❄ Hi there,
let us first figure out what we need to do to find x in this equation.
Since x is
multiplied by 3we will
divide by 3In other words we'll do just the opposite.
[tex]\sf{3x=2}\\\sf{x=\dfrac{2}{3}}[/tex]
That's it!
❄
Sanford's gym coach made him run 20 laps on a 400 m track. How many kilometers did he run? How many miles?
Answer:
8km 5mi
Step-by-step explanation:
20x400=8000meters a km = to 1000meters
8000/1000=8km
A mile is a kilometer/ 1.6 8/1.6=5 miles
Sanford ran approximately 8 kilometers and about 4.97 miles.
Given that a coach made someone run 20 laps on a 400 m track.
We need to find the number of mile he ran as well as number of kilometers he ran.
To find out how many kilometers Sanford ran, we can use the fact that 1 kilometer is equal to 1000 meters.
Similarly, to find out how many miles he ran, we'll use the conversion factor of 1 mile being equal to approximately 1609.34 meters.
Let's calculate it:
1 lap = 400 meters
20 laps = 20 x 400 = 8000 meters
Kilometers:
8000 meters ÷ 1000 meters/kilometer = 8 kilometers
Miles:
8000 meters ÷ 1609.34 meters/mile ≈ 4.97 miles
So, Sanford ran approximately 8 kilometers and about 4.97 miles.
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Geometry question need help finding the answer.
Answer: 1208.96
Step-by-step explanation:
The volume of the cylinder is [tex](\pi)(4^2)(4)=64\pi[/tex]
The volume of the prism is [tex](6)(12)(14)=1008[/tex]
So, the total volume is [tex]1008+64\pi=\boxed{1208.96}[/tex]
Suppose you live in a country with a proportional tax system. you make $20,000 a year and pay $5,000 in taxes. your friend makes twice as much money as you. what amount can your friend expect to pay in taxes this year? $2,500 $5,000 $10,000 $20,000
Answer:
10,000
Step-by-step explanation:
Tbh this was pretty simple. If he makes twice the money as you, he pays twice as much too. Meaning he makes 40k a year and pays 10k for taxes
20 points!! !!
help me
Answer:
The mean absolute deviation (MAD) is 0
Step-by-step explanation:
20 + 16 + 21 + 16 + 22 + 16 + 15
= 126 ÷ 7 = 18
(20 - 18) + (16 - 18) + (21 - 18) + (16 - 18) + (22 - 18) + (16 - 18) + (15 - 18) =
2 +(-2) + 3 + (-2) + 4 + (-2) + (-3) = 0 ÷ 7= 0
The mean absolute deviation (MAD) is 0
A company is considering the purchase of a new machine for $75,660. management predicts that the machine can produce sales of $20,000 each year for the next 10 years. expenses are expected to include direct materials, direct labor, and factory overhead totaling $16,800 per year, including depreciation of $4,600 per year. what is the payback period for the new machine?
The company is considering the purchase of a new machine for $75,660 (based on the available data), and the payback period is 24 years.
What is the payback period?The payback period is the time the company requires to recoup its investment for the new machine.
The payback period can be computed by dividing the investment cash outflows by the annual net cash inflows.
Data and Calculations:Initial investment in new machine = $75,660
Annual depreciation expense = $4,600
Investment period = 10 years
Annual sales revenue = $20,000
Annual expenses = $16,800
Ne annual cash inflow = $3,200 ($20,000 - $16,800)
Payback period = 24 years ($75,660/$3,200)
Thus, since the payback period is 24 years, while the investment period is 10 years, it sounds unwise for the company to continue the investment.
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MN =7. Find AB.
3.5
10.5
14
The length of line segment AB by observation if the diagram in the task content is; 14.
What is the length of line segment AB?It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.
Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.
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What is the result of subtracting the second equation from the first?
- 2x + y = 0
-7x + 3y = 2
The result is [tex]5x-2y=-2[/tex].
