Answer:
each friend would get 1/6 when you divide 1/2 by 3
Step-by-step explanation:
Each friend receives 1/6 of the pie.
The student asked how much pie each of three friends would get if they share 1/2 of a blueberry pie. To find the answer, you simply divide the half of the pie by three, since there are three friends sharing it. That is, 1/2 ÷ 3.
You can think of this division as splitting the 1/2 of the pie into three equal parts. Each friend would get 1/6 of the pie, because 1/2 ÷ 3 = 1/6. This intuitively makes sense because if a pie is cut into six equal slices, three slices (which is half the pie) can be shared by three friends, giving each one slice.
Maryam showed the location of each vertex of a polygon on the grid below. On a coordinate plane, points are at (1, 3), (4, 1), (3, negative 3), (negative 1, negative 3), and (negative 2, 1). If the points are connected, which statements about the polygon are true? Check all that apply. The polygon has six sides. The polygon is a pentagon. The vertices of the polygon are (–2, 1), (1, 3), (4, 1), (3, –3), and (–1, –3). The polygon has five vertices. The polygon is a heptagon.
Answer:
bcd
Step-by-step explanation:
Answer:
B C D
Step-by-step explanation:
A precision instrument is guaranteed to be accurate to within 2 units. A sample of four instrument readings on the same object yielded the measurements 352, 350, 350, and 353. Give the attained significance level for testing the null hypothesis σ = 0.7 versus the alternative hypothesis σ > 0.7. (Round your answer to six decimal places.)
Answer:
[tex]\chi^2 =\frac{4-1}{0.7^2} 1.5^2 =13.776[/tex]
[tex]p_v =P(\chi^2 >13.776)=0.0032[/tex]
In order to find the p value we can use the following code in excel:
"=1-CHISQ.DIST(13.776,3,TRUE)"
If we compare the p value and the significance level assumed we see that [tex]p_v <\alpha[/tex] so on this case we have enough evidence in order reject the null hypothesis. And we can conclude that the true deviation i significantly higher than 0.7
Step-by-step explanation:
Notation and previous concepts
A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"
[tex]n=4[/tex] represent the sample size
We can calculate the sample deviation with this formula:
[tex]s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
[tex]\alpha[/tex] represent the confidence level
[tex]s =1.5 [/tex] represent the sample variance obtained
[tex]\sigma^2 =0.7[/tex] represent the value that we want to test
Null and alternative hypothesis
On this case we want to check if the population deviation is higher than 0.7, so the system of hypothesis would be:
Null Hypothesis: [tex]\sigma \leq 0.7[/tex]
Alternative hypothesis: [tex]\sigma >0.7[/tex]
Calculate the statistic
For this test we can use the following statistic:
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.
[tex]\chi^2 =\frac{4-1}{0.7^2} 1.5^2 =13.776[/tex]
Calculate the p value
In order to calculate the p value we need to have in count the degrees of freedom , on this case 3. And since is a right tailed test the p value would be given by:
[tex]p_v =P(\chi^2 >13.776)=0.0032[/tex]
In order to find the p value we can use the following code in excel:
"=1-CHISQ.DIST(13.776,3,TRUE)"
Conclusion
If we compare the p value and the significance level assumed we see that [tex]p_v <\alpha[/tex] so on this case we have enough evidence in order reject the null hypothesis. And we can conclude that the true deviation i significantly higher than 0.7
How much interest is earned on a principal of $9.02 invested at an interest
rate of 8% for three years?
Final answer:
The interest earned on $9.02 at an 8% interest rate for three years is $2.16.
Explanation:
To calculate the amount of interest earned on a principal of $9.02 at an interest rate of 8% for three years, we would use the formula for simple interest: Interest = Principal imes Rate imes Time. Plugging in the values we get:
Interest = $9.02 imes 0.08 imes 3
Interest = $2.166. Therefore, the interest earned on the principal amount of $9.02 invested at an 8% interest rate for three years would be $2.16, after rounding to the nearest cent.
A recent study reported that high school students spend an average of 94 minutes per day texting. Jenna claims that the average for the students at her large high school is greater than 94 minutes. She will conduct a study to investigate this claim.
