The equation that represents the line that is perpendicular to the graph of 4x + 3y = 9 and passes through (-2,3) is
[tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
Let us revise some rules
1. The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]
2. The slope of a line whose equation is ax + by = c is [tex]m = \frac{-a}{b}[/tex], where a is the coefficient of x and b is the coefficient of y
The equation of the given line is 4x + 3y = 9
[tex]m = \frac{-a}{b}[/tex]
whereas a is the coefficient of x and b is the coefficient of y
Therefore the coefficient of x = 4 and the coefficient of y = 3
a = 4 and b = 3
[tex]m = \frac{-a}{b}[/tex]
The slope of the perpendicular line to the given line is [tex]\frac{-1}{m}[/tex]
That means reciprocal the fraction and change its sign
The slope of the perpendicular line = [tex]\frac{3}{4}[/tex]
The form of the equation is y = mx + b
- Substitute m by [tex]\frac{3}{4}[/tex]
y = [tex]\frac{3}{4}[/tex] x + b
To find b substitute x and y in the equation by the coordinates
of a point on the line
The perpendicular line passes through point (-2 , 3)
x = -2 and y = 3
3 = [tex]\frac{3}{4}[/tex](-2) + b
3 = [tex]\frac{-3}{2}[/tex]+ b
Add to both sides
[tex]\frac{9}{2}[/tex] = b
y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation that represents the line that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Hence the answer is perpendicular to graph of 4x+3y=9 and passes through (-2,3) is [tex]y = \frac{3}{4}x+\frac{9}{2}[/tex]
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The diameter of a circle is 52.6 millimeters. What is the circle's area? Use 3.14 for and round your answer to the nearest hundredth.
the circle's area is approximately 2173.22 mm².We can find the radius of the circle by dividing the diameter by 2
what is diameter ?
Diameter is a straight line passing through the center of a circle or sphere and connecting two points on the circumference. It is the longest chord of the circle.
In the given question,
The diameter of a circle is 52.6 millimeters.
We can find the radius of the circle by dividing the diameter by 2:
radius = diameter/2 = 52.6/2 = 26.3 mm
Now, we can use the formula for the area of a circle:
area = π × radius²
Plugging in the values we have:
area = 3.14 × 26.3² = 3.14 × 691.69 ≈ 2173.21 mm²
Rounding to the nearest hundredth, we get:
area ≈ 2173.21 ≈ 2173.22 mm²
Therefore, the circle's area is approximately 2173.22 mm².
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Find the value of the expression (3x – 12) – (1/2xy-10) for x = 3 and y = 6.
-2
Answer:
When x = 3, y = 6,
[tex][3(3)- 12]-[(\frac{1}{2}(3)(6)) -10] = (9-12)-(9-10)[/tex]
[tex]= (-3)-(-1)[/tex]
[tex]= -3+1[/tex]
[tex]=-2[/tex]
For which values of A, B,
and C
will Ax+By = C be a vertical line
through the point (9, 3)?
Answer:
See below
Step-by-step explanation:
A vertical line is just x =
so if a = 1 b = 0 and c = 9 would be a vertical line through the point
so you wind up with x = 9
What is the solution to n/4 = -12.4?
Answer:
Step-by-step explanation:
-12.4 x 4 = -49.6
n = -49.6
Answer:
n = -49.6
Step-by-step explanation:
1. Multiply both sides of the equation by 4
[tex](4)\frac{n}{4}=(4)-12.4[/tex]2. Simplify the expression
n=(4)-12.4n= -4 * 12.4n=-49.6What is the slope of the function y = -5/4x+1
Answer:-5/4
Step-by-step explanation:
the slope is the number next to the letter X.
what are all the fractions that fit between 1/2 and 1
There are infinitely more possibilities, but the midpoint between 1/2 and 1 is 3/4.
what is fraction?
An element of a whole or, more broadly, any number of equal pieces, is represented by a fraction. When used in conversational English, a fraction indicates the number of components of a particular size, as in one-half, eight-fifths, and three-quarters.
For any two numbers a and b, the average 1/2(a + b) is lies between them.
Here, the given two numbers are 1/2 and 1.
So, to find the fraction between 1/2 and 1 we can form the average:
1/2(1/2 + 1) = 1/2(3/2) = 3/4
Hence, the fraction that fit between 1/2 and 1 is 3/4.
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Mia owns a small business selling bagels. She knows that in the last week 85 customers paid cash, 5 customers used a debit card, and 16 customers used a credit card. Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
The probability that the next consumer will use cash as payment is 85/106
85 customers made cash payments.
5 customers used debit cards in total.
16 customers used credit cards in total.
