The effect on the surface area is best described by the statement "the surface area is multiplied by 1/4." The correct option is D.
Given that the radius of a right cone is 5 ft and the slant height is 9 ft. If the radius and slant height of the cone are both multiplied by 1/2, then the new radius of the cone will be:5 × (1/2) = 2.5 ft
New slant height of the cone will be:9 × (1/2) = 4.5 ft. The surface area of a cone can be given by the formula:
S = πrl + πr² Where r is the radius of the base, l is the slant height of the cone, and π is a constant (3.14). The surface area of the original cone can be calculated as:
S1 = π × 5 × 9 + π × 5² = 141.37 ft². Now, if we multiply the radius and slant height by 1/2, the new surface area of the cone will be:S2 = π × 2.5 × 4.5 + π × 2.5² = 17.67 ft².
Therefore, the ratio of the new surface area to the original surface area will be:S2/S1 = 17.67/141.37 = 0.125Thus, the new surface area is 1/8th (0.125) of the original surface area or multiplied by 1/8th (1/2 × 1/4). So, the surface area is multiplied by 1/4.
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suppose vi pays its phone reps $12 per hour. how many phone reps should it employ if it wants to maximize profit?
Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.
Here,
The formula below can be used to determine the ideal amount of phone representatives:
=> MR = MC
Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.
The following results are obtained by taking the derivative of revenue and cost with regard to n:
=> MR=dR/dn = k
=> dC/dn = 12 for MC.
When we set MR equal to MC, we obtain:
=> k = 12
Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
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what is the probability that 45 or more people in this sample have consumed alcoholic beverages? round your answer to 4 decimal places.
The hot or cold, and they can be served in a variety of containers, including cups, bottles, and cans.
There is no sample size or other information provided in the question, so the probability of 45 or more people in the sample having consumed alcoholic beverages cannot be calculated. More information is needed to solve this problem.What is probability?Probability is a branch of mathematics that deals with calculating the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing impossibility and 1 representing certainty. A probability of 0.5 represents a 50% chance of the event occurring. Probability is used in a variety of fields, including statistics, finance, and engineering.What are beverages?Beverages are drinks that are intended for human consumption. Beverages come in a variety of types, including alcoholic and non-alcoholic. Beverages can be made from a variety of ingredients, including water, fruit juice, and milk. They can be hot or cold, and they can be served in a variety of containers, including cups, bottles, and cans.
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An airliner carries 200 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d).
(A) If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
The probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.
What is probability?
Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify uncertainty and to make informed decisions in the face of incomplete or uncertain information.
We can assume that the heights of male passengers follow a normal distribution with a mean of 69.0 in and a standard deviation of 2.8 in. Let X be the height of a male passenger in inches. Then, we need to find the probability that X is less than or equal to 74 in, which represents the height of the airliner's doors.
(a) Using the standard normal distribution, we can standardize X as follows:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution, and z is the corresponding z-score.
Substituting the values, we get:
z = (74 - 69.0) / 2.8 = 1.75
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to 1.75:
P(Z ≤ 1.75) ≈ 0.9599
Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.
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I have 2 different things for you people to solve. Please say your answer in the order given
2/3a -7+7/18a-5 1/6= (The answer is not 19a-219/18)
-12(5/6a-7/8)+1/14(3 1/2a-1 2/5)= (The answer is not 13(15a-16)/20)
After solving the given equation, the value of variable a is 6.81 respectively.
What is an equation?Every equation is a formula.
Not all equations have formulas. It is the purpose of equations to be solved for a variable.
We analyze formulas.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
2/3a -7 + 7/18a - 5 1/6 = 0
2/3a + 7/18a = 7 + 6/31
12a+7a/18 = 7+6/31
19a/18 = 7+6/31
19a = (7+6/31)18
19a = (217+6/31)18
19a = (223/31)18
19a = 4,014/31
a = 4014/31*19
a = 4014/589
a = 6.81
Therefore, after solving the given equation, the value of variable a is 6.81 respectively.
