Answer:
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1255, \pi = \frac{735}{1255} = 0.5857[/tex]
The point estimate of this proportion is [tex]\pi = 0.5857[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 - 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.5584[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5857 + 1.96\sqrt{\frac{0.5857*0.4143}{1255}} = 0.6130[/tex]
The 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them is (0.5584, 0.6130).
Answer:
The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
Step-by-step explanation:
The interest is the real proportion of Americans who feel that the environment is a major issue with them. The best point of estimate is given by:
[tex]\hat p =\frac{X}{n}= \frac{735}{1255}=0.586[/tex]
Confidence interval
The confidence interval for the true proportion of interest is given by this:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
We want an interval at 95% of confidence, so then the significance level is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value for this case are:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
Replacing into the confidence interval formula we got:
[tex]0.586 - 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.559[/tex]
[tex]0.586 + 1.96\sqrt{\frac{0.586(1-0.586)}{1255}}=0.613[/tex]
And we have 95% of confidence that the true proportion of Americans who feel that the environment is a major issue with them is between 0.559 and 0.613
A 50% tip for a $30 taxi cap ride
Answer:
15 dollars
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
We multiply the tip percentage by the amount billed
50% * 30
Change to decimal form
.50 * 30
15
Question 9 of 20
Find the measure of the missing angle.
14
?
29
Without sufficient context or additional information, it is not possible to accurately determine the measure of the missing angle in the question.
Explanation:The question asks to find the measure of a missing angle but does not provide sufficient context or information such as a diagram or type of geometric figure involved, making it impossible to determine the correct answer without additional information. The provided references include various angle measures and different contexts (e.g., clocks, projectile motion, trigonometry), none of which pertain directly to the question at hand. Due to the lack of relevant details, the measure of the missing angle cannot be calculated or estimated. Mathematics often requires precise information, and without it, we cannot solve for unknown angles or other values.
The mean annual precipitation for a large city in the Midwest is 30.85 inches with a standard deviation of 3.6 inches. Assume that the variable is normally distributed. a) What is the probability that a randomly selected month will have at least 30 inches of precipitation? b) What is the probability that of a random sample of 32 months taken will have a mean amount of precipitation between 30 and 31.5 inches?
Given Information:
Mean annual precipitation = 30.85 inches
Standard deviation of annual precipitation = 3.6 inches
Required Information:
a) P(X ≥ 30) = ?
b) P(30 < X < 31.5) = ?
Answer:
a) P(X ≥ 30) = 59.48%
b) P(30 < X < 31.5) = 16.62%
Explanation:
What is Normal Distribution?
We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.
a) We want to find out the probability that a randomly selected month will have at least 30 inches of precipitation.
At least 30 inches of precipitation means equal to or greater than 30.
[tex]P(X \geq 30) = 1 - P(X \leq 30)\\\\P(X \geq 30) = 1 - P(Z \leq \frac{x - \mu}{\sigma} )\\\\P(X \geq 30) = 1 - P(Z \leq \frac{30 - 30.85}{3.6} )\\\\P(X \geq 30) = 1 - P(Z \leq \frac{-0.85}{3.6} )\\\\P(X \geq 30) = 1 - P(Z \leq -0.24)\\[/tex]
The z-score corresponding to -0.24 is 0.4052
[tex]P(X \geq 30) = 1 - 0.4052\\\\P(X \geq 30) = 0.5948\\\\P(X \geq 30) = 59.48 \%\\[/tex]
Therefore, the probability that a randomly selected month will have at least 30 inches of precipitation is 59.48%
b) We want to find out the probability that of a random sample of 32 months taken will have a mean amount of precipitation between 30 and 31.5 inches.
