.42 × 4.73 which is equal to 1.9866.
Answer:
Callie multiplied incorrectly
Step-by-step explanation:
all the credit goes to guy above me
In a certain region, 15% of people over the age of 50 didn’t graduate from high school. We would like to know if this percentage is the same among the 25-50 year age group. What is the minimum number of 25-50 year old people who must be surveyed in order to estimate the proportion of non-grads to within 6% of the true parameter with 99% confidence?
Answer:
235 people
Step-by-step explanation:
Given:
P' = 15% = 0.15
1 - P' = 1 - 0.15 = 0.85
At 99% confidence leve, Z will be:
[tex] \alpha [/tex] = 1 - 99%
= 1 - 0.99 = 0.01
[tex] \alpha /2 = \frac{0.01}{2} = 0.005 [/tex]
[tex] Z\alpha/2 = 0.005 [/tex]
Z0.005 = 2.576
For the minimum number of 25-50 year old people who must be surveyed in order to estimate the proportion of non-grads to within 6%, we have:
Margin of error, E = 6% = 0.06
sample size = n = [tex] (\frac{Z\alpha /2}{E})^2 * P* (1 - P) [/tex]
[tex] = (\frac{2.576}{0.06}) ^2 * 0.15 * 0.85 [/tex]
= 235.02 ≈ 235
A number of 235 people between 25-30 years should be surveyed .
Answer:
n = 236
Step-by-step explanation:
Solution:-
- The proportion of people over the age of 50 who didn't graduate from high school are, p = 0.15 - ( 15 % )
- We are to evaluate the minimum sample size " n " from the age group of 25-50 year in order to estimate the proportion of non-grads within a standard error E = 6% of the true proportion p within 99% confidence.
- The minimum required sample size " n " for the standard error " E " for the original proportion p relation is given below:
[tex]n = \frac{(Z_\alpha_/_2)^2 * p* ( 1 - p )}{E^2}[/tex]
- The critical value of standard normal is a function of significance level ( α ), evaluated as follows:
significance level ( α ) = ( 1 - CI/100 )
= ( 1 - 99/100 )
= 0.01
- The Z-critical value is defined as such:
P ( Z < Z-critical ) = α / 2
P ( Z < Z-critical ) = 0.01 / 2 = 0.005
Z-critical = Z_α/2 = 2.58
- Therefore the required sample size " n " is computed as follows:
[tex]n = \frac{(2.58)^2 * 0.15* ( 1 - 0.15 )}{0.06^2}\\\\n = \frac{6.6564 * 0.1275}{0.0036}\\\\n = \frac{0.848691}{0.0036}\\\\n = 235.7475\\[/tex]
Answer: The minimum sample size would be next whole number integer, n = 236.
Translate the English phrase into an algebraic expression, then evaluate the expression
Nine less than negative eighteen
Answer:-18-9=-17
Step-by-step explanation:
Answer:
-27
Step-by-step explanation:
Nine less than negative eighteen
[tex] - 18 - 9 = - 27[/tex]
A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The correct null hypothesis for this problem is
Answer:
We need to conduct a hypothesis in order to check if the true mean for sales is significantly higher than 8000, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 8000[/tex]
Alternative hypothesis:[tex]\mu > 8000[/tex]
[tex]z=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2[/tex]
[tex]p_v =P(z>2)=0.0228[/tex]
Step-by-step explanation:
Data given
[tex]\bar X=8300[/tex] represent the sample mean for the sales
[tex]\sigma=1200[/tex] represent the population standard deviation
[tex]n=64[/tex] sample size
[tex]\mu_o =8000[/tex] represent the value that we want to test
z would represent the statistic (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean for sales is significantly higher than 8000, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 8000[/tex]
Alternative hypothesis:[tex]\mu > 8000[/tex]
The statistic to check this hypothesis is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Calculate the statistic
[tex]t=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2[/tex]
P-value
Since is a one right tailed test the p value would be:
[tex]p_v =P(z>2)=0.0228[/tex]
A random sample of 28 plastic items is obtained, and their breaking strengths are measured. The sample mean is 7.142 and the sample standard deviation is 0.672. Conduct a hypothesis test to assess whether there is evidence that the average breaking strength is not 7.000.
