Answers
Answer:
4.2 mi²
Step-by-step explanation:
Volume of a cone = (1/3)πr²h, where r = radius and h = height
(1/3)πr²h
= (1/3)×π×1²×4
= 4π/3
= 4.2 mi² (rounded to the nearest tenth)
Related Questions
Of the three properties, reflexive, symmetric, and transitive that define the relation "is equal to," which one could also apply to "is less than" and "is greater than?" transitive reflexive symmetric
Answers
Answer: Transitive property.
Step-by-step explanation:
First, for the equality we have:
Reflexive:
For all real numbers x, x = x.
Symmetric:
For all real numbers x, y
if x= y, then y = x.
Transitive:
For reals x, y and z.
if x = y, and y = z, then x = z.
Now, let's talk about inequalities.
first, the reflexive property will say that:
x > x.
This has no sense, so this property does not work for inequalities.
Now, the reflexive.
If x > y, then y > x.
Again, this has no sense, if x is larger than y, then we can never have that y is larger than x. This property does not work for inequalities.
Not, the transitive property.
if x > y, and y > z, then x > z.
This is true.
x is bigger than y, and y is bigger than z, then x should also be bigger than z.
x > y > z.
And this also works for the inverse case:
x < y and y < z, then x < z.
So the correct option is transitive property.
Two charged particles, Q1, and Q2, are a distance r apart with Q2 = 5Q1 Compare the forces they exert on one another when F1 is the force Q2 exerts on Q1and F2 is the force Q1 exerts on Q2.
a) F2 = 5F1.
b) F2 =-5F1.
c) F2 = F1.
d) F2 = -F1.
e) 5F2 = F1.
Answers
Answer:
d) F2 = -F1.
Step-by-step explanation:
According to Coulomb's law of forces on electrostatic charges, the force of attraction is proportional to the product of their charges, and inversely proportional to the square of their distance apart.
What this law means is that both particles will experience an equal amount of force on them, due to the presence of the other particle. This force is not just as a result of their individual charges, but as a result of the product of their charges. Also, the force is a vector quantity that must have a direction alongside its magnitude, and the force on the two particles will always act in opposite direction, be it repulsive or attractive.
Century Roofing is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.)
Answers
Question Completion:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Answer:
Century Roofing
Project's NPV is: ($6,578)
Step-by-step explanation:
a) Data and Calculations:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)
Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700
PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)
NPV = Cash inflow minus Cash outflow
= $158,422 - $165,000
= ($6,578)
Negative NPV
b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value. It becomes a present cash outflow. Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.
Complete the function table
Answers
The lines below are parallel. If the slope of the green line is -4, what is the slope of the red line?
Answers
Answer:
-4
Step-by-step explanation:
Hey there!
Well the slopes of 2 parallel lines have the same slope,
meaning if the green line has a slope of -4 then the slope of the red line has a slope of -4.
Hope this helps :)
A grocery store owner asked the first 20 children who visited the store one day about their favorite snack. This is what type of sampling
Answers
Answer:
Non-probability sampling: In non-probability sampling, the researcher chooses members for research at random. This sampling method is not a fixed or predefined selection process. This makes it difficult for all elements of a population to have equal opportunities to be included in a sample.
Step-by-step explanation:
Uses of non-probability sampling
Non-probability sampling is used for the following:
Create a hypothesis: Researchers use the non-probability sampling method to create an assumption when limited to no prior information is available. This method helps with the immediate return of data and builds a base for further research.
Exploratory research: Researchers use this sampling technique widely when conducting qualitative research, pilot studies, or exploratory research.
Budget and time constraints: The non-probability method when there are budget and time constraints, and some preliminary data must be collected. Since the survey design is not rigid, it is easier to pick respondents at random and have them take the survey or questionnaire.
How do you decide on the type of sampling to use?
For any research, it is essential to choose a sampling method accurately to meet the goals of your study. The effectiveness of your sampling relies on various factors. Here are some steps expert researchers follow to decide the best sampling method.
Jot down the research goals. Generally, it must be a combination of cost, precision, or accuracy.