[tex]P(30 < X < 31.5) = P( \frac{x - \mu}{\sigma} < Z < \frac{x - \mu}{\sigma} )\\\\P(30 < X < 31.5) = P( \frac{30- 30.85}{3.6} < Z < \frac{31.5 - 30.85}{3.6} )\\\\P(30 < X < 31.5) = P( \frac{-0.85}{3.6} < Z < \frac{0.65}{3.6} )\\\\P(30 < X < 31.5) = P( -0.24 < Z < 0.18 )\\[/tex]
The z-score corresponding to -0.24 is 0.4052 and 0.18 is 0.5714
[tex]P(30 < X < 31.5) = P( Z < 0.18 ) - P( Z < -0.24 ) \\\\P(30 < X < 31.5) = 0.5714 - 0.4052 \\\\P(30 < X < 31.5) = 0.1662\\\\P(30 < X < 31.5) = 16.62 \%[/tex]
Therefore, the probability that of a random sample of 32 months taken will have a mean amount of precipitation between 30 and 31.5 inches is 16.62%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.2, 2.2, 0.5 etc.)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.24 then go for 0.04 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
If a woman making $35 an hour gets a 10% raise (35 x 0.10 = 3.50 so $35 + $3.50 = $38.50/hour), how much will she now make in a 6 hour work day? (multiply by 6!) *
What is the best first step in solving Negative 4 x + two-fifths greater-than StartFraction 5 over 10 EndFraction? Add Two-fifths to both sides. Subtract Two-fifths from both sides. Multiply both sides by Negative 4 and reverse the inequality symbol. Divide both sides by 10 and reverse the inequality symbol.
Answer:
(B) Subtract 2/5 from both sides.
Step-by-step explanation:
What is the best first step in solving Negative 4 x + two-fifths greater-than StartFraction 5 over 10 EndFraction?
(A) Add Two-fifths to both sides.
(B) Subtract Two-fifths from both sides. <<<<<-------Correct Answer
(C) Multiply both sides by Negative 4 and reverse the inequality symbol.
(D) Divide both sides by 10 and reverse the inequality symbol.
The solution is Option B.
Subtract Two-fifths from both sides and the inequality equation is x < -1/40
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( -4x ) + 2/5 > 5/10
On simplifying the equation , we get
-4x + 2/5 > 1/2
Subtracting 2/5 on both sides of the equation , we get
-4x > ( 1/2 ) - ( 2/5 )
-4x > 1/10
On further simplification , we get
4x < - ( 1/10 )
Divide by 4 on both sides of the equation , we get
x < - ( 1/40 )
Hence , the inequality is x < - ( 1/40 )
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A horticulturist working for a large plant nursery is conducting experiments on the growth rate of a new shrub. Based on previous research, the horticulturist feels the average weekly growth rate of the new shrub is 2cm per week. A random sample of 48 shrubs has an average growth of 1.80cm per week with a standard deviation of 0.50cm. Is there overwhelming evidence to support the claim that the growth rate of the new shrub is less than 2cm per week at a 0.010 significance level
Answer:
[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
And the p value would be:
[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week
Step-by-step explanation:
Information given
[tex]\bar X=1.8[/tex] represent the sample mean for the growth
[tex]s=0.5[/tex] represent the sample standard deviation
[tex]n=48[/tex] sample size
[tex]\mu_o =2[/tex] represent the value that we want to compare
[tex]\alpha=0.01[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 2cm per week, the system of hypothesis are :
Null hypothesis:[tex]\mu \geq 2[/tex]
Alternative hypothesis:[tex]\mu < 2[/tex]
Since we don't know the population deviation the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]
The degrees of freedom are given by:
[tex]df=n-1=48-1=47[/tex]
And the p value would be:
[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week
Ella’s geometry teacher asked each student to devise a problem and write out its solution. Here is Ella’s work:
A triangle has side lengths of 10, 11, and 15. What type of triangle is it?
Procedure:
102 ?? 112 + 152
100 ?? 121 + 225
100 < 346
Conclusion:
This triangle is an acute triangle.
Which statement best summarizes Ella’s work?
Ella’s procedure and conclusion are correct.
Ella’s procedure is correct, but her conclusion is incorrect.
