Answer:
AB = 27
Step-by-step explanation:
AC = AB + BC
[tex]{ \rm{57 = 3x + (4x - 6)}} \\ \\ { \rm{57 = 7x - 6}} \\ \\ { \rm{7x = 57 + 6}} \\ \\ { \rm{7x = 63}} \\ \\ { \rm{x = 9}}[/tex]
Therefore;
[tex]{ \rm{AB = 3x = 3 \times 9}} \\ { \boxed{ \rm{AB = 27}}}[/tex]
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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Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the car was set to 60 miles per hour by cruise control, and the mpg were recorded at random times. Here are the mpg values from the experiment:37.221.017.424.927.036.938.835.332.323.919.026.125.841.434.432.525.326.528.222.1Suppose that the standard deviation of the population of mpg readings of this vehicle is known to be σ=6.5mpga) What is σx¯, the standard deviation of x¯ (x Bar)?b) Based on a 95% confidence level, what is the margin of error for the mean estimate?c) Given the margin of error computed in part (b), give a 95% confidence interval for μμ, the mean highway mpg for this vehicle. The vehicle sticker information for the vehicle states a highway average of 27 mpg. Are the results of this experiment consistent with the vehicle sticker?
The car sticker information indicates a highway average of 27 mpg, while the sample mean's standard deviation is around 1.455 mpg. The mean estimate's margin of error is roughly 3.06 mpg.
How does a car determine its fuel efficiency?The simplest approach to figure out your gas mileage is to simply divide the distance driven by the quantity of petrol your car required to fill up. That amounts to kilometers traveled divided by petrol consumed.
a) The formula for the standard deviation of the sample mean, σx¯, is:
σx¯ = σ / sqrt(n)
where σ is the standard deviation of the population, and n is the sample size. In this case, σ = 6.5 mpg and n = 20. So,
σx¯ = 6.5 / sqrt(20) ≈ 1.455 mpg
b) To find the margin of error for the mean estimate at a 95% confidence level, we can use the following formula:
Margin of error = z* (σx¯)
where z* is the critical value for a 95% confidence interval, which is 1.96.
Therefore, the margin of error = 1.96 * 1.454 = 2.85 mpg.
c) To find the 95% confidence interval for the mean highway mpg for this vehicle, we can use the following formula:
Confidence interval = x¯ ± Margin of error
where x¯ is the sample mean, which can be calculated by adding up all the mpg readings and dividing by the sample size:
x¯ = (37.2+21.0+17.4+29.2+7.4+27.0+36.9+38.8+35.3+32.3+19.0+26.1+25.8+41.4+34.4+32.5+26.5+28.2+22.1) / 20
= 29.231 mpg
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Why is pi important in math?
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.
Question 53 Look at the performance review below, if you know that person 6 has a perfect score, you can calculate each person's score using the graph. If you know that person 3 hasn't achieved any of their goals this year, Person 5 has an excellent personality and very good job knowledge, and Person 4 is more interested in hanging out at the water cooler than in getting work done, then who must the performance review belong to? Total number of points per employee Peson P2 Pesen3Psen 4 PeronS Person Rating Scale Category Ratings General Quality of Work 4 Very Good Good Job Knowledge Fair Communication Skills Personality Management Ability Contribution to Group Poor 4. Achievement of Goals Person5 2. Person 4 3. Person 3
Without specific details it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. So, based on the information we can define some data as below.
Define the term graph?A graph in x-y axis plot is a visual representation of functions or data points. The dependent or vertical variable represented by y-axis, while the independent or horizontal variable represented by the x-axis.
Without the specific details of the performance review or the names of the employees, I cannot provide an exact answer. However, based on the information given, we can infer the following:
Person 6 : has a perfect score.
Person 3 : not achieved any of their goals.
Person 5 : excellent personality and very good job knowledge.
Person 4: more interested in hanging out at the water cooler.
Given this information, it is difficult to determine who the performance review belongs to as we do not have specific scores for each employee. We also do not have enough information to make an informed judgment about the performance of each employee. It is possible that the review could belong to any of the employees, depending on their individual scores and performance.
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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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After 6 new students entered the Happy Hearts Childcare Center and 2 students exited, there were 3 times as many students as before. How many students were present before students entered and exited the center?
Answer: 2
Step-by-step explanation:
If there are three times as many students when there are 6 students you do 6 divided by three to give you two.
find the equation of the line with the given properties. express the equation in general form or slope intercept form. perpendicular to the line -4x+y=43 ; contains the point (-8,10)
The equation of the required line in slope-intercept form is y = -1/4x + 8.
Here are the steps to find the equation of the line:
Step 1: Find the slope of the given line in slope-intercept form
y = mx + c
-4x + y = 43 ⇒ y = 4x + 43... (1)
Here, the slope (m1) of the given line is 4.
Step 2: Find the slope of the required line as the two lines are perpendicular to each other.
m1 × m2 = -1
[As the given line and the required line are perpendicular to each other]
4 × m2 = -1 ⇒ m2 = -1/4
So, the slope (m2) of the required line is -1/4.
