The statement "Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment" is false.
What is a Binomial Experiment?A binomial experiment is an experiment that is repeated multiple times with each repetition having only two potential outcomes. In a binomial experiment, the probability of success remains constant from trial to trial.
The criteria for a binomial experiment are as follows:
The experiment is made up of a fixed number of trials.There are only two possible results for each trial: success and failure.The probability of success for each trial is the same.The trials are all independent of one another.The formula for calculating the probability of x successes in n trials is:P(x) = (ⁿCₓ)(pˣ)(q^(n-x))
Where p is the probability of success, q is the probability of failure (q = 1 - p), and ⁿCₓ is the combination formula.
Therefore, the statement "Ten cards are selected out of a 52-card deck without replacement and the number of Jacks is observed. This is an example of a "Binomial Experiment" being false. This is because the probability of drawing a jack changes with each trial, as the deck's composition changes after each card is drawn.
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1. meredith has 10 reports to file. if each report takes an average of 75 minutes to file, how long will it take her to file 70% of them? a. 5 hours b. 6 hours, 30 minutes c. 8 hours, 45 minutes d. 10 hours
Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.
The time taken by Meredith to file 70% of the 10 reports given, given that each report takes an average of 75 minutes is 6 hours, 30 minutes. Therefore, the correct option is B. 6 hours, 30 minutes. How long will it take Meredith to file 70% of 10 reports, given that each report takes an average of 75 minutes to file?
Here, the total number of reports = 10
Average time to file one report = 75 minutes
To find out the time taken to file 70% of 10 reports, we will need to multiply the average time taken to file one report by the number of reports to be filed, which is 7 in this case:
75 × 7 = 525 minutes
We have calculated the time it will take Meredith to file 7 reports. Now, to convert this time to hours and minutes, we divide the total minutes by 60 to get the hours and then find out the remainder for the minutes:
525 ÷ 60 = 8 hours 45 minutes
Therefore, Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.
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Sally has 3:4 as many beads as Kelly. Kelly has 18 more beads than Sally. Find the average number of beads the girl have
The average number of beads that the girls have is 63
Let's start by using algebra to represent the given information:
Let b be the number of beads that Sally has.
Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.
Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).
Putting these together, we can write the equation:
(3/4)b = b + 18
Solving for b, we get:
b = 72
So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.
The average number of beads that the girls have is (72 + 54)/2 = 63 beads
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a family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. each member of the family averages 8 minutes in the shower per day. in a 30-day period, how many fewer gallons of water will the family use with the new showerheads? responses 60 60 800 800 2,400 2,400 3,600 3,600 7,200
The family will use 3,600 fewer gallons of water with the new showerheads in a 30-day period.
A family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. Each member of the family averages 8 minutes in the shower per day. In a 30-day period, the family will use 3,600 fewer gallons of water with the new showerheads. How many fewer gallons of water will the family use with the new showerheads?
Calculate the number of gallons used per person per shower before:
5 gal/min x 8 min = 40 gallons per person per shower.
The number of gallons used per person per shower after:
2 gal/min x 8 min = 16 gallons per person per shower.
The number of gallons used per person per day before:
40 gallons x 1 shower = 40 gallons per person per day.
The number of gallons used per person per day after:
16 gallons x 1 shower = 16 gallons per person per day
The number of gallons used per family per day before:
40 gallons x 5 people = 200 gallons per day
The number of gallons used per family per day after:
16 gallons x 5 people = 80 gallons per day
The number of gallons used per month before:
40 gallons x 5 people x 30 days = 6,000 gallons per month
The number of gallons used per month after:
16 gallons x 5 people x 30 days = 2,400 gallons per month
The family will use 6,000 - 2,400 = 3,600 fewer gallons of water with the new showerheads in a 30-day period. Therefore, the answer is 3,600.
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4 more than 3 times a number is 5
Answer:
0.33
Step-by-step explanation:
To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5
Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:
3x + 4 = 5
3x + 4 - 4 = 5 - 4
3x = 1
3x/3 = 1/3
x = 0.33
Answer = 0.33
Describe the relationship between n and 4 that makes the equation 7 x n/4 greater that 7
An Inequality is a relationship between two expressions or values that aren't equal. The relationship between n and 4 is given by the inequality n> 4.
