Answer:
can you elaborate
Step-by-step explanation:
I think you're talking about the slope formula so I'll tell you that y=x+b
y2-y1/x2-x1 (x1,y1) is the first coordinate and (x2,y2) is the second coordinate
Answer:
Step-by-step explanation:
1 ) the slope formula for the line passes by : A(XA,YA) B(XB,YB)
the slope is : (YB - YA)/(XB -XA)
2) y intercept for the line when : x = 0
Consider the following information.
1 hour = 3.6 · 103 seconds
1 day = 24 hours
1 year = 3.65 · 102 days
Use scientific notation to calculate the number of seconds in 3 days.
Answer:
2.592×10^5 seconds
Step-by-step explanation:
[tex]3\,days\cdot\dfrac{24\,h}{1\,day}\cdot\dfrac{3.6\cdot 10^3\,s}{1\,h}=3\cdot 24\cdot 3.6\cdot 10^3\,s=2.592\cdot 10^5\,s[/tex]
Answer:
Corrected answer is 8.64 x 10^4 seconds in one day
Step-by-step explanation:
Given triangle ABC with coordinates A(−4, 4), B(−4, 1), and C(−6, 0), and its image A′B′C′ with A′(0, 0), B′(−3, 0), and C′(−4, −2), find the line of reflection.
The line of reflection is at y=
Answer:
y = x + 4
Step-by-step explanation:
The line of reflection is the perpendicular bisector of segment AA', so passes through point (A+A')/2 = (-2, 2) and is perpendicular to the line through A and A'. That line is y = -x, so the point-slope equation of the line of reflection is ...
y = 1(x -(-2)) +2
y = x +4
The line of reflection between triangle ABC and its image A'B'C' is y = -x. The point-slope equation of the line of reflection is y = x+4.
Explanation:To find the line of reflection between triangle ABC and its image A'B'C', we can observe that the corresponding points have the same x-coordinates and their y-coordinates are negatives of each other. Since the line of reflection is the perpendicular bisector of the segment joining each original point and its image, we can use the coordinates of two corresponding points to find the equation of the line. In this case, we can use points A and A', and points B and B' to determine the line of reflection.
Using the coordinates A(-4, 4) and A'(0, 0), we can calculate the slope of the line as (0 - 4) / (0 - (-4)) = -1. The midpoint between A and A' is (-2, 2), which lies on the line. So, the equation of the line is y = -x.
Similarly, using the coordinates B(-4, 1) and B'(-3, 0), we can calculate the slope as (0 - 1) / (-3 - (-4)) = 1. The midpoint between B and B' is (-3.5, 0.5), which also lies on the line y = x. Therefore, the line of reflection is y = -x.
So, the point-slope equation of the line of reflection is:
y = 1(x -(-2)) +2
y = x +4
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The graph for reflection is given below:
Suppose that five ones and four zeros are arranged around a circle. Between any two equal bits you insert a 0 and between any two unequal bits you insert a 1 to produce nine new bits . Then you erase the nine original bits. Show that when you iterate this procedure , you can never get nine zeros . [Hint:work backward, assuming that you did end up with nine zeros.]
Answer:
Using backward reasoning we want to show that "We can never get nine 0's".
Step-by-step explanation:
Basically in order to create nine 0's, the previous step had to have all 0's or all 1's. There is no other way possible, because between any two equal bits you insert a 0.
If we consider two cases for the second-to-last step:
There were 9 0's:
We obtain nine 0's if all bits in the previous step were the same, thus all bit were 0's or all bits were 1's. If the previous step contained all 0's, then we have the same case as the current iteration step. Since initially the circle did not contain only 0's, the circle had to contain something else than only 0's at some point and thus there exists a point where the circle contained only 1's.
There were 9 1's:
A circle contains only 1's, if every pair of the consecutive nine digits is different. However this is impossible, because there are five 1's and four 0's (we have an odd number of bits!), thus if the 1's and 0's alternate, then we obtain that 1's that will be next to each other (which would result in a 1 in the next step). Thus, we obtained a contradiction and thus assumption that the circle contains nine 0's after iteratins the procedure is false. This then means that you can never get nine 0's.
To summarize, in order to create nine 0's, the previous step had to have all 0's or al 1's. As we didn't start the arrange with all 0's, the only way is having all 1's, but having all 1's will not be possible in our case since we have an odd number of bits.
