Answer:
2 + (13/4)x = 1/2 + (11/2)y
Step-by-step explanation:
Let each jar of paint used by Liam be x
Let each jar of paint used by Evan be y.
Liam uses 2 quarts of yellow paints and adds 3 1/4 jars of blue paint. so we have
2 + 3 1/4x
= 2 + (13/4)x
Since Evan also uses 1/2 quarts of yellow paints and add 5 1/2 jar of red paint, we have
1/2 + 5 1/2y
= 1/2 + (11/2)y
Since they end up with the same volume of paint, we have
2 + (13/4)x = 1/2 + (11/2)y
Final answer:
The equation to show that Liam and Evan end up with the same volume of paint, considering all quantities are in quarts, is 2 + 3.25 = 0.5 + 5.5.
Explanation:
To solve the problem where Liam and Evan end up with the same volume of paint, we can write an equation that sets the total volume of paint used by each person equal to each other. Since Liam uses 2 quarts of yellow paint and adds 3 1/4 (which is equivalent to 3.25) jars of blue paint and Evan uses 1/2 quart of yellow paint and adds 5 1/2 (equal to 5.5) jars of red paint, the equation comparing their total amounts of paint in quarts can be written as:
2 + 3.25 = 0.5 + 5.5
Before writing this equation, we need to ensure that both expressions represent quantities in the same unit. We confirm that all the amounts are given in quarts, so there is no need to convert units in this case. The equation illustrates that the total volume of paint used by Liam and Evan is equal.
Susan wants to mail her nephew a christmas gift. She has picked out a hat that is 27 inches long. The only box available is 15-by-20-by-15 inches. Will the bat fit in the box?
Answer:No, the hat will not fit into the box.
Step-by-step explanation:
The length of the hat is 27 inches long. The only box available is 15-by-20-by-15 inches. This represents the height , width and length of the box
Since all sides of the box are lesser than 27 inches, then the hat will not fit into the box.
Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?A. 93%B. 97%C. 100%D. 107%E. 120%
Answer:
A. 93%
Step-by-step explanation:
Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit.
So each children started with 0.2A, in which A is Arthur's fortune.
Alice
In the first year, she earned a profit of 50 percent. In the second year, she earned a profit of 10%. So her part is
0.2A*(1+0.5)*(1 + 0.1) = 0.33A
Bob
In the first year he earned a profit of 50 percent. In the second year, he earned a profit of 10%. So his part is
0.2A*(1+0.5)*(1 + 0.1) = 0.33A
Carol
In the first year, she earned a profit of 50 percent. In the second year, she lost 60 percent. So
0.2A*(1+0.5)*(1-0.6) = 0.12A
Dave
In the first year, he lost 40 percent. In the second, he earned a profit of 25%. So
0.2A*(1-0.4)*(1 + 0.25) = 0.15A
Errol
Lost all the money he had. So he has 0A.
What percentage of Arthur's fortune currently remains?
This is the sum of the results of all five of his children.
0.33A + 0.33A + 0.12A + 0.15A = 0.93A
So the correct answer is:
A. 93%
A sale transaction closes on April 15th. The day oIf a lot contains 48,000 square feet and is 240’ wide, how deep is the lot? closing belongs to the seller. Real estate taxes for the year, not yet billed, are expected to be $2,110. According to the 365-day method, what is the seller's share of the tax bill?
a. $626
b. $675
c. $607
d. $721
Answer:
c =$607
200 ft deep
Step-by-step explanation:
A sale transaction closes on April 15th. The day oIf a lot contains 48,000 square feet and is 240’ wide, how deep is the lot? closing belongs to the seller. Real estate taxes for the year, not yet billed, are expected to be $2,110. According to the 365-day method, what is the seller's share of the tax bill?
a. $626
b. $675
c. $607
d. $721
Since there are 90 days between january and March, we add that to the 15 days in April. which will give us 105 days.
Applying the 365-day method,
therefore 2110/365
5.78*105
606.98
approximately=$607
b. the day golf contains 48000 square feet
then 48000 divided by how wide it is
48,000 sq ft ÷ 240' = 200'
Veronica was recently diagnosed with a heart condition. Her doctor's bill was $4,200 for the diagnostics. Her policy has a $250 deductible and a 80/20 coinsurance provision up to $10,000 and then the insurance pays 100% thereafter. In total, how much will Veronica pay for her diagnosis?
