Answer:
The right answer is below
Step-by-step explanation:
4.7 is the length of LJ
An inlet pipe on a swimming pool can be used to fill the pool in 16
hours. The drain pipe can be used to empty the pool in 24
hours. If the pool is 13
filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer:
Step-by-step explanation:
15. Math. The poissonier receives 30 lb.. 4 oz. of
dressed mahi-mahi. After filleting and skinning.
13 lb.. 12 oz. of fillets were produced. What
is the yield percentage of the fillets? If the
whole dressed mahi-mahi was purchased
for $5.85/b.. what is the per pound cost of
the fillets?
Answer:
To find the yield percentage of the fillets, we need to divide the weight of the fillets by the weight of the dressed mahi-mahi and then multiply by 100 to get a percentage:
Yield percentage = (Weight of fillets / Weight of dressed mahi-mahi) x 100%
First, we need to convert the weights to a common unit, such as ounces:
Weight of dressed mahi-mahi = 30 lb. 4 oz. = 484 oz.
Weight of fillets = 13 lb. 12 oz. = 220 oz.
Now we can calculate the yield percentage:
Yield percentage = (220 oz. / 484 oz.) x 100% = 45.45%
So the yield percentage of the fillets is 45.45%.
To find the per pound cost of the fillets, we need to divide the total cost of the dressed mahi-mahi by its weight in pounds, and then multiply by the yield percentage to get the cost per pound of fillets:
Total cost of dressed mahi-mahi = 30.25 lb. x $5.85/b. = $176.96
Weight of dressed mahi-mahi in pounds = 30.25 lb.
Weight of fillets in pounds = 13.75 lb.
Cost per pound of fillets = (Total cost of dressed mahi-mahi / Weight of dressed mahi-mahi) x Yield percentage / 100%
Cost per pound of fillets = ($176.96 / 30.25 lb.) x 45.45% = $3.04/lb.
Therefore, the per pound cost of the fillets is $3.04/lb.
sams rectangular swimming pool has a volume of 600 cubic feet, the neighbors pools the same length and height but the width is three times larger. what is the volume of the neighbors pool?
Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:
lwh = 600
For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:
l(3w)h = 3lwh = 3(600) = 1800 cubic feet
Therefore, the volume of the neighbor's pool is 1800 cubic feet.
Step-by-step explanation:
To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.
Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
The correct interpretation of the confidence interval is We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27 that is option A.
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.
Given,
Confidence interval, CI = 62.63 +/- 17.64
CI = ( 44.99 , 80.27 )
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
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Complete question:
To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.
Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.We are 95 percent confident that the mean cost of a hospital visit for the parrot owners in the sample is between $44.99 and $80.27.For all parrot owners in the state, 95 percent of hospital visits for parrot care cost between $44.99 and $80.27.There is a 0.95 probability that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.Help what’s the answer
Answer:
Difference=£2.4
Step-by-step explanation:
Here in shop A
130 cm=£1.82
1 cm=£1.82/130
1 cm=0.014
Now
400 cm=0.014*400
=£5.6
Again, In shop B
235cm=£1.88
1 cm=£1.88/235
1 cm=£0.008
Now
400cm=0.008*400
=£3.2
Now,
Difference=£5.6-£3.2
=£2.4
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.
Answer:
To find the probability of getting someone who tested positive given that he or she had the disease, we need to use the formula for conditional probability:
P(positive|disease) = P(positive and disease) / P(disease)
From the given data, we can see that there are 136 individuals who tested positive and actually had the disease. Therefore, P(positive and disease) = 136.
We can also see that there are a total of 136 + 8 = 144 individuals who actually had the disease. Therefore, P(disease) = 144.
Substituting these values into the formula, we get:
P(positive|disease) = 136 / 144
Simplifying, we get:
P(positive|disease) = 0.944
Rounding to three decimal places, we get:
P(positive|disease) ≈ 0.944
Therefore, the probability of getting someone who tested positive given that he or she had the disease is approximately 0.944.
Graph the system of linear equations.
4x + 3y = 24
-2x + 6y = 18
Use the Line tool to graph the lines.