Iliana multiplied 3p – 7 and 2p2 – 3p – 4. Her work is shown in the table. The expression (3 p minus 7)(2 p squared minus 3 p minus 4) is shown above a table with 3 columns and 2 rows. First column is labeled 2 p squared, second column is labeled negative 3 p, the third column is labeled negative 4. First row is labeled 3 p with entries 6 p cubed, negative 9 p squared, negative 12 p. Second row is labeled negative 7 with entries negative 14 p squared, 21 p, 28. Which is the product? 6p3 + 23p2 + 9p + 28 6p3 – 23p2 – 9p + 28 6p3 – 23p2 + 9p + 28 6p3 + 23p2 – 9p + 28
Answer:
the answer is C
Step-by-step explanation:
Answer:
The correct option is C) [tex]6p^3-23p^2+9p+28[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]3p - 7[/tex] and [tex]2p^2 - 3p - 4[/tex]
According to the provided information the table will be like this.
[tex]2p^2[/tex] -3p -4
3p [tex]6p^3[/tex] -9p² -12p
-7 [tex]-14p^2[/tex] 21 p 28
The above table shows the terms after multiplication.
To find the product you just need to add the terms as shown.
[tex]6p^3-9p^2-12p-14p^2+21p+28[/tex]
[tex]6p^3-9p^2-14p^2-12p+21p+28[/tex]
[tex]6p^3-23p^2+9p+28[/tex]
Hence, the product is [tex]6p^3-23p^2+9p+28[/tex].
You can verify this by product as shown.
[tex]3p-7(2p^2-3p -4)[/tex]
[tex]6p^3-9p^2-12p-14p^2+21p+28[/tex]
[tex]6p^3-23p^2+9p+28[/tex]
Hence, the correct option is C) [tex]6p^3-23p^2+9p+28[/tex]
Two trains travel at right angles to each other after leaving the same train station at the same time. Two hours later they are 65.30 miles apart. If one travels 14 miles per hour slower than the other, what is the rate of the slower train? (Round your answer to the nearest integer)
Answer:
15 miles per hour is the speed of the slower train.
Step-by-step explanation:
As given in the figure attached,
Let the speed of train 1 is v and train 2 is u.
Therefore, distance traveled in 2 hours by train 1 will be = 2v miles
and distance traveled by train 2 will be = 2u miles
Now we can see in the figure a right angle triangle is formed by the two trains.
AB² + BC² = AC²
(2v)² + (2u)²= (65.30)²
4v² + 4u² = 4264.09
Now we divide this equation by 4
v² + u² = 1066.02
If speed of the slower train is v miles per hour then as per statement of the question.
u = v - 14
v = u + 14
By putting the value of v in the equation
(u + 14)² + u² = 1066
u² + 196 + 28u + u² = 1066
2u² + 28u + 196 = 1066
2u² + 28u + 196 - 1066 = 0
2u² + 28u - 870 = 0
By diving this equation by 2
u² + 14u - 435 = 0
u² + 29u - 15u - 435 = 0
u(u + 29) - 15(u + 29) = 0
(u + 29)(u - 15) = 0
u = -29, 15
Since speed can not be with negative notation so u = 15 miles per hour will be the speed.
Therefore, 15 miles per hour is the speed of the slower train.
help fast thanks In the figure, prove that m∥n
Complete the proof below by providing the reasons in each blank.
Blank # 1
Blank # 2
Blank # 3
Answer:
See below
Step-by-step explanation:
a + 133 = 180 because they are supplementary angles. (adjacent angles that form a straight angle)
a = 47 (you substract 133 at each side of the previous equation, leaving that a = 47)
m || n Since "a" measure the same as the angle in the figure that measures 47 both are corresponding angles, therefore m and n are parallels
Answer:
Step-by-step explanation:
It is called adjacent angles to all pairs of angles (2 angles) that are consecutive (that is, have the vertex and one side in common) and supplementary ( the sum of both angles results in 180 °; that is, a straight angle). Graphically, two opposite semi-lines are observed. You can see two adjacent angles in the image.
