The situation that is best represented by an exponential distribution is given by the following option:
Tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s?.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
From this, we get that the exponential distribution is used when we want to study the time between events in a distribution, and only the first option in this problem gives it.
As for the other options, the distributions are as follows:
Meteor: Poisson distribution or binomial distribution, mean in a given time, we want to find the probability of a number.Drivers asleep in the highway: Poisson or binomial, also number of events in an interval.People calling in sick: Binomial distribution.Defective tires: Binomial distribution.More can be learned about the exponential distribution at https://brainly.com/question/16371214
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The points (6, -2) and (h, -3) fall on a line with a slope of 1/3. What is the value of h?
======================================================
Work Shown:
m = 1/3 is the given slope
We'll use the slope formula to solve for h.
[tex](x_1,y_1) = (6,-2) \text{ and } (x_2,y_2) = (h,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\\frac{1}{3} = \frac{-3 - (-2)}{h - 6}\\\\\frac{1}{3} = \frac{-3 + 2}{h - 6}\\\\\frac{1}{3} = \frac{-1}{h-6}\\\\1(h-6) = 3(-1)\\\\h-6 = -3\\\\h = -3+6\\\\h = 3[/tex]
-----------------------------
Let's check the answer.
The point (h,-3) updates to (3,-3)
The claim is that the points (6,-2) and (3,-3) fall on a line with slope 1/3.
Use the slope formula to get the following:
[tex](x_1,y_1) = (6,-2) \text{ and } (x_2,y_2) = (3,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - (-2)}{3 - 6}\\\\m = \frac{-3 + 2}{3 - 6}\\\\m = \frac{-1}{-3}\\\\m = \frac{1}{3}\\\\[/tex]
We get a slope of 1/3 as expected.
The answer is confirmed.
A slope of 1/3 means that each time you move up 1 unit (rise), move to the right 3 units (run).
Answer:
17/3
Explanation:
Make it into a fraction like
6-h/-2+3 = 1/3
this equals 6-h/1=1/3
18-3h=1
-18 -18
-3h=17
/-3 /-3
h=17/3
Cannot simplify
h=17/3
I reached my limit so I can't exactly see questions can someone put it in the comments
Answer:
x = 11
Step-by-step explanation:
[tex]3x - 5 = \frac{12 + 4x}{2} [/tex]
Cross multiply expressions
2(3x - 5) = 12 + 4x multiply inside the parenthesis with 2
6x - 10 = 12 + 4x transfer like terms to the same side of the equation
6x - 4x = 12 + 10 add/subtract
2x = 22 divide both sides by 2
x = 11
If there are 6,500 tcf of reserves of natural gas in the world and we are consuming 123 tcf per year, how long until we run out?.
It takes 53 years until we run out of gas.
Given,
Reserves of natural gas = 6500 TCF
Consumption per year = 123 TCF
Therefore,
years left ( x )= Reserves of natural gas / Consumption per year
= 6500/123
= 52.8 years
x = 53 years approximately
So, it takes 53 years until we run out of gas at this rate of consumption.
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Miles owns 25 toy cars and Lee owns 33 toy
cars. How many more toy cars does Lee own
than Miles?
The points (-3, r) and (4, -24) lie on a line with slope -4. Find the missing coordinate r=
If the points (-3, r) and (4, -24) lie on a line with slope -4 then the missing coordinate r = 4.
What is coordinate?
A coordinate in mathematics is any magnitude that is used to define the location of a point, line, or something similar in relation to a fixed figure, system of lines, etc.
Given in the question,
The slope of the line is -4,
The coordinate points on the line are (-3, r) and (4, -23).
The formula to calculate the slope of a line is:
[tex]m = \frac{y_2-y_1} {x_2 - x_1}[/tex]
Here, m = slope, and (x1, y1) ,(x2, y2) are the points on the line
On putting the values given in question in this formula, we get
[tex]-4 = \frac{-24-r} {4 - (-3)}[/tex]
[tex](-4)7 = -24-r[/tex]
[tex]28-24 = r = 4[/tex]
r = 4
Hence, the value of missing coordinate r is 4
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what is the monthly fee being charged? how do you know?
Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.
Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.
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Jordan and his friends bought a few items from a store. a bag of chips is 1/4 the cost of a sandwich . A soda is 3$less than a sandwich.
Write an expression to represent the items
Answer:
I have the same answer and I don't knownit
Find two integers that add up to 2 and multiply to make -15
Answer:
5 and -3
Step-by-step explanation:
You want two integers that have a sum of 2 and a product of -15.
