Pete needs 10.5 ounces of turkey.
Step-by-step explanation:
Given,
Number of friends = 2
One for Pete.
Total sandwiches to be made = 2+1 = 3
Quantity of turkey in one sandwiches = 3.5 ounces
For finding the quantity of turkey for three sandwiches, we will multiply.
Turkey for 3 sandwiches = 3*3.5 = 10.5 ounces
Pete needs 10.5 ounces of turkey.
Keywords: multiplication, addition
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A culture increases by 500 bacteria every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be by after 24 hours?
Answer:
6500
Step-by-step explanation:
In 24 hours, there are 12 times 2 hours, so the bacteria count will increase by 500 twelve times. That is, the increase after 24 hours will be ...
12 × 500 = 6000 . . . bacteria
Since the starting number was 500, the total will be ...
500 + 6000 = 6500 . . . . bacteria after 24 hours
_____
If you like, you can compute the rate of change as 500 bacteria / (2 hours) = 250 bacteria/hour. Then the equation for the number is ...
bacteria = 500 + 250h . . . . . where h is the number of hours.
Filling in h=24, we get
bacteria = 500 + 250(24) = 500 +6000 = 6500 . . . . after 24 hours
Help!!!!!!! Thank you so much
Answer:
18] not a function; (1, 5), (1, -1)
19] is a function
Step-by-step explanation:
The graph of a function will pass the "vertical line test." That is, a vertical line will not intersect the graph at more than one point.
18] There are an infinite number of points where a vertical line will cross the graph twice. Two that are recognizable are the ones at the vertical extremes: (1, 5) and (1, -1). This relation is not a function.
__
19] None of the points on the graph are vertically aligned, so the relation is a function.
Sixty- five percent of men consider themselves knowledgeable football fans.
If 10 men are randomly selected, find the probability that exactly six of them will consider themselves knowledgeable fans.
a) 0.65 b) 0.069 c) 0.600 d) 0.238
Answer: d) 0.238
Step-by-step explanation:
We would assume binomial distribution for the number of men sampled. The formula for binomial distribution is expressed as
P(x =r) = nCr × q^(n - r) × p^r
Where
p represents the probability of success.
q represents the probability of failure.
n represents the number of samples.
From the information given,
n = 10
p = 65% = 65/100 = 0.65
q = 1 - p = 1 - 0.65 = 0.35
The probability that exactly six of them will consider themselves knowledgeable fans is expressed as P(x = 6). It becomes
P(x =6) = 10C6 × 0.35^(10 - 6) × 0.65^6
P(x =6) = 10C6 × 0.35^4 × 0.65^6
P(x =6) = 0.238
Final answer:
Option d) 0.238
Explanation:
To find the probability that exactly six out of 10 men consider themselves knowledgeable football fans, we can use the binomial probability formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
n = total number of trials (in this case, 10 men) k = number of successful trials (in this case, 6 knowledgeable fans) p = probability of success (in this case, 0.65) C(n, k) = combination of n items taken k at a time
Using the formula, we get:
P(X=6) = C(10, 6) * 0.65^6 * (1-0.65)^4
Calculating C(10, 6) which is 210, and then raising 0.65 to the power of 6 and (1-0.65) to the power of 4, simplifies to:
P(X=6) = 210 * 0.1160290625 * 0.1502625 = 0.238
After rounding to three decimal places, we get:
P(X=6) = 0.238
Therefore, the correct answer is (d) 0.238.
How would you define the following ad placed by a broker in NY, "Two-family home, $190,000, Call 212-123-4567"?
Answer:
The ad is about the price of a house which is sufficient for two families to live in it along with the contact details to purchase this house.
According to the ad, the total cost of the home is $190,000. It is sufficient for two families. It may be double story as well. To purchase this house, one can call at the given number which is 212-123-4567. This can be the original number or the format by the editor to show original number. Actual area of the house is not mentioned in the ad.
Suppose 60% of all college professors like tennis, 65% like bridge, and 50% like chess; 45% like any given pair of recreations.
(a) Should you be suspicious if told 20% like all three recreations?
(b) What is the smallest percentage who could like all three recreations?