Identify the effective sampling techniques that might potentially achieve the research goals.
Test each of these methods and examine whether they help in achieving your goal.
Select the method that works best for the research.
Select your respondents
Difference between probability sampling and non-probability sampling methods
We have looked at the different types of sampling methods above and their subtypes. To encapsulate the whole discussion, though, the significant differences between probability sampling methods and non-probability sampling methods are as below:
Probability Sampling Methods Non-Probability Sampling Methods
Definition Probability Sampling is a sampling technique in which samples from a larger population are chosen using a method based on the theory of probability. Non-probability sampling is a sampling technique in which the researcher selects samples based on the researcher’s subjective judgment rather than random selection.
Alternatively Known as Random sampling method. Non-random sampling method
Population selection The population is selected randomly. The population is selected arbitrarily.
Nature The research is conclusive. The research is exploratory.
Sample Since there is a method for deciding the sample, the population demographics are conclusively represented. Since the sampling method is arbitrary, the population demographics representation is almost always skewed.
Time Taken Takes longer to conduct since the research design defines the selection parameters before the market research study begins. This type of sampling method is quick since neither the sample or selection criteria of the sample are undefined.
Results This type of sampling is entirely unbiased and hence the results are unbiased too and conclusive. This type of sampling is entirely biased and hence the results are biased too, rendering the research speculative.
Hypothesis In probability sampling, there is an underlying hypothesis before the study begins and the objective of this method is to prove the hypothesis. In non-probability sampling, the hypothesis is derived after conducting the research study.
[tex]\int\limits^9_3 {\frac{1}{(x+21)\sqrt{x+22} } } \, dx[/tex]
Answers
Let y = x + 22 and dy = dx, so the integral becomes
[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{25}^{31} \frac{\mathrm dy}{(y-1)\sqrt{y}}[/tex]
Now let z = √y, so that z ² = y. Then 2z dz = dy, and the integral becomes
[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{\sqrt{25}}^{\sqrt{31}} \frac{2z}{(z^2-1)z} \\\\ = \int_5^{\sqrt{31}} \frac{2}{z^2-1}\,\mathrm dz[/tex]
Expand the integrand into partial fractions:
[tex]\dfrac{2}{z^2-1} = \dfrac1{z-1}-\dfrac1{z+1}[/tex]
Then we have
[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_5^{\sqrt{31}}\left(\frac1{z-1}-\frac1{z+1}\right)\,\mathrm dz \\\\ = \left(\ln|z-1|-\ln|z+1|\right)\bigg|_5^{\sqrt{31}} \\\\ =\left[\ln\left|\frac{z-1}{z+1}\right|\right]\bigg|_5^{\sqrt{31}} \\\\ =\ln\left(\frac{\sqrt{31}-1}{\sqrt{31}+1}\right) - \ln\left(\frac{4}{6}\right) \\\\ =\ln\left(32-2\sqrt{31}\right) - \ln\left(\frac23\right) \\\\ =\boxed{\ln\left(48-3\sqrt{31}\right)}[/tex]
Last year, Rob set up the Road Runner Race for his school.
The race was 1,200 meters long and 188 people signed up to
run the race. 38 people did not show up to run. This year,
there will be 3 times as many runners as last year. How
many people will run the race this year?
Answers
Answer:
450 people
Step-by-step explanation:
The number of people running a race this year will be 450.
What is an expression?
Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that last year, Rob set up the Road Runner Race for his school. The race was 1,200 meters long and 188 people signed up to run the race. 38 people did not show up to run. This year, there will be 3 times as many runners as last year.
The number of people running a race this year:-
Number = ( 188 - 38 ) x 3
Number = 150 x 3
Number = 450
Therefore, the number of people running a race this year will be 450.
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Installation of certain hardware takes a random amount of time. The installation times form a normally distributed distribution with a standard deviation 5 minutes and a mean of 45 minutes. A computer technician installs the hardware on 31 different computers. You are interested to find the probability that the mean installation time for the 31 computers is less than 43 minutes. What is the probability that the mean installation time for 31 computers is less than 43 minutes.