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Complete question:
Solve the given equation: 2/3a -7 + 7/18a - 5 1/6 = 0
Carrie drove 7 hours to a beach house for spring break. She spent the first hour averaging 30 miles per hour. After that, she spent the next 4 hours at an average speed of 65 miles per hour. She finished the last part of her drive averaging 52 miles per hour. Write a piecewise function to represent that total distance d (in miles) that carrie has traveled after t hours
the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.
To write a piecewise function to represent the total distance Carrie has traveled after t hours, we need to break down her journey into different parts and calculate the distance covered during each part.
Let's define the three different parts of her journey:
•Part 1: The first hour, during which she averaged 30 miles per hour
•Part 2: The next 4 hours, during which she averaged 65 miles per hour
•Part 3: The remaining 2 hours, during which she averaged 52 miles per hour
For Part 1, the distance covered can be calculated as:
d1 = 30t (where t is the time spent in the first hour, t ≤ 1)
For Part 2, the distance covered can be calculated as:
d2 = 260 + 65(t - 1) (where t is the time spent in the next 4 hours, 1 < t ≤ 5)
For Part 3, the distance covered can be calculated as:
d3 = 520 + 52(t - 5) (where t is the time spent in the remaining 2 hours, 5 < t ≤ 7)
Now, we can combine these three equations to form a piecewise function for the total distance traveled by Carrie:
d(t) = 30t, 0 ≤ t ≤ 1
d(t) = 260 + 65(t - 1), 1 < t ≤ 5
d(t) = 520 + 52(t - 5), 5 < t ≤ 7
Therefore, the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.
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a bag is filled with 200 silver coins and 123 gold coins. what is the theoretical probability of not pulling out a silver coin?
The theoretical probability of not picking the silver coin will be 0.38 .
Given,
200 silver coins and 123 gold coins are filled in a bag .
Now,
Total number of coins in a bag = gold + silver coins
Total number of coins in a bag = 200 + 123
Total number of coins in a bag = 323
Further ,
Probability of taking silver coin = 200/323
Probability of taking silver coin = 0.619.
probability of taking gold coin = 123/323
probability of taking gold coin = 0.38
Hence the probability of not selecting silver coin is 0.38 .
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The volume of air in a person's lungs can be modeled with a periodic function,
V (t) = 500 cos ( ² (t – 0.25)) + 1500, where V represents the volume of air, in
mL, in a person's lungs and time t is measured in seconds.
What is the midline and what does it represent in this
context?.
The midline is 1500. The midline in this context represents the average volume of air in a person's lungs over a period of time.
What is the midline and what does it represent in this context?The midline of a periodic function is the horizontal line that passes through the middle of the function's range.
For a function of the form V(t) = A cos(B(t - C)) + D, the midline is given by the equation y = D, which represents the average value of the function over a period.
In this case, the function is V(t) = 500 cos(²(t - 0.25)) + 1500, so the midline is given by the equation:
y = 1500
This represents the average volume of air in a person's lungs over a period of time.
Since the cosine function oscillates between -1 and 1, the actual volume of air in the person's lungs will oscillate around the midline, between 1500 - 500 = 1000 mL and 1500 + 500 = 2000 mL.
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professor salton's research is about the relationship between work and study among college students. in his survey, he asked respondents to report how many hours they work for a non-academic job. professor salton's measure for work is:
Professor Salton's measure for work is the number of hours worked for a non-academic job, as reported by respondents in his survey.
This measure is a simple but effective way to gain an understanding of how work can impact a student's academic studies. It provides a direct measure of the amount of time that students spend working outside their academic pursuits, and can be used to quantify the potential effects of working on their educational success.
By taking this measure, Professor Salton has provided an effective way of analyzing the relationship between work and study. It allows researchers to determine whether working has an impact on student performance and academic outcomes. It also allows researchers to investigate whether certain types of work, such as part-time or full-time employment, have more of an impact than others.
Ultimately, this measure is an invaluable tool for researchers to gain a better understanding of the effects of work on student success.
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The figure shows intersecting lines k and m. What is the measure of angle a?
Type the number in the box.
86°
a
degrees
According to the information provided, k and m are crossing lines with an angle of 86°. We know this because k and m are straight lines.
The angles add up to 180 degrees.
Then we receive,
[tex]a + 86 =180[/tex]
Or, a = 180 -86
Or, a = 94°.
