Answer: First side is 40.5 meters. Second side is 121.5 meters. The third side is 159.
Step-by-step explanation:
x + 3x + 4x -3 = 321
8x - 3 =321
+3 +3
8x = 324
x = 40.5
Second Side: 3(40.5) = 121.5
Third side: 4(40.5) - 3 = 159
Check: 159 + 121.5 + 40.5 = 321
The director of the IRS has been flooded with complaints that people must wait more than 40 minutes before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly selects 400 people entering IRS offices across the country and records the times which they must wait before seeing an IRS representative. The average waiting time for the sample is 60 minutes with a standard deviation of 22 minutes.
(a) Is there overwhelming evidence to support the claim that the wait time to see an IRS representative is more than 40 minutes at a 0.100 significance level?
Answer:
[tex]t=\frac{60-40}{\frac{22}{\sqrt{400}}}=18.18[/tex]
The degrees of freedom are given by:
[tex]df=n-1=400-1=399[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{(399)}>18.18) \approx 0[/tex]
For this case since the p value is a very low value we can conclude that we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly higher than 40 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=60[/tex] represent the sample mean
[tex]s=22[/tex] represent the sample standard deviation
[tex]n=400[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean for this case is higher than 40 minutes, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{60-40}{\frac{22}{\sqrt{400}}}=18.18[/tex]
The degrees of freedom are given by:
[tex]df=n-1=400-1=399[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{(399)}>18.18) \approx 0[/tex]
For this case since the p value is a very low value we can conclude that we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly higher than 40 minutes
On a snow day, Brooklyn created two snowmen in her backyard. Snowman A was built to a height of 60 inches and Snowman B was built to a height of 44 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 5 inches per hour and Snowman B's height decreased by 3 inches per hour. Let A(t)A(t) represent the height of Snowman A tt hours after sunrise and let B(t)B(t) represent the height of Snowman B tt hours after sunrise. Write the equation for each function and determine the number of hours after sunrise when both snowmen have an equal height.
Answer: it will take 9 hours.
Step-by-step explanation:
The rate at which the height of each snowman decreased is linear. This means that it was decreasing in arithmetic progression. The formula for determining the nth term of an arithmetic progression is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference
n represents the number of terms(hours)
Considering snowman A,
Tn = A(t)
n = t
a = 60 inches
d = - 5 inches(since it is decreasing)
Therefore,
A(t) = 60 + (t - 1)-5
A(t) = 60 - 5t + 5
A(t) = 65 - 5t
Considering snowman B,
Tn = B(t)
n = t
a = 44 inches
d = - 3 inches(since it is decreasing)
Therefore,
B(t) = 44 + (t - 1)-3
B(t) = 44 - 3t + 3
B(t) = 47 - 3t
For both snowmen to have an equal height, it means that
65 - 5t = 47 - 3t
- 5t + 3t = 47 - 65
- 2t = - 18
t = - 18/- 2
t = 9 hours
If -3+i is a riot of the polynomial function f(x), which of the following must also be a root of f(x)
Answer:
-3-i
Step-by-step explanation:
imaginary roots always occur in pairs.
so second root=-3-i
Answer:
A) -3-i
Step-by-step explanation:
imaginary roots always occur in pairs.
Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using a calculator with the binompdf and binomcdf​ commands, which of the following is the most efficient way to calculate the probability that more than 60 adults have a​ bachelor's degree, ​P(x?>60)?
a. P(x < 60)=binompdf(100,0 20,59)
b. P(x<60)=binompdf(100.0.20.60)
c. P(x<60)= binomcdf(100,0,20,59)
d. P(x<60)=binomcdf (100.0.20.60)
Answer:
Step-by-step explanation:
Since x is a binomial random variable that counts the number of adults with at least a bachelor's degree, it means that there are only two outcome. It is either an adult has a bachelor's degree or not. The probability of success would be that the adult has a bachelor's degree. Therefore, probability of success, p = 20/100 = 0.2
Number of adults in the sample is 100
The number of success expected is x
We want to determine the probability of P(x ≥ 60)
Therefore, the most efficient way to calculate the probability that more than 60 adults have a bachelor's degree is
b. P(x<60)=binompdf(100.0.20.60)
This is because it is a discrete probability distribution function
A cone and a cylinder have the same base and height, as shown below. A cone is inside of a cylinder with same base and height. The volume of the cylinder is 84 pi inches squared What can be concluded about the volume of the cone? Check all that apply.