Answer:
The test statistic t = 1.126 < 1.703 of '27' degrees of freedom at 0.05 level of significance.
null hypothesis(H₀ ) is accepted
There is evidence that the average breaking strength is 7.000.
Step-by-step explanation:
Step 1:-
Given random sample size (n) =28 <30
small sample size n= 28
The sample mean (x⁻) = 7.142
sample standard deviation (S) =0.672
Step 2:-
Null hypothesis :- there is evidence that the average breaking strength is 7.000.
H₀ : μ =7
Alternative hypothesis:-there is evidence that the average breaking strength is 7.000.
H₁ : μ ≠7
The test statistic [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
Substitute all values and simplification ,
[tex]t = \frac{7.142 -7}{\frac{0.672}{\sqrt{28} } } = \frac{0.142 }{0.1269}[/tex]
t = 1.126
Calculated value is t = 1.126
The degrees of freedom γ = n-1 = 28-1 =27
The tabulated value t= 1.703 at degrees of freedom at 0.05 level of significance.
since calculated t < tabulated value 't' value of 27 degrees of freedom at 0.05 level of significance.
null hypothesis(H₀ ) is accepted
There is evidence that the average breaking strength is 7.000.
What is the median number of pairs of shoes owned by the children ?
Answer:
3
Step-by-step explanation:
Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days. Every match has a winner and a loser. Show that it is possible to select a winning player each day without selecting the same player twice. \\ \\ \textit{Hint: Remember Hall's Theorem}
Answer:
Step-by-step explanation:
given that Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days.
this is going to be proved by contradiction
Let there be a winning player each day where same players wins twice, let n = 3there are 6 tennis players and match occurs for 5daysfrom hall's theorem, let set n days where less than n players wining a day let on player be loser which loses every single day in n days so, players loose to n different players in n daysif he looses to n players then , n players are winnerbut, we stated less than n players are winners in n days which is contradiction.so,we can choose a winning players each day without selecting the same players twice.3x+5=3 solve this equation
Answer:
-3/2
Step-by-step explanation:
Answer: x = -2/3 = -0.667
Choose all that are correct. Choosing the brainliest.
Answer:
A, B and F
Step-by-step explanation:
Area of 2 triangles:
2(½ × 6 × 8)
48 in²
Area of 3 rectangles:
3(18 × 6)
324 in²
Total surface area:
324 + 48
372 in²
Directions for questions 4 & 5: We selected a random sample of 100 StatCrunchU students, 67 females and 33 males, and analyzed their responses to the question, "What is the total amount (in dollars) of credit card debt you have accrued to date?" With more than 30 in each random and independent sample, conditions are met for modeling the distribution of differences in sample means using a T-model. Therefore, we will proceed with finding a confidence interval to estimate the gender difference in credit card debt for StatCrunchU students. Summary statistics for CC Debt: Group by: Gender Gender Mean Std. dev. n Female 2577.75 1916.29 67 Male 3809.42 2379.47 33 Use StatCrunch to find the 95% confidence interval estimating the difference µ1 – µ2, where µ1 is the mean credit card debt for all female StatCrunchU students and µ2 is the mean credit card debt for all male StatCrunchU students. (directions) Since the numbers are dollars, round to two decimal places when you enter your answer. Flag this Question Question 42 pts The lower limit on the confidence interval is
The lower limit of the 95% confidence interval for the difference in mean credit card debt between female and male students can be calculated by formula using sample means, standard deviations, sample sizes, and accounting for the t-value associated with 95% confidence.
Explanation:To calculate the 95% confidence interval for the difference between the mean credit card debt of female and male StatCrunchU students, we use the given information: µ1 (mean credit card debt of females) = 2577.75, µ2 (mean credit card debt of males) = 3809.42, std. dev. of females = 1916.29, std. dev. of males = 2379.47, number of females = 67, number of males = 33.
To calculate the confidence interval, we will use the t-model formula for confidence intervals for difference in means, which is:
(µ1-µ2) ± t*(sqrt([std. dev.1/sqrt(n1)] + [std. dev.2/sqrt(n2)]))
After plugging in the objective values, we would get the confidence range. The lower limit will be (µ1-µ2) - t*(sqrt([std. dev.1/sqrt(n1)] + [std. dev.2/sqrt(n2)])).
