With a plane containing 40 lines, no 2 of which are parallel , here are 43 points where exactly 2 lines intersect.
In a plane that contains 40 lines, we are asked to find the number of points where exactly 2 lines intersect. Let's call this number "x".
Since every line intersects exactly 2 points, the total number of line intersections is equal to 2x. In other words, if we add up the number of intersections at each point, the total number should equal 2x.
The problem states that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, and 6 points where exactly 6 lines intersect. At the same time, it states that there are no points where more than 6 lines intersect.
To calculate the total number of intersections, we need to multiply the number of lines that intersect at each point by the number of points, and then add them up. In mathematical terms:
2x = 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6
Expanding the right side of the equation:
2x = 9 + 16 + 25 + 36
= 86
Dividing both sides of the equation by 2:
x = 43
So there are 43 points where exactly 2 lines intersect.
This is because at each point where exactly 2 lines intersect, the number of intersections is equal to the number of lines. In total, these 43 points account for 86 line intersections, which is half of the total number of line intersections in the plane.
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suppose x is the number of times a woman is selected when 3 people are randomly chosen (without replacement) from a group of 2 women and 2 men. what are the possible values of x?
Suppose x is the number of times a woman is selected when 3 people are randomly chosen from a group of 2 women and 2 men, the possible values of x are 0, 1, 2, and 3.
When 3 people are randomly chosen without replacement from a group of 2 women and 2 men, there are a total of 4C₃ = 4 possible outcomes, which we can list as follows:
WWx (two women and one of either gender)
WMx (one woman, one man, and one of either gender)
MWx (one man, one woman, and one of either gender)
MMx (two men and one of either gender)
In each of these outcomes, x represents the number of times a woman is selected. We can see that the possible values of x are 0, 1, 2, and 3, depending on which outcome occurs.
In outcome 1 (WWx), a woman is selected twice, so x = 2.
In outcomes 2 (WMx) and 3 (MWx), a woman is selected once, so x = 1.
In outcome 4 (MMx), no women are selected, so x = 0.
Therefore, the possible values of x are 0, 1, 2, and 3.
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an urn contains 3 red and 7 black balls. (a) you randonly draw the balls out one by one without replacement. what is the probability that the last red ball was the 8th ball out?
The probability that the last red ball was the 8th ball out is 3/10
Number of red balls = 3 red balls
Number of black balls = 7 black balls
Then you randomly draw the balls out one by one without replacement.
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The equation will be
Probability = Number of favorable outcomes / Total number of outcomes
Total number of outcomes = 3 + 7
= 10
Substitute the values in the equation
The probability that the last red ball was the 8th ball out = 3/10
Therefore, the probability is 3/10
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Create a function table of the function y=−2x−3 for the values listed
All the values of y are calculated, the function table is complete. In this case, the final table looks like this
| x | -2x | -2x-3 | y |
| -2 | 4 | 1 | -3 |
| -1 | 2 | -1 | -5 |
| 0 | 0 | -3 | -3 |
| 1 | -2 | -5 | -7 |
| 2 | -4 | -7 | -9 |
The function y=-2x-3 is a linear equation. This means that the graph of the equation is a line with a constant slope. The slope of this line is -2 and the y-intercept is -3. The table above shows the output of the function for different values of x. To calculate the value of y for a given x, the first step is to calculate -2x. Then subtract 3 from the result to get the value of y. For example, for x=-2, -2*(-2)=-4 and -4-3=-3, so y=-3. For x=1, -2*(1)=-2 and -2-3=-5, so y=-5. In this way, the output of the function can be calculated for any given value of x.
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Davis will plant seeds in row that are 3 feet apart. In each row he will plant seeds about 4 to 6 inches apart. Estimate the number of corn seeds Davis can plant in section 1
Davis can plant a total of about 1555 corn seeds in the section one.
Davis wants to plant in a row that are 3 ft apart each row, plant are about 4 to 6 inches apart from each other.
We have to find out that how many plant can be planted. Section 1 has 12 columns 18 rows.
Each block formed by a row and column will have an area of 9 square feet. Each row will have a total of 86.4 seeds of corn seeds in it.
The total number of columns in the section 1 are 54. So, multiplying the number by 54 will get the total number of counts,
Total corn seeds = 86.4 x 54.3
= 1555 corns seeds.
So, a total of 1555 corn seeds can be planted.
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A culture of bacteria has an initial population of 8300 bacteria and
doubles every 10 hours. Using the formula Pt = P0 2^t/d, where Pt is
the population after t hours, P0 is the initial population, t is the time in
hours and d is the doubling time, what is the population of bacteria in the culture after 3 hours, to the nearest whole number?
