The probability that Anji goes to the cinema on a particular Friday is (2 - √3) / √3. Let's denote the event of Anji going to the cinema as A and the event of Katrina going to the cinema as K.
We are given the following probabilities:
P(A and K) = 1/3 (probability of both Anji and Katrina going to the cinema)
P(A or K) = 5/6 (probability of at least one of them going to the cinema)
We can use the principle of inclusion-exclusion to find the probability of Anji going to the cinema (P(A)).
P(A or K) = P(A) + P(K) - P(A and K)
Since P(A and K) = 1/3, we have:
5/6 = P(A) + P(K) - 1/3
Now, let's consider that Anji and Katrina decide independently, so the events A and K are independent. Therefore, P(A and K) = P(A) * P(K).
Since P(A and K) = 1/3, and assuming equal probabilities for Anji and Katrina going to the cinema (P(A) = P(K) = x), we have: 1/3 = x * x
Solving this equation, we find: x = 1/√3
Now, substituting this value of x into the equation:
5/6 = P(A) + P(K) - 1/3
5/6 = 2x - 1/3
5/6 = 2(1/√3) - 1/3
5/6 = 2/√3 - 1/3
To find P(A), we can subtract P(K) from both sides: P(A) = 2/√3 - 1/3 - P(K)
Since P(K) = x = 1/√3, we have: P(A) = 2/√3 - 1/3 - 1/√3
Simplifying this expression, we get: P(A) = (2 - √3) / √3
Therefore, the probability that Anji goes to the cinema on a particular Friday is (2 - √3) / √3.
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6x+3y=6
8x+9y=-22
Yolanda and Neel play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty
Given 6x + 3y = 6 and 8x + 9y = -22To find out whether Yolanda and Neel play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty, we can find the slope of the given equations and check whether they are the same or not.
Step 1: Find the slope of 6x + 3y = 6Given equation is 6x + 3y = 6Let's write this equation in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.Subtracting 6x from both sides, we get3y = -6x + 6Dividing both sides by 3, we gety = -2x + 2Thus, the slope of 6x + 3y = 6 is -2.Step 2: Find the slope of 8x + 9y = -22Given equation is 8x + 9y = -22Let's write this equation in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.Subtracting 8x from both sides, we get9y = -8x - 22Dividing both sides by 9, we gety = (-8/9)x - (22/9)Thus, the slope of 8x + 9y = -22 is -8/9.Now we can see that the slopes of both the equations are different. Hence, Yolanda and Neel do not play a game in which they earn the same number of points for each goal and lose the same number of points for each penalty.
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Look for Relationships Chris is buying material
for an art project. Two stores have the material she
needs. Compare prices to find which material is the
better value. Explain.
To compare the prices and determine which material offers better value, Chris needs to consider several factors beyond just the price. Here are some key points to consider:
Quality: Compare the quality of the materials offered by both stores. Sometimes, a higher-priced material may offer better quality, durability, or performance, making it a better value in the long run.
Quantity: Check the quantity or size of the materials available for the price. If one store offers a larger quantity or size for a slightly higher price, it might be a better value as it provides more material for the money.
Features: Look for any additional features or benefits offered by the materials. For example, if one material includes extra accessories or tools at a slightly higher price, it may be a better value due to the added value and convenience.
Customer reviews: Research online or ask for recommendations from others who have used the materials from both stores. Their experiences and feedback can provide insights into the overall value and performance of the materials.
By considering these factors, Chris can make an informed decision and choose the material that offers the best overall value for her art project.
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given solid of hemisphere and cylinder having total height 35 cm and radius is 7 cm find the volume of solid
Given a solid of hemisphere and cylinder having a total height 35 cm and radius 7 cm, the volume of the solid is 6105.19 cm³.
So the volume of the solid is 6105.19 cm³.
To begin with, we must identify the volume of each hemisphere and cylinder before we can add them up to find the volume of the entire solid.