Answer:
The volume of the cone = 28 inch³
Step-by-step explanation:
First let's consider the formula for the volume of the shapes
For cylinder
Volume= πr²h
For cone
Volume= 1/3 πr²h
So we'd notice that no much difference except that the volume if a cylinder is divided by two to get that off a cone.
So if the volume of the cylinder is
84π inch
The volume of the cone is 84/3 = 28
The volume of the cone = 28 inch³
The circle above has an area of 144 pi cm^2. What is the area of the blue sector? Use 3.14 for pi . A. 150.72 cm2 B. 25.12 cm2 C. 48 cm2 D. 113.04 cm2
Answer:
A. 150.72 cm2
Step-by-step explanation:
blue sector is 120 deg which is 1/3 of circle
so its area:
1/3*144 pi= 48 pi cm^2= 48*3.14 cm^2= 150.72 cm^2Puerto Rico is a spanish speaking territory of the United States functioning as a self governing _____.
A.commonwealth
B. Settlement
C.state
D. Colony
Answer:
It is a colony. hope i helped :)
Step-by-step explanation:
The length of a rectangle is 8 less than the width. The perimenter is 44 meters. Find the dimension of the rectangle
Answer:
Length = 7
Width = 15
Step-by-step explanation:
L= x
W= x-8
2x+2(x-8)=44
Please answer this correctly I want helping hand people to answer this correctly
Answer:
q = 9
Step-by-step explanation:
Make a ratio equation:
36 : 54 = 6 : q
[tex]\frac{2}{3} =\frac{6}{q}[/tex]
2q = 18
q = 9
Answer:
q = 9
Step-by-step explanation:
These shapes are similar, so set up a proportion like so:
[tex]\frac{54}{36} =\frac{9}{q}[/tex]
→Cross multiply:
[tex]\frac{324}{36q}[/tex]
→Divide 324 by 36:
q = 9
Filmore has invested $10,000 in an account to help pay for his grandson’s education. He expects the account to return 4.5% annually. Use the rule of 72 to estimate how long it will take the $10,000 to double in value.
Answer:
16 years
Step-by-step explanation:
The rule of 72 says you can estimate the doubling time in years by dividing 72 by the interest rate in percent.
__
For an interest rate of 4.5%, the rule of 72 says the doubling time is ...
72/4.5 = 16 . . . years
It will take about 16 years for the investment to double in value.
A study conducted to assist the impact of caffeine consumption, smoking, alchohol consumption, and physical activity on cardiovascular disease. Suppose that 40% of participants consume caffeine and smoke. If 8 participants are evaluated what is the probability that: A. Exactly half of them consume caffene and they smoke?
Answer:
8.4
Step-by-step explanation:
The adjustment of the thickness of the lens to make close vision possible is ca
Answer: Accommodation
Step-by-step explanation:
Accommodation is the adjustment of the optics of the eye to keep an object in focus on the retina as its distance from the eye varies.
Exactly one of the numbers 2,3 5 and 7 is placed in each of the 4 empty regions formed by circles A, B and C so that the sum of the numbers in each circle is the same. Each number is used. What is the sum of the numbers in each circle? *
Answer:
The sum of the numbers in each circle is 17
Step-by-step explanation:
The numbers to choose from are:
2, 3, 5, 7
By this alone the biggest number must be in the overlap of the three circles.
Then just fill in the numbers in such a way that they all are used.
The sum of the numbers in each circle is 17.
See picture for a solution.