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 385 grams and a standard deviation of 8 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value. Round your final answers to 2 decimal places)
URGENT
the weight that corresponds to each of the events are:
a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].
b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].
c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].
How to deal with Normal distribution?Let X be the weight of a small Starbucks coffee. We are given that X is normally distributed with mean [tex]$\mu=385$[/tex] grams and standard deviation [tex]$\sigma=8$[/tex].
We want to find the weight that corresponds to each of the following events:
a) The weight is less than 380 grams.
b) The weight is between 375 and 395 grams.
c) The weight is greater than 400 grams.
To solve these problems, we first standardize the distribution by finding the corresponding z-scores using the formula:
[tex]$z=\frac{X-\mu}{\sigma}$$[/tex]
a) The weight is less than 380 grams.
We want to find P(X<380). We can find the z-score for X=380 as follows:
[tex]$z=\frac{380-385}{8}=-0.625$$[/tex]
Using a standard normal table or calculator, we find that the probability P(Z<-0.625)=0.266. Therefore,
[tex]$P(X < 380)=P\left(Z < -\frac{0.625}{1}\right)=0.266$$[/tex]
b) The weight is between 375 and 395 grams.
We want to find [tex]$P(375 < X < 395)$[/tex]. We can find the z-scores for X=375 and X=395 as follows:
[tex]$z_1=\frac{375-385}{8}=-1.25,\quad z_2=\frac{395-385}{8}=1.25$$[/tex]
Using a standard normal table or calculator, we find that the probability P(-1.25<Z<1.25)=0.7887. Therefore,
[tex]$P(375 < X < 395)=P\left(-1.25 < Z < 1.25\right)=0.7887$$[/tex]
c) The weight is greater than 400 grams.
We want to find P(X>400). We can find the z-score for X=400 as follows:
[tex]$z=\frac{400-385}{8}=1.875$$[/tex]
Using a standard normal table or calculator, we find that the probability P(Z>1.875)=0.0304. Therefore,
[tex]$P(X > 400)=P\left(Z > \frac{1.875}{1}\right)=0.0304$$[/tex]
Therefore, the weight that corresponds to each of the events are:
a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].
b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].
c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].
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I’m the forest there were lions and tigers and bears the ratio of lions to tigers was 3 to 2 the ratio of tigers to bears was 3 to 4 if there were 9 lions how many bears were there
Answer:
There were 8 bears
Step-by-step explanation:
Letting L = number of lions, T = number of tigers and B = number of bears
L : T = 3 : 2
We can rewrite this as
L/T = 3/2
Cross multiply:
L x 2 = 3 x T
Divide by 3 to get
T = 2/3 L
Since L = 9
T = 2/3 x 9 = 6
In the other ratio we have
T : B = 3 : 4 which we can write as
T/B = 3/4
Cross multiply to get
4T = 3B
B = 4/3 T
Since T = 6, B = 4/3 x 6 = 8
Check
L : T = 9 : 6 = 3: 2 (by dividing both sides of : by 3)
T : B = 6 : 8 = 3:4 (by dividing both sides of : by 2)
Please help me on this geometry question. Use a trig function to find the missing side to the nearest 10. Please show step by step
Answer:
x = 42.9
Step-by-step explanation:
We can let 34 represent the reference angle. Using this angle, we see that the side measuring 24 units is the opposite side and the side measuring x is the hypotenuse.
Thus, we can use the sine trig function which is
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
We plug in what we have into the equation above and solve for x:
[tex]sin(34)=\frac{24}{x}\\ x*sin(34)=24\\x=\frac{24}{sin(34)}\\ x=42.9189996\\x=42.9[/tex]
Prove that for every real number if c is the root of a polynomial with rational coefficients then root ofa polynomial with integer coefficients: It may be helpful to suppose that is a solution to the polynomial equation: GnXn An-1xn-1_ +q1* + 4o Where qi € Q
Every real root of a polynomial with rational coefficients is also a root of a polynomial with integer coefficients.