The volume of a hemisphere of radius r is given by the formula;
V = 2/3πr³
And the volume of a cylinder of radius r and height h is given by;
V = πr²h
Hence, the volume of the hemisphere with radius 7cm will be;
V₁ = 2/3π(7)³
= 718.81cm³
And the volume of the cylinder with radius 7cm and height 35cm will be;
V₂ = π(7)²(35)
= 5386.38cm³
The volume of the entire solid is given by the sum of the volumes of the hemisphere and cylinder.
V = V₁ + V₂
= 718.81 + 5386.38
= 6105.19 cm³
Therefore, the volume of the solid is 6105.19 cm³.
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What is the solution to -48 - 3x) 6x - 8?
O X> -4/3
O x<-4/3
O x>4
Ox<4
The solution to the inequality -48 - 3x > 6x - 8 is x < -40/9
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
-48 - 3x > 6x - 8
Collect the like terms in the above inequality
So, we have
-6x - 3x > 48 - 8
When the like terms are evaluated, we have
-9x > 40
Divide both sides by -9
x < -40/9
Hence, the solution to the inequality is x < -40/9
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What is the value of q for which the lines qx−7y+10=20 and 4y+3x+9=0 are parallel to each other?
To determine the value of q for which the lines qx - 7y + 10 = 20 and 4y + 3x + 9 = 0 are parallel to each other, we need to compare their slopes.
First, we'll rewrite the equations in the standard form y = mx + b, where m represents the slope of the line:
For the line qx - 7y + 10 = 20, rearranging the equation gives us:
qx - 7y = 10
-7y = -qx + 10
y = (q/7)x - 10/7
For the line 4y + 3x + 9 = 0, rearranging the equation gives us:
4y = -3x - 9
y = (-3/4)x - 9/4
From the equations, we can see that the slopes are q/7 for the first line and -3/4 for the second line.
For two lines to be parallel, their slopes must be equal. Therefore, we can equate the slopes and solve for q:
q/7 = -3/4
Cross-multiplying, we have:
4q = -21
Dividing both sides by 4, we find:
q = -21/4
Therefore, the value of q for which the lines are parallel to each other is -21/4.
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If 980 = 2x X 5y X 7z, find the values of x, y and z... pls help with working
Answer:
x = 2, y = 1, z = 7-------------------------
We are given that, 980 = 2x × 5y × 7z
We need to find the values of x, y, and z.
Find the prime factorization of 980.
980 can be written as:
980 = 2 × 2 × 5 × 7 × 7Compare the given expression with the prime factorization of 980.
2 × 2 × 5 × 7 × 7 = 2x × 5y × 7zIt can be observed that:
2x = 2 × 2 ⇒ x = 25y = 5 ⇒ y = 17z = 7 × 7 ⇒ z = 7Hence, the values of x, y, and z are 2, 1, and 7 respectively.
A national shipping company advertises that standard shipping can take up to seven days. If you were to write the null hypothesis in words, what would it be?
A) "The true mean shipping time would be 7 days or more"
B) "The true mean shipping time would take 7 days or less"
C) "The true mean shipping days would take more than 7 days"
D) "The true mean shipping time would take less than 7 days"
The null hypothesis, in this case, represents the assumption or statement that there is no significant difference or effect.
In the context of the shipping company and their advertised standard shipping time, the null hypothesis would state that the true mean shipping time is equal to or greater than seven days.
Therefore, the correct choice would be:
A) "The true mean shipping time would be 7 days or more"
This hypothesis assumes that the standard shipping time meets or exceeds the advertised duration of seven days. The null hypothesis is typically used as a baseline or starting point for statistical analysis, and it is the hypothesis that is tested against an alternative hypothesis to determine if there is sufficient evidence to reject or accept it.
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Which function has a greater constan rate of change explain
Fun
Function A FuctionB
Y=-3x+7
The function that has a greater constant rate of change is Function A.
A function that has a constant rate of change means that the function increases or decreases at a steady pace.
Function A has a slope of -3 while Function B does not have a slope.
This indicates that Function A has a constant rate of change that is equal to -3.
This is because -3 is the coefficient of x in the equation of Function A, which represents the slope.
It shows that for every increase of one unit in x, the value of y decreases by three units.
Since Function B does not have a slope, it does not have a constant rate of change.
Therefore, Function A has a greater constant rate of change than Function B.