Write the equation of the line that passes through
the points (-1, 2) and (6, 3) in slope-intercept form.
The equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form is,
[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]
How to find the equation of a passing line?The equation y = mx often denotes a straight line with a gradient of m that passes through the origin. Y = mx is the equation for a straight line with gradient m that passes through the origin.Y = mx + b is the equation for a line with a slope of m and a y-intercept of (0, b). In order to graph a line expressed in slope-intercept form: Draw the coordinate plane's y-intercept. To locate a different point on the line, use the slope.The three main types of linear equations are slope-intercept form, standard form, and point-slope form.Given: [tex](-1,2)[/tex] and [tex](6,3).[/tex]
The slope of the line passing through[tex](x1,y1)[/tex] [tex](x2,y2)[/tex] is [tex]\frac{y^{2} }{x^{2} } -\frac{y^{1} }{x^{1} }[/tex]
The slope of our line[tex]=\frac{(3-2)}{(6+1)} =\frac{1}{7}[/tex]
Slope intercept from the equation would be [tex]y= 1/7 x +C[/tex]
Find C:
Since [tex](-1,2)[/tex] lies on the line, substitute these in the line equation
[tex]2 = \frac{1}{7(-1)} +c[/tex]
[tex]C=2+\frac{1}{7} =\frac{15}{7}[/tex]
Therefore, the equation in slope intercept form is[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]
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1. Use the figure to determine the value of x and y.
Answer:
Step-by-step explanation:
x=100 bc like 180-80=100
y=80 bc vertical angles
Answer:
y = 80*
x = 100*
Step-by-step explanation:
y is the same to the 80* angle and therefore x is 100*
180* - 80 = 100*
Find the length of the line joining the points A(-2,10) and B(-8,2)
Length of the line
= [tex]\sqrt{((-2)-(-8))^{2}+(10-2)^{2} }[/tex]
= [tex]\sqrt{36+64}[/tex]
=[tex]\sqrt{100}[/tex]
= 10
HELPPP ASAP 25PTS! Find the area of the shape
Answer:
480
Step-by-step explanation:
One fifth of the sum of 9 and 6 is multiplied by the quotient of 18 divided by the sum of 2 and 4, find the result.
please tell me.
Answer:
9
Step-by-step explanation:
We can tackle the individual parts and combine
1/5 of the sum of 9 and 6 means 1/5 * (9 + 6)
The quotient of 18 divided by the sum of 2 and 4 is 18 / (2 + 4)
Combing everything gives us (1/5 * (9 +6)) * (18 / (2 + 4)
(1/5 * 15) * 18/6
3 * 3 = 9
To make cream ice pops, nina uses conical molds that each have a height of 15 cm and a radius of 2 cm. how much ice pop mixture can each mold hold when full? a. 30 pi cubic centimeters b. 10 pi cubic centimeters c. 20pi cubic centimeters d. 60pi cubic centimeters
Answer:
C
Step-by-step explanation:
Givens
r = 2 cm
h = 15 cm
pi = 3.14 The question does not expect a number for pi
Formula
V = (1/3) pi r^2 h Substitute givens into formula
Solution
V = 1/3 * pi * 2^2 * 15 Combine. Remember pi is left as it is
V = 1/3 * pi * 4 * 15
V = 1/3 pi * 60 Divide 60 by 3
V = 20 pi
The volume of a sphere is 256/3π cm3.
Work out the surface area of the sphere.
Give your answer in terms of π.
the surface area of the sphere is π/4 cm^3
How to determine the surface areaIt is important to know the formula for surface area and volume of a sphere
Surface area = [tex]\frac{4\pi }{r^2}[/tex]
Volume = [tex]\frac{4}{3} \pi r^3[/tex]
First, let's determine the value of radius, r
The value for volume was given as 256/3π cm3.
