Answer:
5.75 ft ≈ 6 ft
2.47 ft ≈ 2 ft
perimeter of the rectangular counter top = 16 ft
Step-by-step explanation:
The counter top he is installing is a rectangular piece of quartz that is 5.75 ft long and 2.47 ft wide. The length and the width can be rounded off to the nearest whole number as follows.
length = 5.75 ft to the nearest whole number will be 6 ft
width = 2.47 ft to the nearest whole number will be 2 ft
The logic in rounding off the number to the nearest whole number is that the value on the left hand side of the decimal is rounded off to an integer. If the number at the right hand side of the number is greater or equal to 5 we borrow 1 and add to the left hand side number of the decimal number.
Therefore,
Perimeter of the rectangle = 2l + 2w
perimeter of the rectangle = 2 × 6 + 2 × 2
perimeter of the rectangle = 12 + 4
perimeter of the rectangle = 16 ft
Pew Research Center is a nonpartisan polling organization that provides information about issues, attitudes, and trends shaping America. In a poll, Pew researchers found that 47% of American adult respondents reported getting at least some local news on their cell phone or tablet computer (Pew Research website, May 14, 2011). Further findings showed that 42% of respondents who own cell phones or tablet computers use those devices to check local weather reports and 37% use the devices to find local restaurants or other businesses.
a. One statistic concerned using cell phones or tablet computers for local news. What population is that finding applicable to?
b. Another statistic concerned using cell phones or tablet computers to check local weather reports and to find local restaurants. What population is this finding applicable to?
c. Do you think the Pew researchers conducted a census or a sample survey to obtain their results? Why?
d. If you were a restaurant owner, would you find these results interesting? Why? How could you take advantage of this information?
Answer:
a) Population of adults who watch local news
b) Population of adults who use cell phones or tablets.
c) They conducted a sample survey
d) I will find the results interesting.
I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.
Step-by-step explanation:
a) This finding is applicable to the population of adults who watch local news.
This is because the sample will be collected from the population of adults who watch local news to see the percentage that actually get those local news from their cell phones or tablet computers.
b) This finding is applicable to the population of adults who use cell phones or tablets.
The sample will be collected from the population of adults who use cell phones or tablets. A survey can now be carried out to find out what they use their phones or tablets for, whether to search for restaurants or get weather reports.
c) The Pew Researchers conducted a sample survey because a census data cannot contain the information about weather reports, local restaurants or news channel. Precise information can only be gotten from a sample survey.
d) Yes, I will. Having an idea of how large the population of those that search for local restaurants on phones and tablets will enable me to channel my publicity towards this media. I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.
A coin is tossed twice in succession. Let A be the event that the first toss is heads and let B the event that the second toss is heads. Find: (a) P(A) (b) P(B) (c) P(A∩B) (d) P(B /A)
Answer:
Step-by-step explanation:
A coin has two faces, a head (H) or tail (T). Tossing a coin twice in succession would give the following sample size;
{HH, HT, TH, TT}
Given that: A = first toss is heads, B = second toss is heads, then:
i. P(A) = {HH, HT} = 2
ii. P(B) = {TH} = 1
iii. P(A∩B) = {HH} = 1
iv. P(B /A) = [tex]\frac{1}{2}[/tex]
7. 12, 24, 4, 18, 12, 9
Using the data, create a histogram.
Answer:
import pandas as pd
vec = pd.Series([7.12,24,4,18,12,9])
vec.plot(kind = 'hist')
Step-by-step explanation:
You can use python for that.
By doing
import pandas as pd
vec = pd.Series([7.12,24,4,18,12,9])
vec.plot(kind = 'hist')
And this is the result you get
Over several years, students of Professor Robin Lock have flipped a large number of coins and recorded whether the flip landed on heads or tails. As reported in a 2002 issue of Chance News, these students has observed 14,709 heads in a total of 29,015 flips.
Required:
a. What are the observational units for this study?
b. Determine the theory-based p-value for testing whether the long-run proportion of heads differs from 0.50.
c. What conclusion would you draw at the 0.05 significance level?
d. Are your results practically important? Why/why not?
Answer:
a) The observational units for this study are coins
b) The test is a two-tailed test.
c) Since the p-value is < α, we can therefore conclude that long-run proportion of heads significantly differ from 0.50
d) The findings are known as statistically important, due to the very large sample size. But the difference between the 0.50 ratio hypothesized and the 0.51 ratio observed isn't very large. Consequently , the findings are not relevant
Step-by-step explanation:
a) The observational units for this study are coins
b) Number of heads = x = 14709
Number of flips = n = 29015
Sample proportion = [tex]\bar{p}[/tex] = x ÷ n = 14709 ÷ 29015=0.51
H[tex]_{o}[/tex] : p =0.50
H[tex]_{a}:[/tex] p [tex]\ne[/tex] 0.50
z = [tex](\bar{p}-p)/\sqrt{p(1-p)/n} = (0.51-0.50)/\sqrt{0.50 \times (1-0.50)/29015}[/tex]
z = 2.366
Using the normal distribution table, area under the normal curve to the right of z;
z = 2.366 = 0.009
The test is a two-tailed test.