A case of consecutive angles is shown between a"" and 133 °, because they form a straight angle and are separated by a common side. Then "a" and 133 ° add up to 180 °. In this way you can know what is the value of "a".
a+133°=180°
a=180°-133°
a=47°
The relative position of the angles with respect to the straight lines makes those angles receive specific names. Thus, it is called corresponding angles to those that are located on the same side of the parallels and on the same side of the transversal. These angles are equal.
Note that the other angle given as data is 47 °. This angle has the same value as "a" and as both angles are on the same side of the transverse, so that they are corresponding m must be parallel to n.
Mrs. Grundy has two children. Given that Mrs. Grundy has at least one child born on a Monday, what is the probability that both her children were born on Mondays?
Answer: Ok, the chanche of both children were born on a monday is [tex]\frac{1}{7}[/tex]
Step-by-step explanation: Well, we alredy know that one of her children was born on a monday, when they ask the probability of both children were born on a monday, we only need to see the case of the second kid.
So, the week has 7 days, ence the probability for each day (in this case a monday) is 1/7.
Consider the numbers 0, 10, 20, 30, and 40. Multiply each by 4 and compare the result to 60 to determine into which of the following intervals the answer to the question "What number can you multiply by 4 and then add 8 to the product to get 60?" should fall.
Select the interval into which the answer should fall.
a) 0 to 10
b) 10 to 20
c) 20 to 30
d) 30 to 40
Answer:
b) 10 to 20
Step-by-step explanation:
You have to multiply each of the given numbers by 4, and add 8 to that result.
So:
0*4+8 = 810*4+8 = 4820*4+8 = 8830*4+8 = 12840*4+8 = 168And 60 is between the result of 10 and 20, so that's the interval you have to select.
The correct answer is b) 10 to 20
What is the length of Line segment A C? Round to the nearest tenth. Triangle A B C is shown. Angle A C B is 90 degrees and angle B A C is 55 degrees. The length of C B is 15 meters. 10.5 m 12.3 m 18.3 m 21.4 m
Answer:
10.5
Step-by-step explanation:
got it on the test
The length of line segment AC in triangle ABC is 12.3 meters, derived using the sine function and the given angle and side.
Explanation:To find the length of Line segment AC in the given right angle triangle ABC, we can use the trigonometry functions. Since we are given the length of side CB and the measure of angle BAC, we can apply the sine function. The sin of an angle in a right angle triangle is the length of the opposite side (which in this case is the length of AC we're trying to find) divided by the length of the hypotenuse (which in this case is length CB = 15 m).
So, sin(55 degrees) = Length of AC / 15 m. Solving this equation for Length of AC produces: Length of AC = 15 m * sin(55 Degrees). Plugging in the value of sin(55 degrees) approximately as 0.819 gives a Length of AC approximately equal to 12.3 m. "So the length of the line segment AC is 12.3 m".
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Meg constructed triangle POQ and then used compass and straight edge to accurately construct line segment OS, as shown in the figure below. Which could be a measure of POS and angle POQ?
Answer:
The answer is C
Step-by-step explanation:
The measurement of angle POS is 20 and POQ is 40
OS is an angle bisector of ∠POQ. This means it splits ∠POQ into two congruent pieces.
This tells us that ∠POS+∠SOQ = ∠POS+∠POS = ∠POQ.
If m∠POS = 20, this means that m∠POQ = 20+20 = 40°.
Answer:
The correct option is C) m∠POS = 20°, m∠POQ = 40°,
Step-by-step explanation:
Consider the provided figure.
Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS.
From the given figure it is clear that OS is angle bisector of POQ,
[tex]\angle POQ=\angle POS+\angle QOS[/tex]
[tex]\angle POS=\angle QOS[/tex] ∴ angle bisector
[tex]\angle POQ=\angle POS+\angle POS=2\angle POS[/tex]
Thus, the measure of ∠POQ is double the measure of ∠POS.
There is only one option in which m∠POQ is double the m∠POS.
Therefore, the correct option is C) m∠POS = 20°, m∠POQ = 40°,
The picture shows a lorry driver standing next to his lorry.
The lorry driver and the lorry are drawn to the same scale.
The lorry driver wants to drive the lorry into a car park.
The entrance to the car park is 3.1 meters high.
Can the lorry driver safely drive the lorry into the car park?
You must clearly show how you got your answer, explaining any
assumptions you have made.