Suppose that c is a root of the polynomial equation:
[tex]q_n[/tex] × [tex]x^n[/tex] + q_{n-1} × [tex]x^{n-1}[/tex] + ... + q1 × x + q0 = 0
where [tex]q_i[/tex] are rational coefficients. Since c is a root of this polynomial equation, we have:
[tex]q_n[/tex] × [tex]c^n[/tex] + [tex]q_{n-1}[/tex] × [tex]c^{n-1}[/tex] + ... + q1 × c + q0 = 0
Multiplying both sides of the equation by the common denominator of the coefficients [tex]q_i[/tex], we can obtain an equation with integer coefficients. Let d be the least common multiple of the denominators of the coefficients [tex]q_i[/tex]. Then we can write:
d × ([tex]q_n[/tex] × [tex]c^n[/tex] + [tex]q_{n-1}[/tex] × [tex]c^{n-1}[/tex] + ... + q1 × c + q0) = 0
Expanding the left-hand side of the equation, we obtain a polynomial with integer coefficients:
d × [tex]q_n[/tex] × [tex]x^n[/tex] + d × [tex]q_{n-1}[/tex] × [tex]x^{n-1}[/tex] + ... + d × q1 × x + d × q0 = 0
Since c is a root of the original polynomial equation, it is also a root of this polynomial with integer coefficients. Therefore, we have shown that if c is a root of a polynomial with rational coefficients, then it is also a root of a polynomial with integer coefficients.
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Figure ABCD is a parallelogram.Parallelogram A B C D is shown. The length of A D is 5 x + 3 and the length of B C is 38.What is the value of x?6789
ABCD is a parallelogram, the value of x is 7
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.
The opposing sides of a parallelogram are equal and parallel.
AD = BC
5x + 3 = 38
Take 3 away from both sides.
5x + 3 - 3 = 38 - 3
5x = 35
Subtract 5 from both sides.
5x/5 = 35/5
x = 7
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
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Which graph matches the function given:
The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.
What is a piecewise function?A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.
The intervals of the piecewise function are;
f(x) = √(x + 5) if x < -2
f(x) = |x + 1| -2 ≤ x ≤ 2
f(x) = (x - 2)² if x > 2
The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²
The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2
The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.
The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.
The correct option for the graph of the piecewise function is therefore the third option.
Please find the attached the graph of the piecewise function created with MS Excel
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A photography student took portrait photos of people from his hometown. He wants to
develop 21 of the photos, 9 of which were photos of babies.
If he randomly chooses to make 4 of the photos black and white, what is the probability that
all of them are of babies?
Answer: The total number of ways the photography student can choose 4 photos out of 21 is given by the combination formula:
Step-by-step explanation: C(21, 4) = (21!)/((4!)(21-4)!) = 5985
Out of the 21 photos, 9 were photos of babies. The number of ways the student can choose 4 baby photos out of 9 is given by:
C(9, 4) = (9!)/((4!)(9-4)!) = 126
Therefore, the probability that all 4 photos chosen are of babies is:
P = (number of ways to choose 4 baby photos)/(total number of ways to choose 4 photos)
P = C(9, 4)/C(21, 4)
P = 126/5985
P ≈ 0.021
So, the probability that all 4 photos chosen are of babies is approximately 0.021 or 2.1%.
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
√9+25 = 28
π-4 = -0.8571
³√-27 = -3
2 / 3 = 0.6667
18÷2 = 9
√-27 = 5.196
What is surdsIn mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).
We have √9+25 = 28
find the square root of 9 = 3
3 + 25 = 28
π-4 = 3.14 - 4
= -0.8571
³√-27 = ³√3³
= 3
2÷3 = 0.6667
18÷2 = 9
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question:
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
find the value of the terms
A fair coin is tossed five times. What is the theoretical probability that the coin lands on the same side every time?
A) 0.1
B) 0.5
C) 0.03125
D) 0.0625
Answer:
Step-by-step explanation:
The theoretical probability of getting the same side every time in a single coin toss is 1/2. Since we have five independent coin tosses, we can calculate the probability of getting the same side every time by multiplying the probability of getting the same side in each toss:
(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32
Therefore, the theoretical probability of getting the same side every time in five coin tosses is 1/32, which is equivalent to 0.03125. So, the answer is (C) 0.03125.