Hence, p-value = [tex]0.009 \times 2[/tex] = 0.018
c) α = 0.05
p-value < α = 0.05, we reject the null hypothesis.
We can therefore conclude that long-run proportion of heads significantly differ from 0.50
d) The findings are known as statistically important, due to the very large sample size. But the difference between the 0.50 ratio hypothesized and the 0.51 ratio observed isn't very large. Consequently , the findings are not relevant
The volume of a cone is cubic feet. Its height is 12 feet. Ashlyn is finding the area of the base of the cone. Her work is shown below.
Answer:
Step-by-step explanation:
The volume of a cone of height h and a circular base of radius r is given by [tex]V=\frac{\pi r^2 h }{3}[/tex]. Note that [tex]\pi r^2[/tex] is the area of the base, therefore, if we want to find the area of the base we must multiply the equation by 3 and divide by h. Hence
[tex]\pi r^2 = \frac{3V}{h}[/tex]
In this case, h=12. Given a value of V, we can find the area of the base
The value of homes sold in Hampton VA are normally distributed with a mean of $200,000 and a standard deviation of $10,000. If 1216 houses were sold in 2012 what percentage of houses sold fall between $190,000 and 230,000?
Answer:
84%
Step-by-step explanation:
What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.
We have that z is equal to:
z = (x - m) / (sd)
x is the value to evaluate, m the mean, sd the standard deviation
So for 190000 we have:
z = (190000 - 200000) / (10000)
z = -1
and this value represents 0.1587
for 230000 we have:
z = (230000 - 200000) / (10000)
z = 3
and this value represents 0.9987
we subtract:
0.9987 - 0.1587 = 0.84
Which means that it represents 84% of the houses
The dimensions of the base of Box 1 are x by 3x.
The base area of Box 1 is:
3x
3.x2
3r3
4x
Answer:
3x²
Step-by-step explanation:
The area is the product of the dimensions of the base:
area = x(3x) = 3x²
Question 1:Lauren wants to buy 3 shirts at $15.00 each. At home, she calculates the total cost as $46.20, using the sales tax of 8%. At the store, Lisa (the cashier) tells Lauren the total cost is $48.60. Which person is wrong, Lauren or Lisa
Question 2:What’s the cost of the shirts before tax
Question 3:How much is the sales tax for all shirts
Question 4:What is the total cost of the shirts, including tax?
Answer:
Lauren is wrong
Step-by-step explanation:
1. Lauren is wrong
2. What’s the cost of the shirts before tax
Each shirt cost $15 and the total = $15 x 3 = $45
3. How much is the sales tax for all shirts
Sale tax for all shirts is $45 x 0.08 = $3.6
4. What is the total cost of the shirts, including tax?
Total cost = $45 + $3.6 = $48.60
need help pls on circle geometry
Answer:
25
Step-by-step explanation:
AB is a tangent to the circle hence the angle ABO is a right angle !!! With that knowledge we can construct a right-angled triangle with sides AB ,BO and OA .
Applying the Pythagorean theorem we get that OA is the hypotenuse and thus
[tex]oa = \sqrt{ab {}^{2} + ob {}^{2} } [/tex]
can the square root of a rational number be irrational?
Answer:
Yes. Some examples are √2, √3, √5.
You better believe it ! In fact, if you don't count an infinite number of examples, you'll find that MOST of their square roots are irrational.
Let's examine the smallest 1,000 integers . . .
-- They're all rational numbers, but ...
-- only 31 of them have rational square roots !
4ln(3x)=-4
Solve for x
Answer:
4.4=-4
Step-by-step explanation:
just solving maths
The mathematics department at a community college collected data for the number of students enrolled in 40 math classes over the course of one year. The following stem-and-leaf display shows the total number of students enrolled in each class. Choose the statement below that describes the enrollment data. Key: 10|5 denotes 105 students; 7|2 denotes 72 students3 6 6 7 8 9 4 2 3 3 6 6 5 3 3 8 9 6 2 2 3 5 9 7 2 5 7 8 0 0 3 7 7 9 1 3 5 7 10 0 2 5 7 1 1 3 4 12 1 2 2 A. The distribution of the number of students enrolled in each of 40 math courses is skewed to the right, with a typical class size of 69 students. The smallest class size was 36 and the largest was 122. B. The distribution of the number of students enrolled in each of 40 math courses is unimodal and symmetric. The smallest class size was 36 and the largest was 122. The center (as measured by the median) of the distribution was around 73 students. C. The distribution of the number of students enrolled in each of 40 math courses is skewed to the left, with a typical class size of 88 students. The smallest class size was 36 and the largest was 122. D. The distribution of the number of students enrolled in each of 40 math courses is nearly uniform. The smallest class size was 36 and the largest was 122. The center (as measured by the median) of the distribution was around 73 students. E. The distribution of the number of students enrolled in each of 40 math courses is nearly uniform. The smallest class size was 36 and the largest was 122. The center (as measured by the median) of the distribution was around 88 students.