(b) Based on a sample of 32 students, Jenna calculated a sample mean of 96.5 minutes and a sample standard deviation of 6.3 minutes. Assume all conditions for inference are met. At the significance level of α=0.05, do the data provide convincing statistical evidence to support Jenna’s claim? Complete an appropriate inference procedure to support your answer.
Answer:
We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.
Step-by-step explanation:
Jenna claims that the average time of texting at her larger high school is greater than 94 minutes per day.
From here we can see that we have to perform a hypothesis test about a sample mean. The null and alternate hypothesis will be:
Null Hypothesis: [tex]\mu \leq 94[/tex]
Alternate Hypothesis: [tex]\mu > 94[/tex]
Jenna collected data from a sample of 32 students. So, sample size will be:
Sample Size = n = 32
Sample Mean = x = 96.5
Sample Standard Deviation = s = 6.3
We have to perform a hypothesis test, to test Jenna's claim. Since, the value of Population Standard Deviation is unknown and the value of Sample Standard Deviation is known, we will use One Sample t-test in this case.
The formula to calculate the test statistic is:
[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]
Using the values, we get:
[tex]t=\frac{96.5-94}{\frac{6.3}{\sqrt{32} } }=2.245[/tex]
The degrees of freedom will be:
df = n - 1 = 32 - 1 = 31
We have to convert the t-score 2.245 with 31 degrees of freedom to its equivalent p-value. From t-table this value comes out to be:
p-value = 0.0160
The significance level is:
[tex]\alpha =0.05[/tex]
Since, the p-value is lesser than the level of significance, we reject the Null Hypothesis.
Conclusion:
We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.
This p value the significant level 0.05 is given which is higher then the obtained p value. Thus we can reject the null hypothesis. Thus we have convincing statistical evidence to support Jenna’s claim.
Given-
Jenna claims that the average for the students at her large high school is greater than 94 minutes. The null hypothesis is [tex]\mu\leq 94[/tex] and alternate hypothesis [tex]\mu >94[/tex].
Now given that,
The value of sample size [tex]n[/tex] is 32, sample means [tex]x[/tex] is 96.5 and the sample standard deviation [tex]s[/tex] is 6.3.
Here one-sample t-test will be used for the as sample standard deviation is given. The formula for the test statics is,
[tex]t=\dfrac{x-\mu}{\dfrac{s}{\sqrt{n}} }[/tex]
[tex]t=\dfrac{96.5-94}{\dfrac{6.3}{\sqrt{32}} }[/tex]
[tex]t=2.245[/tex]
Now the degrees of freedom is n-1. thus,
[tex]D_f=n-1[/tex]
[tex]D_f=32-1=31[/tex]
Now from the t table the value of t score 2.245 having degree 31 is,
p value[tex]=0.0160[/tex]
For this p value the significant level 0.05 is given which is higher then the obtained p value. Thus we can reject the null hypothesis. Thus we have convincing statistical evidence to support Jenna’s claim.
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A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an additional 5% per man-hour.
Answer:
if you divide 80 and 5 would give you 16
Step-by-step explanation:
A report on a certain fast food restaurant states that μ, the mean order total, is $9. The manager of the restaurant believes the mean is higher. A random sample of orders will be selected. The sample mean x¯ will be calculated and used in a hypothesis test to investigate the belief. Which of the following is the correct set of hypotheses?A. H0:x¯=$9Ha:x¯≠$9B. H0:x¯=$9Ha:x¯>$9 C. H0:μ=$9Ha:μ≠$9 D. H0:μ=$9Ha:μ>$9 E. H0:μ=$9Ha:μ<$9
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $9
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $9
Step-by-step explanation:
We are given that a report on a certain fast food restaurant states that μ, the mean order total, is $9. The manager of the restaurant believes the mean is higher.
A random sample of orders will be selected. The sample mean x¯ will be calculated and used in a hypothesis test to investigate the belief.
Let [tex]\mu[/tex] = the mean order total
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $9
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $9
Here, null hypothesis states that the mean order total is equal to $9 and the manager claim's is not correct.
On the other hand, alternate hypothesis states that the mean order total is higher than $9 and the manager claim's is correct.