Jina rolled a number cube 40 times and got the following results.
Outcome Rolled
1
Number of Rolls 7
2
6
3
9
4
6
5
3
Answer the following. Round your answers to the nearest thousandths.
6
9
(a) From Jina's results, compute the experimental probability of rolling a 3 or 6.
0.45
(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 3 or 6.
0
(c) Assuming that the cube is fair, choose the statement below that is true.
With a small number of rolls, it is surprising when the experimental probability is much
greater than the theoretical probability.
With a small number of rolls, it is not surprising when the experimental probability is much
When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.
what is probability ?The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is used to determine how likely or unlikely an occurrence is to occur. An event's likelihood is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of occurrence. The symbol P stands for the probability of an occurrence A. (A). It is determined by dividing the number of positive results of event A by all the potential outcomes.
given
(a) The result of rolling 3 or 6 times is 6 + 9 = 15.
Experimental chance = (Total number of rolls) / (Number of times 3 or 6 were rolled) = 15/40 = 0.375
(b) The theoretical likelihood of rolling either a 3 or a 6 on a fair number cube is equal to the total of those odds, which is 1/6 + 1/6 = 1/3 = 0.333. (rounded to three decimal places).
(c) When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.
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help ASAP PLSSSS
The table of values represents a linear function.
Enter the rate of change of this function.
The rate of change (or slope) of this linear function is -1/2.
Describe Linear Function?A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.
The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.
Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.
The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
Let's use the points (0, -3) and (2, -4) to calculate the slope:
slope = (-4 - (-3)) / (2 - 0)
slope = -1 / 2
Therefore, the rate of change (or slope) of this linear function is -1/2.
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NEED HELP ASAP!!!
Which polynomial best represents the scenario below? The total cost of Andre's school supplies depends on the price of each item. Each notebook (n) is $5, each folder (f) is $4, and each backpack (b) is $15.
Answer:
C = 5n + 4f + 15b
A joined in a partnership with B after 3 months by investing Rs. 27000. The profit of A is 3/5th of B's share at the end of one year. What was the amount invested by B?
Thus, A’s share is Rs. 2,40,000 and B’s share is Rs. 2,61,000.
What is profit and loss?A profit and loss statement (P&L) is a financial statement that summarizes income, expenses, and expenses incurred during a specified period of time.
Along with the balance sheet and cash flow statement, the income statement is one of the three financial statements issued quarterly and annually by all publicly traded companies.
When used together, the Income Statement, Balance Sheet, and Cash Flow Statement provide detailed insight into the company's overall financial performance.
Accounting is created using the cash method or the accrual method of accounting.
Changes over time are more important than the numbers themselves, so it's important to compare income statements from different accounting periods.
According to our question-
Ratio of their share in profit = Ratio of their investments
Ratio of their share in profit = Ratio of their investments
⇒ 27000 × 5 + 23000 × 15 ∶ 36000 × 9 + 33000 × 6 ∶ 50000 × 6
Thus, ratio of their investments = 480000 ∶ 522000 ∶ 300000 = 480 ∶ 522 ∶ 300 = 80 ∶ 87 ∶ 50
Profit earned after a year = Rs. 6,51,000
A’s share = (80/217) × 651000 = Rs. 240000
B’s share = (87/217) × 651000 = Rs. 261000
Hence, Thus, A’s share is Rs. 2,40,000 and B’s share is Rs. 2,61,000.
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$690 is invested in an account earning 2.2% interest (APR), compounded quarterly.
Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
a) A function showing the value of the account after t years, where the annual growth rate can be found from a constant, is f(x) = 690 (1+0.0055)^4t.
b) The percentage of growth per year (APY) is 2.2%.
What is a function?A function is a mathematical expression that shows the relationship between variables.
An example of a mathematical function is an equation that shows the relationship between y and x variables.
Principal = $690
APR = 2.2%
APR per quarter = 0.0055 (2.2%/4)
Compounding = Quarterly
Investment period = t years
Let f(x) = the value of the account after t years.
Future value function, (FV) = PV × (1 + r) ^ n
Where PV = present value or investment
r = compounding rate per period
n = the investment period
Therefore, f(x) or FV = 690 (1+0.0055)^4t.
