Answer:
The statement translate to 'Every square has three sides'
Step-by-step explanation:
Since P(x) is an open sentence and the domain for x is the set of all squares, its means that whatever that is applicable to one square also applicable to others
A fort had enough food for 80 soldiers for 60 days .How long would the food last if 20 more soliders join after 15 days ?
Answer:
The food would last 51 days
Step-by-step explanation:
After 15 days are over, you could say that the 16th day would be as follows -
80 soldiers, food finished in 60 - 15 = 45 days.
If 20 more soldiers arrive, there would be a total of 100 soldiers, so if 80 soldiers can finish their food in 45 days - 1 soldier can finish = 45 * 80. Respectively, 100 soldiers can consume their food in ( 45 * 80 ) / 100 = 36 days.
As 15 days are already over, adding 36 more days = 51 days
The food would last 51 days if 20 more soldiers join after 15 days
There are several possible ways to answer this question, but I hope that explanation helps!
Answer:
A total of 51 days, or 36 days after the extra soldiers join in.
Step-by-step explanation:
Let's say a soldier eats 1 portion of food in 1 days. That portion may be divided into breakfast, lunch , and dinner, but it is still accounted as 1 portion per soldier per day.
There are 80 soldiers and enough food for 60 days.
The number of portions is
60 * 80 = 4800
The fort started with 4800 portions.
80 soldiers ate their portions for 15 days.
80 * 15 = 1200
After 15 days, they have
4800 - 1200 = 3600 portions left.
After 15 days, 20 more soldiers joined in.
Now there are 80 + 20 = 100 soldiers.
There are 3600 portions left for 100 soldiers.
3600/100 = 36
The food would last 36 days after the 15 days, or a total of 51 days.
Given that (-2,7) is on the graph of f(x), find the corresponding point for the function f(x + 4).
Answer:
(-6, 7)
Step-by-step explanation:
In order to make (x+4) = -2, we must have x = -6. Then the point (-6, 7) will be on the graph of f(x+4).
__
Another way to think about this is that replacing x with x-h causes the graph to be shifted right by h units. Here, we have h=-4, so the graph is shifted left 4 units. Shifting the point (-2, 7) by 4 units to the left moves it to (-2-4, 7) = (-6, 7).
Answer:
PLATO: -6,7
Step-by-step explanation:
I earn $20.00 in 4 hours. At this rate, how much will i earn in 28 hours (show your work)
Answer:
140$
Step-by-step explanation:
4 hours = 20
28 hours divided by 4 is 7
7 x 20 = 140
One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement, "I'm pleased with the way we divide the responsibilities for childcare." The ratings went from 1 (strongly agree) to 5 (strongly disagree). The table below contains ten of the paired responses for husbands and wives. Conduct a hypothesis test at the 5% level to see if the mean difference in the husband's versus the wife's satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife's score 2 2 3 3 4 2 1 1 2 4 Husband's score 2 1 2 3 2 1 1 1 2 4 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
(1) State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom.)
(2) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)
(3) What is the p-value? (Round your answer to four decimal places.)
(4) Alpha (Enter an exact number as an integer, fraction, or decimal.)
α =
Answer:
(a) The test statistic would follow a t distribution with n - 1 = 10 - 1 = 9 degrees of freedom.
(b) The test statistic is -2.2361.
(c) The p-value of the test is 0.026.
(d) α = 0.05.
Step-by-step explanation:
In this case a hypothesis test is to be performed to determine whether the mean difference in the husband's versus the wife's satisfaction level is negative.
(a)
The data provided is paired data.
So a paired t-test would be used.
The test statistic would follow a t distribution with n - 1 = 10 - 1 = 9 degrees of freedom.
The hypothesis can be defined as follows:
[tex]\text{H}_{0}:\ \mu_{d}=0\\\\\text{H}_{a}:\ \mu_{d}<0[/tex]
(b)
Compute the test statistic as follows:
[tex]t=\frac {\bar d-\mu_{d}}{\sigma_{d}/\sqrt{n}}[/tex]
[tex]=\frac{-0.50-0}{0.7071/\sqrt{10}}\\\\=-2.2360894\\\\\approx -2.2361[/tex]
The test statistic is -2.2361.