Factor pairsSolving a problem like this can often be done fairly quickly by listing the factor pairs that make up the product. Only the pairs need be listed that have a sum with the same sign as the sum you're looking for.
Divisors of 15 are 1, 3, 5, and 15. You want a negative product with the largest factor being positive:
-15 = 15(-1) = 5(-3)
The sums of these factor pairs are 14 and 2. The latter pair is the one of interest.
The two integers are 5 and -3.
__
Additional comment
The desired relations can be expressed as a quadratic equation. It generally works well to solve it by completing the square.
If one of the numbers is x, the other is 2-x. Their product is -15:
x(2 -x) = -15
2x -x^2 = -15 . . . . . eliminate parentheses
x^2 -2x = 15 . . . . . . make the leading coefficient positive
Complete the square by adding the square of half the x-coefficient
x^2 -2x +1 = 15 +1
(x -1)^2 = 16
x -1 = √16 = 4 . . . . . . take the square root
x = 5 . . . . . . . . . . . add 1
2-x = 2 -5 = -3 . . . . the other number
evaluate the expression when x=-5. x² + 6x - 9
Answer:
- 14
Step-by-step explanation:
substitute x = - 5 into the expression
x² + 6x - 9
= (- 5)² + 6(- 5) - 9
= 25 - 30 - 9
= - 5 - 9
= - 14
Answer:
-14
Step-by-step explanation:
Step 1: Substitute x = -5
[tex]\displaystyle{x^2+6x-9\to (-5)^2+6(-5)-9}[/tex]
Step 2: Evaluate
Keep in mind that negative times negative is positive and positive times negative is negative.
[tex]\displaystyle{=(-5)(-5)+6(-5)-9}\\\\\displaystyle{=25-30-9}\\\\\displaystyle{=-14}[/tex]
Please let me know if you have any questions!
HELP!! // You need to download 4 games for your math class. Each game is the same price. Since this is your first time downloading a game from the site, you are also charged a one-time $0.75 access fee. You are charged a total of $5.50. What is the cost of each game? Show your work and round your answer to the nearest cent.
Answer:1.2
Step-by-step explanation: subtract the one time fee from the total, 5.5-0.75= 4.75 than divide that by 4, 4.75/4= 1.1875 than just round up to $1.20 for each game
Find the volume of the cone. Round your answer to the nearest tenth. Use 3.14 for it.13 cm16 cmThe volume is aboutcm3
we know that
the volume of the cone is equal to
[tex]V=\frac{1}{3}\cdot\pi^{}\cdot r^2\cdot h[/tex]we have
pi=3.14
r=13 cm
h=16 cm
substitute
[tex]\begin{gathered} v=\frac{1}{3}\cdot3.14\cdot(13^2)\cdot16 \\ v=2,830.2\text{ cm\textasciicircum{}3} \end{gathered}[/tex]Volume is about 2,830.2 cubic centimetersWhat is an example of cultural diffusion that was found in Faiyum?
In the Fayum Basin during the first and third century BCE, Egyptians established a practice of painting pictures of their loved ones on wood or linen panels, which would eventually be glued to their mummified remains.
For centuries, scholars have been fascinated by these Fayum mummy portraits. Humans have attempted to identify their departed family members since the dawn of time.
Egyptians were no exception to this rule. Nonetheless, because of the numerous nations that conquered. The pictures were definitely impacted by the influence of different cultures, and they influenced Egypt.
Each leadership wave carried with it new ambitions and influences. With the exception of the Assyrians, who were infamous for their violent reign, and the Persians, each victorious country before the Amon priests aspired to reestablish a Pharaoh, probably to establish the role of a god-king (Kamil, "Coptic Egypt," 16-18). Despite the ruler changes, there remained a quite stable set of Egyptian ideas and customs.
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Suppose that w and x are points on the number line. if wx= 10 and x lies at -13, where could w be located? if there is more that one location, separate then with comas.
The X can be placed on the line at either 23 or -3 on the axis.
Describe line.
A line, according to Euclid, is the distance between two points and can stretch forever in either direction.
Given:
WX=10
W is now at -13.
Right now, we are unsure of whether W or X comes first.
Taking two cases
Case 1:
W comes first before
X is at
=10-(-13)
=23
Case 2:
X came first before
X is at
=10+(-13)
= -3
Therefore, X can be placed at either at 23 or -3 on the axis respectively
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Based on the 2010 census,the population of Georgia was 9.6x10 6 people . Which state had a larger population?
Answer:
new york
Step-by-step explanation:
1.9 x 70 > 7.1 x 50
plsss help me fill in the blanks
Answer:
m<1=
m=0
m<7
=m7
Tama Po ya
a puzzle piece, in the shape of a triangle, has perimeter 30 cm. two sides of the triangle are each twice as long as the shortest side. find the length of each side.
the shortest side is 6 centimeters and the length of each of the other sides is 12 centimeters each.