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Question 17 1 pts Last year 500 students enrolled in both math and art class. Of these students 82 got an A in math, 73 in art class, and 42 in both statistic and psychology. Find the probability that randomly selected student got an A in math or art class (or both).
To find the probability that a randomly selected student got an A in math or art class (or both), we need to use the principle of inclusion-exclusion.
Let's define the events:
M = Getting an A in math class
A = Getting an A in art class
We are given the following information:
n(M) = 82 (number of students who got an A in math)
n(A) = 73 (number of students who got an A in art)
n(M ∩ A) = 42 (number of students who got an A in both math and art)
To calculate the probability of getting an A in math or art class (or both), we can use the formula:
P(M ∪ A) = P(M) + P(A) - P(M ∩ A)
We need to find the probabilities P(M) and P(A) first.
P(M) = n(M) / total number of students
P(M) = 82 / 500
P(M) = 0.164
P(A) = n(A) / total number of students
P(A) = 73 / 500
P(A) = 0.146
Now, we can calculate the probability of getting an A in math or art class (or both):
P(M ∪ A) = P(M) + P(A) - P(M ∩ A)
P(M ∪ A) = 0.164 + 0.146 - (42 / 500)
P(M ∪ A) ≈ 0.164 + 0.146 - 0.084
P(M ∪ A) ≈ 0.226
Therefore, the probability that a randomly selected student got an A in math or art class (or both) is approximately 0.226, or 22.6%.
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We have to estimate the allocation base and the total manufacturing overhead costs in advance in order to be able to determine a
In order to determine the predetermined overhead rate and allocate manufacturing overhead costs, it is necessary to estimate the allocation base and the total manufacturing overhead costs in advance.
These estimates help in establishing a systematic method for assigning overhead costs to products or services based on a relevant allocation base.
Manufacturing overhead costs include various indirect expenses such as factory rent, utilities, equipment maintenance, and supervision. These costs cannot be easily traced directly to specific products or services. Instead, they are allocated based on a predetermined overhead rate.
The allocation base is a measure or activity that serves as a common denominator for distributing overhead costs. Common allocation bases include direct labor hours, machine hours, or material costs. The choice of allocation base depends on the nature of the business and the activities that drive overhead costs.
To determine the predetermined overhead rate, the total estimated manufacturing overhead costs for a specific period are divided by the estimated allocation base. This rate is then applied to the actual allocation base incurred during production to allocate the overhead costs to individual products or services.
Estimating the allocation base and the total manufacturing overhead costs in advance allows for a more accurate and consistent allocation of overhead expenses. It helps businesses establish a systematic approach to assign costs, aiding in decision-making, cost analysis, and determining product or service pricing.
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150 people are asked how many siblings they have? # of Siblings Frequency Relative Frequency Cumulative Frequency 0 35 0.2333 35 1 29 64 2 0.1533 87 3 29 0.1933 116 4 34 0.2267
Therefore, the answer is:Number of Siblings Frequency Relative Frequency Cumulative Frequency0 35 0.2333 351 29 0.1933 642 0 0 873 29 0.1933 1164 34 0.2267 150
Here is how to calculate the Relative Frequency and Cumulative Frequency based on the data given:
Number of Siblings Frequency Relative Frequency Cumulative Frequency
0 35 0.2333 351 29 0.1933 642 0 0.1533 873 29 0.1933 1164 34 0.2267 150
Relative frequency for 0 siblings:
As per the given data, frequency of 0 siblings = 35
And, total number of people asked = 150
Therefore, relative frequency for 0 siblings = 35/150= 0.2333
Relative frequency for 1 sibling:
As per the given data, frequency of 1 sibling = 29And, total number of people asked = 150Therefore, relative frequency for 1 sibling = 29/150 = 0.1933Relative frequency for 2 siblings:
As per the given data, frequency of 2 siblings = 0And, total number of people asked = 150Therefore, relative frequency for 2 siblings = 0/150 = 0Relative frequency for 3 siblings:
As per the given data, frequency of 3 siblings = 29And, total number of people asked = 150Therefore, relative frequency for 3 siblings = 29/150 = 0.1933Relative frequency for 4 siblings:
As per the given data, frequency of 4 siblings = 34And, total number of people asked = 150Therefore, relative frequency for 4 siblings = 34/150 = 0.2267Cumulative frequency:
To calculate the cumulative frequency, add the frequency of each category to the sum of the frequencies of all categories below it. The last cumulative frequency should equal the total number of observations.So, the cumulative frequency for each category is as follows:For 0 siblings:
35For 1 or fewer siblings:
35+29=64For 2 or fewer siblings: 64+0=64For 3 or fewer siblings:
64+29=93For 4 or fewer siblings:
93+34=127For all 5 siblings:
127+23=150
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Find a number written in binary system that when read as a number in decimal system is five times
smaller than the same number read as a decimal (notice that any binary number can be also
interpret as a decimal, for example 111 can represent a binary number but also can be seen as one
hundred and eleven - a decimal).