(c)
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<t)\\\\=P(t_{9}<-2.2361)\\\\=0.026[/tex]
The p-value of the test is 0.026.
(d)
It is provided that the significance level of the test is, α = 0.05.
what is the volume of a cone with the given dimensions. radius=4 cm; height= 10 cm
Answer:
[tex] 167.47 \: {cm}^{3} [/tex]
Step-by-step explanation:
[tex]V_{cone} = \frac{1}{ 3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \pi \times {4}^{2} \times 10 \\ \\ = \frac{1}{ 3} \times 3.14 \times 16 \times 10 \\ \\ = \frac{1}{ 3} \times \: 502.4 \\ \\ = 167.466667 \\ \\ = 167.47 \: {cm}^{3} [/tex]
A large restaurant is being sued for age discrimination because 15% of newly hired candidates are between the ages of 30 years and 50 years when 50% of all applicants were in that age bracket. You plan to use hypothesis testing to determine whether there is significant evidence that the company's hiring practices are discriminatory. Part A: State the null and alternative hypotheses for the significance test. (2 points) Part B: In the context of the problem, what would a Type I error be
Answer:
See explanation below.
Step-by-step explanation:
Let's take P as the proportion of new candidates between 30 years and 50 years
A) The null and alternative hypotheses:
H0 : p = 0.5
H1: p < 0.5
b) Type I error, is an error whereby the null hypothesis, H0 is rejected although it is true. Here, the type I error will be to conclude that there was age discrimination in the hiring process, whereas it was fair and random.
ie, H0: p = 0.5, then H0 is rejected.
Mary is selling chocolate bars to raise money. She earns $3 for each solid milk chocolate bar sold and $4 for each caramel-filled bar sold. If m represents the number of milk chocolate bars sold, and c represents the number of caramel bars sold, which of the following expressions represents the amount of money that Mary has raised? Question 6 options: A) 3m – 4c B) m∕3 + i∕4 C) 12mc D) 3m + 4c
Answer:
3m + 4c
Step-by-step explanation:
Whenever a word problem says the word earn that means the slope, also known as the rate of change, will be positive. Knowing this you can determine that both the caramel and milk chocolate slopes will be positive. After figuring all that out the only thing left to do is to make the equation. You know you have two slopes, and each slope needs a variable, so you will have to look back at the question. It is given that m represents the milk chocolate and c represents the caramel. Now all you have to do is make the slope the coefficient to the corresponding variable. The milk chocolates are 3 dollars, so the 3 goes in front of the m and the caramel chocolates are 4 dollars, so teh 4 goes in front of the 4. Since both slopes are positive no negatives or minus signs will be used in the equation. Knowing all this information you can now create the expression 3m + 4c.
Answer:
D
Step-by-step explanation:
3m + 4c
In a bag there are 2 red, 3 yellow, 4 green, and 6 blue marbles.
What is the probability of P (yellow or green)?
Answer:
7/15
Step-by-step explanation:
There are 15 marbles total. -->
3 of them are yellow => 4 of them are green
3 + 4 = 7
7/15
Hope This Helps!
Answer: 7/15=46%
Step-by-step explanation:
There is in total of 15 marbles
but 3 of them are yellow and 4 are green.
4+3=7
7/15=0.466...
7/15≈0.46
0.46=46%
Pls answer either of these questions with step by step explanation
Answer:
C and B
Step-by-step explanation:
31. Thrice means 3 times as much. Let's call Rahul and Shivam's present ages r and s respectively. We can write:
r = 3s
r + 8 = 1 + (s + 8) * 2
Simplifying the second equation gives us r + 8 = 2s + 17. When we substitute r = 3s into the second equation we get 3s + 8 = 2s + 17 which gives us s = 9. This means r = 9 * 3 = 27 so Rahul's age 8 years before the present is 27 - 8 = 19.
32. Let's call Ravi and Kishan's ages r and k. We can write:
r + k = 69
r - 8 = 2(k - 8) - 4
Rewriting the first equation gives us r = -k + 69 and when we substitute this into the second equation we get -k + 69 - 8 = 2k - 16 - 4. Solving for k we get k = 27 which means r = 42. 42 - 27 = 15.