The probability that the following consumer will make a cash payment must be calculated as a fraction in its simplest form.
Total clients: 85 + 5 + 16 = 106
There were 85 successful outcomes (Customers who paid cash)
Therefore, the probability will be: =85/106 = 0.801
Therefore, the probability that the following customer will pay with cash is 85/106.
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Answer:
≈ 80%
Step-by-step explanation:
Based on these results, express the probability that the next customer will pay with cash as a percent to the nearest whole number.
85 cash, 5 debit card, and 16 credit card.
85+5+16= 106
There were a toal of 106 customers. 85 paid with cash.
Probability the next customer will pay with cash:
85/106= 0.801886...
0.801886... ×100% ≈ 80.1887%
≈ 80%
Tom needs to buy plastic forks. Brand A has a box of 36 forks for $1.54. Brand B has a box of 48 forks for $1.66. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent. pls answer
Brand B will be the best because it costs less each fork.
Brand B has price of $0.03 per forks .
What is unit price ?The cost per unit of an item is represented by the unit price. To get the unit price of an item, we divide the price of a specific number of units by the number of units.It is computed by multiplying the total number of units produced by the sum of fixed and variable costs.Here given,
Given that Brand A charges $1,54 for a package of 36forks,
Then the price per fork will be:
= $1.54 / 36
= $0.042
Given that Brand B charges $1.66 for a box of 48 forks,
Then the price per fork will be:
= $1.66 / 48
= $ 0.034
Since brand B has lower cost per fork ,
Brand B will therefore be the finest brand with $0.03 per forks price.
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The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. Create a system of equations to find the smallest number of busses the orchestra can rent.
The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given that, Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.
The system of equations to find the smallest number of busses the orchestra can rent is,
The total number of buses :
b + v ≤ 6
The total number of passengers.
25b + 12v ≥ 111 - - - - (2)
Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
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I would like to be walked through this and see if my answer is correct as well as how to do it
Answer:
perimeter = 16 ft
Step-by-step explanation:
You want the perimeter of an isosceles triangle with side length 5 ft and altitude 4 ft.
Base lengthThe side lengths being equal mean the triangle is isosceles. That also means altitude PS bisects the peak angle and segment QR. Once we find the length QS using the Pythagorean theorem, we can double that measure to find QR.
The Pythagorean theorem tells us ...
QS² +PS² = QP²
QS² +(4 ft)² = (5 ft)²
QS² = (25 ft²) -(16 ft²) = 9 ft² . . . . . evaluate squares, subtract 16 ft²
QS = √(9 ft²) = 3 ft
Now we know the base length is ...
QR = 2·QS = 2(3 ft) = 6 ft
PerimeterThe perimeter is the sum of the outside edge lengths:
Perimeter = PQ +QR +RP
Perimeter = (5 ft) +(6 ft) +(5 ft) = 16 ft
The perimeter of ∆PQR is 16 feet.
__
Additional comment
With some practice, you can learn to recognize a 3-4-5 right triangle. That is the triangle used here for each of the right triangles that make up ∆PQR. Once you identify the long side as 4 and the hypotenuse as 5, you know immediately the short side is 3.
The set {3, 4, 5} is called a "Pythagorean triple." Other triples commonly seen in high school problems are {5, 12, 13}, {7, 24, 25}, {8, 15, 17}. Legs of these lengths form a right triangle. Knowing any two (or their ratio) tells you immediately the value of the third. Of course, these triples can be scaled by any factor. (3, 4, 5) scaled by 2 is (6, 8, 10), another commonly seen triple.
There are no isosceles right triangles that have integer values for both the legs and the hypotenuse. If the legs are both 4, the hypotenuse will be 4√2 ≈ 5.657... (an irrational number), not 5.
Louis recorded how many times he could jump rope without stopping. Here is
his data:
50 15 102 64 29 55 100 97 48 81 61
Find the median, upper quartile, and lower quartile of his data.
Write an equation representing the y-intercept (0,4), (4,2)
Answer:
y = -1/2x + 4
Step-by-step explanation:
Use the slope formula (change in y divided by change in x) to find the slope. (-1/2). Then pick one of the points and plug it back into the new equation using -1/2 as your slope.
A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 25500 kilograms. Other shipments weighing 4800 kilograms have already been loaded into the container. What is the greatest number of 40-kilogram crates that can be loaded into the shipping container?
The greatest number of 40-kilogram crates is 517.5.