[tex]\frac{256}{3} \pi = \frac{4}{3} \pi r^3[/tex]
Pi cancels out and we have cross multiply to get the radius
[tex]256 * 3 = 4 * 3 r^3[/tex]
[tex]12r^3 = 768[/tex]
Make r the subject of the formula
[tex]r = \sqrt[3]{\frac{768}{12} }[/tex]
[tex]r = \sqrt[3]{64}[/tex]
r = 4
Let's substitute to find the surface area
Surface area = [tex]\frac{4\pi }{4^2}[/tex]
Surface area = π/4
Surface area = π/4 cm^3
Thus, the surface area of the sphere is π/4 cm^3
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full of sand, the wagon weighs 100 pounds. If the wagon weighs 80 ounces when its empty, how much do the bags of sand weigh?
given,
wagon weight with sand = 100 pounds
wangon weight = 80 ounces ÷ 16 = 5 pounds
sand weight = 100 - 5 = 95 pounds//
A large container holds 4 gallons of chocolate milk that has to be poured into 1-pint bottles. if the ratio of gallons to pints is 1 : 8, how many bottles are needed? a. 2 bottles b. 4 bottles c. 8 bottles d. 32 bottles e. 40 bottles
32 bottles are needed to poured 4 gallons of chocolate milk.
The correct option is D.
What do you know about volume?A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.
According to the given information:Pints to Gallons Ratio: 1:8
Permit x bottles to be present.
There are x bottles required for 4 gallons of chocolate milk.
Because of the direct proportion
4/x = 1/8
x = 4 x 8
x = 32
As a result, 32 bottles are required.
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the vertex of this parabola is at (-5,-2) when the x value is -4 the y value is 2 . what is the coefficient of the squared expression in the parabola's equation
The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.
What is the vertex coefficient of the equation of the parabola?
In this question we must find the vertex coefficient of the equation of the parabola, which is the vertex form of the quadratic equation:
y - k = C · (x - h)²
If we know that (h, k) = (- 5, - 2) and (x, y) = (- 4, 2), then the vertex coefficient is:
2 - (- 2) = C · [- 4 - (- 2)]²
4 = C · (- 2)²
C = 1
The vertex coefficient of the parabola with vertex (- 5, - 2) and the point (- 4, 2) is equal to 1.
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I am playing in a racquetball tournament, and I am up against a player I have watched but never played before. I consider three possibilities for my prior model: we are equally talented, and each of us is equally likely to win each game; I am slightly better, and therefore I win each game independently with probability 0.6; or he is slightly better, and thus he wins each game independently with probability 0.6. Before we play, I think that each of these three possibilities is equally likely.
In our match we play until one player wins three games. I win the second game, but he wins the first, third, and fourth. After this match, in my posterior model, with what probability should I believe that my opponent is slightly better than I am?
Answer: If your opponent is winning 3:1 then they are probably better then you if they are winning more then you are. (or you are just having a bad day)
Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134
Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466
Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400
Let's denote the three possibilities as follows:
A: Equally talented, each player has a 0.5 probability of winning a game.
B: You are slightly better, with a 0.6 probability of winning a game.
C: Your opponent is slightly better, with a 0.6 probability of winning a game.
Given that you won the second game but lost the first, third, and fourth games, we want to find the probability of scenario C given this outcome. Let P(C) represent the prior probability of scenario C being true.
According to the given information, each of the three scenarios (A, B, and C) is equally likely, so P(A) = P(B) = P(C) = 1/3.
Now, let's update the probabilities based on the outcome of the match:
In scenario A:
The probability of winning the second game is 0.5, and the probability of losing the first, third, and fourth games is 0.5 each. Therefore, the overall probability of the observed outcome in scenario A is (0.5 * 0.5 * 0.5 * 0.5) = 0.0625.
In scenario B:
The probability of winning all three games (assuming you are slightly better) is (0.6 * 0.6 * 0.6) = 0.216.