Answer:
$1040
Step-by-step explanation:
As 80/20 insurance policy is a form of coinsurance in which deductible is satisfied first and then the client would pay 20% of additional medical costs and the remaining 80% is paid by the insurance company. Under the current scenario, Veronica will bear an amount of $250 and $790(i.e. 20% of the amount after deductible), totaling to $1040.
How many ways can a person toss a coin 13 times so that the number of tails is between 7 and 9 inclusive
Answer:
3718 ways
Step-by-step explanation:
How many ways can a person toss a coin 13 times so that the number of tails is between 7 and 9 inclusive
Probability is the likelihood for an event to occur or not
The formula for a combination is:
n choose r = n! / (r! x (n-r)!)
n=13
r=7 to 9
We are going to add up the cases for 7 through 9:
[tex]^{n } C_{r}[/tex]
[tex]^{13 } C_{7}[/tex]+[tex]^{13 } C_{8}[/tex]+[tex]^{13 } C_{9}[/tex]
[tex]\frac{n!}{r!(n-r)!}[/tex]
[tex]\frac{13!}{7!(13-7)!}[/tex]+[tex]\frac{13!}{8!(13-8)!}[/tex]+[tex]\frac{13!}{9!(13-9)!}[/tex]
1716+1287+715
3718 ways
A merchant marks his wares 40% more than the real price and allows 20% discount. His profit is?a) 20%
b) 18%
c) 16%
d) 12%
e) None of these
Answer:
D) 12%
Step-by-step explanation:
The merchant marks his wares 40% more than the real price.
The merchant also allows 20% discount.
Let the real price = 100
After a 40% mark up, the price becomes
(40 /100) * 100
= 40
So we have 100 +40= 140
Discount of 20% = (20/100)* 140
= 28
The price is 140 - 28 = 112
Profit = 112 -100
= 12%
Las Cruses, NM, is about 600 mi from Dallas, TX. One plane flies from Dallas to Las Cruses in 1 hr 12 min, and another plane with the same air speed flies from Las Cruses to Dallas in 1 hr 30 min. Find the air speed of the planes and the speed of the wind
Answer: the speed of the plane is 7.4 miles per minute.
the speed of the wind is 0.93 miles per minute.
Step-by-step explanation:
Let x represent the speed of the plane.
Let y represent the speed of the wind.
Distance of Las Cruses, NM from Dallas, TX is 600 miles.
Distance = speed × time
One plane flies from Dallas to Las Cruses in 1 hr 12 min(72 minutes). Assuming the plane flew in the same direction with the wind, then
600 = 72(x + y)
600 = 72x + 72y - - - - - - - - 1
Another plane with the same air speed flies from Las Cruses to Dallas in 1 hr 30 min(90 minutes). Assuming it flew in opposite direction to that of the wind, then
600 = 90x - 90y - - - - - - - 2
Adding equation 1 and equation 2, it becomes. 1200 = 162x
x = 1200/162 = 7.4 miles per minute.
x + y = 600/72 = 8.33
y = 8.33 - x = 8.33 - 7.4 = 0.93 miles per minute
Answer:
Hi am sitting in my post office waiting for you to come over and then I’ll come over to you
Step-by-step explanation:
Inside the post office office became offices when offices are offices
Aaron wants to make a path to guide guest through the conservation area.He uses rolls of rope to make the path.He uses 3/4 of a roll of rope for 1/8. He has 4 rolls.How many more rolls does Aaron need to complete the path
Answer:
Aaron needs 2 more rolls to complete the path.
Step-by-step explanation:
Given:
Total rolls Aaron has = 4
Part of path covered by using [tex]\frac{3}{4}[/tex] of a roll = [tex]\frac{1}{8}[/tex]
So, in order to find the number of rolls required to cover the complete path is given using the unitary method.
Rolls used for [tex]\frac{1}{8}[/tex] of a path = [tex]\frac{3}{4}[/tex]
Therefore, rolls used to cover the whole path is given by dividing the rolls used for one-eighth of the path and the path covered. This gives,
[tex]=\frac{3}{4}\div \frac{1}{8}[/tex]
[tex]=\frac{3}{4}\times \frac{8}{1}[/tex]
[tex]=\frac{3\times 8}{4\times 1}[/tex]
[tex]=\frac{24}{4}[/tex]
[tex]=6\ rolls[/tex]
Now, rolls required to complete the path is 6. But Aaron has only 4 rolls.