APY = 100 [(1 + Interest/Principal)(365/Days in term) - 1]
2.2% = 100 [(1 + $15.18/$690)(365/365) - 1]
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An organization wishing to attract more people decides to base its
membership fees on the age of the member. Also, wanting members to
attend more activities, it gives a reduction on the membership fee for each
activity attended in the previous year.
The following table depicts the corresponding fee and reductions. The
minimum membership fee is $1, even if the member attended a lot of
activities.
Age
6 years or less
7-12 years
13-18 years
Over 18 years
Membership
Fee Reduction per Activity
$0.75
$1.25
$2
$5
$10
$15
$25
$2
Write a program that asks the user to input their age and the number of
activities attended and then displays the corresponding membership fee.
Input Validation: Do not accept a negative value for either the age or the
number of activities
C++
1. Begin the program by including the header file <iostream> which includes basic input/output library functions as well as the <vector> library which is needed for this program.
2. Declare a vector of integer type named 'ageGroups' which will store the age groups and the corresponding membership fee and reductions.
3. Create a void function named 'calculateFee()' which will take a parameters age and activities attended.
4. In the calculateFee() function, use the switch statement for the age group and store the corresponding membership fee and reduction value in variables.
5. Use an if statement to check that the number of activities attended is non-negative.
6. Calculate the membership fee using the variables and store it in a variable named 'fee'.
7. Use an if statement to check if the fee is less than 1 and if yes, assign the fee to 1.
8. Print the fee to the user.
9. End the program.
please help with with this math
The slope of this linear function is equal to: B. -2/9.
The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.
The value of each expression is: C. a) 2, b) 1/2, c) 2/9.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - 10)/(6 - (-3))
Slope (m) = (8 - 10)/(6 + 3)
Slope (m) =
Slope (m) = -2/9.
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the given parameters, we have:
Volume of cylinder, V = 3.14 × 5² × 10
Volume of cylinder, V = 785 m³
(√2)² = 2
(1/√2)² = 1/2
(√2/3)² = 2/9
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Which of the following tables represents a linear relationship that is also proportional?
x 2 3 4
y −3 0 3
x 4 2 0
y −2 −1 0
x −2 1 4
y 0 1 2
x 0 1 2
y −4 0 4
Answer:
This table represents a linear relationship that is also proportional:
x 0 1 2
y −4 0 4
Answer:
The second table represents a linear relationship that is also proportional.
To check if a relationship is proportional, we need to see if the ratio of y to x is constant for all values of x and y. In other words, if we divide any y value by its corresponding x value, we should get the same number for all values.
Let's check the ratio for each table:
Ratio for the first table:
-3/2 = -1.5
0/3 = 0
3/4 = 0.75
The ratio is not constant, so this relationship is not proportional.
Ratio for the second table:
-2/4 = -0.5
-1/2 = -0.5
0/0 = undefined
The ratio is constant (-0.5), so this relationship is proportional.
Ratio for the third table:
0/(-2) = 0
1/1 = 1
2/4 = 0.5
The ratio is not constant, so this relationship is not proportional.
Ratio for the fourth table:
-4/0 = undefined
0/1 = 0
4/2 = 2
The ratio is not constant, so this relationship is not proportional.
Therefore, the second table is the only one that represents a linear relationship that is also proportional.
The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble?
A) 11
B) 33
C) 32
D) 22
Answer:
B) 33 times.
Step-by-step explanation:
The total amount of pebbles is 50. There is 22 yellow pebbles.
Note that 3/2 * 50 is 75. 3/2 * 22 = 33.
He should expect to choose a yellow pebble B) 33 times.
Find the prime factorization of 792. What is the sum of the distinct prime factors?
The sum of the distinct prime factors is 16.
Solution:There are overall 24 factors of 792 among which 792 is the most significant factor and its prime factors are 2, 3, and 11.
Hence sum = 2 + 3 + 11 = 16
Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y = mx + b.
x 1 2 3 4 5 6
y 102 114 131 152 176 206
Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50
What is linear regression?
Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.
To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:
The mean of x is 3.5 and the mean of y is 150.