Let x represent the length of the shortest side of the triangle.
Two sides of the triangle are each twice as long as the shortest side. This means that the length of the two sides would be 2x.
The perimeter of a triangle is the sum of each side of the triangle.
The puzzle piece in the shape of a triangle has perimeter 30 centimeters. This means that
x + 2x + 2x = 30
5x = 30
x = 30/5
x = 6
The length of each of the two sides is
2x = 2 × 6 = 12
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Which of the following could be a real-world description of 2x ?
10
A. The cost of a pizza split by 10 people plus a 2$ tip
B. The cost of a pizza plus a 2$ tip divided by 10 people
C. The cost per pizza for 10 pizzas divided by 2 people
D. The cost per pizza for 2 pizzas divided by 10 people
Step-by-step explanation:
it is not clear what you mean by 2x ? 10.
I assume you mean 2x / 10 (divided).
in any case, D is the only answer that makes sense with a "2x" term.
x would then stand for the price of a single pizza.
2x is then the price for 2 pizzas.
2x / 10 is then the share of the costs of the 2 pizzas per person, if there are 10 people sharing (the costs are evenly split among 10 parties).
What would be the total cost of purchasing the number of shirts needed to use your
coupon—after your coupon is applied and a 7.5% sales tax is charged on the purchase?
Please write a original answer
The total cost of purchasing the number of shirts needed to use your coupon is $40.32.
What is the cost?Discount = 25%
Total price before coupon = $50
Sales tax = 7.5%
Therefore, the calculation based on the information will be:
= Total price - Discount + (Discount × Tax)
= $50 - (50 × 0.25) + (37.5 × 7.5%)
= 50 - 12.5 - 2.82
= $40.32
Therefore, the cost is $40.32.
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Its saying 8/9= w-2 over 6 and the the problem says what is w and then shows improper fractions
To solve this problem we ned to isolate the "w" variable on the left side of the equation, as shown below:
[tex]\begin{gathered} \frac{8}{9}\text{ = }\frac{w}{6}\text{ - }\frac{2}{6} \\ \frac{8}{9}\text{ + }\frac{2}{6}\text{ = }\frac{w}{6} \\ \frac{w}{6}\text{ = }\frac{2\cdot8\text{ + 3}\cdot2}{18} \\ \frac{w}{6}\text{ = }\frac{16+6}{18} \\ \frac{w}{6}\text{ = }\frac{22}{18} \\ w\text{ =}\frac{6\cdot22}{18}\text{ = }\frac{22}{3} \end{gathered}[/tex]The correct answer is the second option.
What is the equation of the line that passes through the point (-2, -2) and has
slope of 3?
A group of people paid a total of $240 to see a concert. The tickets each cost the same amount. There are more than 2 and less than 10 people in the group. What are the possible number of people in the group and the possible amounts paid per ticket?
Using the properties of permutation and combination we can calculate that there are possible 3 ,4 ,5 ,6 or 8 people in the group.
A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.
The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."A combination is a choice of items from a group of different items where the order of the choices is irrelevant.There are 2 to 10 people in the group.
Lets us consider there are 3 people. Ticket price = 240 / 3= $80
Lets us consider there are 4 people. Ticket price = 240 / 4= $60
Lets us consider there are 5 people. Ticket price = 240 / 5= $48
Lets us consider there are 6 people. Ticket price = 240 / 6= $40
Lets us consider there are 8 people. Ticket price = 240 / 3= $30
Hence from the properties of permutation and combination we can see that there could be 3 ,4,5,6 or 8 people.
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Fill in each blank so that the resulting statement is true.
Consider the following long division problem.
3x-4)9x³ +6x² + 13x-5
Begin the division process by dividing
in the dividend.
Begin the division process by dividing
by
by, which obtains
***
which obtains
.Write this result above
.Write this result above in the dividend.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
What are some examples of polynomials?
picture of a polynomial,Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.For instance, the polynomial 3x+2x-5.a description of polynomials.The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. The number 10 is not a polynomial by this definition.However, the polynomial is frequently represented by the number 10 (10,0,0,...).This is an illustration of a symbol that is "overloaded," which can occur in math on sometimes.Ideally, the context will always make the meaning evident. Because whole numbers are singular terms without a variable, they would not be considered polynomials by themselves. However, a whole number could be a part of a polynomial as that polynomial's constant term.The leading coefficient is the first term of a polynomial.4x5+2x2−14x+12.A polynomial is simply a sum of several monomials.A polynomial with only two terms can be referred to as a binomial, and a polynomial with three terms is referred to as a trinomial.(3x-4)9x³+6x²+13x-5
derivative of polynomial
axn-1
3x1-1
3x°
3×1
t=3
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At a local print shop, 10 copies can be made for $4. At this rate, how much would it
cost to make 75 copies?