Answer: no its too big it wont fit
Step-by-step explanation:
its just too big
A researcher reports that the time (in minutes) it takes children who are "picky eaters" to finish their vegetables is negatively skewed, with children finishing their vegetables in 4.2±1.0 (M±SD) minutes. Based on Chebyshev's theorem, we can conclude that68% of children finished their vegetables in 3.2 to 5.2 minutes.50% of children finished their vegetables in at least 3.2 minutes.99.7% of children finished their vegetables in 2.2 to 6.2 minutes.At least 89% of children finished their vegetables in 1.2 to 7.2 minutes.
Answer:
Option d) Chebyshev's rule
Step-by-step explanation:
The Chebyshev's rule state that for a data that is not distributed normally,
atleast [tex](1 - \frac{1}{k^2})\% \text{ of data lies within the interval}~(Mean \pm (k)Standard ~Deviation)[/tex].
Here, k cannot be 1 and is always greater than 2.
For k = 2,
[tex](1 - \frac{1}{4})\times 100\% = 75\%[/tex] of data lies within the range of [tex](\mu \pm 2\sigma)[/tex]
Atleast 75% of children finished their vegetables in [tex](\mu \pm 2\sigma) = (4.2 \pm (2)1.0) = (2.2,6.2)[/tex]
For k = 3,
[tex](1 - \frac{1}{9})\times 100\% = 88.912\%[/tex] of data lies within the range of [tex](\mu \pm 3\sigma)[/tex]
Atleast 89% of children finished their vegetables in [tex](\mu \pm 3\sigma) = (4.2 \pm (3)1.0) = (1.2,7.2)[/tex]
Thus, option d) is correct.
An equation that expresses a relationship between two or more variables, such as Upper H equals nine tenths left parenthesis 220 minus a right parenthesis , is called _______. The process of finding such equations to describe real-world phenomena is called mathematical _______. Such equations, together with the meaning assigned to the variables, are called mathematical _______.
Answer:
An equation that expresses a relationship between two or more variables, such as Upper H equals nine tenths left parenthesis 220 minus a right parenthesis , is called Formula.
A formula is an equation that expresses a relationship between two or more variables.
The process of finding formulas to describe real-world phenomena is called mathematical modeling.
Such equations, together with the meaning assigned to the variables, are called mathematical models.
A mathematical equation expresses a relationship between variables, and the process of finding such equations is called mathematical modeling.
Explanation:An equation that expresses a relationship between two or more variables is called a mathematical equation. The process of finding such equations to describe real-world phenomena is called mathematical modeling. These equations, together with the meaning assigned to the variables, are called mathematical models.
For example, if we have an equation like Upper H equals nine tenths left parenthesis 220 minus a right parenthesis, this equation represents a relationship between a variable H and the expression nine tenths left parenthesis 220 minus a right parenthesis. We can use this equation to calculate the value of H given a specific value for the expression.
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There were 2,605 people at the basketball game. A reporter rounded this number to the nearest hundred for a newpaper aticle. What number did the reporter use
You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture?a 4 inch
Answer:
24/18=1.333
20/16=1.25
6/4=1.5 (the ratio to achieve9
1.333 is more close to 1.5 than 1.25 (11% difference compared to 17%)
Step-by-step explanation:
Answer:
16 in. X 20 in will keep more.
Step-by-step explanation:
Length of picture = 4 inches
Breadth of picture = 6 inches
Area of picture=[tex]length \times breadth[/tex]
=[tex]4 \times 6[/tex]
=[tex]24 inches^2[/tex]
Length of frame 1 = 16 inches
Breadth of frame 1 = 20 inches
Area of frame 1 = [tex]16 \times 20 = 320 inches^2[/tex]
So, % of picture can fit in frame 1= [tex]\frac{\text{original picture area }}{\text{Frame 1 area }} \times 100[/tex]
= [tex]\frac{24}{320} \times 100[/tex]
= [tex]7.5 %[/tex]
Length of frame 2 = 18 inches
Breadth of frame 2 = 24 inches
Area of frame 2 = [tex]18 \times 24 = 432 inches^2[/tex]
So, % of picture can fit in frame 2 = [tex]\frac{\text{original picture area }}{\text{Frame 1 area }} \times 100[/tex]
= [tex]\frac{24}{432} \times 100[/tex]
= [tex]5.56 %[/tex]
Since % of picture can fit in frame 1 is more than frame 2 .