In scenario C:
The probability of winning the second game (assuming your opponent is slightly better) is 0.4, and the probability of losing the first, third, and fourth games is 0.6 each. Therefore, the overall probability of the observed outcome in scenario C is (0.4 * 0.6 * 0.6 * 0.6) = 0.05184.
Now, we can update the probabilities based on Bayes' theorem:
Posterior probability of scenario A: P(A|data) = (P(data|A) * P(A)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))
Posterior probability of scenario B: P(B|data) = (P(data|B) * P(B)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))
Posterior probability of scenario C: P(C|data) = (P(data|C) * P(C)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))
P(data|A) = 0.0625
P(data|B) = 0.216
P(data|C) = 0.05184
Plugging in the values, we get:
Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134
Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466
Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400
So, after the match, the posterior probability that your opponent is slightly better than you is approximately 0.400 or 40%.
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Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centered at a=1. Write the Taylor series in summation notation
Answer:
[tex]e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...[/tex]
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
Step-by-step explanation:
Taylor series expansions of f(x) at the point x = a
[tex]\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...[/tex]
This expansion is valid only if [tex]\text{f}\:^{(n)}(a)[/tex] exists and is finite for all [tex]n \in \mathbb{N}[/tex], and for values of x for which the infinite series converges.
[tex]\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1[/tex]
[tex]\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]
[tex]\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4[/tex]
[tex]\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4[/tex]
[tex]\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4[/tex]
Substituting the values in the series expansion gives:
[tex]e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...[/tex]
Factoring out e⁴:
[tex]e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right][/tex]
Taylor Series summation notation:
[tex]\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n[/tex]
Therefore:
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
A person draws a card from a hat. each card is one color, with the following probabilities of being drawn: 1/25 for white, 1/5 for black, 1/10 for red, and 1/15 for pink. what is the probability of pulling a black or red card, written as a reduced fraction?
The probability of pulling a black or red card = 3/10
We are informed that a card is pulled from a hat.Probability that a white card will be drawn, P(white) = 1/25
Probability that a blue card will be dealt, P(black) = 1/5
Probability that a black card will be dealt, P(red) = 1/10
Probability that a pink card will be revealed, P(pink) = 1/15
All of these occurrences are distinct from one another and do not relate to one another.
The likelihood that any one of any two events, A and B, with probability P(A) and P(B), will occur is:
P( A ∪ B ) = P(A) + P(B)
Here, event A can be compared to getting a black card, and
incident B is comparable to receiving a red card.
So, P(black or red) = P(black) + P (red)
= (1/5) + (1/10)
= ( 2 + 1 )/10
= 3/10
So, the likelihood that a black or red card will be pulled from the hat:
= 3/10
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The data set below has a lower quartile of 13 and an upper quartile of 37.
1, 12, 13, 15, 18, 20, 35, 37, 40, 78
Which statement is true about any outliers of the data set?
The correct option regarding the outliers of the data-set is given by:
The greatest value, 78, is the only outlier.
How to use the quartiles of a data-set to identitfy outliers?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile with the first quartile.Measures that are more than 1.5 IQR from Q1 and Q3 are considered outliers.The IQR for this problem is:
IQR = 37 - 13 = 24.
Hence the bounds for outliers are:
Less than 13 - 1.5 x 24 = -23.Greater than 37 + 1.5 x 24 = 73,The options are:
No outliers.Only 1 is an outlier.Only 78 is an outlier.Both 1 and 78 are outliers.Hence the correct option is that only 78 is an outlier.
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If f(x) = 4x² + 1 and g(x)=x2-5, find (f- g)(x).
0 A. 3x2 + 6
OB. 5x²-6
OC. 5x²-4
OD. 3x² - 4
Answer:
Option A is correct.