We want to find a relation between n and 4 similar that
7 *( n/ 4)> 7
still, we get
If we now divide both sides of the former inequality by 7.
7 *( n/ 4)/ 7>7/7
n/ 4> 1
So n/ 4 must be lesser than 1.
A better way to show the relationship is to multiply both sides of the inequality by 4.
4 *( n/ 4)> 4 * 1
n> 4
So the relationship between n and 4 is that n must be lesser than 4.
In mathematics, an inequality is a relationship that results in an unstable comparison of two figures or other fine expressions. It's frequently used to compare two figures on a number line grounded on their size.
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Dentify the solution to the following system of equations
Identify the solution to the following system of equations
No solution
(0. 29, 2. 73)
(0. 78, 0. 05) and (-4. 32, 12. 80)
( -1, 4. 5)
If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.
To do this, we can set the coefficients of x and y in the two equations equal to each other:
6 - 4m = 2k(2m - 1)
2n - 7 = 3k
Simplifying these equations, we get:
8m - 6 = 4km
2n - 7 = 3k
We can solve the first equation for k:
k = (8m - 6)/(4m)
Substituting this into the second equation and solving for n, we get:
n = (16m - 29)/(8m - 12)
Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.
We find that the expressions for k and n are the same for m = 3/2.
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Complete Question:
Determine the values of m and n so that the following system of linear equations have infinite number of solutions:
(2m−1)x+3y−5=0
3x+(n−1)y−2=0
Please help me with my math!!
Answer:
The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.
Since a = -3 < 0, the parabola opens downwards and has a maximum point.
To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:
x = -3
y = -3(-3+3)^2 + 4 = 4
Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.
Hence, the answer is option C
Answer:
C) Maximum point; 4
Step-by-step explanation:
Given parabola:
[tex]y=-3(x+3)^2+4[/tex]
The given parabola is in vertex form:
[tex]\boxed{y = a(x - h)^2 + k}[/tex]
where:
(h, k) is the vertex of the parabola.a is the leading coefficient.By comparing the given equation with the vertex form, we can see that:
a = -3h = -3k = 4As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.
The vertex of the parabola is (h, k) = (-3, 4).
Therefore, the maximum value of y is 4, which occurs at x = -3.
Help Me Find Y
Show Work
Answer:
y = 12
Step-by-step explanation:
if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is
y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )
y = [tex]\sqrt{144}[/tex] = 12
If Joe has 40 apples and bob steals 5, how many apples does Joe have
Joe aura 35 pommes.
40-5=35
At the book store, you purchased some $5 clearance mystery books and $12 regular-priced science fiction books. How many of each did you buy if you spent a total of $126?
Answer: View answer in explanation below.
Step-by-step explanation: Let's use variables to represent the unknown quantities.
Let x be the number of $5 clearance mystery books purchased.
Let y be the number of $12 regular-priced science fiction books purchased.
We can set up a system of equations based on the given information:
5x + 12y = 126 (total amount spent)
x + y = total number of books purchased
We need to solve for x and y.
Let's use the second equation to solve for one variable in terms of the other:
y = total number of books purchased - x
Now we can substitute this expression for y into the first equation:
5x + 12(total number of books purchased - x) = 126
Simplifying and solving for x:
5x + 12total number of books purchased - 12x = 126
-7x + 12total number of books purchased = 126
-7x = -12total number of books purchased + 126
x = (12total number of books purchased - 126)/7
Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:
If total number of books purchased is 10:
x = (12(10) - 126)/7 = -6/7 (not a whole number)
If total number of books purchased is 11:
x = (12(11) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 12:
x = (12(12) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 13:
x = (12(13) - 126)/7 = 12/7 (not a whole number)
If total number of books purchased is 14:
x = (12(14) - 126)/7 = 18/7 (not a whole number)
If total number of books purchased is 15:
x = (12(15) - 126)/7 = 24/7 (not a whole number)
If total number of books purchased is 16:
x = (12(16) - 126)/7 = 30/7 (not a whole number)
If total number of books purchased is 17:
x = (12(17) - 126)/7 = 36/7 (not a whole number)
If total number of books purchased is 18:
x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)
So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.
a sheet of 8-inch by 10-inch paper is placed on top of a sheet of $8 \frac{1}{2}$-inch by 11-inch paper, as shown. what is the area of the region of overlap in square inches?