A STORY OF RATIOS
A positive, finite decimal s is said to be written in scientific notation if it is expressed as a product d x 10", where d
is a finite decimal so that 1 ≤ d < 10, and n is an integer.
The integer n is called the order of magnitude of the decimal d x 10".
Are the following numbers written in scientific notation? If not, state the reason.
Exercise 1
1.908 x 1017
Exercise 2
0.325 x 10-2
Exercise 3
7.99 x 10³2
EUREKA
MATH
Lesson 9:
Scientific Notation
© 2019 Great Mindeurekamath.org
Exercise 4
4.0701 +10
Exercise 5
18.432 x 5
Lesson 9 Classwork 8.1
Exercise 6
8x 10-¹1
85
Exercise 1: Yes, 1.908 x 10^17 is written in scientific notation.
Exercise 2: Yes, 0.325 x 10^-2 is written in scientific notation.
Exercise 3: No, 7.99 x 10^32 is not written in scientific notation. The decimal d must be between 1 and 10, not between 10 and 100.
Exercise 4: No, 4.0701 + 10 is not written in scientific notation. The correct format is d x 10^n.
Exercise 5: No, 18.432 x 5 is not written in scientific notation. The correct format is d x 10^n.
Exercise 6: No, 8x 10^-11 is not written in scientific notation. The correct format is d x 10^n.
Please help me answer this question 20 points
Answer:
uhhhh
Step-by-step explanation:
is 10/x linear or nonlinear
Answer:
10/x is a nonlinear equation. Linear equations represent a straight line in a graph, whereas nonlinear equations are used to represent curves. In this case, the degree of variable y is 1 and the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.
With the given budget, what’s the farthest distance a truck can travel from the warehouse to the retail outlet?
In a circle, a 315° sector has area 504π in2. What is the radius of the circle?
Let's call the radius of the circle "r". The formula for the area of a sector of a circle is given by:
(θ/360) * π * r^2,
where θ is the central angle of the sector in degrees.
In this case, we know that the central angle is 315° and the area of the sector is 504π, so we can set up an equation as follows:
(315/360) * π * r^2 = 504π
Solving for r, we can isolate it on one side of the equation:
r^2 = 504 / (π * (315/360))
To simplify the expression on the right-hand side, we can divide both the numerator and denominator by 45 (which is a factor of both 315 and 360):
r^2 = 504 / (π * (7/8))
Finally, taking the square root of both sides gives us:
r = sqrt(504 / (π * (7/8)))
So the radius of the circle is approximately 17.14 inches.
question 12
help me asap
Answer:
ED = 4 cm
Step-by-step explanation:
given 2 secants from an external point to the circle, then the product of one secant's external part and the entire secant is equal to the product of the other secant's external part and that entire secant, that is
CD × CE = CB × CA
8(8 + x) = 6(6 + 10) = 6 × 16 = 96 ( divide both sides by 8 )
8 + x = 12 ( subtract 8 from both sides )
x = ED = 4 cm
What is the complete square corresponding to x2 – 6x? A. (x – 1.5)2 B. (x – 3)2 C. (x – 4.5)2 D. (x – 9)
Answer:
So the answer is C. (x - 3)^2.
Step-by-step explanation:
The complete square corresponding to x^2 - 6x is (x - 3)^2.
A complete square is a trinomial that can be written in the form (x - a)^2, where a is a constant. To find the complete square of x^2 - 6x, we need to rewrite x^2 - 6x into the form (x - a)^2. We do this by adding and subtracting a constant term to make the trinomial a perfect square.
x^2 - 6x + 9 = (x - 3)^2
So the answer is C. (x - 3)^2.
Please Answer (Iready)
The expression for the given model will be 3÷2/5.
What exactly are expressions?
Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.
Now,
as shown in figure the model is shaded uptil 3
and in 1 unit there are 5 total boxes which are divided in 2 parts
Therefore, it will be represented by 3÷2/5.
Hence,
The expression for the given model will be 3÷2/5.
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The amount of time required to download a song from Michael's computer to his music player is the same for each song he downloads.
A linear model of this situation contains the values (138 , 96.6) and (238 , 166.6), where x represents the number of songs he wants to download to his music player, and y represents the total amount of time, in minutes, it will take him to download the songs.
What is the rate of change in this linear model?
A.
100 minutes per song
B.
0.35 of a minute per song
C.
1.4 minutes per song
D.