Ella’s procedure is incorrect, but her conclusion is correct.
Ella’s procedure and conclusion are incorrect.
Answer:Ella's Procedure And Conclusion are incorrect
Step-by-step explanation:
Answer:
Ellas procedure and conclusion are incorrect
Step-by-step explanation:
What is the range of this set of data?
111.97, 63, 84, 100, 119,72
Answer:
56
Step-by-step explanation:
The range of a data set is the difference between the largest and the smallest values in that data set. In this case, the largest value in the data set is 119, and the smallest is 63. 119-63=56, which is the range. Hope this helps!
The measures of angle Y is 45 degrees and the measures of angle Z is 70 whg is the measure of angle W
Answer:
65 degrees
Step-by-step explanation:
I assume this shape is a triangle. The sum of the three angles in a triangle always equals 180 degrees. So, you add the angles that we have the measurements of and subtract it from 180 to get your answer of 65 degrees. hope this helps:)
In preparation for upcoming wage negotiations with the union, the managers for the Bevel Hardware Company want to establish the time required to assemble a kitchen cabinet. A first line supervisor believes that the job should take 40 minutes on average to complete. A random sample of 120 cabinets has an average assembly time of 42 minutes with a standard deviation of 8 minutes. Is there overwhelming evidence to contradict the first line supervisors belief at a 0.05 significance level
Answer:
[tex]t=\frac{42-40}{\frac{8}{\sqrt{120}}}=2.739[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(z>2.739)=0.0616[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.
Step-by-step explanation:
Information provided
[tex]\bar X=42[/tex] represent the sample mean for the assembly time
[tex]s=8[/tex] represent the sample deviation
[tex]n=120[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We want to conduct a hypothesis in order to see if the true mean is equal to 40 minutes or not, the system of hypothesis would be:
Null hypothesis:[tex]\mu =40[/tex]
Alternative hypothesis:[tex]\mu \neq 40[/tex]
The statistic for this case is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{42-40}{\frac{8}{\sqrt{120}}}=2.739[/tex]
The p value for this case would be given by:
[tex]p_v =2*P(z>2.739)=0.0616[/tex]
Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.
The hypothesis testing does not provide sufficient evidence to contradict the supervisor's belief that the job should take 40 minutes on average.
Explanation:The subject matter refers to the concept of hypothesis testing in statistics, where in context, we are checking whether the actual average assembly time of a kitchen cabinet contradicts the believed assembly time. Hypothesis testing works on a null hypothesis and an alternative hypothesis. In this case, the null hypothesis (H0) can be that the average assembly time equals 40 minutes. The alternative hypothesis (H1) would be that the average assembly time does not equal 40 minutes.
At a 0.05 significance level, we calculate the test statistic (z-score) which represents how many standard deviations a data-point (the sample mean) is from the mean (the supervisor's claimed mean). The z-score is calculated as:
(Sample Mean - Claimed Mean) / (Standard Deviation/ √Number of Observations)
In this case, this becomes: (42-40)/(8/√120) = 1.732. The corresponding p-value for this z-score is 0.083.
Since the p-value is greater than the significance level of 0.05, we cannot reject the null hypothesis. Hence, there isn't overwhelming evidence to contradict the supervisor's belief that the job should take 40 minutes on average.
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Kate baked some cookies. She put 12 cookies on each cookie sheet. If she baked 24 cookie sheets of cookies, how many cookies did she bake in all?
Answer:
She baked 288 cookies
Step-by-step explanation:
24 X 12 equals 288
Answer:
288 cookies
Step-by-step explanation:
Write an expression that means the sum of six and the product of three and d
Final answer:
The expression representing the sum of six and the product of three and a variable 'd' is written as 6 + 3d.
Explanation:
The expression that means the sum of six and the product of three and d is written as 6 + 3d.
This expression shows that you first multiply the number three by the variable d, and then add six to the result of that multiplication.
The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), instructs us to perform the multiplication before the addition.
Use the distributive property to write an equivalent expression without parentheses.