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Consider rolling two number cubes, each of which has its faces numbered
from 1 to 6. The cubes will be rolled and the sum of the numbers landing
face up will be recorded. Let the event E represent the event of rolling a sum
of 5. How many outcomes are in the collection for event E?
Answer: 4 outcomes
Step-by-step explanation:
For two number cubes, the total possible outcomes are:
6 events for the first and 6 events for the second, then the total number of combinations is 6*6 = 36
If the dice are different, the possible outcomes are:
Dice 1 = 3, Dice 2 = 2
Dice 1 = 2, Dice 2 = 3
Dice 1 = 4, Dice 2 = 1
Dice 1 = 1, Dice 2 = 4
Then we have 4 outcomes in the collection for event E.
Answer:
4
Step-by-step explanation:
I did it on college board
Based on these tables, what can you determine about the students in this class? Check all that apply.
There are 35 students in the class.
11 of the students are boys who have summer birthdays.
19 of the students are boys.
There is not enough information shown to determine how many girls have summer birthdays.
Answer:
Step-by-step explanation:
It’s 1 3,and 4
Answer:
1,3,4
Step-by-step explanation:
A recent study reported that 18- to 24-year-olds average 192 restaurant visits per year. Assume that the standard deviation for number of visits per year for this age group is 56.5. To validate these findings, a random sample of forty 18- to 24-year-olds was selected and found to average 212 restaurant visits per year. Which of the following statements is correct
A.)The interval that contains 95% of the sample means is 170.3 and 213.7 visits. Because the sample mean is between these two values, we have support for the results of the May 2011 study.
B.)The interval that contains 95% of the sample means is 170.3 and 213.7 visits. Because the sample mean is between these two values, we do not have support for the results of the May 2011 study.
C.)The interval that contains 95% of the sample means is 174.5 and 209.5 visits. Because the sample mean is not between these two values, we have support for the results of the May 2011 study.
D.)The interval that contains 95% of the sample means is 174.5 and 209.5 visits. Because the sample mean is not between these two values, we do not have support for the results of the May 2011 study.
Answer:
Option C) is the correct answer.
Step-by-step explanation:
We are given the following in the question:
Mean = 192
Sample mean, [tex]\bar{x}[/tex] = 212
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 56.5
95% Confidence interval:
[tex]\mu \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
[tex]192 \pm 1.96(\dfrac{56.5}{\sqrt{40}} ) = 192 \pm 17.5 = (174.5,209.5)[/tex]
Thus, the correction answer is
Option C)
"The interval that contains 95% of the sample means is 174.5 and 209.5 visits. Because the sample mean is not between these two values, we have support for the results of the May 2011 study."
Braydon, a scuba diver, has a tank that holds 6 liters of air under a pressure of 220 pounds per square inch (psi).
Write the equation that relates pressure, P, to volume, V.
If the pressure increases to 330 psi, how much air is held in Braydon’s tank?
Answer: 4 litres of air is held in Braydon’s tank.
Step-by-step explanation:
The law relating pressure to volume is the Boyle's law. It states that the volume of a given mass of gas is inversely proportional to its pressure as long as temperature remains constant. It is expressed as
P1V1 = P2V2
Where
P1 and P2 are the initial and final pressures of the gas.
V1 and V2 are the initial and final volumes of the gas.
From the information given,
V1 = 6 litres
P = 220 psi
P2 = 330 psi
Therefore,
6 × 220 = 330V2
V2 = 1320/330 = 4 litres
Answer:
V=1320/p
the tank holds 4 liters
Step-by-step explanation:
Which solids can have vertical cross sections that are circles? Check all that apply
-cones
-cylinders
-spheres
cones
cylinders
spheres
Step-by-step explanation:
The question was worded incorrectly and instead of giving the options it gave you the answers
The following stem-and-leaf plot represents the test scores for 22 students in a class on their most recent test. Use the data provided to find the quartiles.