Answer:
a) yes we should get suspicious
b) smallest percentage to like all three sports= 60
Step-by-step explanation:
Let the total professors be =100
n(tennis) = 60
n( bridge) = 65
n( chess)= 50
n( T U B) = 45, n(BU C) = 45, n(T UC)=45
n( T U B U C)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) + [tex]n(T\cap B\cap C)[/tex]
100 = 60 + 65 + 50 - 45-45-45 + [tex]n(T\cap B\cap C)[/tex]
[tex]n(T\cap B\cap C)[/tex] = 60
Therefore,
a) yes we should get suspicious
b) smallest percentage to like all three sports= 60
Final answer:
The given information suggests that we should be suspicious if told that 20% of all college professors like all three recreations. The smallest percentage who could like all three recreations is 0%.
Explanation:
(a) Yes, we should be suspicious if told that 20% of all college professors like all three recreations. This is because the given information states that 45% of college professors like any given pair of recreations. If 20% of them like all three, it means that the remaining 25% (45% - 20%) would have to like two recreations, which contradicts the given data.
(b) The smallest percentage who could like all three recreations is 0%. Since the information states that 50% of college professors like chess and 65% like bridge, it means that at most, 50% (the percentage who like chess) can like both chess and bridge. Therefore, there is no overlap between those who like chess and bridge, and those who like tennis. Hence, the smallest percentage who could like all three recreations is 0%.
If a current mortgage payment of $792 per month can be reduced to $578 per month by refinancing, how many months would you need to remain in the house to recoup refinancing charges of $3,784? (Round up to the nearest month.)
Answer:
[tex]Months =\frac{3784}{214 /month}=17.682months\approx 18 months[/tex]
As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months
Step-by-step explanation:
Notation
[tex]P_f =792[/tex] current mortgage payment
[tex]P_i = 578[/tex] reduced mortgage payment
R= 3784 represent the rfinancing charges
Solution to the problem
In order to solve this question we need to find first the difference between the two mortgage payments like this:
[tex]P_f- P_i = 792-578=214[/tex]
And then since the refinancing charges is $3784 we can find the number of months that we will need to remain in the house like this:
[tex]Months =\frac{3784}{214 /month}=17.682months[/tex]
As we can see after cancel the units we got 17.682 months that can be rounded up to approximately 18 months
What is GE ?
Enter your answer in the box.
_____units
Good evening ,
Answer:
GE = 10.Step-by-step explanation:
GE=2×ZE
Since ZE=XY then ZE=5
therefore GE=2×5=10.
:)
Write an equation of the line containing the given point and perpendicular to the given line:
(4,- 9); 2x+9y=5
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
2x+9y=5
9y = - 2x + 5
y = -2x/9 + 5/9
Comparing with the slope intercept form, slope = -2/9
If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (4,-9) is 9/2
To determine the intercept, we would substitute m = 9/2, x = 4 and y = -9 into y = mx + c. It becomes
- 9 = 9/2×4 + c = 18 + c
c = - 9 - 18 = - 27
The equation becomes
y = 9x/2 - 27
Which definition best describes Pythagorean triples? A. Sets of three whole numbers (a, b, and c) that satisfy the equation
B. Pairs of numbers, a and b, such that a2 = b2
C. Any three numbers, each of which is squared
D. Sets of three whole numbers (a, b, and c) that satisfy the equation
Answer:
Option C) Any three numbers, each of which is squared is correct
Step-by-step explanation:
By using Pythagorean Theorem:
Pythagorean theorem is also called as Pythagoras' theorem. It is a fundamental relation among the three sides of a right triangle.
It states that the length of the square of hypotenuse side is equal to the sum of the lengths of the squares of the opposite side and adjacent side.
[tex]a^{2}+b^{2}=c^{2}[/tex]
where c is the length of the hypotenuse side and a and b are the lengths of the opposite and adjacent sides of triangle's.
Therefore Option C) Any three numbers, each of which is squared is correct
Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem.
Explanation:Pythagorean triples are sets of three whole numbers (a, b, and c) that satisfy the equation a² + b² = c². This equation is derived from the Pythagorean theorem, which relates the lengths of the legs of a right triangle to the length of the hypotenuse. In a Pythagorean triple, the square of the larger numbers is equal to the sum of the squares of the smaller numbers. For example, the triplet (3, 4, 5) is a Pythagorean triple because 3² + 4² = 5² (9 + 16 = 25).