Treat this question like a puzzle, just try different numbers and this way guess the answer.
Considering, the binary number to be represented is a two-digit number, the binary number to be represented is 0101.
Let us assume that the binary number to be represented is a two-digit number.
Therefore, it can be represented as xy where x and y are either 0 or 1.
We know that any binary number can also be interpreted as a decimal number.
For example, 111 can represent a binary number but also can be seen as one hundred and eleven - a decimal.
The number written in the binary system is thus 2x + y.
The number written in the decimal system is = x × 10 + y, which is 5 times greater than the binary number when the binary number is written in the decimal system.
5(2x + y) = x × 10 + y
10x - 9y = 0
y = 0, 10, 20, 30, ... are some solutions, but y cannot be greater than 10, as it is a two-digit number in the binary system.
As a result, the only feasible solution is y = 0.5(2x)
= 10x
x = 5
Therefore, the binary number to be represented is 0101.
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A model is made of a car. The car is 9 feet long and the model is 7 inches long. What is the ratio of the length
of the car to the length of the model?
a 7:9
b. 9:7
c. 7: 108
d. 108: 7
The correct answer is d) 108:7. This ratio indicates that for every 108 inches the car measures, the model measures 7 inches. It represents the proportional relationship between the two lengths.
To find the ratio of the length of the car to the length of the model, we need to convert both lengths to the same units. Let's convert them both to inches for consistency.
Given:
Length of the car = 9 feet
Length of the model = 7 inches
To convert feet to inches, we know that 1 foot is equal to 12 inches. Therefore, the length of the car in inches is:
Length of the car = 9 feet * 12 inches/foot = 108 inches
Now we have the lengths in the same unit: 108 inches for the car and 7 inches for the model.
The ratio of the length of the car to the length of the model is:
108:7
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$16000 is invested for 5 years with an APR of3 % and quarterly compounding
The accumulated value in 5 years of the investment compounded quarterly is approximately: $18578.946
How to find the compound interest?Compound interest differs from simple interest in that the interest received in one period will itself accrue in the next period. As a result, the amount in the account increases exponentially.
The future value of a compounding account depends on the number of compounding periods per year. Another factor is the annual interest rate. The higher the APR, the greater the cumulative value over time.
The formula for compound interest is:
FV = P(1 + (r/m))^(mt)
where:
FV is the future value of the investment.
P is the principal or initial amount invested.
r is the annual interest rate.
m is the number of compounding per year.
t is the time in years,
P = $16000
t = 5
m = 4
r = 3% = 0.03
Thus:
FV = 16000(1 + (0.03/4))^(4 * 5)
FV = $18578.946
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Complete Question is:
$16000 is invested for 5 years with an APR of3 % and quarterly compounding.
Write a numerical expression that would compute the value of the investment after 5 years.
A child flies a kite at a height of ft, the wind carrying the kite horizontally away from the child at a rate of. How fast must the child let out the string when the kite is ft away from the child?
To find the rate at which the child must let out the string, we can use the concept of related rates.