So, he will need 6 - 4 = 2 rolls more to complete the path.
Aaron can cover 6 portions of the path with his 4 rolls. Since the path has 8 portions, he needs 2 more rolls of rope to complete the path.
Explanation:In this question, Aaron uses 3/4 of a roll for 1/8 of the path. Therefore, he will need one roll for (1/8) / (3/4) = 2/3 of the path. Now, we want to know how many rolls he needs for the complete path. The full path will be 1/(2/3) = 3/2 = 1.5 times bigger than the amount of path he can cover with one roll. Since he has four rolls to start with, he can cover 4 * 1.5 = 6 portions of the path. But to cover a full path, he would need 8 portions (as 1/8 of the path corresponds to one portion). So, he needs 8 - 6 = 2 more rolls.
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The wind speed near the center of a tornado is represented by the equation S=93logd+65, where d is the distance, in miles, that the tornado travels and S is the wind speed, in miles per hour. If the wind speed was 130 miles per hour, which equation could be used to find the distance that the tornado traveled?
Final answer:
To find the distance that the tornado traveled, rearrange the equation S = 93log(d) + 65 to solve for d. The equation to find the distance is d = 10^(65/93), where d is the distance in miles.
Explanation:
To find the distance that the tornado traveled, we can rearrange the equation S = 93log(d) + 65 to solve for d.
First, subtract 65 from both sides of the equation: 130 - 65 = 93log(d). Now, divide both sides by 93: 65/93 = log(d). Finally, take the inverse logarithm of both sides to find d: 10^(65/93) = d.
Therefore, the equation to find the distance that the tornado traveled is d = 10^(65/93), where d is the distance in miles.
We can find the value of [tex]\( d \)[/tex]. This equation is the one that would be used to determine the distance traveled by the tornado corresponding to a wind speed of 130 miles per hour.
To find the distance that the tornado traveled when the wind speed is known, we need to solve the given equation for [tex]\( d \)[/tex]. The original equation is [tex]\[ S = 93\log d + 65 \][/tex]
Given that [tex]\( S = 130 \)[/tex] miles per hour, we substitute this value into the equation:
[tex]\[ 130 = 93\log d + 65 \][/tex]
Now, we need to isolate [tex]\( \log d \)[/tex]:
[tex]\[ 130 - 65 = 93\log d \] \[ 65 = 93\log d \][/tex]
Next, we divide both sides by 93 to solve for [tex]\( \log d \)[/tex]:
[tex]\[ \frac{65}{93} = \log d \][/tex]
To find [tex]\( d \)[/tex], we need to use the inverse of the logarithm function, which is the exponential function. The base of the logarithm is 10 (common logarithm) because it is not specified otherwise. Thus, we have:
[tex]\[ 10^{\frac{65}{93}} = d \][/tex]
This is the equation that could be used to find the distance[tex]\( d \)[/tex] that the tornado traveled when the wind speed is 130 miles per hour.
To find the numerical value of [tex]\( d \)[/tex], we calculate:
[tex]\[ d = 10^{\frac{65}{93}} \][/tex]
Lina wants to find the least common denominator of 4/32 and 5/8 so that she can add the fractions.What is the least common denominator?Rewrite the fractions with a common denominator.Explain your reasoning
Answer:
Least common denominator = 32
Step-by-step explanation:
We are given the following in the question:
Lina wants to find the least common denominator of two fractions so she can add them.
[tex]\dfrac{4}{32}\text{ and }\dfrac{5}{8}[/tex]
To find the LCM of the fractions:
[tex]8 = 2\times 2\times 2\\32 = 2\times 2\times 2\times 2\times 2\\\text{Common factors = }2\times 2\times 2\\LCM = 2\times 2\times 2\times 2\times 2 = 32[/tex]
The fractions can be added in the following manner:
[tex]\dfrac{4}{32} + \dfrac{5}{8}\\\\=\dfrac{4\times 1}{32\times 1} + \dfrac{5\times 4}{8\times 4}\\\\= \dfrac{4}{32} + \dfrac{20}{32}\\\\=\dfrac{4+20}{32}\\\\=\dfrac{24}{32}[/tex]
Tex wants to make a lawn in the front of his house. The total yards are 30 by 30 yards he gets 20 by 10 yards. Is that enough and if so how much more does he need?