Answer:
D.
Step-by-step explanation:
Sky and Natalia shared some money in the ratio 6:5.
Sky gets £3 more than Natalia.
How much does Natalia receive?
Let the amount that Sky receives be S, and the amount that Natalia recieves be N.
[tex] \dfrac{s}{n} = \dfrac{6}{5} [/tex]
[tex]s = n + 3 \\ \\ \dfrac{n + 3}{n} = \frac{6}{5} \\ \\ 5n + 15 = 6n \\ \\ n = 15[/tex]
15 euros
Help! Which of the following side lengths would NOT make a right triangle?
Answer:
The Answer is 10, 50, and 54
Step-by-step explanation:
You want to figure this answer out by using the Pythagorean Theorem. If 10 squared plus 50 squared does not equal 54 squared, then those side lengths can not make a triangle.
We have two fractions,
and
and we want to rewrite them so that they have a common denominator
12 4.
(and whole number numerators).
imi
What numbers could we use for the denominator?
ent
Choose 2 answers:
A
12
ond
8
Band
nom
24
18
Answer:
Options (A) and (C).
Step-by-step explanation:
There are two fractions given as
[tex]\frac{5}{12},\frac{3}{4}[/tex]
If we rewrite the fractions by making denominators common we can convert the fraction as,
[tex]\frac{5}{12}, \frac{3\times 3}{3\times 4}[/tex]
Or [tex]\frac{5}{12}, \frac{9}{12}[/tex]
Similarly, both the fractions with common denominators may be[tex]\frac{5\times 2}{12\times 2},\frac{3\times 6}{4\times 6}[/tex]
Or [tex]\frac{10}{24},\frac{18}{24}[/tex]
Therefore, denominators of both the fractions will be 12 and 24.
Options (A) and (C) will be the answer.
Choose the best answer to explain whether the question is statistical or not statistical. How far from work do all the employees live?
Answer: statistical
Step-by-step explanation: A statistical – is a question that can be answered by collecting data and that anticipates variability in those data • Statistics – the science of collecting, reviewing, and analyzing data
If the average ago of retirement for a random sample of 87 retired persons is 66 years with a standard deviation of 2 years.a. b. c. d.e.f.g. Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more. Find all values to 3 decimal places.
Answer:
0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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 [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214[/tex]
Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
This probability is 1 subtracted by the pvalue of Z when X = 66.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{66.5 - 66}{0.214}[/tex]
[tex]Z = 2.336[/tex]
[tex]Z = 2.336[/tex] has a pvalue of 0.99.
1 - 0.99 = 0.01
0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.
Determine whether the following relation represents a function. Give the domain and range for the relation. StartSet (7 comma 2 )comma (5 comma negative 4 )comma (3 comma 3 )comma (negative 4 comma negative 4 )EndSet
Answer:
is a functiondomain: {-4. 3. 5. 7}range: {-4, 2, 3}Step-by-step explanation:
Given:
{(7, 2), (5, -4), (3, 3), (-4, -4)}
__
The domain is the set of first numbers:
{7, 5, 3, -4} . . . domain
The range is the set of second numbers:
{2, -4, 3} . . . range
No domain values are repeated, so this relation is a function.
Find the circumference
Answer:
C = pi or approximately 3.14
Step-by-step explanation:
The circumference is equal to
C = 2 * pi *r
C = 2 * pi *.5
C = pi
We can approximate pi by 3.14
C = pi or approximately 3.14
The floor manager of the factory earns €45,000 annually. She has a standard rate cut-off point of €28,000 and a tax credit of €4,000. If the standard rate of income tax is 20% and the higher rate is 41%, how much income tax does she have to pay a year?
Answer:
She has to pay income tax of 8,570 Euros
Step-by-step explanation:
On the 28,000 Euros,the floor manager would pay taxes at the rate of 20% which is computed thus:
tax at 20%=28,000 Euros*20%=5,600 Euros
The remaining earnings would be charged to tax at higher tax rate of 41% as follows:
tax at 41%=45,000 Euros-28,000 Euros=17,000 Euros*41%=6,970 Euros
Total amount of taxes=5,600+6970 = 12,570 Euros
Taxes payable =total taxes -tax credit
The manager has a tax credit of 4,000 Euros
taxes payable= 12,570-4,000=8,570 Euros
What’s the correct answer for this?