So, this would be the correct set of hypotheses for testing.
Based on the null hypothesis, the mean order to total is $9, and the manager's belief is wrong. Based on alternate hypothesis, the mean order total is more than $9, and the manager is right.
Given information:
A report on a certain fast food restaurant states that μ, the mean order total, is $9.
The manager of the restaurant believes the mean is higher.
So, according to the null hypothesis, [tex]H_0[/tex]
[tex]\mu=9[/tex]
And, according to alternate hypothesis, [tex]H_a[/tex]
[tex]\mu>9[/tex]
Therefore, based on the null hypothesis, the mean order to total is $9, and the manager's belief is wrong. Based on alternate hypothesis, the mean order total is more than $9, and the manager is right.
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A computer program has a bug that causes it to fail once in every thousand runs, on average. In an effort to find the bug, independent runs of the program will be made until the program has failed six times. What is the standard deviation of the number of runs required?
Answer:
The standard deviation of the number of runs required is 2447.26
Step-by-step explanation:
For each run, there are only two possible outcomes. Either the program fails, or it does not. The probability of the computer failing during a run is independent of other runs. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation for the expected number of trials for r sucesses is:
[tex]\sqrt{V(X)} = \sqrt{\frac{r(1-p)}{p^{2}}}[/tex]
A computer program has a bug that causes it to fail once in every thousand runs, on average.
This means that [tex]p = \frac{1}{1000} = 0.001[/tex]
In an effort to find the bug, independent runs of the program will be made until the program has failed six times. What is the standard deviation of the number of runs required?
This means that r = 6. So
[tex]\sqrt{V(X)} = \sqrt{\frac{6*0.999}{(0.001)^{2}}} = 2447.26[/tex]
The standard deviation of the number of runs required is 2447.26
Find the volume of the rectangular prism
Answer:
40 and 1/2
Step-by-step explanation:
Multiply 4 1/2 by 1 1/2. Then multiply the product of 4 1/2 and 1 1/2 by 6.
A quality inspector inspect random box of 50 tablets. He discovers 2 are defective. In an order of 2,000 tablets,how many are likely to be defective
Answer:
80
Step-by-step explanation:
So if 50 tablets are made and 2 are defective then it’s 50:2. That means for every 50 tablets are made 2 are defective. And since 50 goes into 2000 40 times, you would multiply 40 x 2 to get 80, the number defective tablets
One number is eight more than twice another. If their difference is 25, what is the larger number?
17
42
35
Answer: The largest number was 42
7. Certain car manufacturers install a gauge that tells the driver how many miles they can drive
until they will run out of gas. A study was conducted to test the accuracy of these gauges.
Each driver was assigned a certain gauge reading until empty to watch for. When their car
announced it had that many miles remaining until empty, they began to measure their
distance traveled. After they ran out of gas, they reported the distance they were able to dove
(in miles) as well as the gauge reading they were assigned (in miles). Here is computer output
showing the regression analysis:
Regression Analysis: Distance versus Gauge Reading
Predictor Coef SE Coef
Constant -0.7928 3.2114
-0.2469 0.8060
Gauge 1.1889 0.0457
26.0310 0.0000
5 - 7.0032
R-Sq -0.9326 R-Sqladj) - 0.9312
Identify and interpret the slope of the regression line used for predicting the actual distance
that can be driven based on the gauge reading
(A) Slope - 1.1889. The predicted distance the drivers were able to drive increases by 1.1889
miles for each additional mile reported by the gauge.
(B) Slope - 0.0457. The predicted distance the drivers were able to drive increases by 0.0457
miles for each additional mile reported by the gauge.
(C) Slope - -0.7928. The predicted distance the drivers were able to drive decreases by
0.7928 miles for each additional mile reported by the gauge.
(D) Slope - 1.1889. For each additional mile reported by the gauge, the drivers were able to
drive an additional 1.1889 miles
(E) Slope -0.0457. For each additional mile reported by the gauge, the drivers were able to
drive an additional 0.0457 miles,
Answer:
A) Slope - 1.1889. The Predicted distance the drivers were able to drive increases by 1.1889
Step-by-step explanation:
According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most recent month. Let's assume the standard deviation is 4.5% of students. Joseph collects data from 186 students at a medium-sized school in Iowa and finds that only 11% reported this rate of bullying. What is his 95% confidence interval?