Let's assign variables to the given quantities: Let h represent the height of the kite in feet. Let x represent the horizontal distance of the kite from the child in feet. Let dh/dt represent the rate at which the height is changing in feet per second. Let dx/dt represent the rate at which the horizontal distance is changing in feet per second. We are given that the height of the kite is h ft, the horizontal distance is x ft, and the rate of change of the horizontal distance is dx/dt ft/s. By using the Pythagorean theorem, we have the equation: x^2 + h^2 = d^2. Differentiating both sides of the equation with respect to time t, we get: 2x(dx/dt) + 2h(dh/dt) = 2d(dd/dt). Since the child is not letting out or pulling in the string, the rate at which the length of the string (d) is changing is zero. Therefore, dd/dt is equal to 0. Now, we can substitute the given values: 2x(dx/dt) + 2h(dh/dt) = 0. Solving for dx/dt, the rate at which the child must let out the string, we get: dx/dt = -h(dh/dt) / x.
Therefore, the child must let out the string at a rate of (-h(dh/dt)) / x feet per second when the kite is x feet away from the child.
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There are 254 counties in Texas. Zane rounds the number to nearest ten. What is the difference between actual number of counties and Zane rounded number of counties and zane's rounded number? solve this problem using an equation and an unknown.
The difference between the actual number of counties in Texas and Zane's rounded number of counties can be found by subtracting Zane's rounded number from the actual number. Let's represent the actual number of counties as "x" and Zane's rounded number as "y". The equation representing the difference is x - y.
Let's assume that the actual number of counties in Texas is "x". Zane rounds the number to the nearest ten, so his rounded number of counties can be represented as "y". The difference between the actual number and Zane's rounded number can be calculated by subtracting Zane's rounded number from the actual number, which gives us the equation x - y. Substituting the given values, where x = 254 (actual number of counties) and y is the rounded number, we can find the difference.
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You can get some great new space for $126,000 per year. You will be leasing 3,900 square feet. What will your rent be per square foot per year?
Given that a space is leased for $126,000 per year and 3,900 square feet leased area.
What will be the rent per square foot per year?
We can obtain the rent per square foot per year by using the following formula;`
Rent per square foot per year = Total rent per year / Total area leased`
Using the formula above, the rent per square foot per year can be calculated as follows;
`Rent per square foot per year = 126,000 / 3,900 = $32.31
`Therefore, the rent per square foot per year is $32.31.
let's do it in more detail:
To calculate the rent per square foot per year, you can divide the total annual rent by the total square footage.
Rent per square foot per year = Total annual rent / Total square footage
Given:
Total annual rent: $126,000
Total square footage: 3,900 square feet
Rent per square foot per year = $126,000 / 3,900 square feet
Using a calculator, we can compute:
Rent per square foot per year ≈ $32.31
Therefore, the rent per square foot per year would be approximately $32.31.
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A bag of pennies, nickels, dimes and quarters contains 120 coins with a total weight 240, worth a total of $12.30. If pennies and dimes weigh 1, nickels weigh 2 and quarters 3, how many coins of each type are there
Let the number of pennies, nickels, dimes, and quarters be P, N, D, and Q respectively.There are a total of 120 coinsTherefore:[tex]P + N + D + Q = 120[/tex] [Equation 1]and let the weight of a nickel and a quarter be 2N and 3N respectively. the bag contains 19 pennies, 3 nickels, 24 dimes, and 7 quarters.
According to the question, the total weight is 240. Therefore,[tex]1P + 1D + 2N + 3Q = 240[/tex] [Equation 2]Let the value of a penny, nickel, dime, and quarter be 1C, 5C, 10C, and 25C respectively.According to the question, the total value is [tex]$12.30[/tex]. Therefore,[tex]1P + 5N + 10D + 25Q = 1230[/tex] [Equation 3]
From Equation 1,[tex]P = 120 - N - D - Q.[/tex]
we can substitute [tex]N = 3A and D = 3B[/tex] in the equation above.
This gives: [tex]4(3A) + 9(3B) + 24Q = 1110[/tex] Simplifying this,
we get:[tex]4A + 3B + 8Q = 370[/tex]
From here, we can substitute Q = 1, 2, 3, ... and check which values of A and B satisfy this equation. After some calculations, we find that Q = 7, A = 19, and B = 8.