Answers
To solve this question, the normal distribution and the central limit theorem are used.
Doing this, there is an 0.0129 = 1.29% probability that the mean installation time for 31 computers is less than 43 minutes.
------------------------------------
First, these concepts are presented, then we identify mean, standard deviation and sample size, and then, we find the desired probability.
------------------------------------
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
------------------------------------
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
------------------------------------
Mean of 45, standard deviation of 5:
This means that [tex]\mu = 45, \sigma = 5[/tex]
Sample size of 31:
This means that [tex]n = 31, s = \frac{5}{\sqrt{31}}[/tex]
------------------------------------
Probability the sample mean is less than 43:
This is the p-value of Z when X = 43, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{43 - 45}{\frac{5}{\sqrt{31}}}[/tex]
[tex]Z = -2.23[/tex]
[tex]Z = -2.23[/tex] has a p-value of 0.0129.
Thus, 0.0129 = 1.29% probability that the mean installation time for 31 computers is less than 43 minutes.
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Determine the positive integer values of k for which the following polynomia
over the integers given: c^2 – 7c+ k
Answers
Explanation:
c^2 - 7c + 10
= (c -5)(c-2)
c^2 - 7c + 12
= (c - 4)(c -3)
c^2 - 7c + 6
= (c - 1)(c - 6)
I need help with this please if anyone know I will appreciate it
Answers
Answer:
290.44
Step-by-step explanation:
The whole figure area can be calculated by assuming that the whole floor is a complete square of 18.2 x 18.2 and subtracting the area of the rectangular cutout which is 10.2 x 4
Area of the the flooring=18.2 x 18.2 - (10.2*4)=290.44
What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot 6 StartRoot 2 EndRoot 18 StartRoot 2 EndRoot 30 StartRoot 2 EndRoot 36 StartRoot 2 EndRoot
Answers
Answer:
[tex]18\sqrt2[/tex]
Step-by-step explanation:
To simplify:
[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }[/tex]
First of all, let us write 18 and 162 as product of prime factors:
[tex]18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}[/tex]
The pairs are underlined as above.
While taking roots, only one of the numbers from the pairs will be chosen.
Now, taking square roots.
[tex]\sqrt{18} =3 \sqrt2[/tex]
[tex]162 = 3 \times 3 \times \sqrt 2 = 9 \sqrt2[/tex]
So, the given expression becomes:
[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}[/tex]
So, the answer is:
[tex]18\sqrt2[/tex] or 18 StartRoot 2 EndRoot
Answer:
its B. 18 sqrt(2)
Step-by-step explanation:
just took test
A tin of tennis balls costs $6.99, and each tin contains 4
tennis balls.
If the tennis balls were sold individually, then
approximately how much would one tennis ball cost?
$
Answers
Answer:
About $1.75 per tennis balls
Step-by-step explanation:
A tin of 4 tennis balls costs $6.99. We are asked to find the price of one tennis ball.
We need to find the unit price, or price per ball.
Divide the cost by the number of tennis balls.
cost / tennis balls
cost = $6.99
tennis balls = 4 tennis balls
$6.99 / 4 tennis balls
Divide 6.99 by 4.
$1.7475 / 1 tennis ball
Round to the nearest cent or hundredth. The 7 in the thousandth place tells us to round the 4 to a 5 in the hundredth place.
$1.75 / 1 tennis ball
It would cost approximately $1.75 for one tennis ball.
I need help with these
Answers
Answer:
2. 20 oranges
3. 18 yellow tulips
4. 23 students
All 20 children at a party were given one cookie, and then some were given an additional cookie. If a total of
32 cookies were given out, how many children received an additional cookie?
8
O 10
О о о
O 12
o 14
Answers
Answer:
If there were 20 children at a party, and each were given one cookie, then a total of 20 cookies were given out.
However, this is not the case, as 32 cookies were given out. So, we can see that 32 - 20 children, or 12 children, received one additional cookie.
Let me know if this helps!
A research center project involved a survey of 851 Internet users. It provided a variety of statistics on Internet users. (a) The sample survey showed that 92% of respondents said the Internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. (Round your answers to four decimal places.)