As a result, an is 94°.
The angle an is 94 degrees.
Supplementary angle are formed when two angles add to 180 degrees. When additional angles are added together, they form a straight angle, or 180 degrees. In these other words, if indeed the sum of angles 1 and 2 equals 180 degrees, angles 1 and 2 are supplementary. Angles 1 and 2 are referred to as "supplements" to one another in this context.
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In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student chosen randomly from the class is an only child?
The probability that a student chosen randomly from the class is an only child is 0.23 or 23%.
What is the probability?
To find the probability that a student chosen randomly from the class is an only child, we need to add up the number of students who do not have a brother and do not have a sister, and then divide by the total number of students in the class.
From the table, we can see that there are 6 students who do not have a sister and do not have a brother. Therefore, the probability that a student chosen randomly from the class is an only child is:
P(only child) = number of only children / total number of students
= 6 / (2 + 13 + 5 + 6)
= 6 / 26
= 0.23 (rounded to two decimal places)
Therefore, the probability that a student chosen randomly from the class is an only child is 0.23 or 23%.
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Simplify the following: 2(√12 + 2√3)
Answer:
[tex]2 \sqrt{2(6 + \sqrt{3} )} [/tex]
Step-by-step explanation:
There's your answer.
what is this expression in simpliest form? 3^√-729
A. -243
B. -18
C. -81
D. -9
Answer:
-9
Step-by-step explanation:
[tex](-9)^3 = -729[/tex]
[tex]-9 = \sqrt[3]{-729}[/tex] (taking cube root on both sides)
Hopefully this answer helped you!!!
Evaluate the following expression. You should do this problem without a calculator. e^In 5
a. 1
b. 5
c. 10
d. 0
The value of [tex]e^{In 5}[/tex] is equal to 5 which of option B. According to the property of logs and logarithm rules the given equation is done.
The natural log, or log to the base e, is denoted by ln. ln can also be written as [tex]log_{e}[/tex].
So, we can write the given expression as:
[tex]e^{log_{e}^(5) }[/tex]
The property of logs is:
[tex]a^{log_{a}^(x) } = x[/tex]
This means that if the number an is raised to a log whose base is the same as the number a, the answer will be equal to the log's argument, which is x.
The number e and the base of log are the same in the given case. As a result, the answer to the expression will be the log argument, which is 5.
Therefore, the value of [tex]e^{log_{e}^(5) }[/tex] = [tex]e^{In 5}[/tex] = 5. Correct option is option B.
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what are the null and alternative hypotheses? let the probability the shares held will be worth more after the split.
Null hypothesis: No statistically significant relationship between stock splits and the value of shares held
Alternative Hypothesis: Statistically significant relationship between stock splits and the value of shares held
Probability of the shares held being worth
The null and alternative hypotheses are as follows:Null Hypothesis (H0): There is no statistically significant relationship between stock splits and the value of shares held.Alternative Hypothesis (Ha): There is a statistically significant relationship between stock splits and the value of shares held.The probability that the shares held will be worth more after the split can be determined through statistical analysis. The null hypothesis assumes that there is no relationship between stock splits and the value of shares held, while the alternative hypothesis suggests that there is a statistically significant relationship between the two variables.Therefore, the probability of the shares held being worth more after the split is based on the results of the statistical analysis of the null and alternative hypotheses.
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hey there mide helping me⭒What is the missing numerator and denominator? Three (?) times (?) fourths equals nine twentieths⭒ this is for my ↣⭒exam⭒↢ (=^･ｪ･^=)⭒meow⭒ will get brainiest
The answer is in numerator = 3 and denominator = 5
What are numbers?Numbers are present in every part οf οur everyday lives, including the number οf laps we cοmplete οn the racetrack, the number οf hοurs we sleep at night, and many οther things.
In math, a number can be even, οdd, prime, cοmpοsite, decimal, fractiοnal, ratiοnal, irratiοnal, natural, integer, real, whοle, οr any cοmbinatiοn οf these.
Numbers are the basis οf mathematics
We must learn abοut numbers if we are tο understand math.
There are many different kinds οf numbers.