9 (a + 8)
Check all that apply.
Distribute 9, by multiplication, to the variable, a, and to the constant, 8.
Write the two multiplications, 9(a) + 9(8)
The expression 9(a) is written as 9a.
The expression 9(8) equals 72.
The equivalent expression is 9a + 8.
The equivalent expression is 9a + 72.
Answer:
A.Distribute 9, by multiplication, to the variable, a, and to the constant, 8.
B.Write the two multiplications, 9(a) + 9(8)
C.The expression 9(a) is written as 9a.
D.The expression 9(8) equals 72.
F.The equivalent expression is 9a + 72.
Step-by-step explanation:
or rather 9+72
Área of panel 5ft by 16ft
he following probabilities are based on data collected from U.S. adults during the National Health Interview Survey 2005-2007. Individuals are placed into a weight category based on weight, height, gender and age. Probability Underweight 0.019 Healthy weight 0.377 Overweight (not obese) 0.35 Obese 0.254 Based on this data, what is the probability that a randomly selected U.S. adult weighs more than the healthy weight range?
Answer:
60.4% probability that a randomly selected U.S. adult weighs more than the healthy weight range
Step-by-step explanation:
We have these following probabilities:
1.9% probability that a randomly selected U.S. adult is underweight.
37.7% probability that a randomly selected U.S. adult has healthy weight.
35% probability that a randomly selected U.S. adult is overweight.
25.4% probability that a randomly selected U.S. adult is obese.
Based on this data, what is the probability that a randomly selected U.S. adult weighs more than the healthy weight range?
More than the healthy weight range: overweight or obese
35% + 25.4% = 60.4%
60.4% probability that a randomly selected U.S. adult weighs more than the healthy weight range
Match the type of valuation with the factors used in its calculation.
cash flows
profit
NOPAT
earnings
total cost of financing
weighted average
cost of capital
EVA
Here's the matching of the valuation types with the factors used in their calculation:
1. Cash flows: The actual cash generated or received by a business.
2. Profit: The amount of money a company makes after subtracting its expenses from its revenue.
3. NOPAT (Net Operating Profit After Tax): It is a company's operating profit after deducting taxes.
4. Earnings: The amount of money a company makes after subtracting its expenses from its revenue. It's often used interchangeably with profit.
5. Total cost of financing: The total cost associated with raising capital, including interest payments and other financing costs.
6. Weighted average: A calculated average where each value is weighted according to its significance.
7. Cost of capital: The cost of obtaining funds, which is typically the weighted average cost of debt and equity.
8. EVA (Economic Value Added): A measure of a company's financial performance based on the residual wealth calculated by deducting its cost of capital from its operating profit.
These factors are used in various combinations to perform different types of valuations, such as discounted cash flow analysis, earning-based valuation models, and economic value-added analysis.
The question is:
Match the type of valuation with the factors used in its calculation.
Types of valuation:
Cash flowsProfitNOPATEarningsTotal cost of financingWeighted averageCost of capital EVAFactors used:
Actual cashExpenses - RevenueProfit after deducting taxesProfitInterest paymentsCalculated averageAverage cost of debt and equityMeasure of a company's financial performancewhat is the equation of the line that passes through the point (8,-8) and has a slope of -1 ?
The equation of the line that passes through the point (8,-8) and has a slope of -1 is y = -x.
Explanation:The equation of the line that passes through the point (8,-8) and has a slope of -1 can be found using the point-slope form: y - y1 = m(x - x1).
Using the given point (8,-8) and slope -1, the equation becomes y - (-8) = -1(x - 8).
Simplifying the equation, we have y + 8 = -x + 8. Rearranging the terms gives us the final equation: y = -x.
Last week, Ida bought 8 cartons of raspberries for $7. How many cartons of raspberries can Ida
buy this week if she has $21?