Tyrell's SAT math score was in the 64th percentile. If all SAT math scores are normally distributed with a mean of 500 and a standard deviation of 100, what is Tyrell's math score? Round your answer to the nearest whole number
Answer:
[tex]P(x < 535.8) = 0.64[/tex]
[tex]P_{64} = 535.8[/tex]
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 500
Standard Deviation, σ = 100
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.64
P(X<x) = 0.64
[tex]P( X < x) = P( z < \displaystyle\frac{x - 500}{10})=0.64[/tex]
Calculation the value from standard normal z table, we have, [tex]p(z<0.358) = 0.64[/tex]
[tex]\displaystyle\frac{x - 500}{100} = 0.358\\x = 535.8[/tex]
[tex]P(x < 535.8) = 0.64[/tex]
[tex]P_{64} = 535.8[/tex]
Tyrell's math score is 554.
Explanation:To find Tyrell's math score, we need to use the z-score formula. The z-score formula is given as z = (x - μ)/σ. In this case, we want to find x, so we rearrange the formula to solve for x: x = zσ + μ. Given that Tyrell's score is in the 64th percentile, we can use the z-score table to find the corresponding z-score. The z-score for the 64th percentile is approximately 0.355. Plugging this into the formula, we get: x = 0.355(100) + 500 = 53.55 + 500 = 553.55. Rounding to the nearest whole number, Tyrell's math score is 554.
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A running back was the MVP (most valuable player) in 0.14 of the first 50 Super Bowls. A. What percent of the MVPs were running backs? % were running backs. B. What fraction of the MVPs were not running backs? Were not running backs.
Answer:
A. 14%.
B. [tex]\frac{43}{50}[/tex]
Step-by-step explanation:
We have been given that a running back was the MVP (most valuable player) in 0.14 of the first 50 Super Bowls.
A. To find the percent, when the MVPs were running backs, we need to convert 0.14 into percent by multiplying by 100 as:
[tex]0.14\times 100=14\%[/tex]
Therefore, 14 percent of the MVPs were running backs.
B. To find the fraction of the MVPs were not running backs, we will subtract 0.14 from 1 to find the MVPs, who were not running backs. Finally, we will convert the answer into fraction as:
[tex]1-0.14=0.86[/tex]
Now, we will multiply and divide 0.86 by 100 as:
[tex]0.86\times \frac{100}{100}=\frac{86}{100}[/tex]
Reduce the fraction by dividing numerator and denominator by 2:
[tex]\frac{43}{50}[/tex]
Therefore, [tex]\frac{43}{50}[/tex] of the MVPs were not running backs.
14% of the MVPs in the first 50 Super Bowls were running backs. Yet, 43 out of 50 MVPs (or 86%) were not running backs.
Explanation:The running back was the MVP in 0.14 of the first 50 Super Bowls according to the question. To find the percent of the MVPs that were running backs, we simply convert the 0.14 to percentage by multiplying it by 100. Hence, 14% of the MVPs were running backs.
For the fraction of the MVPs that were not running backs, we need to calculate the remaining part not covered by the running backs. Given as 1 (entirety) minus 0.14 gives 0.86. In fraction terms, this is same as 86/100 which simplifies to 43/50.
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Yuvraj planned to give a party to 24 people. He ordered food in separate packages for each of the 24 people. But only 15 people turned up and had their food. What percentage of food was left?
The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 500 feet of fencing available, what is the maximum possible area of the corral?
Answer:
[tex]A= 125*250=31250 ft^2[/tex]
Step-by-step explanation:
Let's define some notation first :
w= width , l = length , A= Area, P perimeter
For this case we want to maximize the Area given by this function:
A= l w (1)
With the following restriction P=500 ft
We know that the perimeter on this case is given by:
[tex]P=2w +l[/tex]
Since they are using the creek as one side.
So then we have this:
[tex]500 =2w +l[/tex] (2)
Now we can solve w in terms of l from eqaution (2) and we got:
[tex]w=\frac{500-l}{2}[/tex] (3)
And we can replace this condition into equation (1) like this:
[tex]A= \frac{500-l}{2} l =250l - \frac{1}{2} l^2[/tex]
And we can maximize this function derivating respect to l and we got:
[tex]\frac{dA}{dl}= 250 -l=0[/tex]
And then we got that [tex]l=250[/tex]
And if we solve for w from equation (3) we got:
[tex]w=\frac{500-250}{2}=125[/tex]
And then the dimensions would be:
[tex] l =250ft , w=125ft[/tex]
And the area would be:
[tex]A= 125*250=31250 ft^2[/tex]
To maximize the area of the corral, we can solve a mathematical optimization problem. By expressing the length in terms of the width, we can find the derivative of the area formula and set it to zero. Substituting the resulting value of the width into the area formula gives us the maximum area.