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A survey asked people of different ages whether they get their news by reading the paper. What is the probability that a person surveyed gets the news by reading the paper, given that he or she is under 40? If necessary. round your answer to the nearest percent. HELP HELP ME HELP
the example of a permutation is: A) The number of ways 3 people can win 3 different prizes.
A) The number of ways 3 people can win 3 different prizes.
This scenario involves the arrangement of 3 people winning 3 different prizes. Since the order in which the people win the prizes matters, this is an example of a permutation. For instance, if we have three people named A, B, and C, the possible permutations of them winning the prizes could be A winning the first prize, B winning the second prize, and C winning the third prize. Therefore, option A is an example of a permutation.
B) Picking 10 CDs to lend to a neighbor from a collection of 35.
This scenario involves selecting 10 CDs out of a collection of 35. The order in which the CDs are selected does not matter; only the selection itself is important. Therefore, this is an example of a combination rather than a permutation. Option B does not represent a permutation.
C) The number of ways 8 books can be selected from 10 to take on a trip.
Similarly to option B, this scenario involves selecting 8 books out of a group of 10 books. The order of the selected books does not matter; only the selection itself is relevant. Thus, this is also an example of a combination rather than a permutation. Option C does not represent a permutation.
D) Selecting 4 students to represent their class for the school.
This scenario involves selecting 4 students from a group to represent their class. Since the order in which the students are selected does not matter, this represents a combination rather than a permutation. Option D does not represent a permutation.
Option A
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Your bathtub holds 80 gallons of water. The cold faucet adds water to the tub at 2142 and 1 fourth gallons per minute. The hot water faucet adds water to the tub at 1121 and 1 half gallon per minute. The drain lets water out at a rate of 343 over 4 gallon per minute. You start the bath by turning both faucets on, but forget to close the drain. The tub fills in 27 minutes. How large is the bathtub?
How will you solve the question?
To determine the size of the bathtub, we can use the information provided about the fill rate of the cold and hot water faucets, the drain rate, and the time it takes to fill the tub. The size of the bathtub is 42,471 gallons.
To determine the size of the bathtub, we can use the information provided about the fill rate of the cold and hot water faucets, the drain rate, and the time it takes to fill the tub. By subtracting the drain rate from the combined fill rate of the faucets and multiplying it by the time, we can find the net fill rate. Dividing the total amount of water filled in the given time by the net fill rate will give us the size of the bathtub.
First, we calculate the net fill rate per minute: (2142 1/4 + 1121 1/2) - (343/4) = 2142 1/4 + 1121 1/2 - 343/4.
Next, we multiply the net fill rate per minute by the time in minutes (27) to find the total water filled in that time.
To compute the net fill rate per minute, we need to convert the mixed numbers to improper fractions and perform the necessary calculations:
2142 1/4 + 1121 1/2 - 343/4 = 2149/4 + 2243/2 - 343/4 = 2149/4 + 4486/4 - 343/4 = (2149 + 4486 - 343)/4 = 6292/4 = 1573/1 = 1573.
The net fill rate per minute is 1573 gallons.
Next, we calculate the total water filled in 27 minutes:
Total water filled = net fill rate per minute × time in minutes = 1573 × 27 = 42,471 gallons.
Therefore, the size of the bathtub is 42,471 gallons.
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An airplane cruises 1 kilometer in112of a minute. What is its cruising speed?Simplify your answer and write it as a proper fraction, mixed number, or whole number
The cruising speed of the airplane can be determined by dividing the distance it traveled by the time it took. In this case, the airplane cruised 1 kilometer in 1/12 of a minute. Therefore, its cruising speed is 12 kilometers per minute.
To calculate the cruising speed of the airplane, we divide the distance traveled (1 kilometer) by the time it took (1/12 of a minute). Dividing these values yields a cruising speed of 12 kilometers per minute.
It's important to note that the speed of an object is defined as the distance traveled per unit of time. In this case, the distance traveled by the airplane is given as 1 kilometer, and the time taken is 1/12 of a minute. Dividing these values provides us with the cruising speed of the airplane.
The cruising speed of 12 kilometers per minute represents the rate at which the airplane covers distance during its cruise phase. It is essential to simplify the answer and express it as a whole number or fraction to provide a clear and concise representation of the cruising speed.