So, 16 in. X 20 in will keep more.
An unknown radioactive element decays into non-radioactive substances. In 30 days the radioactivity of a sample decreases by 12%. When will a sample of 50 mg decay to 10 mg? Round your final answer to 1 decimal place.
Answer:
Time to decay will be 377.7 days.
Step-by-step explanation:
Decay of an radioactive element is represented by the formula
[tex]A_{t}=A_{0}e^{-kt}[/tex]
where [tex]A_{t}[/tex] = Amount after t days
[tex]A_{0}[/tex] = Initial amount
t = duration for the decay
k = decay constant
Now we plug in the values in the formula
[tex](1-0.12)x=xe^{-30k}[/tex]
[tex](0.88)x=xe^{-30k}[/tex]
[tex]0.88=e^{-30k}[/tex]
Now we take natural log on both the sides
ln(0.88) = [tex]ln(e)^{-30k}[/tex]
ln(0.88) = -30k(lne)
-30k = -0.1278
k = [tex]\frac{.1278}{30}[/tex]
k = [tex]4.261\times 10^{-3}[/tex]
Now we have to calculate the duration for the decay of 50 mg sample to 10 mg.
[tex]A_{t}=A_{0}e^{-kt}[/tex]
We plug in the values in the formula
10 = 50[tex]e^{-4.261\times 10^{-3}\times t}[/tex]
[tex]e^{-4.261\times 10^{-3}\times t}=\frac{10}{50}[/tex]
[tex]e^{-4.261\times 10^{-3}\times t}=0.2[/tex]
We take (ln) on both the sides
[tex]ln(e^{-4.261\times 10^{-3}\times t})=ln(0.2)[/tex]
[tex]-4.261\times 10^{-3}\times t=-1.6094[/tex]
t = [tex]\frac{1.6094}{4.261\times 10^{-3} }[/tex]
t = 0.37771×10³
t = 377.7 days
Therefore, time for decay will be 377.7 days.
Luis purchased a laptop computer that was marked down by 25 of the original price. What fractional part of the original price did Luis pay? A 15 B 45 C 35 D 25
Answer:
75%
Step-by-step explanation:
100%-25%= 75%
He would have paid 75% of the original price..
Answer:
C. [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Let x be the original price of laptop computer.
We have been given that Luis purchased a laptop computer that was marked down by 2/5 of the original price.
The price of laptop computer after mark-down would be x minus 2/5 of x.
[tex]\text{The price of laptop computer after mark-down}=x-\frac{2}{5}x[/tex]
[tex]\text{The price of laptop computer after mark-down}=\frac{5}{5}x-\frac{2}{5}x[/tex]
[tex]\text{The price of laptop computer after mark-down}=\frac{5-2}{5}x[/tex]
[tex]\text{The price of laptop computer after mark-down}=\frac{3}{5}x[/tex]
Therefore, Luis paid [tex]\frac{3}{5}[/tex] of the original price.
A discrete mathematics class contains 1 mathematics major who is a freshman, 12 mathematics majors who are sophomores, 15 computer science majors who are sophomores, 2 mathematics majors who are juniors, 2 computer science majors who are juniors, and 1 computer science major who is a senior. Express each of these statements in terms of quantifiers and then determine its truth value.
a) There is a student in the class who is a junior.
b) Every student in the class is a computer science major.
c) There is a student in the class who is neither a mathematics major nor a junior.
d) Every student in the class is either a sophomore or a computer science major.
e) There is a major such that there is a student
Answer and Step-by-step explanation:
As quantifiers, we can settle:
x is a student
M(x) is a math major student
C(x) is a computer science major student
F(x) is a freshman student
S(x) is a sophomore student
J(x) is a junior student
N(x) is a senior student
∃ exists
∀ every
¬ negation
∧ and
∨ or
a) There is a student in the class who is a junior.
∃xJ(x) value: True. There are 4 juniors
b) Every student in the class is a computer science major.
∀xC(x) value: False. There are math students
c) There is a student in the class who is neither a mathematics major nor a junior.
∃x¬M(x)∨¬C(x) value: False. All students are math ou computer science majors
d) Every student in the class is either a sophomore or a computer science major.