An object is dropped off a building that is 144 feet tall. After how many seconds does the object hit the ground? (
Answer:
t = 3 seconds
Step-by-step explanation:
16t^2=144
Simplify by dividing both sides by 16:
t^2=9
t=3
Hope this helped!
64 less than y is no less than −128 Written in interval notation
Answer:
[tex]y\in [-64,\infty)[/tex] .
Step-by-step explanation:
The given statement is "64 less than y is no less than −128". It means 64 less than y is greater than or equal to −128.
[tex]y-64\geq -128[/tex]
Add 64 both sides.
[tex]y-64+64\geq -128+64[/tex]
[tex]y\geq -64[/tex]
It means possible value of y is greater than or equal to -64.
[tex]y\in [-64,\infty)[/tex]
Therefore, the required interval is [tex][-64,\infty)[/tex].
2. Is -1/3-4/5 positive,negative, or zero ?
Molly, Nathan, and Sam own a
bookstore. They agree to share
the profit equally. If the profit is
$8,822, which is the best estimate
of each owner's share?
A $2,000
B $3,000
C $4,000
D $5.000
PLEASE HELP QUICKLY ! THANK YOU
At least 2,000
Step-by-step explanation:
I divided 8,822 by 3 and got 2940.66666....
If you basically round that, you get to 2,000
You could get 3,000 but they need to share their profit equally
(hopefully this helped :P)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Answer:
question wrong
Step-by-step explanation:
2 same angles
[tex]\frac{13+5}{z} = \frac{z}{5} \\\\z^{2} = 5 * 18\\z^{2} = 90\\z = \sqrt{90} = 9,4[/tex]
A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim. Group of answer choices 0.3264 0.1736 0.3409 0.1591
Answer:
[tex]z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.415[/tex]
Now we can find the p value with the following probability:
[tex]p_v =P(z<-0.415)=0.3409[/tex]
Step-by-step explanation:
Information given
n=97 represent the random sample taken
[tex]\hat p=0.05[/tex] estimated proportion of defective
[tex]p_o=0.06[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to tests
We want to tet if the true proportion is less than 6%, the system of hypothesis are:
Null hypothesis:[tex]p\geq 0.06[/tex]
Alternative hypothesis:[tex]p < 0.06[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.415[/tex]
Now we can find the p value with the following probability:
[tex]p_v =P(z<-0.415)=0.3409[/tex]
Reduce the fraction to lowest terms. Do not use spaces in your answer.
Answer:
(r-s)/(r+s)
Step-by-step explanation:
Factor out the 5
Use properties of multiplication to show why 4 x 50 = 8 x 25.
Enter your answers in the boxes.
4 x 50 = 4 x
x 25) = (4 x
1) x 25 =
D) x 25
Answer: use the app: photomath
Step-by-step explanation:
a village is 20 miles away from Belfast. Connor drives from the village to Belfast at an average speed of 40mph. Kelly drives from the village to Belfast at an average speed of 50mph. How much longer will the journey take Connor in minutes?.
Answer:
6 minutes
Step-by-step explanation:
Connor drives from the village to Belfast at an average speed of 40mph.
The distance covered is 20 miles.
Time = distance/ speed
Time = 20/40
Time = 0.5 hours
Time = 30 minutes.
Kelly drives from the village to Belfast at an average speed of 50mph.
Time = distance/speed
Time = 20/50
Time = 0.4 hours
Time = 24 minutes
It will take Conor 30 - 24 = 6 minutes longer than Kelly
which multiplication equation can be used to explain the solution to 15 divided by 1/3
1) 5 x 3 =15
2) 45 x 1/3
3) 1/3 x 15 =5
4) 1/5 x 15 =3
Answer:
Step-by-step explanation:
"15 divided by 1/3" comes out to:
15 15 3
------- = -----* ----- = 45
1/3 1 1
Recall that to divide 15 by 1/3 we invert 1/3, obtaining 3, and then multiply 15 by 3. The correct result is 45.
Multiplication equation B can be used to explain the solution to 15 divided by 1/3. Option 2 is correct.