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Estimate the total cost of 32 printers at £198 each and 58 ink cartridges at
£31. 15 each.
The estimated total cost of 32 printers at £198 each and 58 ink cartridges at £31.
to estimate the total cost, we can multiply the quantity of each item by its respective cost and then sum them together.
the cost of 32 printers at £198 each can be calculated as follows:32 printers * £198/printer = £6336
the cost of 58 ink cartridges at £31.15 each can be calculated as follows:
58 cartridges * £31.15/cartridge = £1805.70
to find the total cost, we add the cost of the printers and the cost of the ink cartridges:total cost = £6336 + £1805.70 = £8141.70 15 each is £8141.70.
the total cost of 32 printers at £198 each and 58 ink cartridges at £31.
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What is the place value and value of the digit 5 in 48.56
The digit 5 in the number 48.56 holds the place value of hundredths and has a value of 0.05.
In the decimal number system, each digit has a specific place value based on its position in the number. The digit 5 in the number 48.56 is located in the hundredths place. This means that it represents a fraction of one hundredth or 0.01.
The digit 5 contributes to the overall value of the number by adding 0.05 to it. The place value system allows us to understand the positional significance of digits in a number, enabling accurate representation and computation of values.
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Pls can i get help need help to find out the numbers that made this box plot
The box plot or any additional information regarding the data. Without any context, it is impossible to determine the numbers that made up the box plot.
A box plot displays a summary of a set of data, including the minimum and maximum values, the median, the first quartile, and the third quartile.
It provides a visual representation of the distribution of data and helps in identifying outliers in the data.In order to find the numbers that made up the box plot, you need to have the actual data set from which the box plot was created.
Once you have the data set, you can use it to calculate the minimum and maximum values, the median, the first quartile, and the third quartile.
These values can then be plotted on a box plot to create a visual representation of the data distribution. Alternatively, you can use a software or an online tool that can generate a box plot from a given data set.
The numbers that made up the box plot will vary depending on the data set. The box plot is a useful tool for visualizing data, but it is important to understand the context and characteristics of the data in order to interpret the plot accurately.
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Luci cuts a board that is 3/5 yard long into pieces that are 3/10 yard long how many pieces does she cut
Luci cuts a board that is 3/5 yard long into pieces that are 3/10 yard long.
Let's determine how many pieces she has cut.
Each piece will be 3/10 yard long;
thus, we can divide the total length of the board by the length of each piece to determine how many pieces we have:
3/5 ÷ 3/10 = 3/5 × 10/3 (multiplying by the reciprocal to divide)
= 2
Therefore, Luci has cut the board into 2 pieces.
Luci cuts a board that is 3/5 yard long into pieces that are 3/10 yard long. We can determine how many pieces she cut by dividing the length of the board by the length of each piece.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Thus, if we have 3/5 ÷ 3/10, we can multiply 3/5 by 10/3, which equals 2.
Therefore, Luci cut the board into 2 pieces that are 3/10 yard long each.
It's important to understand fractions and how to divide them, especially when working with measurements like yards or feet. In this case, we need to make sure the fractions have the same denominator before dividing. Once we have a common denominator, we can divide the fractions by dividing the numerators and denominators separately. We can also simplify the fraction if possible, which may make it easier to work with. Thus Luci cut the board into 2 pieces that are 3/10 yard long each.
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Write each series as a summation in sigma notation. 12+4+ 4/3 + 4/9 + 4/27
The given series can be expressed in sigma notation as follows:
∑ (12 + 4/n²)
The two series are:-
Series 1: 12 + 4 + 4/3 + 4/9 + 4/27
Series 2: 12 + 4 + 4/3 + 4/9 + ...
Summation, denoted by the symbol "∑" (sigma), is a mathematical notation used to represent the sum of a series of terms. It is commonly used when we want to express the sum of a sequence of numbers or a pattern that can be described mathematically.
Let's break down each term of the series and represent them in sigma notation.
Series 1: 12 + 4 + 4/3 + 4/9 + 4/27
Where n starts from 0 and goes to 4.