From the question, we have
Weight of the crate = 40 kg
Greatest weight that the container can load = 25500 kilograms
Weight of the other shipments on the container = 4800 kg
So the greatest number of 40 kg crates = c
Therefore, the weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container
4800 + 40c ≤ 25500
40c ≤ 25500 - 4800
40c ≤ 20700
c ≤ 517.5
Hence, the greatest number of 40-kilogram crates is 517.5.
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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In triangle ABC, angler A is 35 degrees, and angle b is 20 degrees. Select all triangles which are similar to triangle ABC
The triangle which are similar to ABC are:
Triangle DEF where ∠D is 35° and ∠E is 20°.Triangle JKL where ∠J is 35° and ∠L is 125°.Triangle MNO where ∠N is 20° and ∠O is 125°.The connecting of three non-collinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.
We know that the when we sum all the interior angles of a triangle, we get 180°.
Given that, A triangle ABC has ∠A = 35° and ∠B = 20°.
∴ ∠C = 180° - 35° - 20°.
∠C = 125°.
Triangle will be similar if every corresponding angle of different triangles has the same measure. So, Triangles that are similar to triangle ABC is triangle DEF where ∠D is 35° and ∠E is 20° and triangle JKL where ∠J is 35° and ∠L is 125° and triangle MNO where ∠N is 20° and ∠O is 125°.
Therefore, triangle DEF, JKL and MNO are similar to triangle ABC.
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The given question is incomplete. Here is the complete Question:
The number of members on the basketball team
increased from 9 to 12. What was the percent
increase?
I may be incorrect.
Answer: 33.333333333333%
Step-by-step explanation:
The difference is 1/3. Twelve by three is four. Nine by three is three. The different from 9 to 12 is 1/3.
The velocity v of an object rolled down an inclined plane is given by the formula v= √48d, where d is the distance the object has rolled. Solve the formula for d
d=(Simplify your answer. Use integers or fractions for any numbers in the expression.)
The formula for d is d = v/√48
What is a formula?
In science, a formula is a compact manner of symbolically describing information, such as a mathematical formula or a chemical formula. In physics, the phrase formula refers to the general construct of a connection between given quantities. In mathematics, a formula is an identity that equates one mathematical statement to another, the most significant of which are mathematical theorems. A formula (also known as a well-formed formula) is a logical object that is produced utilizing the symbols and formation rules of a specific logical language. For example, calculating the volume of a sphere necessitates extensive use of integral calculus or its geometrical equivalent, the method of exhaustion.
The equation is given as v= √48d
Hence, the formula for d is, d = v/√48
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Terry deposits a principal amount of $500 in a savings account that earns an annual rate of simple interest. If he makes no deposits or withdrawals, he will earn $40 in simple interest in 4 years. What is the annual rate of simple interest?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$40\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases} \\\\\\ 40 = (500)(\frac{r}{100})(4) \implies 40=20r\implies \cfrac{40}{20}=r\implies \stackrel{\%}{2}=r[/tex]
sample Response: The sample is from the right population, his customers. However, because he is surveying such a small number of people and only asking his best customers (who are probably the most satisfied, or they would not buy so much from him), the results are going to be biased, most likely positive, and not representative of his entire customer base.
What did you include in your response? Check all that apply.
The sample size is too small.
Only sending the survey to his best customers will yield biased results, most likely in the positive direction.
The sample is not representative of the entire population.
The thing to include in the response regarding the sampling include:
The sample size is too small.Only sending the survey to his best customers will yield biased results, most likely in the positive direction.The sample is not representative of the entire population.What is sampling?Sampling is the process of selecting the group from which you will collect data for your research. For example, if you want to know what students think at your university, you could survey 100 of them. In statistics, sampling allows you to test a hypothesis about a population's characteristics.
The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study.
In this case, the sample size wasn't a true reflection of the customers.
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Write an equation that makes it easier to find the number of vertices in an
octahedron, which has 8 faces.
Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.
Given:
Octahedron has 8 faces
Let F be the faces of octahedron
Let V be the vertices of octahedron
we know that:
V + F = 14
Given F = 8 substitute
V + 8 = 14
V = 14 - 8
V = 6
Therefore Equation that makes it easier to find the number of vertices in an Octahedron is V + F = 14 with 8 faces there are 6 vertices.
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Given the parent function y=x. Find the equation of a second line that has a negative y intercept and a positive slope.
For the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.
What is the slope-intercept form of a line?
When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula y = mx + b. (0, b). The y value of the y-intercept point is represented by b in the formula.
For the given parent function y = x.
Comparing with the slope-intercept form y = mx + c, we get
slope(m) = 1, and the y-intercept is c = 0;
So we can make one line such that it has a negative y-intercept and a positive slope.
y = mx + c, where c < 0 and m > 0.