Explanation:To find the maximum area of the corral, we need to determine the dimensions of the rectangle. Let's assume the length of the corral is L and the width is W.
Since one side of the corral is the creek, we only need to use fencing for the other three sides. This implies that 2W + L = 500 (since there are two widths and one length that need fencing).
To maximize the area, we can express L in terms of W using the formula L = 500 - 2W and substitute it into the area formula A = LW. Simplifying, we get A = W(500 - 2W). To find the maximum area, we can take the derivative of A with respect to W, set it equal to zero, and solve for W. The resulting value of W can be substituted back into the equation to find the corresponding value of L. The maximum area is obtained by multiplying these two dimensions together.
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If y=sin(x-sinx), what is the smallest positive value of x for which the tangent line is parallel to the x-axis
(a) 1.677
(b) 2.310
(c) 3.142
(d) 3.973
(e) 6.283
Answer:
Option b ) 2.310
Step-by-step explanation:
Given that the function is
[tex]y = sin (x-sinx)[/tex]
For finding when the tangent is parallel to x axis, we must find the least positive value of x for which y' i.e. derivative =0
Differentiate y with respect to x using chain rule.
[tex]y' = cos(x-sinx) * (1-cosx)[/tex]
Equate this to 0
Either one factor should be zero.
[tex]cos(x-sinx)=0\\x-sinx =\frac{\pi}{2} \\[/tex]
x=2.31 satisfies this
For the other root,
[tex]1-cos x =0\\cos x =1\\x =0\\[/tex]
Since positive least value is asked we can say
x =2.310
Option b
The auditorium at P.S 104 has 28 rows in all each consists of 95 unfortunately, 30 seats are broken calculate the total number of seats that are broken in the auditorium
Answer:
30 seats
Step-by-step explanation:
The problem statement tells you 30 seats are broken.
___
It does not say 30 seats in each row are broken.
Need some help with this
Answer:
Step-by-step explanation:
The total number of outcomes the two fair number cubes are thrown is 36. This can be seen by counting the outcomes shown on the table.
a) for a sum of 4, there are only 3 possible outcomes. They are 3,2 2,2 and 1,3
Therefore, the probability of getting a sum of 4 will be
3/36 = 1/12
b) for a sum of 5, there are only 4 possible outcomes. They are 4,1 3,2 2,3 and 1,4
Therefore, the probability of getting a sum of 4 will be
4/36 = 1/9
c)for a sum of 6, there are only 5 possible outcomes. They are 5,1 4,2 3,3 2,4 and 1,5
Therefore, the probability of getting a sum of 6 will be
5/36 = 5/36
The probability that the sum of the results of the throw is 4,5 or 6 would be
1/12 + 1/9 + 5/36 = (3 + 4 + 5)/36 = 12/36 = 1/3
What is the value of cos A?
Answer:
The answer to your question is cos A = [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Process
1.- Write the formula
[tex]cos A = \frac{adjacent side}{hypotenuse}[/tex]
2.- Identify the legs of the triangle
opposite side = 12
adjacent side = 9
hypotenuse = 15
3.- Substitute the values in the formula
[tex]cos A = \frac{9}{15}[/tex]
4.- Simplification and result
[tex]cos A = \frac{3}{5}[/tex]
Explanation of finding the value of cos A using trigonometric identities and scalar products.
Cosine function: The value of cos A can be determined using trigonometric identities. For example, from the given expressions like cos 4A=8cos^4A-8cos^2A+1, we can find the value of cos A for specific angles.
Trigonometric identities: By manipulating the given equations and using trigonometric relationships like 1 - cos A = 2sin^2A, you can solve for cos A for different angles.
Scalar products: Understanding the concept of scalar products involving cosine functions like AB cos(θ) will help in applying trigonometry in real-world applications.
HELP ASAP PLEASE!!!!
The image shows the rational equation from part A with an incorrect solution process that a student performed. Explain the error the student made, and give the correct solution.
Only problem is with the simplifying.
We all know that 5/5 = 1, it is natural to assume (x+a)/(x+a) is also 1, but in some cases where x+a=0, it is undefined. In this equation, where they simplify (x-2) and (x-6), you must say that x is not 2 nor 6 or, you just delete 0/0 which is undefined.