The area of the region of overlap between the 8-inch by 10-inch paper and the 8(1/2)-inch by 11-inch paper measures 12 square inches.
The area of the region of overlap between an 8-inch by 10-inch paper and an 8(1/2)-inch by 11-inch paper can be found in the following steps:
Step 1: Calculate the area of each paper. The area of an 8-inch by 10-inch paper is:
[tex]$$\text{Area} = \text{length} \times \text{width} = 8 \text{ in.} \times 10 \text{ in.} = 80 \text{ sq. in.}$$[/tex]
The area of an 8 1/2-inch by 11-inch paper is:
[tex]$$\text{Area} = \text{length} \times \text{width} = \left( 8 \frac{1}{2} \right) \text{ in.} \times 11 \text{ in.} = 93.5 \text{ sq. in.}$$[/tex]
Step 2: Find the horizontal and vertical lengths of the region of overlap.
The horizontal length is the length that is common to both papers, which is 8 inches.
The vertical length is the amount by which the two papers overlap, which is 8(1/2) inches - 10 inches = -1(1/2) inches. However, since the region of overlap cannot have a negative length, we take the absolute value of this result, which is 1(1/2) inches.
Step 3: Calculate the area of the region of overlap.
The area of the region of overlap is the product of the horizontal and vertical lengths:
[tex]$$\text{Area of the region of overlap} = 8 \text{ in.} \times 1 \frac{1}{2} \text{ in.} = 12 \text{ sq. in.}$$[/tex]
Therefore, the area of the region of overlap in square inches is 12 square inches.
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Solve the following simultaneous equations algebraically
xy = 6
y-x=1
Step-by-step explanation:
xy=6
x=6/y (1)
now,
XY=6
6/y-y=6
In the figure below, m 24 = 106°. Find mZ1, m/2, and m 23. 1 X 3 2 ترا = 0° m 22 = ° m2 1 = m 23 = °
Answer:
m<1=74
m<2=106
m<3=74
Step-by-step explanation:
m<1:
=180-106
=74
m<2:
=106
m<3;
if m<1 is 74, m<s will also be 74
80% off of the sale price $90 what is the original price
Answer: So that means the answer is $112.5
Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.
YES THIS IS RIGHT!!!!
write the force equation for the following system b and b are the coefficient of viscious friction and force case by this friction is
The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.
Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b
F is the opposing force of friction. Together, these two forces determine the net force acting on the object.
Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.
Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.
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9(-14)(−2)=
A -15
B 128
C 252
D -252
Answer:
the answer is c
Step-by-step explanation:
add 14 9 times and then whatever that number is double it and remove the negative sign
Suppose 30% of the restaurants in a certain part of a town are in violation of the health code. A health inspector randomly selects nine of the restaurants for inspection. (Round your answers to four decimal places.)
(a) What is the probability that none of the restaurants are in violation of the health code?
(b) What is the probability that one of the restaurants is in violation of the health code?
(c) What is the probability that at least two of the restaurants are in violation of the health code?
a)The probability that none of the restaurants are in violation of the health code is approximately 0.0482.
b)The probability that one of the restaurants is in violation of the health code is approximately 0.3729.
c)The probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.
(a) Probability that none of the restaurants are in violation of the health code:
Let E be the event that a restaurant is in violation of the health code, and let F be the event that a restaurant is not in violation of the health code. Therefore, probability that a restaurant is in violation of the health code is:
P(E) = 0.30
,then the probability that a restaurant is not in violation of the health code is:
P(F) = 1 - P(E) = 1 - 0.30 = 0.70
The health inspector selects 9 restaurants. The probability that none of the restaurants are in violation of the health code is:
P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^9 ≈ 0.0482.
Therefore, the probability that none of the restaurants are in violation of the health code is approximately 0.0482.