4. The area of a rhombus with one diagonal is 8.72 cm long is the same as the area of a square of side 15.6 cm. Find the length of the other diagonal of the rhombus.
Answer:
55.82 cm
Step-by-step explanation:
d1= 8.72 cm
a= 15.6 cm
A rhombus= 1/2*d1*d2 = A square
A square= 15.6²= 243.36 cm²
d2= 2A/d1= 2*243.36/8.72 ≈55.82 cm
Find the x-intercepts for the quadratic function y= -1/2(x+3)^2 +4
Answer:
x= -3 +√2 ≈ -0.1716, and x = - 3 -2√2 ≈ -5.8284
Step-by-step explanation:
y= -1/2(x+3)² +4
For x -intercept, y = 0.
0 = - 1/2(x+3)² + 4 /*(-2)
0 = (x+3)² - 8
(x+3)² = 8
√(x+3)² = +/-√8
x+3 = +/-√8
x = - 3+/- 2√2
x= -3 +√2 ≈ -0.1716, and x = - 3-2√2 ≈ -5.8284
A tooth-whitening gel is to be tested for effectiveness. A group of 85 adults have volunteered to participate in the study. Of these, 43 are to be given a gel that contains the tooth-whitening chemicals. The remaining 42 are to be given a similar-looking package of gel that does not contain the tooth-whitening chemicals. A standard method will be used to evaluate the whiteness of teeth for all participants. Then the results for the two groups will be compared. 1. After the treatment period, compare the whiteness of the 43 treated adults. 2. A placebo is not being used. 3. After the treatment period, compare the whiteness of the two groups. 4. Randomly select 85 adults to be given the treatment gel. 5. The remaining 42 adults receive the placebo gel. 6. Randomly select 43 adults to be given the treatment gel.
Answer:
(a) 3, 5 and 6
Step-by-step explanation:
In the experiment, 43 are to be given a gel that contains the tooth-whitening chemicals while the remaining 42 are to be given a placebo. Therefore, a placebo is used.
The 43 that will receive the gel are to be selected randomly.
After the experiment, the whiteness of the two groups will be compared to see the effect of the gel.
Therefore for the experiment to be completely random, 3, 5, and 6 apply.
(b)
For the experiment to be double-blind, the researchers who will evaluate the whiteness and interact with the subjects, and the subjects would not know which subjects received either the whitening gel or the placebo.
The television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast. Find the probability that none of the households are tuned to 50 Minutes.
Answer:
The probability that none of the households are tuned to 50 Minutes is 0.04398.
Step-by-step explanation:
We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.
A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.
The above situation can be represented through binomial distribution;
[tex]P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........[/tex]
where, n = number of samples (trials) taken = 14 households
r = number of success = none of the households are tuned to 50 min
p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%
Let X = Number of households that are tuned to 50 Minutes
So, X ~ Binom(n = 14, p = 0.20)
Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)
P(X = 0) = [tex]\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}[/tex]
= [tex]1 \times 1 \times 0.80^{14}[/tex]
= 0.04398
Which polynomial function could be represented by the graph below? On a coordinate plane, a cubic function crosses the x-axis at (negative 3, 0), (0, 0), (2, 0). f(x) = x3 + x2 – 6x f(x) = x3 – x2 – 6x f(x) = –2x3 – 2x2 + 12x f(x) = –2x3 + 2x2 + 12x
Answer:
third one
Step-by-step explanation:
when
x=0, y=0
x=1, y=8
x=2 y=0
and so on.
Answer:
C. f(x)= -2x^3 -2x^2 +12x
Step-by-step explanation:
edge 2020
Write the equation represents the line.
Answer:
y = 3/4x+2
Step-by-step explanation:
The change in y over change in x of the two points given is 3/4, which is the slope. The line intersects with the y axis at 2, making 2 the y-int
In a recent household telephone survey of 2,550 adults in a certain country, 27% reported that they own at least one gun. The researchers want to estimate the true percentage of adults in that country that own at least one gun. Complete parts a through f below a. Identify the population of interest to the researchers. Choose the correct answer below.
a. The set of adults that responded to the survey
b. The set of guns in the country
c. The set of adults in the country that own a gun (CMD.
d. The set of all gun ownership status (yes/no) values for all adults in the country.