Therefore the only solution would be x=-1
The error that the student made in the rational equation simplification is that; She made 6 and -1 to be a solution but 6 is not a solution but only x = -1 because 6 makes the function undefined
Simplifying Rational EquationsFrom the simplification of the rational equation, the solution the person got is; x = 6 or -1
Now, when we put 6 for x in the rational equation, it is discovered that the denominator becomes zero for two of the expressions.
Now, when the denominator of a fraction is zero, that fraction is said to be undefined.
Whereas when x = -1, we don't get an undefined function. Thus, the mistake the student made is that 6 is not a solution but only x = -1
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Oscar has a piece of pie would that is 9‘ x 9‘ explain how we can divided into two smaller pieces of plywood would the area of the smaller pieces equal to the area of the larger piece
Answer:
1. with the aid of a saw
2.No
Step-by-step explanation:
A. The 9‘ x 9‘ can be divided into two with the aid of a saw .
we have to take into account the area of the shape wic 9'x9'. and then saw the piece at the middle.
b.there are two sides to the second answer
1. the area of the smaller pieces will be smaller than the area of the larger piece
2. when the smaller pieces are placed side by side aain , tere area combined together will be the same as the original piece
Answer:
Part A. Using a handsaw.
Part B. Yes, the area of the two smaller pieces together equal the are of the large piece
Step-by-step explanation:
Part A. Explain how Oscar can divide it into two smaller pieces of plywood?
He can use a handsaw and cut the plywood in two smaller pieces of several measures, not necessarily the two smaller pieces need to be equal.
Part B. Would the area of the smaller pieces equal the area of the large piece?
Yes, the area of the two smaller pieces together equal the are of the large piece.
i. Let's suppose we have two pieces of 4.5 feet by 9 feet, then the combined area of these two pieces would be:
A = 4.5 *9 + 4.5 * 9
A = 40.5 + 40.5 = 81 ft² that is the same than 9 * 9 = 81 ft²
ii. Now let's suppose we divide the plywood into a piece of 6 ft by 9 ft and a second one of 3 ft by 9 ft, then the combined area of these two pieces would be:
A = 6 * 9 + 3 * 9
A = 54 + 27 = 81 ft² that is the same than 9 * 9 = 81 ft²
iii. Finally, let's suppose we divide the plywood into a piece of 1 ft by 9 ft and a second one of 8 ft by 9 ft, then the combined area of these two pieces would be:
A = 1 * 9 + 8 * 9
A = 9 +72 = 81 ft² that is the same than 9 * 9 = 81 ft²
What is the average rate of change of the function on the interval from x = 0 to x = 5 f(x)=
1/2(3)x
What is the average rate of change of the function on the interval from x = 0 to x = 5 ; f(x)= 1\2 (3)^x
Answer:
Average rate of change of the function on the interval from x = 0 to x = 5 is 24.2
Solution:
Given function is:
[tex]f(x) = \frac{1}{2}(3^x)[/tex]
We have to find the average rate of change of function from x = 0 to x = 5
The formula for average rate of change can be expressed as follows:
[tex]{A\left( x \right) = \frac{{f\left( b \right) - f\left( a \right)}}{{b - a}}}[/tex]
So for rate of change of function from x = 0 to x = 5 is:
[tex]{A\left( x \right) = \frac{{f\left( 5 \right) - f\left( 0 \right)}}{{5 - 0}}}[/tex]
Let us find f(0) and f(5)
To find f(0), substitute x = 0 in f(x)
[tex]f(0) = \frac{1}{2}(3^0) = \frac{1}{2}[/tex]
To find f(5), substitute x = 5 in f(x)
[tex]f(5) = \frac{1}{2}(3^5) = \frac{1}{2}(243) = \frac{243}{2}[/tex]
Therefore,
[tex]A(x)=\frac{\frac{243}{2}-\frac{1}{2}}{5-0}=\frac{242}{\frac{2}{5}}=\frac{242}{2} \times \frac{1}{5}=24.2[/tex]
Therefore average rate of change of the function on the interval from x = 0 to x = 5 is 24.2
A recent survey showed that 102 adults out of a sample of 400 do not like cold weather. However, 115 of those studied said that they had interest in taking skiing lessons. Based on this sample, if an adult is chosen at random, what is the probability that he or she has no desire to take skiing lessons? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that a randomly chosen adult from the survey has no desire to take skiing lessons is 57/80, or as a decimal, 0.7125.