Test Scores by Student
Stem Leaves
6 1 6 6 6
7 1 3 4
8 1 1 5 5 7 8 8 9
9 1 3 3 3 7 7 7
Key: 6||1=61
Step 1 of 3 : Find the second quartile.
Using the median concept, it is found that the second quartile is of 86.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile. The median is also called the second quartile, as [tex]\frac{2}{4} \times 100 = 50[/tex].
In this problem, there are 22 scores, which is an even number, hence the median is the mean of the 11th and the 12th scores.
From the stem-and-leaf plot, we have that:
The 1st score, in an increasing way, is 61.The 2nd, 3rd and 4th is 66.The 11th score is 85.The 12th score is 87.Then:
(85 + 87)/2 = 86
The second quartile is of 86.
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To find the quartiles of a dataset, arrange the data in ascending order, determine the median (Q2), split the data into a lower half and an upper half (excluding the median if the number of data points is odd), and find Q1 and Q3 as the medians of these subgroups.
Explanation:To find the quartiles for a set of test scores, first arrange the data from lowest to highest and then divide the dataset into four equal parts. The second quartile (Q2), also known as the median, separates the data into two halves. In this case, because we have 22 data points, the median will be the average of the 11th and 12th data points.
To calculate the first quartile (Q1), we find the median of the lower half of the data, which consists of the 10 scores below the overall median. Since we have an even number of data points in the lower half, Q1 will be the average of the 5th and 6th smallest scores.
Similarly, the third quartile (Q3) is the median of the upper half, consisting of the 10 scores above the overall median. Q3 will be the average of the 5th and 6th highest scores within this upper half.
Use a one-sample t ‑test, based on the data below, to test the null hypothesis H0:µ=100.63 against the alternative hypothesis H1:µ>100.63 . The sample has a mean of x⎯⎯⎯=101.09 and a standard deviation of s=0.4887 . 100.68,101.23,100.82,101.15,100.96,100.70,102.09 Calculate the standard error (SE) and the t ‑statistic for this test. Give the standard error to four decimal places and t to three decimal places.
Answer:
The standard error (SE) is 0.1847.
The t-statistic for this test is 2.490.
Step-by-step explanation:
We are given that the sample has a mean of [tex]\bar X[/tex] = 101.09 and a standard deviation of s = 0.4887 .
Also, the 7 sample values are also given.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 100.63
Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] > 100.63
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 101.09
s = sample standard deviation = 0.4887
n = sample values = 7
The Standard Error (SE) is given by = [tex]\frac{s}{\sqrt{n} }[/tex] = [tex]\frac{0.4887}{\sqrt{7} }[/tex] = 0.1847
So, test statistics = [tex]\frac{101.09-100.63}{\frac{0.4887}{\sqrt{7} } }[/tex] ~ [tex]t_6[/tex]
= 2.490
The value of t test statistics is 2.490.
rectangle 2 is a scale drawing of rectangle b and has 25% of its area if rectangle A has side lengths of 4cm and 5cm what are the side lengths of rectangle b ?
Answer:
24 324
Step-by-step explanation:
21334 fda adf
Answer: 24, 324
Step-by-step explanation:
Find the perimiter of both sides
A 90% confidence interval for the mean height of students
is (60.128, 69.397). What is the value of the margin of error?
a) m = 129.525
b) m = 4.635
c) m = 64.763
d) m = 9.269
Answer:
[tex] ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635[/tex]
And the best answer on this case would be:
b) m = 4.635
Step-by-step explanation:
Let X the random variable of interest and we know that the confidence interval for the population mean [tex]\mu[/tex] is given by this formula:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}} [/tex]
The confidence level on this case is 0.9 and the significance [tex]\alpha=1-0.9=0.1[/tex]
The confidence interval calculated on this case is [tex]60.128 \leq \mu \leq 69.397[/tex]
The margin of error for this confidence interval is given by:
[tex]ME =t_{\alpha/2} \frac{s}{\sqrt{n}} [/tex]
Since the confidence interval is symmetrical we can estimate the margin of error with the following formula:
[tex] ME = \frac{Upper -Lower}{2}[/tex]
Where Upper and Lower represent the bounds for the confidence interval calculated and replacing we got:
[tex] ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635[/tex]
And the best answer on this case would be:
b) m = 4.635
An Individual Retirement Account (IRA) has $17 comma 000in it, and the owner decides not to add any more money to the account other than interest earned at 4%compounded daily. How much will be in the account 30years from now when the owner reaches retirement age?