Answers
Answer:
The answer is "(0.9193924 , 0.9206076)".
Step-by-step explanation:
[tex]\text{sample proportion}\ (SP) = 0.92\\\\\text{sample size}\ n = 851\\\\\text{Standard error} \ SE = \sqrt{\frac{(SP \times(1 - SP)}{n})}\\\\[/tex]
[tex]= \sqrt{\frac{(0.92 \times (0.08)}{851})}\\\\= \sqrt{\frac{0.0736}{851}}\\\\= \sqrt{8.648\times 10^{-5}}\\\\=0.00031[/tex]
[tex]\text{CI level is}\ 95\% \\\\\therefore\\\\ \alpha = 1 - 0.95 = 0.05\\\\\frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\ Z_c = Z_{(\frac{\alpha}{2})} = 1.96[/tex]
Calculating the Margin of Error:
[tex]ME = z_{c} \times SE\\\\[/tex]
[tex]= 1.96 \times 0.00031\\\\ = 0.0006076[/tex]
[tex]CI = (SP - z*SE, SP + z*SE)[/tex]
[tex]= (0.92 - 1.96 * 0.00031 , 0.92 + 1.96 * 0.00031)\\\\ = (0.92 - 0.0006076 , 0.92 + 0.0006076)\\\\= (0.9193924 , 0.9206076)[/tex]
GIVING 15 POINTS PLS FAST
Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
-24 8 + 30
131.87
28.98+(-52.22)
65
45%+39
-23.24
56.75 +75.12
Reset
Next
Next
Answers
Answer:
Hope this helps! All you needed to do was add and subtract. Go through the slides, I added the step by step explanation, as well as the final table which contains the answers.
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
We have,
Expressions:
-24(5/9) +30(7/9)
Simplifying the fractions.
This can be written as,
= (-24 + 30) +(-5/9 + 7/9)
= 6 + 2/9
= 6(2/9)
45(2/9) +39(3/9)
= (45 + 39) + (2/9 + 3/9)
= 84 + 5/9
= 84(5/9)
28.98 + (-52.22)
= 28.98 - 52.22
= -23.24
56.75 + 75.12
= 131.87
Thus,
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
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Suppose that a random sample of 16 measures from a normally distributed population gives a sample mean of x=13.5 and a sample standard deviation of s=6. the null hypothesis is equal to 15 and the alternative hypothesis is not equal to 15. using hypothesis testing for t values do you reject the null hypothesis at alpha=.10 level of significance?
Answers
Answer:
Step-by-step explanation:
The summary of the statistics given include:
population mean [tex]\mu[/tex] = 15
sample mean [tex]\oerline x[/tex] = 13.5
sample size n = 16
standard deviation s = 6
The level of significance ∝ = 0.10
The null and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o: \mu = 15} \\ \\ \mathtt{H_1 : \mu \neq 15}[/tex]
Since this test is two tailed, the t- test can be calculated by using the formula:
[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]
[tex]t = \dfrac{13.5 - 15}{\dfrac{6}{\sqrt{16}}}[/tex]
[tex]t = \dfrac{- 1.5}{\dfrac{6}{4}}[/tex]
[tex]t = \dfrac{- 1.5\times 4}{6}}[/tex]
[tex]t = \dfrac{- 6.0}{6}}[/tex]
t = - 1
degree of freedom = n - 1
degree of freedom = 16 - 1
degree of freedom = 15
From the standard normal t probability distribution table, the p value when t = -1 at 0.10 level of significance, the p - value = 0.3332
Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.10
Conclusion: Therefore, we can conclude that there is insufficient evidence at the 0.10 level of significance to conclude that the population mean μ is different than 15.
will give 5 stars and thanks for correct answer Richard starts high school every day at 7:45 A.M.. How many seconds is Richard in school each day of school dismissed at 2:15 P.M.
Answers
Is the constant of proportionality in gallons per minute the same for every row? What does this say about the relationship of the amount of water to time?
Answers
Answer:
Yes, the constant of proportionality is the same for the three rows.