Hence, for the parent function y = x, the equation of the line has a negative y-intercept and a positive slope will be y = mx + c where c < 0 and m > 0.
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Read the description of a proportional relationship. Ever since Brian was a small child, his favorite food has always been carrots. He likes them so much he wants to plant a garden in his backyard just to grow carrots. There is a proportional relationship between the size of Brian's garden (in square feet), x, and the number of carrots he can grow at a time, y. The equation that models this relationship is y=4x. What size garden does Brian need to grow 20 carrots at a time?
The size of the garden That Brian need to grow 20 carrots at a time is 5 square feet
The size of the Brian's garden in square feet = x
The number of carrots that he can grow at a time = y
The equation that models the relationship is
y = 4x
The means the number of carrots that he can grow at a time is directly proportional to the size of the Brian's garden,
The number of carrots that he need to grow = 20 carrots
Substitute the values in the equation and find the value of x
20 = 4x
The size of the garden x = 20/4
= 5 square feet
Hence, the size of the garden That Brian need to grow 20 carrots at a time is 5 square feet
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The difference between a two digit number and the reverse of that number is 18
Answer:
64
Step-by-step explanation:
Meldie made a cube whose side is (3x - 2) inches. Find its volume in cubic inches.
Answer:
x^2(3x-2) cubic inches OR in^3
OR
3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3
I AM UNAWARE IF YOU ASKED THAT ONE SIDE IS (3X-2) OR ALL. I WILL ANSWER BOTH PARTS
-
NOTE: '^' MEANS TO THE POWER OF..
-
Volume = v, abc = 3 sides of cube (height, width, length)
Using the formula for volume in a cube,
[tex]v = abc[/tex]
We can solve this.
If one side is (3x-2)in,
(3x-2)(x)(x) = v.... x are the other two sidesx^2(3x-2) = vx^2(3x-2) cubic inches OR in^3
If all sides are (3x-2)in,
Use the formula,
[tex](a - b) ^{3} = {a}^{3} + 3ab(b - a) - {b}^{3} [/tex]
We can solve this.
(3x-2)(3x-2)(3x-2) = v(3x-2)^3 = v.... 3x = a and -2 = b(3x)^3 + [(3)(3x)(2)][2-3x] - (2)^3 = v27x^3 + 18x(2-3x) -8 = v(27x^3 + 36x - 54x^2) - 8 = v.. Terms inside brackets - take 3x as common and leave out 83x(9x^2 -18x +12) = v... Take 3 as common again in the brackets3x [ 3 ([3x^2 -6x] + 4) -8 = v....Take 3x common in the terms in square brackets3x [ 3 [ 3x (x-2) + 4 ]] - 8 = v3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 = v3x { 3 [ 3x ( x - 2 ) + 4 ] } - 8 cubic inches OR in^3
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___
Which set of ordered pairs represents a function?
A. {(1, 7), (8, -9), (1, -2), (-6, -1)\}{(1,7),(8,−9),(1,−2),(−6,−1)}
B. {(9, 0), (7, 9), (3, -4), (3, -6)\}{(9,0),(7,9),(3,−4),(3,−6)}
C. {(-2, -6), (-5, -6), (9, -2), (7, 3)\}{(−2,−6),(−5,−6),(9,−2),(7,3)}
D. {(4, 7), (8, 1), (-6, -1), (-6, -5)\}{(4,7),(8,1),(−6,−1),(−6,−5)}
The set of ordered pairs that is a function is (c) {(-2, -6), (-5, -6), (9, -2), (7, 3)}
How to determine the ordered pair that is a function?The list of options represents the given parameter
As a general rule, for an ordered pair to be a function;
The y values on the ordered pair must point to different x values
In (a) the y values -1 and 7 have the same x value of 1
So, it is not a function
In (b) the y values -4 and -6 have the same x value of 3
So, it is not a function
In (c) all the y values have different x values
So, it is a function
In (d) the y values -5 and -1 have the same x value of -6
So, it is not a function
Hence, the ordered pair that is a function is (c)
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Answer:
The answer would be C. {(-2, -6), (-5, -6), (9, -2), (7, 3)\}{(−2,−6),(−5,−6),(9,−2),(7,3)}
Step-by-step explanation:
a university found that of its students withdraw without completing the introductory statistics course. assume that students registered for the course. a. compute the probability that or fewer will withdraw (to 4 decimals). 0.2061 b. compute the probability that exactly will withdraw (to 4 decimals). 0.2182 c. compute the probability that more than will withdraw (to 4 decimals). 0.5886 d. compute the expected number of withdrawals.