3x^2+6
Step-by-step explanation:
We have to find (f-g)(x):
We can write it f(x)-g(x), so substitute the values:
f(x)-g(x)=(4x^2+1)-(x^2-5)
=4x^2+1-x^2+5
=3x^2+6
20 POINTS
Data Analysis and Probability - Computing mean absolute deviation from a list of numerical values
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15
Answer:
2.571428
Step-by-step explanation:
The mean absolute deviation of a dataset is the average distance between each data point and the mean.
Find the length of one edge of a cube if its lateral surface area is 144 square centimeters. a. 4 cm b. 8 cm c. 6 cm d. 3 cm
The length of one edge of the cube exists 6 centimeters.
What is the lateral surface area of a cube?The lateral surface area of a cube exists
[tex]$A=4 a^{5}$[/tex]
where a stands the length of one edge of a cube.
It exists given that the lateral surface area of the square stands at 144 square centimeters.
Substitute A = 144 in the above formula.
[tex]$144=4 a^{2}[/tex]
Divide both sides by 4.
[tex]$36=a^{2}[/tex]
Taking square root on both sides.
[tex]$\sqrt{36}=\sqrt{a^{2}}[/tex]
6 = a
The length of one edge of the cube exists 6 centimeters.
Therefore, the correct answer is option c. 6 cm.
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Sarah attempt to convert 8 miles in to kilomiters explain her error and then provide a correct conversion
Answer:
12.8 km
Step-by-step explanation:
each mile has 1.6 km in it so in order to find the total distance in km we need to multiply the miles by 1.6= 8 miles x 1.6 =12.8 km
PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP
Answer:
5/52
Step-by-step explanation:
There are 52 cards in a deck, with 26 red and 26 black cards. There are 2 red ones, 2 black threes, and 1 six of hearts. The # of favorable outcomes is 2 + 2 + 1 = 5, so the answer is 5/52.
Which of the following is NOT a monomial? -11x
x - 4
3
22xy
Answer:
x - 4
Step-by-step explanation:
monomial is one term
-11x is only one term
x-4 isn't
3 is one term
22xy is only one term
only x-4 isn't a monomial
Find the surface area of the cone to the nearest square unit. Use π = 3.14.
6 cm
3 cm
The surface area of the cone exists as πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
How to find the surface area of the cone?
The surface of the cone consists of the lateral surface and the base area. So,
1. the lateral surface exists equal to πrs, where r exists the radius of the base and s exists the slant height of the cone.
2. the base area exists πr² (since the base exists a circle with radius r).
Then the surface area exists SA = πrs + πr²
The surface area of the cone exists as πr² + πrl
where "r" exists the radius, "l" exists the slant height
The radius of the cone exists at 6 cm
The slant height of the cone exists at 3 cm
To find the surface area of a cone
The surface area of a cone = πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
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Find, leave your answers in terms of pie,
a) the area of the shaded region,
b) the perimeter of the shaded region
A die is rolled. if it rolls to a 1 or 2, you win 2 usd. if it rolls to a 3, 4, 5, or 6, you will lose 1 usd. what is the expected payoff from rolling this die?
The expected payoff from rolling the die is 0 usd.
According to the given question.
A die is rolled.
So, the possiblbe outcomes for a dice = {1, 2, 3, 4, 5, 6}
⇒ Total number of outcomes = 6
Also, it is given that
If a die is roll to a 1 or 2, we win 2usd and if it rolls to 3, 4, 5, or 6 we lose 1 usd.
As, we know that "Probability denotes the possibility of the outcome of any random event". And probability of any event can be calculated as
P(E) = total number of favorable outcomes/ Total number of outcomes
So,
The probability that die rolls 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3
And, the probability thet die rolls 3, 4, 5, or 6
= 1/6 + 1/6 + 1/6 + 1/6
= 4/6
= 2/3
Therefore, the excepted payoff from rolling this die
= [tex]2\times\frac{1}{3} - 1\times\frac{2}{3}[/tex]
[tex]= \frac{2}{3} - \frac{2}{3}[/tex]
= 0 usd
Hence, the expected payoff from rolling the die is 0 usd.
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