Answer
option D
Step-by-step explanation:
The population of interest to the research is the set of all gun ownership status (yes/no) values for all adults in the country. Or all total adults in a country including those that own a gym or not. This is the population of interest. The sample is the 2550 individuals adults surveyed in the household telephone survey.
(m-3)/(7)=(m)/(m+8) Solve the proportion.
Answer: m=6, m=-4
Step-by-step explanation:
To solve this proportion, we have to cross multiply.
[tex]\frac{m-3}{7} =\frac{m}{m+8}[/tex]
[tex](m-3)(m+8)=7m[/tex]
Now that we have cross multiplied, we actually need to FOIL the left side to expand the equation.
[tex]m^2+8m-3m-24=7m[/tex]
Combine like terms.
[tex]m^2+5m-24=7m[/tex]
We can move all terms to one side and then solve for m.
[tex]m^2-2m-24=0[/tex]
We can actually factor this to:
[tex](m-6)(m+4)=0[/tex]
We set each factor equal to 0 to find m.
m-6=0
m=6
m+4=0
m=-4
Using the order of operations, what should be done first to evaluate 12 divided by (negative 6) (3) + (negative 2)? Divide 12 by 5. Multiply –6 and 3. Divide 12 by –6. Add 3 and –2.
Answer:
first you need to multiply -6 and 3
Answer:
-6 and 3
Step-by-step explanation:
sorry it was an late answer I'm just tryna gain points :D
Can some help me if your good at maths
Answer:
36=2×3×3×3
36=2×3³Answer
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
Step-by-step explanation:
First write the prime factors of 36 that you can see here
[tex]2 \: \: \: 2 \: \: \: 3 \: \: \: 3[/tex]
Now write 36 as a product of its prime factors.
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
(d) A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 100ml of coffee. The machine actually dispenses a mean amount of 105ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispenses into each cup is normally distributed, find the standard deviation of the amount of coffee dispensed per cup in ml.
Answer:
The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Step-by-step explanation:
Let the random variable X denote the amount of coffee dispensed by the machine.
It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.
It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.
And 10% of the cups contain less than the amount stated on the sign.
To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of z for the above probability is, z = -1.28.
*Use a z-table
Compute the value of standard deviation as follows:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]-1.28=\frac{100-105}{\sigma}[/tex]
[tex]\sigma=\frac{-5}{-1.28}[/tex]
[tex]=3.90625\\\\\approx 3.91[/tex]
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Some equilateral triangles are not isosceles.
O A. True
O
B. False
Answer: B. false
Step-by-step explanation:
An equilateral triangle has 3 equal sides
Isosceles triangle has two equal sides.
Which means that equilateral triangles cannot become isosceles.
Answer:
False
Step-by-step explanation:
An equilateral triangle has all three sides equal
An isosceles triangle has at least 2 sides equal
An equilateral triangle is a special isosceles triangle
Jack works in a supermarket. He earns $186 a week. How much does he earn in a 52 week year?
Answer:
9672 per year
Step-by-step explanation:
Take the amount he earns per week times the number of weeks he works
186* 52
9672 per year
Answer:
$9672
Step-by-step explanation:
Jack earns $186 in 1 week.
In 52 weeks,
186 × 52 = 9672
He earns $9672.
The formula for the area of a parallelogram is A = bh,
where b is the base and h is the height.
(x-4) cm
(2x2 + 2x-6) cm
(Not drawn to scale)
Answer:
B) 2x³ – 6x² – 14x + 24 square centimetersStep-by-step explanation:
The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.
"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"
Area of a parallelogram = Base * Height.
Given the height of the parallelogram = (x-4)cm
Base = (2x² + 2x-6) cm
Area of the parallelogram = (x-4)cm * (2x² + 2x-6) cm
Area of the parallelogram = (x-4)(2x²+2x-6)
Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24
= 2x³+2x²-8x²-6x-8x+24
= (2x³-6x²-14x+24)cm²
HELP! What is the solution to the equation below? Round your answer to two decimal places. 4x = 20 A. x = 2.99 B. x = 0.46 C. x = 1.30 D. x = 2.16
Answer:
X = 5
Step-by-step explanation:
If 4x = 20
And we are asked to find the solution.