Answer:
24 cartons
Step-by-step explanation:
8c=7
7/8=0.875
21/0.875=24
which shows the numbers from greatest to least? 9.5 9 3/8 9.125 9 3/4
Answer:
I think the answer is 9 3/4, 9.5, 9 3/8, 9.125
Jay wants his money to double in eight years. What interest rate does he need to earn? *
Answer:
The rate of interest is 12.5%
Step-by-step explanation:
Let the principal be P
We are given that Jay wants his money to double in eight years.
So, Amount = 2P
Simple interest = Amount - Principal = 2P-P = P
Time taken to double the money is 8 years
So,[tex]SI = \frac{P \times T \times R}{100}\\P=\frac{P \times 8 \times R}{100}\\100=8 \times R\\\frac{100}{8}=R\\12.5 =R[/tex]
Hence The rate of interest is 12.5%
Select all the correct answers. What were the three main social reform movements of the nineteenth century in United States? abolitionist movement labor reform movement mental health reform movement women’s rights movement
Answer:
What were the three main social reform movements of the nineteenth century in United States?
abolitionist movement
mental health reform movement
women’s rights movement
Step-by-step explanation:
what does an individual's effective tax rate indicate?
The effective tax rate signifies the actual percentage of an individual's total income that is paid in taxes. It reflects the overall tax burden an individual faces, considering all forms of income and tax provisions. It gives a comprehensive view of the tax situation of an individual.
Explanation:An individual's effective tax rate refers to the percentage of their total income that they pay in taxes. It is calculated by dividing their total tax paid by their total income counts from all sources such as wages, profits, interest, rental income, and government transfers. The effective tax rate provides an accurate picture of an individual's tax burden and gives a holistic view of one's tax situation, considering all factors and tax code complexities.
For example, in the federal income tax, a progressive tax system, people with higher incomes tend to have a higher effective tax rate. To illustrate, in 2009, top 1% of households with an average income of $1,219,700 per year in pre-tax income had an average federal tax rate of 28.9%, but their effective tax rate was 20.4%. This is because the effective tax rate considers all sources of income and provisions like the earned income tax credit, not just tax from wages.
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Final answer:
An individual's effective tax rate represents the percentage of their total income that is paid in taxes, which may be different from the marginal tax rate applied to their last dollar of income.
Explanation:
An individual's effective tax rate indicates the proportion of their total income that is paid in taxes. This rate is calculated by dividing the tax liability by the total income. It contrasts with the marginal tax rate, which is the tax rate applied to an additional dollar of taxable income.
For example, with an income of $20,000 and a tax payment of $2,581.25, the effective tax rate would be $2,581.25 divided by $20,000, equaling 12.9 percent. This rate reflects the average percentage of income paid in taxes, as opposed to the marginal tax rate, which in this case could be higher, such as 15 percent. The marginal tax rate is particularly important for understanding economic decisions, as it affects the tax paid on any additional income earned.
The diameters of computer parts made in a factory followed a normal distribution with a mean diameter of 6.5 inches and a standard deviation of 0.24 inches. The company considers all parts that are below the 16th percentile and all parts that are above the 84th percentile defective. What are the diameters of those defective parts? Show all of your work for full credit.
Answer:
The diameters below 0.41 inches and above 0.89 inches are considered as defective.
Step-by-step explanation:
Let X = diameters of computer parts.
The random variable X is normally distributed with mean, μ = 6.5 inches and standard deviation, σ = 0.24 inches.
The pth percentile is a data value such that at least p% of the data set is less than or equal to this data value and at least (100 - p)% of the data set are more than or equal to this data value.
Compute the 16th percentile of X as follows:
P (X < x) = 0.16
⇒ P (Z < z) = 0.16
The value of z for this probability is:
z = -0.99
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-0.99=\frac{x-6.5}{0.24}\\\\x=0.65-(0.99\times 0.24)\\\\x=0.4124\\\\x\approx 0.41[/tex]
The value at the 16th percentile is 0.44 inches.