(b) Probability that one of the restaurants is in violation of the health code:
The health inspector selects 9 restaurants. We want to find the probability that one of the restaurants is in violation of the health code. We can use the product rule of probability for this. Let us assume that the health inspector selects the first restaurant and that it is in violation of the health code. The probability of that happening is:
P(E) = 0.30
Then the probability that the other eight restaurants are not in violation of the health code is:
P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^8
Then, the health inspector could have selected the restaurant that is in violation of the health code from any of the 9 restaurants. So, we have to multiply by 9.
P(one restaurant in violation of health code) = 9 × P(E) × P(F)^8≈ 0.3729
Therefore, the probability that one of the restaurants is in violation of the health code is approximately 0.3729.
(c) Probability that at least two of the restaurants are in violation of the health code:
Let X be the random variable that denotes the number of restaurants that are in violation of the health code. Then, X can take on values 0, 1, 2, 3, ..., 9.The probability that at least two of the restaurants are in violation of the health code is the same as the probability that two or more are in violation of the health code:
P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)
We can use the sum rule of probability for this.Let us calculate the probability that exactly k of the 9 restaurants are in violation of the health code:
P(X = k) = (9Ck) P(E)k P(F)9−k = (9Ck) (0.30)k (0.70)9−k
Then:P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)= ∑ (9Ck) (0.30)k (0.70)9−k, where k = 2, 3, ..., 9
= 1 − [P(X = 0) + P(X = 1)]= 1 − [1 × (0.70)^9 + 9 × (0.30)(0.70)^8]≈ 0.4681
Therefore, the probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.
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It measure the degree of accuracy of the sample mean as an estimate of the population mean
Answer:
The answer is the standard error is a measure of the accuracy of the sample mean as an estimate of the population mean.
Step-by-step explanation:
A computer store sells Ultra Fast brand desktop and laptop computers. They tracked the sales of both kinds of computers over five days. The table shows the sales data. Make a double-line graph of the data.
The resulting double-line graph should show the sales data for desktop and laptop computers over the five days, with a line for each type of computer.
What is double-line graph?A double-line graph is a graph that displays two sets of data on the same graph, using two lines to show how each set of data changes over time or some other variable.
To create a double-line graph of the sales data for desktop and laptop computers over five days, follow these steps:
Draw a graph with two perpendicular axes, the horizontal axis (x-axis) representing the days, and the vertical axis (y-axis) representing the number of computers sold.
Label the horizontal axis with the days from Day 1 to Day 5.
Label the vertical axis with the heading "Number of Computers Sold".
Plot the data points for desktop computer sales. For Day 1, plot a point at (1, 4), for Day 2 plot a point at (2, 1), for Day 3 plot a point at (3, 2), for Day 4 plot a point at (4, 5), and for Day 5 plot a point at (5, 1).
Connect the data points for desktop computer sales with a line.
Plot the data points for laptop computer sales. For Day 1, plot a point at (1, 5), for Day 2 plot a point at (2, 2), for Day 3 plot a point at (3, 3), for Day 4 plot a point at (4, 7), and for Day 5 plot a point at (5, 3).
Connect the data points for laptop computer sales with a line.
Use a different color or style for the line representing desktop sales and the line representing laptop sales.
Add a legend to the graph to indicate which line corresponds to desktop sales and which corresponds to laptop sales.
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1 Write a positive or negative number to represent each change in the high temperature. Tuesday's high temperature was 4 degrees less than Monday's high temperature.
Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.
Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.
The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.
As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.
using the formula no.
Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.
Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
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the complete question is
Write a positive or negative number to represent each change in the high temperature.
1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?
2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?
3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?
4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?
A grading machine can grade 96 multiple choice test in 2 minutes. if a teacher has 300 multiple choice test to grade, predict the number of minutes it will take the machine the grade the tests. please answer with details please
Answer:
6.25 minutes
Step-by-step explanation:
So, if there are 96 tests being graded in 2 minutes, the average per minute (using the equation 96/2 = average) would be 48 per minute. Next you would do 300/48 to get the number of minutes that it would take to grade that amount. The answer to that would be 6.25, So it would take approximately 6.25 minutes.