The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Compute the probability that 2 or fewer will withdraw,To determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:Then, multiply this quantity by, = 190Which is the number of ways to choose 2 students from the total of 20. Therefore:The probability that exactly 2 students withdraw is Following an process determine that: The probability that exactly 1 student withdraw is The probability that exactly none students withdraw is Finally, the probability that 2 or fewer students will withdraw is,= 0.355Compute the expected number of withdrawals.Hence ,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.hence,The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
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Consider a bank with two tellers. Three people, Alice, Betty, and Carol enter the bank at almost the same time and in that order. Alice and Betty go directly into service while Carol waits for the first available teller. Suppose that the service times for each customer are exponentially distributed with mean of 4 minutes. Betty finishes and leaves the bank. Carol goes to the available teller. What's the probability Alice leaves before carol?
The probability that Alice leaves before Carol is 0.5 according to the given information.
What is meant by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur.
If X1 and X2 are both exponential distributions with parameters 1 and 2, respectively, then
P(X₁< X₂)= λ₁/(λ₁+λ₂ )
And P(X>s+t/x>s)=P(X>t), if X≈exp(μ)
Here, Let [tex]X_{A}[/tex], [tex]X_{C}[/tex] denote the service times for Alice and Carol
And also given that,
E[ [tex]X_{A}[/tex]]=1/μ
E[ [tex]X_{A}[/tex]]=4
E[ [tex]X_{C}[/tex]]=4
E[ [tex]X_{A}[/tex]]=E[ [tex]X_{C}[/tex]]=4
So, [tex]X_{A}[/tex], [tex]X_{C}[/tex] ≈exp(1/4)
Now, when Betty completes his service, Alice is still being served, and the remaining time required to complete his service is exp(1/4).
Because the exponential distribution has no memory.
So, P( [tex]X_{A}[/tex]< [tex]X_{C}[/tex] )= λ₁/ λ₁+ λ₂
=(1/4)/((1/4)+(1/4))
=(1/4)/(1/2)
=0.5
As a result, the probability that Alice leaves before Carol is 0.5.
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Write an equation in point-slope form of the line that passes through the point (1, 0) with slope -1/4
Answer:
y = -1/4(x-1)
Step-by-step explanation:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) From the point given [tex]y_{1}[/tex] = 0 and [tex]x_{1}[/tex] = 1
m = slope -1/4 Plug these in and get
y - 0 = -1/4(x - 1) y-0 is just y
Jocelyn and her children went into a movie theater and she bought $75.50 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.50. She bought a total of 18 candies and pretzels altogether. Determine the number of candies and the number of pretzels that Jocelyn bought.
The number of candies bought = 10
The number of pretzels bought = 8
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let,
x = number of candies bought
y = number of pretzels bought.
The equations that describe the given problem are:
4.75 x + 3.5 y = 75.50..........(1)
x + y = 18
x = 18 - y.................(2)
Substitute equation 2 in equation 1,
4.75 (18 - y) + 3.5 y = 75.50
85.5-4.75y+3.5y=75.50
85.5-1.25y=75.50
1.25y=85.5-75.50=10
y=8
Substitute y=8 into x = 18 - y.
x=18-8=10
The number of candies bought is 10, and the number of pretzels bought is 8.
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An angle measures 37.6 degrees less than the measure of its complementary angle. What is the measure of each angle
Answer:
x = 27.1 y = 62.9 x + y = 90
Explaination:
Let's say you have 2 complimentary angles, x and y
So x + y = 90
if x is 35.8 degrees less than the measure of a complementary angle, then x = y - 35.8
Putting this into our x + y = 90 equation, we get (y - 35.8) + y = 90
2y - 35.8 = 90
2y = 90 + 35.8
2y = 125.8
y = 125.8/2 = 62.9 degrees.
so x = 62.9 - 35.8 = 27.1 degrees.
A random sample of 85 printers discovered that 35 of them were being used in small businesses. Find the 99% confidence interval for the population proportion of printers that are used in small businesses
The 99% confidence interval for the population proportion of printers that are used in small businesses, using the z-distribution, is of:
(0.2743, 0.5493)
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the equation presented next:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the point estimate of the parameter.z is the critical value of the z-distribution.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
(the critical value can be found either with the z-table or with a z-distribution calculator).
The sample size and the estimate are listed as follows:
[tex]n = 85, \pi = \frac{35}{85} = 0.4118[/tex]
The lower bound of the interval is obtained as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4118 - 2.575\sqrt{\frac{0.4118(0.5882)}{85}} = 0.2743[/tex]
The upper bound of the interval is obtained as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4118 + 2.575\sqrt{\frac{0.4118(0.5882)}{85}} = 0.5493[/tex]
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