The relationship between amount of water (W) in terms of time (t) can be written as:
W = 16.5 t
Step-by-step explanation:
To find the constant of proportionality, find the number of gallons per minute for each row:
First row: 16.5 gal in 1 minute means: 16.5 Gal/min
Second row: 24.75 gallons in 1.5 minutes means 24.75/1.5 = 16.6 Gal/min (same proportionality as above)
Third row: 33 gallons in 2 minutes means: 33/2 = 16.5 Gal/min (again same proportionality)
Then: Yes, the constant of proportionality is the same for the three rows.
Therefore the amount (W) of water in gallons per time (t) in minutes can be written as the product of 16.5 times time (t):
W = 16.5 t
Answer:
The numbers prove that there is a proportional relationship between the gallons of water and the time in minutes. The bathtub fills at a constant rate.
Step-by-step explanation:
Subtract 750 -389 plzzz help
Answers
Therefore, 361
How do you write 5.44 in words?
Answers
Answer:
five and forty-four hundredths
Step-by-step explanation:
Answer:
five point four four
Step-by-step explanation:
Martin writes down 4
numbers.
Their mean is 8.
The range is 6.
The largest value is 11.
There is no mode.
Write down the four
numbers.
Answers
Answer:
5, 7, 9, 11
or
5, 6, 10, 11.
Step-by-step explanation:
The mean is 8 so the total value of the 4 numbers = 4*8 = 32.
Range is 6 so largest number - smallest = 6
The largest value is 11 so the smallest is 11-6 = 5
The middle 2 numbers add up to 32-(11+5) = 32 - 16
= 16.
- and as there is no mode they must be 7 and 9
or 6 and 10.
look at the image for the question
Answers
Answer:
3166.7
Step-by-step explanation:
V = πr²h
V = π * (12 km)² * 7 km
V ≈ 3166.7 km³
Hey there!
First, let's review the formula for finding a cylinder's volume.
Formula: [tex]\pi r^2h[/tex]
Our new equation would look like this: [tex]\pi[/tex] x [tex]12^{2}[/tex] x 7.
The original answer would be 3166.72539482, but the question states that it want it rounded to the nearest tenth. So, your answer would be 3166.7.
Hope this helps! Have a great day!
If ABCD is dilated by a factor of 3 the coordinates of A would be
Answers
Answer:
A'=(-9, - 3)
Step-by-step explanation:
A' will be 3*(the coordinates of A), A'=(-9, - 3)
Coordinates of A' are given by (-9,-3).
What is Coordinates?Coordinates of a point suggest the position of that particular point in the Cartesian Plane.
If the coordinates of a point are (x,y) then x is the distance of the point from Y-axis and y is the distance from the X-axis.
Here in the given graph, we can see that the coordinates of A of quadrilateral ABCD are (-3,-1)
ABCD is dilated by a factor of 3.
So the coordinates of the A' which is the point A after dilating by 3 are given by the product of 3 and corresponding original coordinations.
Hence the coordinates of A' are = (3*(-3),3*(-1)) = (-9,-3)
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Write 11 numbers in a row so that the sum of any 3 consecutive numbers is negative, while the sum of all the numbers is positive. Is it possible?
Answers
Explanation:
Let the 11 numbers be {a1, a2, ..., a11} such that a1 is the smallest and a11 is the largest. So, a1 < a2 < ... < a11. Furthermore, these numbers are consecutive.
If we add consecutive numbers to get a negative result, then each of the numbers must be negative. So every value in the set {a1, a2, ..., a11} is a negative value which makes it impossible to have a1+a2+...a11 be a positive sum.
The table shows data collected on the relationship between time spent playing video games and time spent with family. The line of best fit for the data is ý = -0.363 +94.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables.