Answer:
Step-by-step explanation:
Tex wants to make a lawn in the front of his house. The total yards are 30 by 30 yards. This means that the total area of the lawn is
30 × 30 = 900 yards^2
he gets 20 by 10 yards. This means that the total area of what he got would be
20 × 10 = 200 yards^2
Since what he needs is 900 yards^2 and it is greater than what he got, 200 yards^2, then it won't be enough.
What he needs more would be
900 - 200 = 700 yards^2
Jill filled up the gas tank in her new hybrid car.Jill put 10.3 gallons of gas in her car and she has driven 473.8 miles. Determine how many miles per gallon her car achieved
Jill put 10.3 gallons of gas into her car. She drove for 473.8 miles.
So we have to find how many miles per gallon she drove.
473.8 into 10.3 = 46
To make sure= 10.3 x 46 = 473.8
So Jill drove 46 miles per gallon.
Solve this problems: a company has two office building that hold 30000 employees. Their headquarters contains 14 times as many employees as their overseas branch. Therefore, their headquarters contains employees
Their headquarters contains 28000 employees.
Step-by-step explanation:
Given,
Total number of employees = 30000
Let,
Number of employees in headquarters = x
Number of employees in overseas branch = y
According to given statement;
x+y=30000 Eqn 1
x = 14y Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]14y+y=30000\\15y=30000\\[/tex]
Dividing both sides by 15
[tex]\frac{15y}{15}=\frac{30000}{15}\\y=2000[/tex]
Putting y=2000 in Eqn 2
[tex]x=14(2000)\\x=28000[/tex]
Their headquarters contains 28000 employees.
Keywords: linear equation, division
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The overseas branch has 2,000 employees, and since the headquarters has 14 times as many employees, it contains 28,000 employees.
We need to determine the number of employees at the headquarters of a company given that the headquarters has 14 times as many employees as the overseas branch, and the total number of employees in both buildings is 30,000.
Let's denote the number of employees in the overseas branch as x. Then, the number of employees in the headquarters is 14x. According to the problem, the total number of employees in both buildings is:
x + 14x = 30,000
Combining the terms:
15x = 30,000
To find x, we divide both sides by 15:
x = 30,000 / 15
x = 2,000
This means the overseas branch has 2,000 employees.
Now, since the headquarters contains 14 times as many employees as the overseas branch, we calculate:
14x = 14 * 2,000 = 28,000
Therefore, their headquarters contains 28,000 employees.
what is the lateral area of a square pyramid with side length 11.2 and slant height 20
Answer:
The lateral surface area of square pyramid is 448 square units.
Step-by-step explanation:
We are given the following in the question:
Side length of square pyramid = 11.2 units
Slant height of square pyramid = 20 units
Lateral area of a square pyramid =
[tex]L = \dfrac{1}{2}Ph[/tex]
where P is the perimeter of square base and h is the slant height.
Perimeter of square base =
[tex]P = 4\times \text{Base edge}\\= 4\times 11.2 = 44.8\text{ units}[/tex]
Putting the values, we get:
[tex]L = \dfrac{1}{2}\times 44.8\times 20 = 448\text{ square units}[/tex]
Thus, the lateral surface area of square pyramid is 448 square units.