It simply means looking for the value of x
So
4x = 20
X = 20/4
X = 5
X is simply the solution
X = 5
Answer:
D 2.16
Step-by-step explanation:
a p e x just use log
Birth weights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birth weights between 125 oz and 140 oz is:
Answer:
The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 110, \sigma = 0.15[/tex]
The proportion of infants with birth weights between 125 oz and 140 oz is
This is the pvalue of Z when X = 140 subtracted by the pvalue of Z when X = 125. So
X = 140
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 110}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 125
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 110}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.9772 - 0.8413 = 0.1359
The proportion of infants with birth weights between 125 oz and 140 oz is 0.1359 = 13.59%.
Find the volume of the following solid figure. Use = 3.14.
V = 4/313. A sphere has a radius of 3.5 inches.
Answer:
V = 51.3 in.³
Step-by-step explanation:
Volume of Sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r = 3.5
So,
V = [tex]\frac{4}{3} (3.14)(3.5)^3[/tex]
V = [tex]\frac{4}{3} (3.14)(12.25)[/tex]
V = [tex]\frac{153.9}{3}[/tex]
V = 51.3 in.³
Identify the steps used in Algorithm 1 to find the maximum element in the following finite sequence 1, 8, 12, 9, 11, 2, 14, 5, 10, 4.
Algorithm 1 procedure max(a1, a2, . . . , an : integers) max :______
Answer:
max(1, 8, 12, 9, 11, 2, 14, 5, 10, 4) = 14
Step-by-step explanation:
Here is the algorithm to find the maximum element:
procedure max(a1, a2, . . . , an : integers)
max := a1
for i := 2 to n
if max < ai then max := ai
return max{max is the largest element}
Now lets see how this algorithm works with the given sequence. 1, 8, 12, 9, 11, 2, 14, 5, 10, 4.
The value of max is set to 1. So max = 1.Now the for loop starts. The loop variable i which works as an index moves throughout the sequence i.e. from 2 to n. The value of n is 10 since the total number of elements in the sequence are 10. The first iteration: i=2. Now the IF condition if max < ai inside this FOR loop checks if the value of max is less than the element at i-th position. As the current value of max=1 and the value at i=2 is 8 which means the second element of the sequence. So this condition evaluates to true as 1 < 8. So the IF part is executed which has a statement max := ai which means if the value of max is less than the element at i-th index then the value of max is set to that element. So max = 8.The second iteration: at i = 3. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 8 and current value of i=3 means the third element of the sequence which is 12. So this condition evaluates to true as 8 < 12. So the IF part is executed which has a statement max := ai which means if the value of max is less than the element at i-th index then the value of max is set to that element. So max = 12.The third iteration at i = 4. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 12 and current value of i=4 means the fourth element of the sequence which is 9. Now the IF condition evaluates to false because 12 > 9. Hence the value of max remains the same. So max = 12.The fourth iteration at i = 5. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 12 and current value of i=5 means the fifth element of the sequence which is 11. Now the IF condition evaluates to false because 12 > 11. Hence the value of max remains the same. So max = 12.The fifth iteration at i = 6. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 12 and current value of i=6 means the sixth element of the sequence which is 2. Now the IF condition evaluates to false because 1 2> 2. Hence the value of max remains the same. So max = 12.The sixth iteration at i = 7. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 12 and current value of i=7 means the seventh element of the sequence which is 14. So this condition evaluates to true as 14 < 12. So the IF part is executed which has a statement max := ai which means if the value of max is less than the element at i-th index then the value of max is set to that element. So max = 14.The seventh iteration at i = 8. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 14 and current value of i=8 means the eighth element of the sequence which is 5. Now the IF condition evaluates to false because 1 4> 5. Hence the value of max remains the same. So max = 14.The eighth iteration at i = 9. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 14 and current value of i=9 means the ninth element of the sequence which is 10. Now the IF condition evaluates to false because 1 4> 10. Hence the value of max remains the same. So max = 14.The ninth iteration at i = 10. Now the IF condition if max < ai checks if the value of max is less than the element at i-th position. As the current value of max= 14 and current value of i=10 means the tenth element of the sequence which is 4. Now the IF condition evaluates to false because 1 4> 4. Hence the value of max remains the same. So max = 14.Now the loop ends as the value of i now becomes 11 because the loop is execute at i from 2 to n and value of n = 10. So the loop breaks and the next statement return max{max is the largest element} is executed which returns the current value of max. This means it returns the largest element in the sequence. Since the current value of max = 14. Hence max = 14 is the largest element.Find the center (h,k) and radius r of the circle. Graph the equation. x^2 + y^2 - 2x - 10y + 1 = 0
Answer:
Center: (1, 5)
Radius: r = 5
Step-by-step explanation:
Step 1: Rewrite equation
x² - 2x + y² - 10y = -1
Step 2: Complete the Square (x2)
x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25
(x - 1)² + (y - 5)² = 25
Step 3: Find answers
Center = (h, k)
(1, 5) as Center
Radius = r
r² = 25
r = 5
Answer: Center = (1, 5)
Radius = 5
Step-by-step explanation:
The standard form for a circle is: (x - h)² + (y - k)² = r² where
Center = (h, k)Radius = rFirst, group the x's and group the y's in order to complete the square.