Out of a sample of 400 adults, 115 expressed an interest in taking skiing lessons. Therefore, to find the number of adults who have no interest in skiing lessons, we subtract the number interested (115) from the total number surveyed (400).
The calculation is as follows: 400 - 115 = 285 adults who have no interest in taking skiing lessons. The probability that a randomly selected adult has no desire to take skiing lessons is the number of adults with no interest divided by the total number surveyed. This gives us:
Probability = (Number of adults with no desire to take skiing lessons) / (Total number of adults surveyed)Probability = 285 / 400
To simplify this fraction, we find that both numbers are divisible by 5:Probability = 57 / 80
If we want to express this as a decimal rounded to the nearest millionth, we perform the division:
Probability = 0.7125
This result is already rounded to the fourth decimal place, which is more precise than rounding to the nearest millionth.
someone please help me with this math problem quickly!
Answer:
(fоgоh)(x)=2x³+1
Step-by-step explanation:
Function composition is an operation where two functions, say f(x) and g(x), a new function h(x)=(fоg)(x)=f(g(x)) is generated. In this operation, the function g is applied to the result of the function f. Hence, function f:X→Y and g:Y→Z are joined to form a new function h:X→Z
Given [tex]f(x)=x+1[/tex]
[tex]g(x)=2x[/tex]
[tex]h(x)=x^{3}[/tex]
(fоgоh)(x)=[tex]f(g(h(x)))[/tex]
=[tex]f(g(x^{3}))[/tex]
=[tex]f(2x^{3})[/tex]
=2x³+1
If 15 of the students are male and 18 of the students are female in a mathclass, what fractional part of the class is female?
Answer:
6/11
Step-by-step explanation:
Assuming all students are accounted for, the fraction that is female is ...
female/total = 18/(15+18) = 18/33 = 6/11
The speedometer in Kevin's car reads in both miles/hour and kilometers/hour. What information is needed to convert between these two units?a) the number of miles in 1 kilometerb) the number of kilometers that are traveled in 1 hourc) the number of miles that are traveled in 1 hourd) the number of hours per 1 kilometer
Answer:
a) the number of miles in 1 kilometer
Step-by-step explanation:
The car converts from miles/hour to kilometers/hour, if we see the time measurement (hours) it stays the same in both units.
So to make the conversion it is enough to know how many miles are in one kilometer.
For example, lets convert 10miles/hour to kilometers/hour.
there are 0.621371 miles in 1 kilometer, so if we divide 10miles/hour by 0.621371 we get kilometers/hour units:
[tex]\frac{10miles}{hour} (\frac{1kilometer}{0.621371miles} )=16.0934\frac{kilometers}{hour}[/tex]
Thus to make the conversion between the two units is needed the number of miles in 1 kilometer.
Clara visita the aquarium while on vacation. The aquarium is 2 1/2 miles from her hotel. She walks 1/4 mile to the bus stop, takes the bus for 1 3/4 miles, and walks the rest of the way to the aquarium. How far did Clara walk after getting off the bus?
Answer:
Step-by-step explanation:
The aquarium is 2 1/2 miles from her hotel. Converting 2 1/2 miles into improper fraction, it becomes 5/2 miles.
She walks 1/4 mile to the bus stop, takes the bus for 1 3/4 miles. Converting 1 3/4 miles to improper fraction, it becomes 7/4 miles. Therefore the total distance covered by walking and boarding the bus would be
1/4 + 7/4 = 8/4 = 2 miles
She walks the rest of the way to the aquarium. Therefore, the distance that Clara walked after getting off the bus would be
5/2 - 2 = 1/2 miles
Determine whether the degree of the function is even or odd and whether the function itself is even or odd.
Answer:
There are Even, Odd and None of them and this does not depend on the degree but on the relation. An Even function: [tex]f(-x)=f(x)[/tex] And Odd one: [tex]-f(x)=f(-x)[/tex]
Step-by-step explanation:
1) Firstly let's remember the definition of Even and Odd function.