Answer:
[tex]448 cm^{2}[/tex]
Step-by-step explanation:
s = 11.2; l = 20
L.A. = [tex]4 (\frac{1}{2} sl)[/tex]
L.A.= [tex]\frac{1}{2}(4 * 11.2)20[/tex] Multiply 4 * 11.2 to get perimeter 44.8
L.A. = [tex]\frac{1}{2} pl[/tex]
L.A. = [tex]\frac{1}{2} (44.8)20\\[/tex] Simplify 44.8 * 20
L.A. = [tex]\frac{1}{2}(896)\\[/tex] Divide 896 by 2
L.A. = [tex]448cm^{2}[/tex]
Martin has a combination of 33 quarters and dimes worth a total of $6. Which system of linear equations can be used to find the number of quarters, q, and the number of dimes, d, Martin has?A) q + d = 625q + 10d = 33B) q + d = 60.25q + 0.1d = 33C) q + d = 3325q + 10d = 6D) q + d = 330.25q + 0.1d = 6
Answer:
D) q + d = 330
0.25q + 0.1d = 6
Step-by-step explanation:
Let q= numbers of quarters
d = number of dimes
q + d = 33 ...........(1)
q = 33 - d
xq + yd = 6 ..........(2)
We will consider the options to know the correct answer
From option A
q +d = 6
25q + 10d = 33
This is wrong
Option B
q + d = 60
0.25q + 0.1d = 33
This is also wrong
Option C
q+d = 33
25q + 10d = 6
Put q = 33 -d in equation 2
25(33 - d) + 10q = 6
825 - 25d + 10d = 6
825 - 15d = 6
-15d = 6-825
-15d = -819
d = -819/-15
d= 54.6
This is also wrong because d exceeds the combination.
Option D
q+d = 33
0.25q + 0.1d = 6
Put q = 33 -d in equation 2
0.25(33 - d) + 0.1d = 6
8.25 - 0.25d + 0.1d = 6
8.25 - 0.15d = 6
-0.15d = 6 - 8.25
-0.15d = -2.25
d = -2.25/ -0.15
d = 15
q = 33 - 15
q = 18
This is correct
Answer:
It's D.
Step-by-step explanation:
Edge 2020;)
A machine shop is manufacturing a pair of gears that need to be in a ratio as close to 1.1839323 as possible, but they can’t make gears with more than 50 teeth on them. How many teeth should be on each gear to best approximate this ratio?
Answer: Driven gear will have 50 teeth, and driver gear will have 42 teeth
Step-by-step explanation: First we have to know the formula of gear ratio which is started below
(No of teeth on driven)/(No of teeth on driver)
Note: we should all know in the combination of a gear system, we have two gears, the driver gear and the driven gear
So since the least amount of teeth for any gear is 50, we assume the no of teeth on the driven is 50
And no of teeth on the driver is x
50/x = 1.1839323
Cross multiply
x x 1.1839323 = 50
x = 50/1.1839323
x = 42.23
To the nearest whole number = 42
So therefore, number of teeth on the driver gear is 42
To approximate the gear ratio of 1.1839323 with gear teeth not exceeding 50, gears with 42 and 50 teeth can be used, resulting in an actual ratio of approximately 1.1904762, which is a close approximation to the desired value.
To find the number of teeth on each gear for a ratio as close to 1.1839323 as possible with a maximum of 50 teeth on a gear, we can start by recognizing that gear ratios are a form of fraction. Since the ratio must not exceed the limit of 50 teeth on each gear, the numbers must be integers within this boundary. The ratio can be approximated by finding two numbers close to the target ratio when divided, while not exceeding the maximum teeth number of 50 for either gear.
For an initial approximation, we can multiply the ratio by a number that will give us an integer closest to 50. For example, multiplying 1.1839323 by 42 (because 50 / 1.1839323 is approximately 42.245) gives us approximately 49.725, which we can round to 50. Thus, the other gear would have 42 teeth (as we multiplied by 42 to stay within the boundary of 50 teeth on a gear).
Now, to check the obtained ratio, we divide 50 by 42, which gives us approximately 1.1904762. This is a very close approximation to the desired ratio of 1.1839323. Therefore, the gears should have 42 and 50 teeth, respectively, to best approximate the desired gear ratio.
Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively. How many times will they ring together at the same second in one hour excluding the one at the end?
Answer:
60 times will they ring together at the same second in one hour excluding the one at the end.
Step-by-step explanation:
Given : Five bells begin to ring together and they ring at intervals of 3, 6, 10, 12 and 15 seconds, respectively.
To find : How many times will they ring together at the same second in one hour excluding the one at the end?
Solution :
First we find the LCM of 3, 6, 10, 12 and 15.
2 | 3 6 10 12 15
2 | 3 3 5 6 15
3 | 3 3 5 3 15
5 | 1 1 5 1 5
| 1 1 1 1 1
[tex]LCM(3, 6, 10, 12,15)=2\times 2\times 3\times 5[/tex]
[tex]LCM(3, 6, 10, 12,15)=60[/tex]
So, the bells will ring together after every 60 seconds i.e. 1 minutes.
i.e. in 1 minute they rand together 1 time.