∀xS(x)∨C(x) value: False. There are some students who are neither, for example mathematics majors who are juniors
e) There is a major such that there is a student*
∃M(x)C(x)x value: True. All majors have students.
*This one seems incomplete, but I answered the way it is writen.
The expression of the statement based on the quantifiers show that the truth value will be:
True FalseTrue False FalseWhat is a quantifier?It should be noted that quantifies are the words or expressions that indicate the number of elements which a statement pertains to.
From the information, there is a student in the class who is a junior. It can also be deduced that not every student in the class is a computer science major. This is because there are mathematics majors too.
Furthermore, there is a student in the class who is neither a mathematics major not a junior but not every student in the class is either a sophomore or a computer science major.
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solve the equation -36 = -6(2x - 14)
Answer:
x = 10
Step-by-step explanation:
-36 = -6(2x-14)
6 = 2x-14
20 =2x
10 = x
Answer:
-x = -10
Step-by-step explanation:
-36 = -12x + 84
-120 = -12x
-10 = -x
If AD = 12 units, BD = 15 units, and AC = 4 units, what is the length of BC?
Answer:
The answer to your question is: BC = √65 or 8.05 u
Step-by-step explanation:
Data
AD = 12 u
BD = 15 u
AC = 4 u
BC = ?
First calculate the length of AB using the pythagorean theorem
BD² = AB² + AD²
AB² = BD² - AD²
AB² = 15² - 12²
AB² = 225 - 144
AB² = 81
AB = 9 u
Now, use the pythagorean theorem to find BC
AB² = BC² + AC²
BC² = AB² - AC²
BC² = 9² - 4²
BC² = 81 - 16
BC² = 65
BC = √65 or 8.05 u
A bathtub can hold a maximum of 50 gallons of water. Water can be drained out of the tub at a rate of 2 gallons per minute. If the tub is initially completely filled by a faucet at a rate of 1 gallon per minute, how long will it take to drain the full tub if the drain is opened but the faucet is kept on?
Answer:
50 minutes
Step-by-step explanation:
Given,
Water can be drained out of the tub at a rate of 2 gallons per minute,
So, the drained water in 1 minute = 2 gallon,
That is, change in 1 minute = -2 gallon
( negative sign shows losing water)
Also, it is filled by a faucet at a rate of 1 gallon per minute,
So, the filled water in 1 minute = 1 gallon,
That is, change in 1 minute = + 1 gallon
( Positive sign shows additional water ),
Thus, total change in 1 minute = -2 + 1 = -1 gallon,
Let x be the time after which the bathtub will be emptied completely,
Total change in x minutes = -x gallon,
Bathtub will be emptied, if,
Initial volume of water + total change in water = 0
50 - x = 0 ( given volume of tub is 50 gallon )
[tex]\implies x = 50[/tex]
Hence, it will take 50 minutes to drain the full tub.
Final answer:
To drain a bathtub initially filled with 50 gallons, with an incoming rate of 1 gallon per minute and a draining rate of 2 gallons per minute, it takes 50 minutes.
Explanation:
The question involves calculating the time it takes to drain a bathtub that is being filled and drained simultaneously. Initially, the bathtub is completely filled with 50 gallons of water. The faucet fills the tub at a rate of 1 gallon per minute, while the drain can remove water at a rate of 2 gallons per minute. Therefore, the net rate at which water is being drained is 1 gallon per minute (2 gallons out - 1 gallon in). To completely drain the tub of its initial 50 gallons, at a net rate of 1 gallon per minute, it would take 50 minutes.
Therefore, as per the above explaination, the correct answer is 50 min.
suppose Tinsel Town Videos lowers the price of its movie club membership by 10 percent and as a result, CineArts Videos experienced a 16 percent decline in its movie club membership. What is the value of the cross- price elasticity between the two movie club memberships
Answer: The value of cross price elasticity is 1.6.
Step-by-step explanation:
Since we have given that
Percent change in price = 10%
Percent change in quantity = 16%
So, we need to find the cross price elasticity between the two movie club memberships.
As we know the formula for cross price elasticity :
[tex]\dfrac{\%\text{change in demand}}{\%\text{change in price}}\\\\=\dfrac{16}{10}\\\\=1.6[/tex]
Hence, the value of cross price elasticity is 1.6.