Using the formula for a 95% confidence interval and a Z score of 1.96, Joseph's 95% confidence interval for the percentage of students reporting bullying at their school is roughly 10.1% to 11.9%.
Explanation:The subject of this problem is statistics, specifically the creation of a 95% confidence interval based on collected data. A confidence interval is a type of estimate computed from the statistics of observed data. This gives a range of values for an unknown parameter (in this case, the number of students experiencing bullying).
In this case, the mean (or average) is 0.15 or 15%. The standard deviation is 0.045 or 4.5%. The sample size, often denoted as 'n', is 186.
Based on the 95% confidence interval, we will use a Z score of 1.96. We can start to calculate our interval using the formula for the confidence interval: sample mean ± (Z * (standard deviation/sqrt(n))).
Using these numbers:
The lower end of the confidence interval is 0.11 - (1.96 * (0.045 / sqrt(186))) = about 0.101 or 10.1%.
The upper end of the confidence interval is 0.11 + (1.96 * (0.045 / sqrt(186))) = about 0.119 or 11.9%.
So, the 95% confidence interval for the percentage of students who reported experiencing bullying one to three times within the most recent month is approximately 10.1% to 11.9%.
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A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. At \alpha = .05, we would reject the null hypothesis.
a. True
b. False
Answer:
b) False
Calculated value Z = 1.635 < 1.96 at 0.05 level of significance.
The null hypothesis is accepted.
Step-by-step explanation:
Explanation:-
Step:- (1)
Given data the opinion poll recently sampled 1500 voting age citizens.
Given sample size 'n' = 1500
Given data the opinion poll recently sampled 1500 voting age citizens in selected 1020 of the sampled citizens were in favor of an increase in cigarette taxes.
The sample proportion[tex]'p' = \frac{1020}{1500} = 0.68[/tex]
Given data the state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66
Population proportion 'P' =0.66
Q = 1-P
Q = 1-0.66 = 0.34
Null hypothesis :H₀: 'P' >0.66
Alternative hypothesis: H₀: 'P' <0.66
Level of significance ∝=0.05
Step:-(2)
The test statistic
[tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.68-0.66}{\sqrt{\frac{0.66 X 0.34}{1500} } }[/tex]
Z = 1.635
The calculated value Z = 1.635
The tabulated value Z = 1.96 at ∝=0.05 level of significance.
Therefore Z = 1.635 < 1.96 at 0.05 level of significance.
The null hypothesis is accepted.
The alternative hypothesis is rejected.
Conclusion:-
The null hypothesis is accepted at 0.05 level of significance.
The proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66
A labourer is paid #1000 for5 days work. what is his pay for 22days work
Final answer:
To calculate the labourer's pay for 22 days, divide the total pay for 5 days by 5 to get the daily wage, and then multiply this by 22. The labourer would earn #4400 for 22 days of work.
Explanation:
The question posed is regarding the calculation of a laborer's pay for a certain number of days based on a known daily wage rate.
If a labourer is paid #1000 for 5 days work, to find out his pay for 22 days work we follow these steps:
Firstly, we calculate the daily wage by dividing the total pay by the number of days worked. That is, #1000 / 5 days = #200 per day.Next, we multiply the daily wage by the number of days in question to get the total pay for that period. So for 22 days: #200 per day * 22 days = #4400.In conclusion, the labourer's pay for 22 days of work would be #4400.
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Answer:
Step-by-step explanation:
y=4x−2 (What does Y and X equal?
y=x+3
Answer:
x = 5/3
y = 14/3
Step-by-step explanation:
y=4x−2
y=x+3
Since they are both equal to y, we can set them equal to each other
4x-2 = x+3
Subtract x from each side
4x-2-x = x+3-x
3x-2 =3
Add 2 to each side
3x-2+2 = 3+2
3x =5
Divide each side by 3
3x/3 =5/3
x = 5/3
Now we need to find y
y = x+3
y =5/3+3
y = 5/3+9/3
y = 14/3
Answer:
x=5/3; y=14/3
Step-by-step explanation:
Subtract the following:
-4x+y=-2
-x+y=3
= -3x=-5
x=5/3
substitute x into one of the given equations.
y=5/3+3
y= 14/3
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 39.9 σ=39.9. You would like to be 99% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?