Compute the 84th percentile of X as follows:
P (X < x) = 0.84
⇒ P (Z < z) = 0.84
The value of z for this probability is:
z = 0.99
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\0.99=\frac{x-6.5}{0.24}\\\\x=0.65+(0.99\times 0.24)\\\\x=0.8876\\\\x\approx 0.89[/tex]
The value at the 84th percentile is 0.89 inches.
Thus, the diameters below 0.41 inches and above 0.89 inches are considered as defective.
can someone plz answer this quick
It takes Andre 4 minutes to swim 5 laps. How many laps per minute is that?
A. 1 1/4
B. 4/5
C. .75
D. 5/4
E. 1.25
The number of laps per minute is equal to 1.25 laps.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, time is 4 minutes and the number of laps is 5.
We can calculate as Number of laps per minute = Total number of laps/Number of minutes
= 5/4
= 1.25 laps
Hence, the number of laps per minute is 1.25 laps.
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Find the vector equations for medians from the vertices to the three midpoints of triangle ABC with vertices A(-1,5), B(5,-2) and C(3,5).
Answer:
The equation is
2y + 85x + 75 = 0
Step-by-step explanation:
Given vertices A(-1,5), B(5,-2) and C(3,5).
Suppose we want to find the median from A
First, we find the midpoint of side BC
Let the midpoint be M = ((x1 + x2)/2, (y1 + y2)/2)
= ((5+3)/2, (-2-5)/2)
= (8/2, -7/2)
= (4, -7/2)
Next, we write the equation of median with A(-1,5) and midpoint M(4,-7/2)
y = mx + c
The slope m = (y2 - y1)/(x2 - x1)
= (-7/2 - 5)/(4 + 1)
= (-17/2)/5
m = -85/2
We find the y-intercept, using A(-1,5)
x = -1, y = 5, m = -85/2
y = mx + c
5 = (-85/2)(-1) + c
c = 5- 85/2
= -75/2
y = -85x/2 - 75/2
Multiply through by 2
2y = -85x - 75
2y + 85x + 75 = 0
And this is the equation
Which of the following statements is true?
O A) The number 135 is not divisible by 3 or 5.
OB) The number 135 is divisible by 3, 5 and 9.
OC) The number 135 is divisible by 3 and 5, but not by 9.
OD) The number 135 is divisible by 3 and 9, but not by 5.
Answer:
B)
Step-by-step explanation:
If you try to divide 135 with each number,every number is divisible by 135 XD
Please help me .which number is less than 4.703
Answer:
4.7
Step-by-step explanation:
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2 : Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.
Answer:
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.3583 , 0.4579)
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 517
Given data Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured.
'x' =211
The sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{211}{517} =0.4081[/tex]
[tex]q^{-} = 1-p^{-} = 1- 0.4081 = 0.5919[/tex]
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
[tex](p^{-} - Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} + Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} }{n} } )[/tex]
[tex](0.4081 - 2.326 \sqrt{\frac{0.4081 (0.5919 )}{517} } , 0.4081+ 2.326\sqrt{\frac{0.4081(0.5919 }{517} } )[/tex]
(0.4081-0.0498 , 0.4081 +0.0498)
(0.3583 , 0.4579)
Conclusion:-
98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list
(0.3583 , 0.4579)
what’s the circumference of a circle with radius of 18 in.
Answer:
C = 36 pi or approximately 113.04
Step-by-step explanation:
The circumference of a circle is given by
C = 2*pi*r
C = 2*pi*18
C = 36 pi
We can approximate pi by 3.14
C = 36*3.14
C =113.04
Bryan's mom spent $46.20 filling up her gas tank if her gas tank can hold 12 gallons of gas how much did each gallon cost
Answer: Each gallon costs $3.85
Step-by-step explanation:
We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:
$46.20 ÷ 12 = $3.85
Each gallon costs $3.85
I hope this helps!
Answer:
Each gallon costs $3.85
Step-by-step explanation: We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:$46.20 ÷ 12 = $3.85Each gallon costs $3.85I hope this helps!