PLEASE HELP!!! Consider this bag of marbles. What is the probability of drawing a green marble versus the ODDs of drawing a green marble? What is the difference in these two things?
https://lh3.googleusercontent.com/HGdB_Oa4buUyXgZbq38nPvDmZEK9J5FLEqrQ1NsfckiHy9N2VTd3wEpjuEpI8rrp5LtZMw=s100
Answer:
Probabilities are usually given in percentages.
Odds can have a value of 0-infinity & are in the form of a ratio. Odds can be given in 2 different ways: Odds in favor & Odds against.
*Probability of drawing a green
marble is 50%
*Odds if drawing a green marble
are 5:5
The probability of drawing a green marble is 1/2 and the odds are 1:1. The difference between probability and odds is explained.
The probability of drawing a green marble from the bag can be calculated by dividing the number of green marbles by the total number of marbles in the bag. In this case, there are 5 green marbles and a total of 10 marbles, so the probability is 5/10 or 1/2.
Odds, on the other hand, represent the ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, since there are 5 green marbles and a total of 5 marbles that are not green (3 blue marbles and 2 red marbles), the odds of drawing a green marble are 5:5 or 1:1.
The difference between probability and odds is that probability is a measure of the likelihood of an event occurring, while odds represent the ratio of favorable to unfavorable outcomes.
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The probable question may be:
Consider this bag of marbles, where we have 5 green marbles, 3 blue marbles and 2 red marbles. What is the probability of drawing a green marble versus the ODDs of drawing a green marble? What is the difference in these two things?
Select the correct answer. The number of scented candles packaged in a box can vary by at most two from an average of 80 candles per box. If the cost of producing a candle is two dollars, what is the range of the possible production costs, x, for 50 boxes of candles? A. 78 ≤ x ≤ 82 B. 156 ≤ x ≤ 164 C. 3,900 ≤ x ≤ 4,100 D. 7,800 ≤ x ≤ 8,200
Answer:
Step-by-step explanation:
From the problem statement, each box of candles has the following range of candles:
[tex]78 \leq x \leq 82[/tex]
We also know that we have 50 boxes of candles, so we multiply the above range by 50 to get the range of candles:
[tex]3900 \leq x \leq 4100[/tex]
Finally, each candle costs $2, so we have the final range of cost:
[tex]7800 \leq x \leq 8200[/tex]
By calculating the cost of producing the minimum and maximum number of candles that can be packaged in 50 boxes, we determine the range of possible production costs, x, is $7,800 to $8,200.
Explanation:The student needs to calculate the range of possible production costs for 50 boxes of candles, given that each box contains an average of 80 candles and the number of candles can vary by at most two from this average. Since each candle costs two dollars to produce, we can find the minimum and maximum number of candles in one box by subtracting and adding two to the average, respectively (78 and 82 candles). Multiplying these numbers by the cost per candle gives us the cost per box, and then multiplying by the number of boxes (50) gives us the total production cost range for all boxes.
To calculate the minimum cost, we use the minimum number of candles per box: 78 candles per box × $2 per candle × 50 boxes = $7,800. To calculate the maximum cost, we use the maximum number of candles per box: 82 candles per box × $2 per candle × 50 boxes = $8,200. Therefore, the range for the possible production costs, x, for 50 boxes of candles is $7,800 ≤ x ≤ $8,200, which corresponds to answer choice D.
Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance. In a study of a weight loss program, 4 subjects lost an average of 48 lbs. It is found that there is about a 32% chance of getting such results with a diet that has no effect.
Answer:
Step-by-step explanation:
Given that in a study of a weight loss program, 4 subjects lost an average of 48 lbs.
It is found that there is about a 32% chance of getting such results with a diet that has no effect.
The results do not appear to have statistical significance. The reasons are
1) Sample size of 4 is very small not even meeting the bare minimum
2) Sample of 4 cannot be taken to represent the population
3) Whether bias was there in the selection of sample is not known.
4) Std deviation is not considered which is very important while concluding results.
A theater gives away one free ticket to every 10th customer and two free tickets to every 25th customer. The manager wants to give away four free tickets when the customer is both a 10th and a 25th customer. Who is the first customer that will recieve four free tickets
Answer:
The first customer that will get four free tickets is 50th customer
Step-by-step explanation:
Find the least common multiple of numbers 10 and 25. First, factorize these numbers:
[tex]10=2\cdot \underline{5}\\ \\25=\underline{5}\cdot 5\\ \\LCM(10,25)=\underline{5}\cdot 2\cdot 5=50[/tex]
When finding LCM, first write the all common multiples (underlined 5) and then multiply them by remaining multiples (2 and 5). You get 50 as LCM(10,25). This means that each 50th customer will get four free tickets.