There is a lengthy list that includes whοle numbers, οrdinal numbers, οrdinal numbers, natural numbers, οdd numbers, even numbers, cοnsecutive numbers, and sο οn.
3*3 = 9
5*4=20
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help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex] .
What dimensions are expressed in linear units?The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that [tex]ZF = ZD + DF = 24 + 28 = 52[/tex] and [tex]FH = ZG = 30 and ZH = 36.[/tex]
As a result, Fard ZH's perimeter is as follows:
perimeter = [tex]= ZF + FH + ZH + ZG[/tex]
perimeter [tex]= 52 + 30 + 36 + 30[/tex]
perimeter [tex]= 148[/tex]
So the perimeter of Fard ZH is [tex]148[/tex] .
(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:
[tex]V = (xB - xA, yB - yA)[/tex]
Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.
Plugging in the given values, we get:
[tex]V = (5 - 10, 2 - 14)[/tex]
[tex]V = (-5, -12)[/tex]
Therefore, The V's direction is [tex](-5, -12)[/tex] .
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5-1 Additional Practice 1. Look at the paper to the right. a. Write an equation to represent the description. 8 more than 4 times number 28 b. Describe a real-world situation the equation could represent.
HELP I CANT GET LUNCH DETENTION
linear Equation to represent the description "8 more than 4 times number 28" is: y = 4x + 8
What is linear equation ?
A linear equation is an algebraic equation that describes a straight line relationship between two variables, typically denoted as x and y. The general form of a linear equation is:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).
The slope, m, represents the rate of change of y with respect to x, or how steep the line is. It is calculated as the change in y divided by the change in x between any two points on the line.
According to the question:
a. An equation to represent the description "8 more than 4 times number 28" is:
y = 4x + 8
where x represents the number 28, and y represents the result of multiplying 28 by 4 and then adding 8.
b. A real-world situation that this equation could represent is the cost of purchasing a certain number of items. For example, if the price of one item is $28, and there is a discount of 8 dollars for every four items purchased, the equation y = 4x + 8 could be used to calculate the total cost y of purchasing x items. The 4x term represents the cost of the items before the discount, and the +8 term represents the discount. For instance, if a customer wants to purchase 12 items, they would pay 4 * $28 = $112 for the first 12 items, minus $8 for the discount, resulting in a total cost of $104.
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what is the numerical value of the product of the lengths of all diagonals of a regular hexagon of side length $1$?
Answer: 2.8%
Step-by-step explanation: 2.8%
£80 :))
for a ride, a taxi driver charges an initial fare of $3.00 plus $0.40 for each 1 5 of a mile driven. if the total charge for a ride is $27.00, what is the distance traveled, in miles?
The taxi driver charges an initial fare of $3.00 plus $0.40 for each 1/5 of a mile driven. If the total charge for a ride is $27.00, the distance traveled, in miles is 9.
The data given in the question is, The taxi driver charges an initial fare of $3.00 plus $0.40 for each 1/5 of a mile driven. The total charge for a ride is $27.00.
Let's calculate the distance traveled:
Let d be the distance traveled. The given data in the problem is in dollars and cents. Therefore, let's first change it to the same units (cents). We know that 1 dollar is equal to 100 cents. Thus $27.00 is equal to 27 * 100 cents.
Therefore, $27.00 is equal to 2700 cents.
Now, we know that the driver charges $3.00 as an initial fare.
So, he charged 300 cents. Therefore, the remaining amount of money he charged for the distance is (2700 - 300) cents.
Hence, he charged 2400 cents for the distance traveled. The driver charges $0.40 for each 1/5 of a mile. That is 40 cents for each 1.2 km.
Therefore, he charges 200 cents for each 1.2 km of distance traveled.
Hence, he charges (2400/200) * 1.2 km of distance traveled.
Therefore, the distance traveled is 14.4 km or 9 miles. Accordingly, the distance traveled, in miles, is 9.
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help!
It’s the pythagorean theorem
Answer:
17.8
Step-by-step explanation:
a^2+b^2=c^2
To find the distance between Tallahassee and Miami we need to find the distance from...