Answer: The owner reaches at Rs. 56438.28 after 30 years.
Step-by-step explanation:
Since we have given that
Sum = Rs. 17000
Rate of compounded daily = 4%
Number of years = 30 years
So, Using "compound interest formula" we get that :
[tex]A=P(1+\dfrac{r}{n})^{nt}\\\\A=17000(1+\dfrac{0.04}{365})^{365\times 30}\\\\A=17000(1.000109589)^{10950}\\\\A=56438.28[/tex]
Hence, The owner reaches at Rs. 56438.28 after 30 years.
The population in the city of Millstone was approximately 2 million in 2010 and 2.2 million in 2015. What is the percent increase from 2010 to 2015
Answer:
10%
Step-by-step explanation:
Percentage increase for any change is calculated by formula
{(Final value - initial value)/initial value} * 100
Given
population in 2010 = 2 million ----------->initial value
population in 2015 = 2.2 million ----------->Final value
[tex]Percentage \ \ increase = {(2.2 - 2)/2} *100= (0.2/2)*100 = 10%[/tex]
Answer:
10%
Step-by-step explanation:the population in 2010 - 2015 is grown though 10%
as a percent incease the number willl incease in increase will increase and increase until the number can increase to 2.2 million or 2 millions and also the population would probably decrease
Paulo works at the United Nations. He researched what percent of the world's population lives on each continent. He surveys a sample of employees at the United Nations about their continent of origin to see if the distribution in the sample agrees with the percentages he researched.
Which of these inference procedures is most appropriate?
Answer:
confidence interval using a two sample t test between percents
Step-by-step explanation:
confidence interval using a two sample t test between percents This can be used to compare percentages drawn from two independent samples in this case employees. It is used to compare two sub groups from a single sample example the population on the planet
An experiment is carried out 400 times the possible outcomes are void fail and success if the frequency of void is 96 and the relative frequency is 0.24 then how much is the frequency of fail and success
the frequency of success is 244.
part b's answer is 240.
A relative frequency distribution shows the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.
Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario. The relative frequency formula is given as:
Relative Frequency = Subgroup frequency/ Total frequency.
1. Frequency of success
=400 - 96 - 60
=244
relative frequency of fail
=60/400= 0.15
Relative Frequency of success
=1-0.15 - 0.24
=0.61
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A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 8 type B balls, and 3 type C balls, find the probability that the golf ball is not a type A ball.
Final answer:
The probability that a randomly selected golf ball from the bag is not a type A ball is 11/16, as we calculate this by dividing the number of non-type A balls (11) by the total number of balls (16).
Explanation:
The probability that the golf ball selected at random is not a type A ball can be found by first determining the total number of balls in the golf bag and then subtracting the number of type A balls to obtain the number of non-type A balls. The total number of balls is 5 type A balls + 8 type B balls + 3 type C balls = 16 balls. The number of non-type A balls is 8 type B balls + 3 type C balls = 11 balls.
To find the probability that the selected ball is not a type A ball, we divide the number of non-type A balls by the total number of balls, which gives us a probability of 11/16.
Final answer:
The probability that a randomly selected golf ball from the bag is not a type A ball is 0.6875 or 68.75%.
Explanation:
To find the probability that the golf ball selected at random is not a type A ball, we need to determine the total number of non-type A balls in the golf bag and divide it by the total number of balls in the bag. The golf bag contains 5 type A balls, 8 type B balls, and 3 type C balls, so the total number of balls in the bag is 5 + 8 + 3 = 16. There are 8 + 3 = 11 non-type A balls (type B and type C).
The probability of selecting a non-type A ball is then given by the number of non-type A balls divided by the total number of balls:
Probability = Number of non-type A balls / Total number of balls
We calculate it as:
Probability = 11 / 16 = 0.6875
Thus, the probability that the selected golf ball is not a type A ball is 0.6875 or 68.75%.
what is 81,007-26,318?