An Even function satisfies this relation:
[tex]f(-x)=f(x)[/tex]
An Odd function satisfies that:
[tex]-f(x)=f(-x)[/tex]
2) Since no function has been given. let's choose some nonlinear functions and test with respect to their degree:
[tex]f(x)=x^{2}-4, g(x)= x^{5}+x^{3}[/tex]
[tex]f(x)=x^2 -4\Rightarrow f(-x)=(-x)^{2}-4\Rightarrow f(-x)=x^{2}-4\therefore f(x)=f(-x)[/tex]
[tex]g(-x)=-(x^{5}+x^{3})\Rightarrow g(-x)=-x^{5}-x^{3}\Rightarrow g(-x)=-g(x)[/tex]
3) Then these functions are respectively even and odd, because they passed on the test for even and odd functions namely, [tex]f(-x)=f(x)[/tex] and [tex]-f(x)=f(x)[/tex] for odd functions.
Since we need to have symmetry to y axis to Even functions, and Symmetry to Odd functions, and moreover, there are cases of not even or odd functions we must test each one case by case.
Final answer:
The degree of a polynomial indicates whether it is even or odd based on the highest power of x. Even functions exhibit symmetry across the y-axis, while odd functions show symmetry with respect to the origin. The derivative of an even function is odd due to the horizontal flip property during differentiation, and the integral of an odd function over a symmetric interval is zero.
Explanation:
To determine whether the degree of a function is even or odd, and whether the function itself is even or odd, one must understand the definitions and properties of even and odd functions. An even function satisfies the property f(-x) = f(x), implying symmetry across the y-axis. A classic example is the cosine function, cos x, or any power function x^n where n is an even number. Conversely, an odd function is defined by the property f(-x) = -f(x), indicating symmetry with respect to the origin. The sine function, sin(x), and x^n where n is odd, are examples of odd functions.
Regarding derivatives, it is interesting to note that the derivative of an even function results in an odd function due to the horizontal flip property of the derivative. This is because differentiation involves a limit process that inherently flips the sign of any even function's symmetric components, resulting in an odd function.
Moreover, both even and odd functions display specific behaviors when integrated over symmetric intervals: the integral of an odd function is zero due to its antisymmetric nature while even functions do not necessarily share this property. For instance, when considering a function expressed as a product, such as f(x) = (x^3 - 3x)e^{-x^2}, where one function is odd and the other even, the resulting function will be odd, based on the product of their respective eigenvalues with respect to the inversion operator.
In triangle abc, bc=4cm, ad=3cm. The triangle abc moves upward at the speed of 4cm per seconds. What is the area swept by the triangle in three seconds?
Answer:
Step-by-step explanation:
Area Of Triangle And Rectangle
Given a triangle of base b and height h (perpendicular to b), the area can be computed by
[tex]\displaystyle A=\frac{bh}{2}[/tex]
A rectangle of the same dimensions has an area of
[tex]A=bh[/tex]
We have a triangle of base 3 cm and a height of 4 cm. Its area is
[tex]\displaystyle A=\frac{(3)(4)}{2}=6\ cm^2[/tex]
That triangle moves upward at 4 cm per second for 3 seconds. It means that the triangle 'sweeps' upwards three times its height forming a rectangle of base 3 cm and height 12 cm. The area of the swept area is
[tex]A=(3)(12)=36\ cm^2[/tex]
The triangle stays in the top of this rectangle, so its area is part of the total swept area:
Total swept area = 6 + 36 = [tex]42\ cm^2[/tex]
Find the four vertices of the cube, starting with (1, 1, 1), that form a regular tetrahedron. Confirm your answer by finding the length of an edge and explaining why all edges have the same length.
Answer:
the vertices (1,1,1), (1,0,0), (0,1,0) and (0,0,1) form a tetrahedron. The length of each side is √2
Step-by-step explanation:
The cube has 8 vertices: (0,0,0), (1,1,0), (0,1,0), (1,0,0), (0,0,1), (0,1,1), (1,0,1), (1,1,0) and (1,1,1). The first four of them are the vertices of the bottom square and the last four are the vertices of the upper square of the cube.
We will take two non-consecutive vertices from each square. For the upper one we take (1,1,1) as the problem suggests, and (0,0,1), which is not consecutive from (1,1,1) and its distance is √2. The non consecutive vertices from the bottom square respect to the vertex (1,1,1) are (0,0,0), (0,1,0) and (1,0,0).
We take (0,1,0) and (1,0,0) because (0,0,0) is consecutive from (0,0,1) hence its distance from it is not √2, but 1.
Note that we take (1,1,1), (0,0,1), (0,1,0) and (1,0,0). If we take any two vertices and compare them toguether we will notice that both of those vertices differ in two places and are equal in the other. In the places where they differ one has the value 1 and the other 0, so the distance between those vertices is √(1²+1²) = √2.