(10,17) and (10,3)
as well as (10,3) and (21,3)
The distance from the point (10,17) to (10,3) is the difference in y or 17-3, which gives you 14
The distance from the point (10,3) to (21,3) is the difference in x or 21-10, which gives you 11
Now you can plug in the values in the pythagorean theorem like so:
14^2+11^2=c^2
196+121=c^2
317=c^2
Square root both sides
The sqrt of 317 is approximately 17.804, rounding to 17.8 to the nearest tenths place.
Suppose that the value of an investment in the stock market has increased at an average compound rate of about 5% since 1900. It is now 2019 a. If your great grandfather invested $1,000 in 1900, how much would that investment be worth today? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment b. If an investment in 1900 has grown to $1 million, how much was invested in 19007 (Enter your answer in dollars. Do not round Intermediate calculations. Round your answer to 2 decimal places.) Present value
where P is the principal amount, r is the interest rate, and n is the number of years. In this case, A is $1,000,000, r is 0.05, and n is 119. Thus, P = [tex]$1,000,000/(1+0.05)119 = $66,059.19.[/tex]
A. The investment of $1,000 in 1900 would be worth $97,792.96 today. This can be calculated by using the compound interest formula A=P(1+r)n, where P is the principal amount, r is the interest rate, and n is the number of years. In this case, P is $1,000, r is 0.05, and n is 119.
Thus, A = [tex]$1,000(1+0.05)119 = $97,792.96.[/tex]
B. If the investment has grown to $1 million in 2019, the principal amount invested in 1900 would be $66,059.19. This can be calculated by using the compound interest formula [tex]A=P(1+r)n[/tex]
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Help, please!
The answer is presented on the image, thank you!
Answer:
PQ = 3QR = 5EF = 10Step-by-step explanation:
You want to know the side lengths of the triangles shown if DE = 8.
Value of xSide DE is marked as x+6. If its length is 8, then we have ...
x +6 = 8
x = 2 . . . . . subtract 6
Side lengthsThe unknown side lengths are then ...
PQ = x+1 = 3
QR = x+3 = 5
EF = x+8 = 10
__
Additional comment
These are both 3:4:5 right triangles. The larger is twice the size of the smaller. You can guess this because a 3:4:5 right triangle is the only one with a side length of 4 and integer lengths for the other sides.
construct a pushdown automata that recognizes { wwr | w is a string over {0, 1} such that w does not contain 0110 as a substring }.
A pushdown automata that recognizes {wwr | w is a string over {0, 1} such that w does not contain 0110 as a substring} can be constructed as follows:
We construct the PDA in two stages:
First, we design a machine that accepts the language (0 + 1)*0110(0 + 1)*.
We can construct a machine that accepts this language as follows:
Initially, we push a marker $ onto the stack.
For each 0 we read, we push a symbol A onto the stack.
For each 1 we read, we remove a symbol A from the stack. When we read 01 in the input, we push B onto the stack. When we read 10 in the input, we replace a single symbol A on the stack with a B.
Finally, when we read 0110 in the input, we remove B from the stack if it is on top. If we reach the end of the input and the stack is empty, the machine accepts. Otherwise, it rejects.
Now, let us turn our attention to the problem at hand. We want to create a machine that accepts {wwr | w is a string over {0, 1} such that w does not contain 0110 as a substring}.
It is equivalent to constructing a PDA that accepts the language
L = { wwr | w is a string over {0, 1} and w does not contain 0110 as a substring}.
First, we divide the string w into two parts: a prefix and a suffix.
For w to be a word in L, the suffix must be the reverse of the prefix, and w cannot contain 0110 as a substring.Next, we try to use the PDA that accepts (0 + 1)*0110(0 + 1)* to ensure that w does not contain the substring 0110.
We maintain a buffer on the stack, and the input is processed one symbol at a time. Initially, we push $ onto the stack. If we read 0 or 1, we push the symbol A onto the stack.
If we read 01, we push B onto the stack. If we read 10, we replace an A with B. Finally, when we read 0110, we pop B from the stack. If we reach the end of the input and the stack is empty, we accept.
If we reach the end of the input and the stack is non-empty, we reject.