Video Games (Minutes) Time with Family (Minutes)
40 80
55 75
70 69
85 64
Required:
a. According to the line of best fit, what would be the predicted number of minutes spent with family for someone who spent 36 minutes playing video games?
b. The predicted number of minutes spent with family is:_________
Answers
Answer:
81.432 minutes
Step-by-step explanation:
Given the following :
Video Games (Mins) - - - Time with Family(Mins)
40 - - - - - - - - - - - - - - - - - - - 80
55 - - - - - - - - - - - - - - - - - - - 75
70 - - - - - - - - - - - - - - - - - - - 69
85 - - - - - - - - - - - - - - - - - - - 64
Best fit line:
ý = -0.363x +94.5
For someone who spent 36 minutes playing video games, the predicted number of minutes spent with family according to the best fit line will be:
Here number of minutes playing video games '36' is the independent variable
ý is the dependent or predicted variable ;
94.5 is the intercept
ý = -0.363(36) +94.5
ý = −13.068 + 94.5
ý = 81.432 minutes
Which is about 81 minutes to the nearest whole number.
A research center claims that % of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of adults in that country, % say that they would travel into space on a commercial flight if they could afford it. At , is there enough evidence to reject the research
Answers
Complete Question
A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At , is there enough evidence to reject the research center's claim
Answer:
Yes there is sufficient evidence to reject the research center's claim.
Step-by-step explanation:
From the question we are told that
The population proportion is p = 0.30
The sample proportion is [tex]\r p = 0.34[/tex]
The sample size is n = 700
The null hypothesis is [tex]H_o : p = 0.30[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.30[/tex]
Here we are going to be making use of level of significance = 0.05 to carry out this test
Now we will obtain the critical value of [tex]Z_{\alpha }[/tex] from the normal distribution table , the value is [tex]Z_{\alpha } = 1.645[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \r p - p }{ \sqrt{ \frac{ p (1-p)}{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.34 - 0.30 }{ \sqrt{ \frac{ 0.30 (1-0.30 )}{ 700} } }[/tex]
[tex]t = 2.31[/tex]
Looking at the values of t and [tex]Z_{\alpha }[/tex] we see that [tex]t > Z_{\alpha }[/tex] hence the null hypothesis is rejected
Thus we can conclude that there is sufficient evidence to reject the research center's claim.
Which of the following correctly shows the quotient of 80 divided by 5 ?
Answers
Answer:16
Step-by-step explanation:
Just divide 80 by 5 or skip count by fives.
1. What happened when you had a negative plus a negative, (-a) + (-b)?
I
2. What happened when you had a positive plus a negative, a + (-b)?
***Is this the same as a positive minus a positive, a - b?
3. What happened when you had a positive minus a negative, a - (-b)?
4. What happened when you had a negative minus a negative, (-a) - (-b)?
Answers
Answer:
See Explanation
Step-by-step explanation:
1.
What happens when negative adds to negative; e.g (-a) + (-b)
First, we need to simplify the expression
[tex](-a) + (-b)[/tex]
Open the brackets
[tex]-a - b[/tex]
Factorize
[tex]-(a+b)[/tex]
So, what happens is that: the two numbers are added together and the result is negated;
E.g.
[tex](-5) + (-3) = -(5 + 3) = -8[/tex]
2.
What happens when positive is added to negative; e.g. a + (-b)
First, we need to simplify the expression
[tex]a + (-b)[/tex]
Open the brackets
[tex]a - b[/tex]
So, what happens is that: the negative number is subtracted from the positive number
And Yes; [tex]a + (-b)[/tex] is the same as [tex]a - b[/tex] (As shown above)
E.g.
[tex]5 + (-3) = 5 - 3 =2[/tex]
3.
What happens when to positive minus a negative; e.g. a - (-b)
First, we need to simplify the expression
[tex]a - (-b)[/tex]
Open the brackets
[tex]a + b[/tex]
So, what happens is that; the two numbers are added together.
E.g.
[tex]5 - (-3) = 5 + 3 = 8[/tex]
4.
What happens when negative minus a negative; e.g. (-a) - (-b)
First, we need to simplify the expression
[tex](-a) - (-b)[/tex]
Open the brackets
[tex]-a + b[/tex]
Reorder
[tex]b - a[/tex]
So, what happens is that; the first number is subtracted from the second.
E.g.
[tex](-5) - (-3) = 3-5 = -2[/tex]