We know, 1 hour = 60 minutes
So, in 60 minute they rang together 60 times.
Therefore, 60 times will they ring together at the same second in one hour excluding the one at the end.
The measures of the angles of the triangle are 32, 53, 95 based on the side lengths, what are the measure of each angle?
Answer:
angle measures are 32°, 53°, 95°.
Step-by-step explanation:
The problem statement asks you to report the angle measures after telling you what they are. The mention of side lengths (without any numbers for them) seems irrelevant.
"The measures of the angles of the triangle are 32, 53, 95."
The length of a rectangle is the sum of the width and 3. The area of the rectangle is 54 units. What is the width, in units, of the rectangle?
Answer:
Step-by-step explanation:
let width=x
length=x+3
x(x+3)=54
x²+3x-54=0
x²+9x-6x-54=0
x(x+9)-6(x+9)=0
(x+9)(x-6)=0
x=-9,6
x=-9 (rejected)
as width can't be negative.
hence width=6 units
HELP ME PLZZZ ITS PRECALC
Answer:
8
Step-by-step explanation:
We observe that the logarithm bases are ...
5√5 = √125 . . . . . 125 is the 2nd power of this
2√2 = √8 . . . . . . . 8 is the 2nd power of this; 64 is the 4th power of √8
If we define ...
[tex]p=\sqrt{125}\\q=\sqrt{8}[/tex]
Then our logarithms are ...
[tex]\log_{p}{p^2}=x=2\\\\\log_{q}{q^4}=y=4\\\\xy=2\cdot 4=8[/tex]
The product of x and y is 8.
Loren is flying round trip from Dallas, Texas, to Minneapolis, Minnesota. The fare for her ticket is $308. Each airport charges a $16 airport fee. There is also a tax of $12 on the fare. What is the total cost of Loren's ticket?
Answer:The total cost of Loren's ticket is $352
Step-by-step explanation:
Loren is flying round trip from Dallas, Texas, to Minneapolis, Minnesota. The total fare for her ticket is $308.
Each airport charges a $16 airport fee. This means that the total airport charges would be 16 × 2 = $32
There is also a tax of $12 on the fare.
The total cost of Loren's ticket would be
308 + 32 + 12 = $352
The total cost of Loren's round-trip ticket from Dallas to Minneapolis, including the fare, airport fees, and tax, is $352.
To find the total cost of Loren's round-trip ticket from Dallas to Minneapolis, we need to add the base fare, airport fees, and the tax.
The base fare for the ticket is $308.Each airport charges a $16 fee, and since she uses two airports, the total fee is $16 × 2 = $32.A tax of $12 is also applied to the fare.We then add these amounts together to find the total cost:
$308 (fare) + $32 (airport fees) + $12 (tax) = $352
Therefore, the total cost of Loren's ticket is $352.
A circle has its center at the origin and has a diameter of 24 units.
What is the standard equation of the circle?
Answer:
B
Step-by-step explanation:
radius=24/2=12
eq. of circle is
x²+y²=12²
Answer:
b. x² + y² = 12²
Step-by-step explanation:
A circle has a general equation of:
(x + h)² + (y – k)² = r²
where h and k are the center (h,k) and r is the radius.
The circle is centered at origin (0, 0), so h=0, k=0.
The diameter is 24, but we want the radius instead. So divide the diameter by 2 to get the radius. r = 24/2 = 12
Plug it into the equation
(x + h)² + (y – k)² = r²
(x + 0)² + (y – 0)² = 12²
x² + y² = 12²
For how many positive values of n are both n3 and 3n four-digit integers?
Answer:
No positive value of n
Step-by-step explanation:
we have to find out for how many positive values of n are both
[tex]n^3 , 3^n[/tex] our-digit integers
Let us consider first cube
we get 4digit lowest number is 1000 and it has cube root as 10.
Thus 10 is the least integer which satisfies four digits for cube.
The highest integer is 9999 and it has cube root as 21.54
or 21 the highest integer.
Considering 3^n we get,
3^10 is having 5 digits and also 3^21
Thus there is no positive value of n which satisfy that both n cube and 3 power n are four digits.