Answer: $30 for 75 copies.
Step-by-step explanation:
We will set up a proportion to help us solve. Let x be equal to the amount for 75 copies.
[tex]\displaystyle \frac{10 \ copies}{\$4} = \frac{75 \ copies}{\$x}[/tex]
Cross-multiply:
10 * x = 75 * 4
10x = 300
Divide:
x = $30
An asteroid travels 25 kilometres per second how far does it travel in a hour
Answer:
The asteroid will travel 90000 km in an hourStep-by-step explanation:
GivenThe speed of the asteroid is 25 km/secTo find The distance traveled in an hour.SolutionFirst, convert hour into seconds:
1 hour = 60 min = 60*60 sec = 3600 secNow find the distance:
25 km/sec * 3600 sec = 90000 km5. The monthly membership fee at a gym
increased by 10% this year. Last year,
the cost of a monthly membership was
$28.50. What is the total yearly cost for a
membership at the gym this year?
A $307.80
C $334.20
B $319.20
D $376.20
Answer:
D $376.20
Step-by-step explanation:
The monthly membership fee at a gym increased by 10% this year. Last year, the cost of a monthly membership was $28.50. What is the total yearly cost for a membership at the gym this year?
A $307.80
C $334.20
B $319.20
D $376.20
28.50 × 1.10 = $31.35 per month this year
there are 12 months per year so:
$31.35 × 12 = $376.20
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Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?
Group of answer choices
y = x – 2
y = x + 2
y = x + 3
y = x – 5
Answer:
y = x-2
Step-by-step explanation:
slope = 1, point = (5,3)
y-3=x-5
y=x-2
:]
A business breaks even when its production costs are equal to its revenue. The expression 120 + 4x represents the cost of producing x items. Decide on a selling price for each item, and write an expression for the revenue generated by selling x items. How many items would you need to sell at your chosen price to break even? Write an equation and solve it.
The number of items you would need to sell at your chosen price to break even is; 120 items
How to Solve Algebra Word Problems?
We are given the expression that represents the cost of producing x items as;
Cost of producing x units: C = 120 + 4x.
Now, we are told to decide on a selling price for each item. If we decide that the selling price for each item is $5, then it means that;
Revenue generated by selling x units at the rate of $5 per unit is;
R = 5x
For the chosen price to break even, it means that revenue must be equal to cost. Thus;
R = C
Thus;
5x = 120 + 4x
x = 120
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Determine whether each function is an example of exponential growth or decay. Then, find the y-intercept. y=0.5(1/4)^x
Because the base is 1/4, which is smaller than 1, we conclude that this is an exponential decay.
Is the function an exponential growth or decay?
A general exponential function is of the form:
y = A*(b)^x
Where A is the initial value, b is the base, and x is the variable.
If 0 < b < 1, then we have an exponential decay.
if b > 1, then we have an exponential growth.
In this case, the function is:
y = 0.5*(1/4)^x
So b =1/4 < 1.
Then we have an exponential decay.
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Write the equation of the circle given the following information.Center: (-4,3)Diameter: 9
The equation of a circle is given by:
[tex]\lparen x-h)\placeholder{⬚}^2+\left(y-k\right)^2=r^2[/tex]where (h,k) is the center and r is the radius.
In this case we know that the center of the circle is (-4,3). To find the radius we just need to remember that the radius is half the diameter, hence:
[tex]r=\frac{9}{2}[/tex]Plugging the values for the center and the radius we have that:
[tex]\begin{gathered} \lparen x-\left(-4\right))\placeholder{⬚}^2+\left(y-3\right)^2=\lparen\frac{9}{2})^2 \\ \lparen x+4)\placeholder{⬚}^2+\left(y-3\right)^2=\frac{81}{4} \end{gathered}[/tex]Therefore, the equation of the circle is:
[tex]\operatorname{\lparen}x+4)\placeholder{⬚}^2+\left(y-3\right)^2=\frac{81}{4}[/tex]-2(4-3х)-6x = 10
Please show how to check work too
Answer:
No solution
Step-by-step explanation:
-2 ( 4 - 3x ) - 6x = 10
→ Expand brackets
-8 + 6x - 6x = 10
→ Simplify
-8 = 10 ⇒ No solution