x² - 2x + y² - 10y = -1
↓ ↓
(-2/2)²=1 (-10/2)²=25
Add those values to BOTH sides:
x² - 2x + 1 + y² - 10y + 25 = -1 + 1 + 25
Rewrite the left side as perfect squares and simplify the right side.
(x - 1)² + (y - 5)² = 25
We end up with (h, k) = (1, 5) this is the center
and r² = 25 --> r = 5 this is the radius
To graph the circle, place an x at the center (1, 5). Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.
1.5 * 10 exponent -5 covert to decimal form
Answer:
The decimal form of [tex]1.5\times 10^{-5}[/tex] is [tex]0.000015[/tex].
Step-by-step explanation:
We need to convert [tex]1.5\times 10^{-5}[/tex] into decimal form. It is given in the standard form. The following steps are to be done to convert it into decimal form.
[tex]1.5\times 10^{-5}\\\\=\dfrac{15}{10}\times 10^{-5}\\\\=15\times 10^{-5}\times 10^{-1}\\\\\=15\times 10^{-5-1}\\\\=15\times 10^{-6}\\\\=\dfrac{15}{1000000}\\\\=0.000015[/tex]
So, the decimal form of [tex]1.5\times 10^{-5}[/tex] is [tex]0.000015[/tex]. Hence, this is the required solution.
A simulated exercise gave n = 20 observations on escape time (sec) for oil workers, from which the sample mean and sample standard deviation are 370.42 and 25.74, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 min. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using a significance level of .05. (Give t to 2 decimal places and the p-value to 3 decimal places.)t =P-value =ConclusionReject the null hypothesis, there is significant evidence that true average escape time exceeds 6 min. Reject the null hypothesis, there is not significant evidence that true average escape time exceeds 6 min. Fail to reject the null hypothesis, there is not significant evidence that true average escape time exceeds 6 min. Fail to reject the null hypothesis, there is significant evidence that true average escape time exceeds 6 min.
Answer:
Reject the null hypothesis, there is significant evidence that true average escape time exceeds 6 min.
Step-by-step explanation:
In this case we need to test whether the data contradict the prior belief that the true average escape time for oil workers would be at most 6 min or 360 seconds.
The information provided is:
[tex]n=20\\\bar x=370.42\\s=25.74\\\alpha =0.05[/tex]
The hypothesis for the test can be defined as follows:
H₀: The true average escape time for oil workers is more than 360 seconds, i.e. μ > 360.
Hₐ: The true average escape time for oil workers is at most 360 seconds, i.e. μ ≤ 360.
As the population standard deviation is not known we will use a t-test for single mean.
Compute the test statistic value as follows:
[tex]t=\frac{\bar x-\mu}{\s/\sqrt{n}}=\frac{370.42-360}{25.74/\sqrt{20}}=1.81[/tex]
Thus, the test statistic value is 1.81.
Compute the p-value of the test as follows:
[tex]\text{p-value}=P(t_{n-1}<t)[/tex]
[tex]=P(t_{20-1}<1.81)\\\\=P(t_{19}<1.81)\\\\=0.044[/tex]
*Use a t-table.
Thus, the p-value of the test is 0.044.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.044 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Thus, concluding that the true average escape time would be at most 6 min.