Series 2: 12 + 4 + 4/3 + 4/9 + ...
where n is a positive integer. Note that the series starts with n = 0 because the first term is 12, and subsequent terms involve n in the denominator.
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Find the slope of the line.
Select the correct choice below and, if necessary, fill
in the answer box to complete your choice.
A. The slope of the line is N
(Simplify your answer. Type an integer or a fraction.)
B. The slope is undefined.
A. The slope of the line is 2.
To find the slope of a line, we need to have two distinct points on the line. The slope represents the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates) between the two points.
Let's consider an example to illustrate this concept:
Suppose we have two points on a line: Point A with coordinates (2, 3) and Point B with coordinates (5, 9).
To find the slope, we can use the slope formula:
slope = (change in y-coordinates) / (change in x-coordinates)
In this case, the change in y-coordinates is 9 - 3 = 6, and the change in x-coordinates is 5 - 2 = 3.
Therefore, the slope of the line passing through these two points is:
slope = 6 / 3 = 2
So, the correct answer would be:
A. The slope of the line is 2
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2. In Canada, 63% of households speak English as their primary language, and 23% speak French as their primary language. If two Canadian households are selected at random, what is the probability that the first household speaks French, but the second household speaks English?
A. (0.23)(0.63) = 0.1449
B. 0.23 + 0.63 = 0.86
C. 0.23 + 0.63 – (0.23)(0.63) = 0.7451
D. 0.23/0.63=0.3650
The probability that the first household speaks French, but the second household speaks English is 0.1449
Let A be the event that the first household speaks French, and B be the event that the second household speaks English.
P(A) = probability that the first household speaks French
= 0.23
P(B|A) = probability that the second household speaks English given that the first household speaks French= 0.63
P(A and B) = probability that the first household speaks French and the second household speaks English
= P(A) × P(B|A)
= 0.23 × 0.63
= 0.1449
The correct option is (A) (0.23)(0.63) = 0.1449.
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In ΔABC, c = 5. 4, a = 3. 3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer. 2. 0 units and 4. 6 units 2. 1 units and 8. 7 units 2. 3 units and 7. 8 units 2. 6 units and 6. 6 units.
To find the approximate length of b in ΔABC, we will use the law of sines. Using the law of sines, we can write: b / sin B = c / sin C, where B is the angle opposite b and C is the angle opposite c.
We know the value of c, a, and A. Thus, we can find the value of sin C using the sine rule,i.e. c / sin C = 2R, where R is the radius of the circumcircle of ΔABC. The value of sin C can be found as sin C = c / 2R. Now, using the value of sin C, we can write:
b / sin B = c / sin C
b / sin B = c / (c / 2R)
b / sin B = 2R
Therefore, sin B = b / (2R)Now, we can find the value of R by using the formula
R = a / (2 sin A), where A is the angle opposite a. Putting the values in this formula, we get:
R = a / (2 sin A) = (3.3) / (2 sin 20°) = 5.004 units
Now, using the value of R, we can find the value of sin B, i.e. sin B = b / (2R)Using the formula, we get:
sin B = b / (2R)
sin B = b / (2 × 5.004)
sin B = b / 10.008
Therefore, we get: b = 10.008 sin B
Now, we can find the range of values of b by finding the range of values of sin B. The value of sin B can range from 0 to 1. Thus, the value of b can range from 0 to 10.008.
Therefore, the possible approximate lengths of b are between 0 and 10.008 units. Hence, the correct answer 2. 6 units and 6. 6 units.
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A drawing of a cereal box, as shown, has a scale of 1 inch to 1 foot.
What is the actual height, in inches, of the cereal box?
The actual height of the cereal box is 12 inches.
In the given scale of 1 inch to 1 foot, it means that every 1 inch on the drawing represents 1 foot in reality. Since there are 12 inches in a foot, the height of the cereal box in inches can be determined by multiplying the height shown on the drawing by 12.0
As a result, the actual height of the cereal box can be calculated by multiplying the height of the cereal box on the drawing by 12. For example, if the height of the cereal box on the drawing is 1 inch, then the actual height of the cereal box would be 1 inch multiplied by 12, which equals 12 inches.
Therefore, in this case, the actual height of the cereal box is 12 inches.
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