What is the definition of arithmetic operation?Arithmetic is a branch of mathematics that studies numbers and the various operations that can be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.
The solution of the expression is;
[tex]x= \frac{15}{\frac{1}{3} } \\\\\ x= 15 \times 3\\\\ x=45[/tex]
The answer of the given equation resembles the option B. Multiplication equation B can be used to explain the solution to 15 divided by 1/3
Hence, option 2 is correct.
To learn more about the arithmetic operation, refer;
brainly.com/question/20595275
#SPJ2
Burnwood Tech plans to issue some $50 par preferred stock with a 8% dividend. A similar stock is selling on the market for $65. Burnwood must pay flotation costs of 6% of the issue price. What is the cost of the preferred stock? Round your answer to two decimal places.
Answer:
6.5%
Step-by-step explanation:
The formular used to calculate the cost of preferred stock is:
= Fixed dividend/Net proceeds
Fixed dividend= $50 × 8/100
= $50×0.08
=$4
Net proceeds= Market price-Flotation costs
= $65-(6/100×$65)
= $65-(0.06×$65)
= $65-3.9
= $61.1
Therefore cost of preferred stock is
= 4/61.1 ×100
= 0.065×100
= 6.5%
Hence the cost of preferred stock is 6.5%
Brainliest for anyone who gets this correct , Which of the graphs below would result if you made the leading term of the following function negative?
Answer:
i think its D. i might be wrong sorry.
Step-by-step explanation:
Answer:D
Step-by-step explanation:
ones that go down are negative, and this is a cubic function
How many fluid ounces are there in 3 pints and 12 fluid ounces?
Answer:
60 fluid ounces
Mark my as brainliest please
In a recent survey, 70% of HR directors thought that it was very important for business students to take a course in business ethics. For a sample of 12 HR directors, what is the probability that at least one of them does not think it very important for business students to take a business ethics course
Answer:
0.9862
Step-by-step explanation:
Given: According to 70% of HR directors, business students should take a course in business ethics.
To find: the probability that at least one of a sample of 12 HR directors does not think it very important for business students to take a business ethics course
Solution:
Probability refers to chances of occurrence of an event.
According to 70% of HR directors, business students should take a course in business ethics.
Therefore,
Probability that at least one of a sample of 12 HR directors does not think it very important for business students to take a business ethics
= 1 - Probability that everyone of a sample of 12 HR directors think that it very important for business students to take a business ethics
= [tex]1-\left ( \frac{70}{100} \right )^{12}[/tex]
[tex]=1-\left ( \frac{7}{10} \right )^{12}[/tex]
[tex]=1-(0.7)^{12}\\=1-0.0138\\=0.9862[/tex]
Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) x + y = 6 x − y = 2
Answer:
(4,2). DEPENDENT
Step-by-step explanation:
As each equation consist on two variable, both can be represented graphically on a cartesian plane. First, each expression is rewritten in explicit form:
[tex]y = 6 - x[/tex] (red line) and [tex]y = x - 2[/tex] (blue line)
By the resource of graphing software, the solution is (4,2). The representation is presented below as attachment. As solution exists, both expression are linearly DEPENDENT.
A garage charges $24 an hour for labour. The garage charges Nigel $336 labour to replace the engine in his car. For how many hour labours was he charged?
Answer:
14 hours
Step-by-step explanation:
336/$24 = 14 hours
Answer: 14 hours
Step-by-step explanation:
Total charges = 336
Rate per hour = 24
No. of hours worked
= 336 / 24 = 14 hours
Marco bought 5 gallons of gasoline for $17.70.
To find the unit price, the cost by the number of gallons.
The unit price is .
To find the unit price we need to all price divide by number of gallons, so
[tex]17.70\div5=3.54[/tex]
Answer: The unit price is $3.54
Answer:
Unit price = 3.54$
Step-by-step explanation:
By using criss-cross method:
5 gallons -> $17.70
1 gallon -> ?
Unit price = 1x17.70 / 5 = 3.54$
Hope this helps..