What is the measure of arc AC? PLS help
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the probability that you turn to page 45? You can write your answer as a fraction, decimal, or percent What is the probability that you turn to an even numbered page? You can write your answer as a fraction, decimal, or percent
Answer:
(a) Since there are 428 equally likely pages, the probability of randomly turning to page 45 is 1/428, which is approximately 0.00234 or 0.234%.
(b) There are two possible cases for an even numbered page: either the last digit is 0, 2, 4, 6, or 8, or the page number ends in 00.
For the first case, there are 5 possible digits for the units place, and each of these digits can be followed by any one of the 5 possible digits for the tens place. So there are 5x5 = 25 even numbered pages that end in a non-zero digit.
For the second case, there are 4 possible digits for the hundreds place, and each of these digits can be followed by 00. So there are 4 even numbered pages that end in 00.
Therefore, there are 25 + 4 = 29 even numbered pages in total. Since there are 428 pages in the book, the probability of randomly turning to an even numbered page is 29/428, which is approximately 0.06776 or 6.776%.
Step-by-step explanation:
(a) Оскільки існує 428 рівноймовірних сторінок, ймовірність випадкового переходу на сторінку 45 дорівнює 1/428, що становить приблизно 0,00234 або 0,234%.
(b) Існує два можливих випадки, коли сторінка має парний номер: або остання цифра 0, 2, 4, 6 або 8, або номер сторінки закінчується на 00.
У першому випадку є 5 можливих цифр для позначення одиниць, і за кожною з цих цифр може слідувати будь-яка з 5 можливих цифр для позначення десятків. Таким чином, існує 5x5 = 25 парних сторінок, які закінчуються на ненульову цифру.
У другому випадку є 4 можливі цифри для сотень, і за кожною з цих цифр може стояти 00. Отже, є 4 парні сторінки, які закінчуються на 00.
Таким чином, всього є 25 + 4 = 29 парних сторінок. Оскільки в книзі 428 сторінок, ймовірність випадкового переходу на парну сторінку дорівнює 29/428, що становить приблизно 0.06776 або 6.776%.
Can you help me with this?
16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.
What is equatiοn οf line?The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.
16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.
Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:
x + 2y = 14
2y = -x + 14
y = (-1/2)x + 7
The slοpe οf the line is -1/2.
Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.
Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:
y - y1 = m(x - x1)
where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.
y - 5 = (-1/2)(x - (-6))
y - 5 = (-1/2)x - 3
y = (-1/2)x + 2
17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)
perpendicular equations slope would be negative reciprocal to the current line.
The slope in y = -(2/3)x + 4, is m = -(2/3),
The negative reciprocal of -(2/3) is 3/2
Now, applying the x and y values in pοint-slοpe fοrm
y - 6 = 3/2(x - (-4))
y = 3/2(x+4) + 6
y = (3/2)x + 6 + 6
y = (3/2)x + 12
18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.
Lets find the slope using slope formula
[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]
[tex]\rm m = \dfrac{1}{3}[/tex]
Now, using the point slope form
y - 1 = 1/3(x - 3)
y = 1/3(x - 3) + 1
y = (1/3)x - 1 + 1
y = (1/3)x
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Why is pi important in math?
If you walk for 1. 5 hours and at 3mph then for the next 0. 5 hours how fast do you run for an average of 4 mph
In order to have an average speed of 4 mph for the entire trip, you would need to run at a speed of 7 mph for the next 0.5 hours after walking for 1.5 hours at 3 mph.
Let's begin by calculating the total distance covered during the entire trip, which is:
distance = (time walked) x (walking speed) + (time ran) x (running speed)
We know that the time walked is 1.5 hours and the walking speed is 3 mph, so the distance covered during walking is:
distance walked = (time walked) x (walking speed) = 1.5 x 3 = 4.5 miles
We also know that the average speed for the entire trip is 4 mph, and that the total time for the trip is 2 hours. Therefore, the distance covered during the entire trip is:
distance = (average speed) x (total time) = 4 x 2 = 8 miles
So the distance covered during running is:
distance ran = distance - distance walked = 8 - 4.5 = 3.5 miles
Now we can use the formula for average speed:
average speed = total distance / total time
To find the running speed, we need to solve for the running time, which is:
time ran = distance ran / running speed
Substituting this expression into the average speed formula, we get:
4 = (distance walked + distance ran) / (1.5 + time ran)
4 = (4.5 + 3.5) / (1.5 + distance ran / running speed)
Simplifying this expression, we get:
1.5 + distance ran / running speed = 2
distance ran / running speed = 0.5
Substituting the values we calculated, we get:
3.5 / running speed = 0.5
Solving for the running speed, we get:
running speed = 3.5 / 0.5 = 7 mph
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Baseball hats are on sale for 12% off the original price of the sale price is $12.50 what was the original price? round the answer to the nearest cent
The original price of the baseball hat before 12% off in the sale was $14.20.