Step 3: Write the equation of the required line in point-slope form.
y - y1 = m(x - x1)
[Using the point-slope formula]
Let (x1, y1) = (-8, 10)m = -1/4
Putting the values in the above formula, we get
y - 10 = -1/4(x - (-8)) ⇒ y - 10 = -1/4(x + 8)... (2)
Step 4: Simplify the above equation to get the required equation of the line in slope-intercept form.
y - 10 = -1/4x - 2 ⇒ y = -1/4x + 8... (3)
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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
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
If Joe has 40 apples and bob steals 5, how many apples does Joe have
Joe aura 35 pommes.
40-5=35
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:
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
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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help me pls♀️♀️♀️. is the function linear, quadratic, or exponential
Answer: Quadratic (not 100% sure)
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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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%.
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.
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. ?
3:27 PM Mon Mar 13
Acellus
Law of Cosines
26
Solve for C.
50
29
C = [?]°
Round your final answer
to the nearest tenth.
Law of Cosines: c²= a² + b² - 2ab-cosC
Measure of Angle C
Enter
3
ဇာ
Help Resources
Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.
what is angle ?A geometric figure known as an angle is created by two lines that share an endpoint and are referred to as the angle's sides and vertex, respectively. The quantity of rotation required to align one side with the other side around the vertex is the angle's unit of measurement. Typically, angles are expressed as degrees or radians, where a complete rotation equals 360 degrees or 2 radians. Angles are frequently used to define the position and orientation of lines and shapes in geometry, trigonometry, and other branches of mathematics.
given
As a result of the Rule of Cosines, we have:
A2 Plus B2 - 2ab cos = c2 (C)
Adding the specified values:
c² = 26² + 29² - 2(26)(29) cos(50°)
c² = 676 + 841 - 1508 cos(50°)
c² = 1517 - 1508 cos(50°)
c ≈ √(1517 - 1508 cos(50°))
c ≈ 17.2° (rounded to the closest tenth)
Consequently, C = 17.2° as by the result of the Rule of Cosines , rounded to the nearest tenth.
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Answer:
C= 23.22
This is the answer this question.
Which of these subsets are subspaces ofM2×2? For each one that is a subspace, write it as a span. For each one that is not a subspace, state the condition that fails. (a). A = {((a, 0), (0, b)): a+b = 5}
Let X and Y be two matrices in A. We can write X = ((x,0),(0,y)) and Y = ((z,0),(0,w)). If we add X and Y, we get((x+z,0),(0,y+w)). The sum is in A if and only if x+z+y+w=5.
Subset of M2x2:A subset of M2x2 is a set that contains some elements of M2x2.
A subset of M2x2 can be considered as a subspace if it meets the following conditions:
it contains the zero vector, it is closed under addition, and it is closed under scalar multiplication.M2x2 is a set of 2x2 matrices with real entries. M2x2 has 4 elements, which are (1,0), (0,1), (0,0), and (1,1).Let A = [tex]{((a,0),(0,b)):a+b=5}.[/tex]To determine if A is a subspace of M2x2, we need to verify that A meets the following conditions:
it contains the zero vector, it is closed under addition, and it is closed under scalar multiplication.Zero vector:To find the zero vector, we need to find a matrix in A such that [tex]a+b=0.[/tex] We can easily see that this is not possible because (a,0) and (0,b) are non-negative, and their sum cannot be zero. Therefore, A does not contain the zero vector.Addition:A is closed under addition if the sum of any two matrices in A is also in A. Let X be a matrix in A and c be a scalar. We can write X = ((x,0),(0,y)). If we multiply X by c, we get((cx,0),(0,cy)). The product is in A if and only if cx+cy=5c. Therefore, A is not closed under scalar multiplication.for such more questions on subset matrices
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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
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
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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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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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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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.
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Conditional probabilities. Suppose that P(A) = 0.5, P(B) = 0.3, and P{B \ A) = 0.2. Find the probability that both A and B occur. Use a Venn diagram to explain your calculation. What is the probability of the event that B occurs and A does not? Find the probabilities. Suppose that the probability that A occurs is 0.6 and the probability that A and B occur is 0.5. Find the probability that B occurs given that A occurs. Illustrate your calculations in part (a) using a Venn diagram.
The probability that both A and B occur is given by P(A and B) = P(B | A) * P(A) = 0.2 * 0.5 = 0.1.
This can be visualized using a Venn diagram, where the intersection of A and B represents the probability of both events occurring, which is equal to 0.1 in this case.
The probability of B occurring and A not occurring is given by P(B and not A) = P(B) - P(B | A) * P(A') = 0.3 - 0.2 * 0.5 = 0.2. This represents the area of the B circle outside of the A circle.
Given that P(A) = 0.6 and P(A and B) = 0.5, we can use Bayes' theorem to find P(B | A) as follows: P(B | A) = P(A and B) / P(A) = 0.5 / 0.6 = 0.83. This means that the probability of B occurring given that A has occurred is 0.83.
We can also visualize this using a Venn diagram, where the overlap between A and B represents the probability of both events occurring, and the B circle represents the probability of B occurring given that A has occurred.
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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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