Answer:
CO = 15
Step-by-step explanation:
Since it's a right Angled Triangle (because of the tangent) so using Pythagoras theorem
OC² = CW²+OW²
CO²=(9)²+(12)²
CO²=81+144
CO²=225
Taking square root on both sides
CO = 15
Find the volume of the rectangular prism in cubic centimeters.
(V2 Lowoh)
a. 30
b. 210
7 cm
c. 70
d. 280
10 cm
3 cm
Please answer this correctly without making mistakes
Answer:
i think its da second image!!!
Step-by-step explanation:
happy to help ya!
Find the probability that a value randomly selected from this population will have a value greater than 130. b. Find the probability that a value randomly selected from this population will have a value less than 95. c. Find the probability that a value randomly selected from this population will have a value between 95 and 130.
Answer:
a) 0.0668
b) 0.3085
c) 0.6247
Question:
A population is normally distributed with μ = 100 and σ= 20.
a. Find the probability that a value randomly selected from this population will have a value greater than
130.
b. Find the probability that a value randomly selected from this population will have a value less than 90.
c. Find the probability that a value randomly selected from this population will have a value between 90
and 130.
Step-by-step explanation:
a) The probability that a value randomly selected from this population will have a value greater than 130 = P(X >130)
A z-score also referred to as a standard normal table shows the number of standard deviations a raw score lays either above or below the mean.
Let's determine the z-score using:
z = (x - µ)/σ
µ = 100
σ = 20
z = (130-100)/20
z = 30/20 = 1.5
The probability from the standard normal table associated with z = 1.50 is 0.4332. This is the area between z = 1.50 and the mean.
The total area under any normal curve is 1. Due to the fact that the normal curve is symmetric about the mean, the area on either sides of the mean is 0.5.
The desired probability = 0.5000 - 0.4332
= 0.0668
Find attached the diagram.
b) The probability that a value randomly selected from this population will have a value less than 90 = P(X<90)
Using the z-score formula:
z = (x - µ)/σ
z = (90-100)/20
z = (-10)/20 = -0.5
The probability from the standard normal table associated with
z = -0.50 is 0.1915. This is the area between z = -0.50 and the mean.
The desired probability = 0.5000 - 0.1915
= 0.3085
Find attached the diagram.
c) The probability that a value randomly selected from this population will have a value between 90 and 130 = P(90≤X≤130)
We earlier found the z score when P(X<90) = -0.5
And the probability associated with
z = -0.50 is 0.1915.
The z score when P(X>130) = 1.5
And the probability associated with z = 1.50 is 0.4332.
The desired probability is the addition of the two probabilities:
P(90≤X≤130) = 0.1915+0.4332
P(90≤X≤130) = 0.6247
KLA=120x KLM=168x ALM=48. Find x
Answer:
Step-by-st
respond poorfa
Answer:
180-168=12
12+48=60x
Step-by-step explanation:
f(x) = 2x - 2
Find f(3)
Step-by-step explanation:
Replace x = 3
f(3) = 2(3) - 2
= 6 - 2
= 4
Answer:
f(3) =4
Step-by-step explanation:
f(x) = 2x - 2
Let x=3
f(3) = 2*3 - 2
= 6-2
= 4
Please answer this correctly
Answer:
9 5/7
Step-by-step explanation:
You add all the 13/14 then divided it by 14
Then add all the while numbers then add then add them all together
On the dietitians beverage tray are 16 filled six ounce glasses. Four glasses contain prune juice and two glasses contain apple juice. What fractional part of the glasses contain some other beverage?( perhaps, H2O) than prune juice and apple juice?
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Given:
Total number of glasses = 16
Number of glasses containing prune juice = 4
Number of glasses containing apple juice = 2
To find: fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice
Solution:
A fraction refers to the parts of a whole. In a fraction, a top number is the numerator, and a bottom number is the denominator.
Number of glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = 16 - 4 - 2 = 10
Total number of glasses = 16
So,
Fractional part of the glasses that contain beverages ( perhaps, H2O) other than prune juice and apple juice = [tex]\frac{10}{16}=\frac{5}{8}[/tex]
plss help bring up my grade
Answer:
117 units cubed.
Step-by-step explanation:
I have attached the work to your problem.
Please see the attachment below.
I hope this helps!
Answer:
117
Step-by-step explanation:
find all the shown surface area
What is the length of AC?
Answer:
Step-by-step explanation:
the triangles are proportional
9/81=1/3
140-x/x=1/3
3(140-x)=x
420-3x=x
4x=420
x=420/4 = 105