What is a percentage?A number can be expressed as a fraction of 100 using a percentage. It frequently serves to indicate a portion of a total and is represented by the sign %. We may state that 25% of the class is made up of guys, for instance, if there are 100 pupils in the class and 25 of them are male.
The Roman term per centum, which meaning "by the hundred," is where the word "percent" originates.
Let us suppose the original price of the baseball hat = x.
Given that, baseball hats are on sale for 12% off the original price.
That is,
12.50 = x(1 - 12/100)
12.50 = x(100 - 12)/100
12.50 = x(0.88)
x = 14.2
Hence, the original price of the baseball hat was $14.20.
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Consider a system with one component that is subject to failure, and suppose that we have 120 copies of the component. Suppose further that the lifespan of each copy is an independent exponential random variable with mean 25 days, and that we replace the component with a new copy immediately when it fails.(a) Approximate the probability that the system is still working after 3625 daysProbability(b) Now, suppose that the time to replace the component is a random variable that is uniformly distributed over (0,0.5). Approximate the probability that the system is still working after 4250 days.Probability
We have that, given the system with a component that can fail, we can find the following probabilities
a) Probability that the system continues to function after 3625 days is 0.091b) Probability that the system is still working after 4250 days is 0.018How do we calculate probability using the exponential distribution?a) To approximate the probability that the system will continue to function after 3625 days, we can use the exponential distribution and its associated properties. The probability that the system is still working after 3625 days is equal to the probability that none of the 120 components have failed, which is equal to:
Probability = e(-120*(3625-25)/25) = 0.091
b) To approximate the probability that the system will continue to function after 4250 days, we must take into account the time required to replace a defective component. Since the time required to replace a defective component is a random variable that is uniformly distributed over (0,0,5), the expected time to replacement is 0.25. Therefore, the probability that the system is still working after 4250 days is equal to:
Probability = e(-120*(4250-25)/25) * e(-120*(0.25)/25) = 0.018
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Part of your summer job is to count the number mosquitoes that get caught in traps around your city. At one trap, you count mosquitoes each week ("week 0" means the first day you counted) and record the following numbers:
Use a calculator or graphing technology to determine which of the following functions matches the numbers you counted in these first few weeks.
A) M (w) = 4(w) + 8
B) M (w) = 1.5 (8^w)
C) M (w) = 8 (1.5^w)
D) w = 8 (1.5^M)
Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).
by the question.
To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:
Week Mosquito Count
0 8
1 20
2 50
3 125
4 312
Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:
mosquito graph
Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.
To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.
Option B gives us the following mosquito counts for the first five weeks:
Week Mosquito Count
0 8
1 19.5
2 47.25
3 114.19
4 276.32
Option C gives us:
Week Mosquito Count
0 8
1 12
2 18
3 27
4 40.5
Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.
Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.
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HELP PLEASE !!
Use the information given in the figure to find the length RV.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
5
13
R
T
11
15
0
The length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
so by Pythagoras rule we can evaluate for the length RV by considering the following right triangles:
For ∆TVU:
13² = 5² + TV²
TV = √(13² - 5²) {make TV the subject}
TV = √(169 - 25)
TV = √144
TV = 12
For ∆TVS:
15² = 12² + SV²
SV = √(15² - 12²) {make SV the subject}
SV = √(225 - 44)
SV = √81
SV = 9
For ∆RVS:
11² = 9² + RV²
RV = √(11² - 9²) {make RV the subject}
RV = √(121 - 81)
RV = √49
RV = 6.3246
Therefore, the length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.
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