Answer:
54689
Step-by-step explanation:
What is the area of a triangle with a base of 7 cm and a height of 4cm
Answer:
14 sq cm
Step-by-step explanation:
7 × 4 = 28
28 ÷ 2 = 14
brainliest?
A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)equals72 comma 000 plus 70 x and p (x )equals 300 minus StartFraction x Over 20 EndFraction , 0less than or equalsxless than or equals6000. (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company $4 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
Answer:
Part (A)
1. Maximum revenue: $450,000Part (B)
2. Maximum protit: $192,5003. Production level: 2,300 television sets4. Price: $185 per television setPart (C)
5. Number of sets: 2,260 television sets.6. Maximum profit: $183,8007. Price: $187 per television set.Explanation:
0. Write the monthly cost and price-demand equations correctly:
Cost:
[tex]C(x)=72,000+70x[/tex]
Price-demand:
[tex]p(x)=300-\dfrac{x}{20}[/tex]
Domain:
[tex]0\leq x\leq 6000[/tex]
1. Part (A) Find the maximum revenue
Revenue = price × quantity
Revenue = R(x)
[tex]R(x)=\bigg(300-\dfrac{x}{20}\bigg)\cdot x[/tex]
Simplify
[tex]R(x)=300x-\dfrac{x^2}{20}[/tex]
A local maximum (or minimum) is reached when the first derivative, R'(x), equals 0.
[tex]R'(x)=300-\dfrac{x}{10}[/tex]
Solve for R'(x)=0
[tex]300-\dfrac{x}{10}=0[/tex]
[tex]3000-x=0\\\\x=3000[/tex]
Is this a maximum or a minimum? Since the coefficient of the quadratic term of R(x) is negative, it is a parabola that opens downward, meaning that its vertex is a maximum.
Hence, the maximum revenue is obtained when the production level is 3,000 units.
And it is calculated by subsituting x = 3,000 in the equation for R(x):
R(3,000) = 300(3,000) - (3000)² / 20 = $450,000Hence, the maximum revenue is $450,000
2. Part (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.
i) Profit(x) = Revenue(x) - Cost(x)
Profit (x) = R(x) - C(x)[tex]Profit(x)=300x-\dfrac{x^2}{20}-\big(72,000+70x\big)[/tex]
[tex]Profit(x)=230x-\dfrac{x^2}{20}-72,000\\\\\\Profit(x)=-\dfrac{x^2}{20}+230x-72,000[/tex]
ii) Find the first derivative and equal to 0 (it will be a maximum because the quadratic function is a parabola that opens downward)
Profit' (x) = -x/10 + 230 -x/10 + 230 = 0-x + 2,300 = 0x = 2,300Thus, the production level that will realize the maximum profit is 2,300 units.
iii) Find the maximum profit.
You must substitute x = 2,300 into the equation for the profit:
Profit(2,300) = - (2,300)²/20 + 230(2,300) - 72,000 = 192,500Hence, the maximum profit is $192,500
iv) Find the price the company should charge for each television set:
Use the price-demand equation:
p(x) = 300 - x/20p(2,300) = 300 - 2,300 / 20p(2,300) = 185Therefore, the company should charge a price os $185 for every television set.
3. Part (C) If the government decides to tax the company $4 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
i) Now you must subtract the $4 tax for each television set, this is 4x from the profit equation.
The new profit equation will be:
Profit(x) = -x² / 20 + 230x - 4x - 72,000Profit(x) = -x² / 20 + 226x - 72,000ii) Find the first derivative and make it equal to 0:
Profit'(x) = -x/10 + 226 = 0-x/10 + 226 = 0-x + 2,260 = 0x = 2,260Then, the new maximum profit is reached when the production level is 2,260 units.
iii) Find the maximum profit by substituting x = 2,260 into the profit equation:
Profit (2,260) = -(2,260)² / 20 + 226(2,260) - 72,000Profit (2,260) = 183,800Hence, the maximum profit, if the government decides to tax the company $4 for each set it produces would be $183,800
iv) Find the price the company should charge for each set.
Substitute the number of units, 2,260, into the equation for the price:
p(2,260) = 300 - 2,260/20p(2,260) = 187.That is, the company should charge $187 per television set.