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16. Find the area AND perimeter of a rectangle that has a length of (5x²y) and a width of (3x²y). (Hint: draw a picture)
can u solve only perimeter
Answer:
Sure! The perimeter of a rectangle is calculated by adding the lengths of all four sides. Since the length of the rectangle is given as (5x²y) and the width is given as (3x²y), we can calculate the perimeter as follows:
Perimeter = 2 * Length + 2 * Width = 2 * (5x²y) + 2 * (3x²y) = 10x²y + 6x²y = 16x²y
So, the perimeter of this rectangle is 16x²y.
Step-by-step explanation:
5 Ahmid used the total number of people who bought a
hot dog and the total number of people who did not
buy a hot dog to make the relative frequency table
below. Does it provide evidence that there is an
association between buying a hot dog and buying a
drink at a baseball game? Explain why or why not.
Drink
No Drink
Total
Hot Dog
70.2%
29.8%
100%
No Hot Dog
38.5%
61.5%
100%
The frequency table shows that there is a relationship between buying a hot dog and buying a drink at a baseball game. The huge 70.2% is evidence of this.
What does the table show?The frequency table is meant to show the relationship between variables. Of all the values provided, the relationship with the highest percentage is 70.2%.
This shows that the number of people who purchased a hot dog while also purchasing a drink constituted the highest number. None of the figures come close to this one. So, there is a strong relationship between the variables.
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Find the value of x in a triangle, 142 degrees and 112 degrees
The value of x in the triangle can be found by using the fact that the sum of all angles in a triangle is 180 degrees. Simplifying the equation 142 degrees + 112 degrees + x = 180 degrees, we get x = 26 degrees.
To find the value of x in the triangle, we use the fact that the sum of all angles in a triangle is 180 degrees.
Let's call the third angle of the triangle "x".
Then, we have:
142 degrees + 112 degrees + x = 180 degrees
Simplifying this equation, we get:
x = 180 degrees - 142 degrees - 112 degrees
x = 26 degrees
Therefore, the value of x in the triangle is 26 degrees.
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9.
Find the values of x and y.
to
35 degrees
(i need
work shown please)
end answers should b x: 145
y: 35
Step-by-step explanation:
y is a corresponding angle to the 35 degree angle so y = 35°
'x' + the 35 degree angle form a straight line = 180 degrees
x + 35 = 180
x = 145°
Format your answer as needed
find the value of the determinants | 5 3 |
|7 9 |
The value of the determinants of the matrix | 5 3 | |7 9 | is 24
What is a Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns which is used to represent a mathematical object or a property of such an object.
Also, It provides two benefits: compact notation for describing sets of data and sets of equations as well as efficient methods for manipulating sets of data and solving sets of equations.
For the given matrix, the determinant Det is:
Det = (5*9) - (7*3)
So, we have
det. = 45 - 21
Evaluate the difference
det = 24
herefore the determinant is equal to 24
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HELP!!!
Write the word sentence as an inequality.
A number z
is no less than 9
Answer:
z ≥ 9
Step-by-step explanation:
z ≥ 9
(The number z is greater than or equal to 9)
...
you get an average rate of two visits per minute at your website. what is the probability that you will have at least one visit during a given minute?
The probability of at least one visit during a given minute is 86.47%.
Given that the average rate of visits per minute is two.
To find the probability of at least one visit during a given minute, we can use Poisson distribution.
Poisson distribution is a probability distribution that is used to determine the probability of a certain number of events occurring in a fixed time period when the events are rare and random.
The Poisson probability distribution is given by;
[tex]P(X=x) = (e^{-\lambda} \times \lambda ^x) / x![/tex]
Where; λ is the average rate of events, x is the number of events that occurred, and e is the base of the natural logarithm,
e ≈ 2.7183
We can find the probability of at least one visit in a minute using the complement rule.
The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
Therefore;
P(at least one visit) = 1 - P(no visit)P(no visit)
= P(X=0) = [tex](e^{-\lambda} \times \lambda^0) / 0![/tex] = [tex]e^{-\lambda}[/tex] = [tex]e^{-2}[/tex] = 0.1353
Therefore;
P(at least one visit) = 1 - P(no visit)
= 1 - 0.1353
= 0.8647 = 86.47%
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