Answer:
large of a sample size n = 2645
Step-by-step explanation:
Explanation:-
The population standard deviation 'σ' = 39.9
Given data the estimate is within 2 of the true population mean so given the margin of error = 2
we know that margin of error is determined by
Margin of error = [tex]\frac{z_{\alpha }S.D }{\sqrt{n} }[/tex]
cross multiplication , we get
[tex]\sqrt{n} = \frac{2.578 X S.D}{M.E}[/tex]
[tex]\sqrt{n} = \frac{2.578 X 39.9}{2}= 51.4311[/tex]
squaring on both sides , we get
n = 2645.15
n = 2645
Conclusion:-
large of a sample size n = 2645
An expression equal to 8x + 24
Answer:
8 ( x + 3 ) , Need more details , hope this was answer
Step-by-step explanation:
Final answer:
The expression 8x + 24 can be factored to 8(x + 3) by taking out the common factor of 8, which is a usual step in simplifying algebraic expressions.
Explanation:
The expression 8x + 24 is a linear algebraic expression with two terms. Typically in algebra, when simplifying expressions or solving equations, we might look for ways to factor or combine like terms. However, in this expression, there's no immediate algebraic simplification other than factoring out a common factor if we wanted to rewrite the expression in a different form.
If we observe that 24 is divisible by 8, we might factor out the number 8 to express the original expression in the form of 8(x + 3). This shows that the expression can be seen as the product of 8 and the quantity (x + 3), which is particularly useful when solving equations or simplifying further expressions that include 8x + 24.
Jenny has a toy which is in the shape of a right prism with triangular bases. The sides of its bases are each 5 feet and its approximate height is 4.3 feet. The length of the prism between the bases is 12 feet. What is the approximate surface area of this right prism?
A. 150ft2 B. 201.5ft2
C.210ft2 D.225.4ft2
Answer:
B
Step-by-step explanation:
split the triangle in to 5 different shapes
3 of them are rectangles, and 2 are triangles
all of the rectangles are the same size being:
12 by 5 so 12 times 5. then do this 3 times for each rectangle.
Now take the triangles and find the area for those.
which is 1/2 or base times height . so half of 5 multiplied by height (4.3)
being 2.5 times 4.3 giving you 10.75
now take the area of the rectangles and triangles and add them together
60+60+60+10.75+10.75= 201.5 ft2
The diameter of a mason jar is 3 inches but can be as large as 3.03 inches and as small as 2.97 inches. Twenty-five samples of mason jars are taken and it is discovered that these components have a grand mean of 3.01 inches and a standard deviation of 0.02 inches. What is the probability of producing a bad product? (4pts)
Answer:
18.15% probability of producing a bad product
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 problem, we have that:
[tex]\mu = 3.01, \sigma = 0.02[/tex]
What is the probability of producing a bad product?
Less than 2.97 or more than 3.03.
Less than 2.97
pvalue of Z when X = 2.97. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.97 - 3.01}{0.02}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
More than 3.03
1 subtracted by the pvalue of Z when X = 3.03. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.03 - 3.01}{0.02}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
1 - 0.8413 = 0.1587
Then
0.0228 + 0.1587 = 0.1815
18.15% probability of producing a bad product
A poll is conducted the day before a state election for Senator. There are only two candidates running for this office. The poll results show that 59% of the voters favor the Republican candidate, with a margin of error of 4 percentage points. Should the Republican expect to win? Why or why not? Choose the correct answer below.
Answer:
The lower limit of the confidence interval is 55%, which is above 50%, so the Republican should expect to win.
Step-by-step explanation:
A confidence interval of proportions has two bounds, a lower bound and an upper bound.
These bounds depend on the sample proportion and the margin of error.
The lower bound is the sample proportion subtracted by the margin of error.
The upper bound is the margin of error added to the sample proportion.