Final answer:
The first customer who will receive four free tickets is the 100th customer.
Explanation:
To determine the first customer who will receive four free tickets, we need to find the smallest positive integer that is divisible by both 10 and 25. This is called the least common multiple (LCM). To find the LCM of 10 and 25, we can list the multiples of each number until we find a common multiple:
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Multiples of 25: 25, 50, 75, 100
The LCM of 10 and 25 is 100. Therefore, the first customer who will receive four free tickets is the 100th customer.
Todd wants to make a snack of a number of grapes and slices of cheese. He knows that each grape has 2 calories. The slice of cheese is 155 calories. Todd wants calorie snack using both grape and cheese. What equation could he use to determine the number of grapes he can eat? Part 2: how many grapes can he eat for his 205 calorie snack? Part 3: Todd's friend Francis brings more slices of cheese. How many total slices of cheese are required to make a 515 calories snack if the number of grapes remain the same?
Answer:
The answer to your question is:
a) C = 2g + 155c
b) g = 25 grapes
c) c = 3
Step-by-step explanation:
Data
grapes = g = 2 calories
cheese = c = 155 calories
a) Equation, we consider the amount of grapes and the calores given.
Total calories = C = 2g + 155c
b) We consider that the slices of cheese stays the same
2g + 155 = 205
2g = 205 -155
2g = 50
g = 50/2 = 25 grapes
c) Then the number of grapes stays the same
2(25) + 155c = 515
50 + 155c = 515
155c = 515 - 50
155c = 465
c = 465/155
c = 3 slices of cheese
Assume that one day's labor in Argentina can produce either 20 units of cloth or 2 units of wine, while in Chile one day's labor can produce either 24 units of cloth or 12 units of wine. If Argentina transfers 2 units of labor from wine to cloth and Chile transfers 1 unit of labor from cloth to wine, the increase in combined output by those two workers will be: A. 16 wine; 8 cloths B. 16 wine; 16 cloths C. 12 wine; 12 cloths D. 8 wine; 16 cloths
(D). 8 Wine, 16 Cloth
Step-by-step explanation:Cloth production by Argentina = 20 units
Wine production by Argentina = 2 units
Cloth production by Chile = 24 units
Wine production by Chile = 12 units
Now,
2 units of labor was transferred by Argentina from Wine to Cloth and 1 unit of labor was transferred by Chile from Cloth to Wine.
Therefore,
Increase in Cloth production = Argentina's total cloth produced - Cloth produced by Chile (before transfer)
Now,
We can say that total cloth produced by Argentina is = 2 x 20 = 40 units
So,
Increase in Cloth production = 40 - 24 = 16 units
Therefore, the increase in Cloth Production is 16 units.
Similarly,
Increase in Wine production = Chile's total Wine produced - Wine produced by Argentina (before transfer)
Now,
We can say that total Wine produced by Chile is = 1 x 12 = 12 units
Wine produced by Argentina before transfer = 2 x 2 = 4 units
So,
Increase in Wine production = 12 - 4 = 8 units
Therefore, the increase in Wine Production is 8 units.
Hence, the correct option is (D).
According to Greg, perfect cherry pies have a ratio of 240240240 cherries to 333 pies. How many cherries does Greg need to make 999 perfect cherry pies?
999 is 3 times 333, so the ratio will have to be multiplied by three.
No of cherries needed = 240240240 * 3 = 720720720 cherries
15=3n+6p solve for n
15=3n+6p
We need to isolate n.
15 - 6p = 3n
(15 - 6p)/3 = n
5 - 2p = n
To solve for n in the equation 15 = 3n + 6p, isolate n by subtracting 6p from both sides, and then divide both sides by 3.
Explanation:To solve for n in the equation 15 = 3n + 6p, we can start by isolating the variable n. First, subtract 6p from both sides of the equation to get 15 - 6p = 3n. Then, divide both sides by 3 to solve for n, yielding: n = (15 - 6p) / 3.
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