Mia starts with a piece of paper 6 cm long she folds the paper into a dragon that is 2 1/2 cm long. How much longer was the original paper than the dragon
Answer: the original length was
3 1/2 cm longer than the length of the dragon
Step-by-step explanation:
The original length of the paper is
6 cm. Mia folds the 6 cm piece of into a dragon that is 2 1/2 cm long. Converting 2 1/2 cm to decimal, it be comes 2.5cm
To determine How much longer the original paper was than the dragon, we would determine difference in length between the original paper and the dragon. It would be
6 - 2.5 = 3.5 = 3 1/2 cm
Answer: The original paper is longer by the difference btw the length
6cm - 2½cm
3½cm
Step-by-step explanation:
The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given:Old SeedNumber of Seeds = 11Average Length = 6.25 inchesStandard Deviation = 1.0 inchesNew SeedNumber of Seeds = 16Average Length = 5.95 inchesStandard Deviation = 0.80 inchesBased on these data, if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is:______
Answer:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]
[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]
Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.
Step-by-step explanation:
Data given and notation
[tex]n_1 = 11 [/tex] represent the sampe size for the Old
[tex]n_2 =16[/tex] represent the sample size for the New
[tex]\bar X_1 =6.25[/tex] represent the sample mean for Old
[tex]\bar X_2 =5.95[/tex] represent the sample mean for the New
[tex]s_1 = 1.0[/tex] represent the sample deviation for Old
[tex]s_2 = 0.8[/tex] represent the sample deviation for New
[tex]\alpha=0.05[/tex] represent the significance level provided
Confidence =0.95 or 95%
F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:
[tex]F=\frac{s^2_2}{s^2_1}[/tex]
Solution to the problem
System of hypothesis
We want to test if the variation for New sample it's lower than the variation for the Old sample, so the system of hypothesis are:
H0: [tex] \sigma^2_2 \geq \sigma^2_1[/tex]
H1: [tex] \sigma^2_2 <\sigma^2_1[/tex]
Calculate the statistic
Now we can calculate the statistic like this:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]
Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =11-1=10[/tex] and the F statistic have 15 degrees of freedom for the numerator and 10 for the denominator. And the P value is given by:
P value
Since we have a left tailed test the p value is given by:
[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]
And we can use the following excel code to find the p value:"=F.DIST(0.64,15,10,TRUE)"
Conclusion
Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.
if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is 1.56. The option (d) is correct.
To test whether the new seed results in less variability in individual potato length compared to the old seed, we can perform an F-test for comparing variances.
The F-test statistic for comparing two variances is given by:
[tex]\[ F = \frac{s_1^2}{s_2^2} \][/tex]
where [tex]\( s_1^2 \)[/tex] is the variance of the old seed and [tex]\( s_2^2 \)[/tex] is the variance of the new seed. The larger variance should be the numerator to ensure the F-value is greater than or equal to 1.
Given data:
- Old Seed:
[tex]- \( n_1 = 11 \)\\ - \( \bar{x}_1 = 6.25 \) inches\\ - \( s_1 = 1.0 \) inch[/tex]
- New Seed:
[tex]- \( n_2 = 16 \)\\ - \( \bar{x}_2 = 5.95 \) inches\\ - \( s_2 = 0.80 \) inch[/tex]
First, calculate the variances:
- Variance of old seed, [tex]\( s_1^2 = (1.0)^2 = 1.0 \)[/tex]
- Variance of new seed, [tex]\( s_2^2 = (0.80)^2 = 0.64 \)[/tex]
Since [tex]\( s_1^2 \)[/tex] (old seed) is larger than [tex]\( s_2^2 \)[/tex] (new seed), we use:
[tex]\[ F = \frac{s_1^2}{s_2^2} = \frac{1.0}{0.64} \][/tex]
Now, calculate the F-value:
[tex]\[ F = \frac{1.0}{0.64} = 1.5625 \][/tex]
The calculated test statistic is approximately 1.56. Therefore, the correct answer is (d) 1.56.
The complete question is:
The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: Old Seed - Number of Seeds = 11, Average length = 6.25 inches , Standard Deviation = 1.0 inches New Seed - Number of Seeds = 16, Average length = 5.95 inches Standard Deviation = 0.80 inches. On this data, if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is:
(a) 1.25
(b) 0.80
(c) 0.64
(d) 1.56
For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. Hypertension is commonly defined as a systolic blood pressure above 140. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.