In this problem, we have that:
Sample proportion 59%
Margin of error 4%
59 - 4 = 55%
59 + 4 = 63%
The lower limit of the confidence interval is 55%, which is above 50%, so the Republican should expect to win.
Final answer:
The Republican candidate can neither be certain of victory nor of defeat based on the poll with a margin of error of 3 percentage points. The poll suggests a favorable leaning towards the Republican, but the actual support could range from 53% to 59%, implying the election could be close. Historical examples illustrate that polls are not foolproof predictors of election outcomes.
Explanation:
Whether the Republican candidate should expect to win based on a poll showing 56% favoritism with a margin of error of 3 percentage points cannot be said with certainty. The margin of error indicates that the true support could theoretically range from 53% to 59%.
To understand the implication, consider that if the candidate's actual support is at the lower end of the margin of error (53%), then it is possible that the race is very close, depending on the percentage of voters favoring the Democratic candidate. If the Democratic candidate has close to 47% support, the election could go either way. Conversely, if the Republican candidate's support is at the higher end (59%), then it is more likely, though not guaranteed, that the Republican would win. Polls provide a snapshot of voter preferences at a particular time and have limitations, including potential sampling errors, nonresponse bias, and inability to predict who will actually turn out to vote.
Historical polls and election outcomes show that while polls can be predictive, they are not always accurate reflections of election results. An example is the 2000 election between George W. Bush and Al Gore, which was a toss-up based on polls but ended with a narrow victory. Similarly, in a hypothetical situation where a state's population is largely liberal, a conservative might still win if the liberal vote is split between two candidates.
Which are the solutions of the quadratic equation ? x ^ 2 = - 5x - 3 - 5, 0 (- 5 - sqrt(13))/2, (- 5 + sqrt(13))/2 (5 - sqrt(13))/2, (5 + sqrt(13))/2 5, 0
Answer: b
Step-by-step explanation:
The solutions to the quadratic equation x^2 = -5x - 3 are (-5 - sqrt(13))/2 and (-5 + sqrt(13))/2, calculated using the quadratic formula -b ± √(b² - 4ac) / (2a).
Explanation:The subject of this question is Mathematics, specifically, the solution of quadratic equations. A quadratic equation is in the form ax²+bx+c = 0. You can find the solutions or roots of any quadratic equation using the formula: -b ± √(b² - 4ac) / (2a).
Let's apply this formula to the quadratic equation, x^2 = -5x - 3. Here, a = 1, b = 5, and c = 3. Substituting these values into the formula, the solutions to this quadratic equation are (-5 - sqrt(13))/2 and (-5 + sqrt(13))/2. However, in the question, there seems to be multiple options. It's essential to note that the correct solutions match the ones derived from our calculations.
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What is .54444 as a fraction?
Answer:
.54444 = .54444/1 = 5.4444/10 = 54.444/100 = 544.44/1000 = 5444.4/10000 = 54444/100000, any one of those works
Answer:
54/99
Step-by-step explanation:
A marine sales dealer Önds that the average price of a previously owned boat is $6492. He decides to sell boats that will appeal to the middle 66% of the market in terms of price. Find the maximum and minimum prices of the boats the dealer will sell. The standard deviation is $1025, and the variable is normally distributed.
Answer:
The maximum price that the dealer will sell is $7471 and the minimum is $5513.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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 problem, we have that:
[tex]\mu = 6492, \sigma = 1025[/tex]
Middle 66%
50 - (66/2) = 17th percentile
50 + (66/2) = 83rd percentile
17th percentile
X when Z has a pvalue of 0.17. So X when Z = -0.955.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.955 = \frac{X - 6492}{1025}[/tex]
[tex]X - 6492 = -0.955*1025[/tex]
[tex]X = 5513[/tex]
83rd percentile
X when Z has a pvalue of 0.83. So X when Z = 0.955.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.955 = \frac{X - 6492}{1025}[/tex]
[tex]X - 6492 = 0.955*1025[/tex]
[tex]X = 7471[/tex]
The maximum price that the dealer will sell is $7471 and the minimum is $5513.