The variance of x is 2.5 and the variance of y is 2203.5.
The covariance of x and y is 607.5.
Using these values, we can calculate the slope of the regression line:
m = covariance of x and y / variance of x = 607.5 / 2.5 = 243
We can also calculate the y-intercept of the regression line:
b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5
Therefore, the equation for the linear function that best fits the given data is:
y = 243x - 16.5
Rounding both numbers to two decimal places, we get:
y = 243x - 16.50
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Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50
What is linear regression?
A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.
To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:
The mean of x is 3.5 and the mean of y is 150.
The variance of x is 2.5 and the variance of y is 2203.5.
The covariance of x and y is 607.5.
Using these values, we can calculate the slope of the regression line:
m = covariance of x and y / variance of x = 607.5 / 2.5 = 243
We can also calculate the y-intercept of the regression line:
b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5
Therefore, the equation for the linear function that best fits the given data is:
y = 243x - 16.5
Rounding both numbers to two decimal places, we get:
y = 243x - 16.50
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You are the marketing manager at The Best Candy Shop where the top sales item is the Dream Pop bags of flavored candies. You have been getting complaints from customers that there are not enough lemon or blueberry flavored candies, which are favorites, and too many grape and strawberry flavored candies. Your boss wants you to create an advertisement indicating, “all bags have equally likely flavors.” (That is, the probability of getting a strawberry flavored candy piece is the same as getting a blueberry flavored candy piece, etc.). As the marketing manager, you want to make sure you are advertising truthful information, so you pull a sample bag of Dream Pop candy and find the following pieces: • 16 grape flavors • 12 strawberry flavors • 6 lemon flavors • 6 blueberry flavors • Explain how you could communicate to your boss that his advertising suggestion (all bags have equally likely flavors) would be incorrect. You must include at least two (2) probabilities from your sample bag of candy that would deem his advice inaccurate.
We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Based on the sample bag of Dream Pop candy, we can calculate the probability of getting each flavor.
If all bags have equally likely flavors, then each flavor should have the same probability of being selected.
However, we can see from the sample that this is not the case.
To communicate this to the boss, we can calculate the probability of getting two different flavors and compare them.
For example:
The probability of getting a grape flavor is 16/40 or 0.4
The probability of getting a lemon flavor is 6/40 or 0.15
These probabilities are not equal, indicating that the flavors are not equally likely.
We can also compare the probabilities of getting two other flavors, such as:
The probability of getting a strawberry flavor is 12/40 or 0.3
The probability of getting a blueberry flavor is 6/40 or 0.15
Again, these probabilities are not equal, further indicating that the flavors are not equally likely.
Therefore,
We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.
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First-year students at a university must take history or philosophy during their first semester. 400 are enrolled in both out of a total of 1200 first-year students. If 600 are enrolled in philosophy, how many are taking history?
Answer: I really don't know I'm just trying to get a quest done sorry
Determine whether the subset of M is a subspace of M with the standard operations of matrix addition and scalar inn nn multiplication The set of all n x n invertible matrices O subspace O not a subspace
The set of all n×n invertible matrices with the standard operations of matrix addition and scalar multiplication is (b) not a subspace.
A Subspace is defined as a subset of a vector space that is itself a vector space under the same operations of addition and scalar multiplication defined on the original vector space.
To be a subspace of Mₙ,ₙ, a subset of Mₙ,ₙ must satisfy three conditions:
(i) The subset must contain the zero matrix,
(ii) The subset must be closed under matrix addition, meaning that if A and B are in the subset, then (A + B) is also in the subset.
(iii) The subset must be closed under scalar multiplication, meaning that if A is in the subset and c is any scalar, then cA is also in the subset.
The set of all n×n invertible matrices does not contain the zero matrix, as the zero matrix is not invertible.
Therefore, it fails to meet the first condition and cannot be a subspace, the correct option is (b).
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The given question is incomplete, the complete question is
Determine whether the subset of Mₙ,ₙ is a subspace of Mₙ,ₙ with the standard operations of matrix addition and scalar multiplication.
The set of all n×n invertible matrices is
(a) Subspace
(b) Not a subspace.