Answer: 0.0001
Step-by-step explanation:
Given : For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.
i.e. [tex]\mu=114.8\ \ \ \&\ \ \sigma=13.1[/tex]
Sample size =4
Let x be the sample mean systolic blood pressure.
Then the probability that their mean systolic blood pressure is greater than 140 will be
[tex]P(x>140)=1-P(x\leq140)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{140-114.8}{\dfrac{13.1}{\sqrt{4}}})\\\\\ =1-P(z\leq3.85)\ \ [\because \ z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9999\ \ \text{[By z-table]}\\\\= 0.0001[/tex]
Hence, the required probability = 0.0001
Answer:
Hence, the required probability = 0.0001
Step-by-step explanation:
The times to process orders at the service counter of a pharmacy are exponentially distributed with mean 1 0 minutes. If 100 customers visit the counter in a 2-day period, what is the probability that at least half of them need to wait more than 10 minutes?
Answer:
Therefore, the probability that at least half of them need to wait more than 10 minutes is 0.0031.
Step-by-step explanation:
The formula for the probability of an exponential distribution is:
P(x < b) = 1 - e^(b/3)
Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:
p = P(x > 10)
= 1 - P(x < 10)
= 1 - (1 - e^(-10/10) )
= e⁻¹
= 0.3679
The z-score is the difference in sample size and the population mean, divided by the standard deviation:
z = (p' - p) / √[p(1 - p) / n]
= (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]
= 2.7393
Therefore, using the probability table, you find that the corresponding probability is:
P(p' ≥ 0.5) = P(z > 2.7393)
P(p' ≥ 0.5) = 0.0031
Therefore, the probability that at least half of them need to wait more than 10 minutes is 0.0031.
A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded. What is the probability that one spin of the spinner will land in a shaded sector?
Answer:
2/3
Step-by-step explanation:
A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded.
Probability is the likelihood that an event will occur. Probability is a selection over the number of observation.
There are 4 shaded portion of the spinner and two unshaded portion.
The probability that when the spinner is spinned the portion will liand on four is simply
4/6, divided to its lowest term.
2/3
The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].
Given information:
A certain spinner is divided into [tex]6[/tex] sectors of equal size, and the spinner is equally likely to land in any sector. Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.
According to question,
[tex]P(E)=\frac{\rm{No\;of\;favourable\;outcomes}}{\rm{Total\;no\;of\;outcomes}}[/tex]
Four of the [tex]6[/tex] sectors are shaded, and the remaining sectors are not shaded.
There are [tex]4[/tex] shaded portion of the spinner and two unshaded portions.
[tex]P(E)=\frac{4}{6}=\frac{2}{3}[/tex]
Hence, The probability that when the spinner is spined the portion will land on four is simply [tex]\frac{2}{3}[/tex].
Learn more about Probability here:
https://brainly.com/question/10198002?referrer=searchResults
A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?(A) 0.8(80 – y)(B) 0.8 + 0.0025y(C) 80/y – 1.25(D) 80/1.25y(E) 80 – 0.25y
Answer:
(B) 0.8+0.0025y
Step-by-step explanation:
Total houses =80
First y houses was painted at the rate of x hours per week
Remaining houses was painted at 1.25x hours per week
Remaining houses= 80-y
Rate = quantity/ time
Time = quantity/ rate
Time for the first painting = y/x
Time for the second painting = 80-y/1.25x
Total time y/x + 80-y/1.25x
= 0.25y +80/1.25x
If it was being painted at the original rate
Time = 80/x
The time to paint in this scenario as a fraction of the time it will take to paint in the original rate.
(0.25y+80/1.25x) /(x/80)
=( 0.25y +80)/100
=0.0025y +0.8
A carnival booth made $88 selling popcorn in one day . It made 22 times as much selling cotton candy how much money did the carnival booth make selling popcorn and cotton candy?
Answer:
Total money made by carnival booth selling popcorn and cotton candy = $2024
Step-by-step explanation:
Money made by carnival booth selling popcorn = $88
Money made by selling cotton candy was 22 times the money made by selling popcorn.
Thus, money made selling cotton candy = [tex]22\times \$88=\$1936[/tex]
Total money made by carnival booth selling popcorn and cotton candy = [tex]\$88+\$1936=\$2024[/tex]