Given the length of a word (wordLen) and the maximum number of consecutive vowels that it can contain (maxVowels), determine how many unique words can be generated. Words will consist of English alphabetic letters a through z only. Vowels are v: {a, e, i, o, u}; consonants are c: remaining 21 letters. In the explanations, v and c represent vowels and consonants.
Vowels are defined as sound repeated as a, e, i, o, u and the rest 21 letters are classified as consonants.
The given words are generated from English alphabet as a combination of Vowels and alphabets. Thus the combination of vowels and consonant help in the formation of words. There are n number of unique letters are formed.
1) Speed is fast = SPEEFAS
2) Minimum number of participants = MINIPART
3) Sum of excess = SUMCESS
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To find the number of unique words that can be generated with a given word length and maximum number of consecutive vowels, multiply the number of possible vowel arrangements by the number of possible consonant arrangements.
Explanation:To determine the number of unique words that can be generated given the length of a word (wordLen) and the maximum number of consecutive vowels (maxVowels), we need to consider the different possibilities for the arrangement of vowels and consonants in the word. Since vowels can be repeated consecutively up to maxVowels times, we can have up to maxVowels + 1 vowels in a row in any word. Similarly, we can have up to wordLen - maxVowels + 1 consonants in a row in any word. Therefore, the total number of unique words that can be generated is (maxVowels + 1) * (wordLen - maxVowels + 1).
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Casey has a total of 18 pens. Twelve of these pens are blue, and the rest are red.
What is the ratio of blue pens to red pens?
Answer: For every 12 blue pens, she has 6 red pens 12:6
Simplifying this would be: 2:1
Answer:
3 : 1
Step-by-step explanation:
18 : 6
simplified ratio is
3 : 1
The product of two given numbers is 126 both of them are divisible by 3 but neither of them is 3.The larger of the two numbers is
I believe the answer is 21
21 × 6 = 126
and both numbers are divisible by 3
The product of three consecutive odd integers is 75.
1. Determine the variable.
x = first odd integer
2. Identify key words and translate their meanings.
1st odd integer = x
2nd odd integer = x + 2
3rd odd integer = x + 4
3. Write the multistep equation for the scenario.
What is the equation that represents the scenario?
Answer:
(D)
x (x + 2) × (x + 4) = 75
Answer:
D.)x (x + 2) · (x + 4) = 75
Step-by-step explanation:
Well, the easiest way to look at this is by first placing both the 2nd odd integer and the 3rd odd integer into parenthesis finally you simply add the 1st integer to the beginning of the equation. You simply just use the information given and piece it all together into an equation usually written in the same order that the information was given.
Also, to find out the operations in the equations you simply use the keywords given in the problem itself. In this problem, they used the phrase "The product of three consecutive odd integers is 75." since we know that product means to multiply then we also know that we are multiplying all of the integers together to give us our final answer of 75.
Having issues solving
Answer:
Step-by-step explanation:
Labor: 40.55 x 4 = $162.20 for total Labor.
Total Charges: 25.75 + 38.75 + 162.20 = $226.70 Total charges.
a bag contains 3 red marbles, 8 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th. that both marbles drawn will be blue
Answer:
0.233
Step-by-step explanation:
There are a total of 16 marbles.
The probability the first marble is blue is 8/16.
Assuming the marble isn't replaced, the probability the second marble is blue is 7/15.
So the probability of both marbles being blue is 8/16 × 7/15 = 7/30 ≈ 0.233.
The probability of drawing two blue marbles without replacement is 0.233 to the nearest thousandth, calculated by multiplying the individual probabilities of the first and second draws.
Explanation:The probability of drawing two blue marbles from a bag without replacement involves a two-step calculation because the outcome of the first draw affects the second. Since there are 3 red, 8 blue, and 5 green marbles, the total number of marbles is 16. The probability of drawing a blue marble first is 8/16 or 1/2.
After drawing one blue marble, there would be 7 blue marbles left in a bag of 15 total marbles. The probability of drawing a blue marble on the second draw is then 7/15. To find the combined probability of both events occurring, we multiply the two probabilities: (1/2) × (7/15) = 7/30, which is approximately 0.233 to the nearest thousandth.
Thus, the probability of drawing two blue marbles in a row without replacement is 0.233 to the nearest thousandth.