Thus, the vertices (1,1,1), (1,0,0), (0,1,0) and (0,0,1) form a tetrahedron.
Final answer:
Explaining how to find the vertices of a cube forming a regular tetrahedron and confirming why all cube edges have the same length.
Explanation:
To find the four vertices of a cube that form a regular tetrahedron starting with (1, 1, 1), we can consider the cube's diagonals. The vertices of the regular tetrahedron can be located at the center of each face of the cube, which are at coordinates (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2).
The length of an edge of a cube is the distance between two adjacent vertices. To calculate the edge length, we can use the distance formula. Since all edges of a cube connect two adjacent vertices, they have the same length due to the cube's symmetry.
Therefore, all edges of the cube have the same length because each connects two adjacent vertices with equal coordinates.
The random variable X, representing the number of cherries in a cherry puff, has the following probability distribution:x: 4 - 5 - 6 - 7 P(X=x): 0.2 - 0.4 - 0.3 - 0.1 (a) Find the mean μ and the variance σ² of X.(b) Find the mean [tex]\mu_{\bar X}[/tex] and the variance [tex]\sigma^2_{\bar X}[/tex] of the mean [tex]\bar X[/tex] for random samples of 36 cherry puffs.(c) Find the probability that the average number of cherries in 36 cherry puffs will be less than 5.5.
Answer:
Step-by-step explanation:
Given is the probability distribution of a random variable X
X 4 5 6 7 Total
P 0.2 0.4 0.3 0.1 1
x*p 0.8 2 1.8 0.7 5.3
x^2*p 3.2 10 10.8 4.9 28.9
a) E(X) = Mean of X = sum of xp = 5.3
[tex]Var(x) = 28.9-5.3^2=0.81[/tex]
Std dev = square root of variance = 0.9
------------------------------------
b) For sample mean we have
Mean = 5.3
Variance = var(x)/n = [tex]\frac{0.81}{{36} } \\=0.0225[/tex]
c) [tex]P(\bar X <5.5)\\= P(Z<\frac{5.5-5.3}{\sqrt{0.0225} } \\= P(Z<1.33)\\=0.908[/tex]
The mean and the variance from the data about the cherries will be 5.3 and 0.81.
How to calculate the mean and variance?The required mean from the information given will be:
= (4 × 0.2) + (5 × 0.4) + (6 × 0.3) + (7 × 0.1)
= 0.8 + 2.0 + 1.8 + 0.7
= 5.3
The variance will be calculated thus:
= (4² × 0.2) + (5² × 0.4) + (6² × 0.3) + (7² × 0.1) - (5.3)²
= 3.2 + 10 + 10.8 + 4.9 - (5.3)²
= 0.81
The variance is 0.81.
The probability that the average number of cherries in 36 cherry puffs will be less than 5.5 will be:
= P(x = 4( + P(x = 5)
= 0.2 + 0.4
= 0.6
Learn more about mean on:
https://brainly.com/question/1136789
Martina creates the graph of function g by applying a transformation to function f.
f(x) = 4x-2
g(x) = 4x+7
Which transformation did Martina apply?
A.a vertical shift of 9 units down
B.a vertical shift of 9 units up
C. a horizontal shift of 9 units left
D. a horizontal shift of 9 units right
Answer:
B.a vertical shift of 9 units up
Step-by-step explanation:
Given [tex]f(x) = 4x-2\\g(x) = 4x+7[/tex]
[tex]g (x) = f (x) + k[/tex]
It means shifting [tex]f (x)\ k[/tex] unit vertically.
Now, we will find the value of [tex]k[/tex] for the given function
[tex]g(x) = 4x+7\\\\add\ 2\ and\ subtract\ 2\\\\g(x) = 4x+7+2-2\\g(x) = 4x-2+9\\\\We\ have\ f(x)=4x-2\\\So,\ g(x)=f(x)+9[/tex]
[tex]k=9[/tex]
Hence, vertical shift of 9 units.
Answer:
C. a horizontal shift of 9 units left
Step-by-step explanation:
Look at this helpful chart:
Vertical Translations
translation up k units: g(x) = f(x) + k, where k > 0
translation down k units: g(x) = f(x) – k, where k > 0
Horizontal Translations
translation left k units: g(x) = f(x + k), where k > 0
translation right k units: g(x) = f(x – k), where k > 0
The change happening in Martina's graph is therefore a horizontal translation to the left.