0.7 of a minute per song
This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).
What is a linear model?A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.
A linear equation is so named because plotting the graph of a given linear model yields a straight line.
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Shade ______ line
for greater than (>).
[tex]above \: the \: line[/tex]
PART A
How many solutions does the system have? Explain.
PART B
Identify the slope and y-intercept of each line. What do you notice about
the slopes of the lines?
The slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
In the given graph two lines are plotted.
Part A: From the graph, the two equations are intersected at (-1.5, 0) and the solution is (-1.5, 0).
Part B: Slope and y-intercept
Equations of lines from the graph are y=3/4 x+1 and y= -4/3 x-2.
For the equation y=3/4 x+1,
Compare, y=3/4 x+1 with y=mx+c, we get
Slope (m)= 3/4 and the y-intercept (c)=1
For the equation y= -4/3 x-2,
Compare, y= -4/3 x-2 with y=mx+c, we get
Slope (m)= -4/3 and the y-intercept (c)=-2
Therefore, the slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.
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in exchange of a square plot of side 96m,a man wants toaccquire a rectangular plot 180m long and of the same area of the square plot . find the width of the rectangular plot
If the length of the rectangular plot is 180m , then the width of the rectangular plot is 51.2 m .
The Area of square plot is ⇒ Area = (Side) × (Side),
In this case, Side is = 96m,
So , the area of the square plot is : A = 96m x 96m = 9216 m² .
The Area of Rectangular Plot is ⇒ A = (Length) × (Width) ;
We know that the area of the rectangular plot is the same as that of the square plot,
that means ⇒ Length × Width = 9216 m² ;
We also know that Length = 180m, so we substitute this value in the equation above ;
⇒ 180m × Width = 9216 m² ;
Dividing both sides by 180m ;
we get ;
⇒ Width = 9216/180 ;
⇒ Width = 51.2 m ;
Therefore, the width of the rectangular plot is 51.2 meters.
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The given question is incomplete , the complete question is
In exchange of a square plot of side 96 m, a man wants to acquire a rectangular plot of 180m long and of the same area of the square plot .
Find the width of the rectangular plot .
Camden is working two summer jobs, making $10 per hour babysitting and making $18 per hour lifeguarding. In a given week, he can work no more than 14 total hours and must earn no less than $180. If Camden worked 9 hours lifeguarding, determine the minimum number of whole hours babysitting that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.
Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
Let's call the number of hours Camden works babysitting "x".
We know that x + 9 (hours of lifeguarding) cannot be more than 14 and that his total earnings must be at least $180. So we can write two equations based on these conditions:
x + 9 ≤ 14 (hours worked can't exceed 14)
10x + 18 × 9 ≥ 180 (earnings must be at least $180)
Now we can substitute the first equation into the second:
10x + 18 × 9 ≥ 180
10x + 162 ≥ 180
10x ≥ 18
x ≥ 1.8
Since x has to be a whole number of hours, we round up to find that Camden must work at least 2 hours babysitting.
So, Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.
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What is the area of this compound figure?
Answer:
(24) + (20) + (8) = 52 ft^2
Step-by-step explanation:
This figure is a compound of 3 rectangles that can be split up like in my attached picture.
The top, horizontal rectangle is 8x3 = 24 sq ft.
The bottom, almost square rectangle is 4x5 = 20 sq ft.
The middle rectangle has a height of 4 feet and a width of (8-6) = 2 feet.
So, its area is 4x2= 8 sq ft.
The compound figure is the sum of all of these areas:
24 + 20 + 8 = 52
The area of the compound figure is 52 sq ft.
Area of 1 = 8 * 3 = 24
Area of 2 = 4 * 2 = 8
Area of 3 = 5 * 4 = 20
Total area = 24 + 8 + 20 = 52
A large data set includes samples of body temperatures. Analyzing one sample of body temperatures results in n=107, x=98.19°F, and s=0.624°F. It is
commonly believed that humans have a mean body temperature of 98.6°F. If the analysis is repeated with a different sample and it is found that for 100
randomly generated samples, 38 of these generated samples have a mean that is as extreme as the mean of the actual sample, what should be concluded
about the assumed mean of 98.6°F? (Assume that an event is significant if it has a probability of 0.05 or less.)
Since 38 of the 100 samples have means that are as much as the sample mean, then that sample mean
strong evidence against the assumed mean of 98.6°F. It appears the population mean
▼98.6°F.
so there
The profanity filter refused my answer.
Please find it in the txt file.
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Simplify the expression below:
14^2 - 24 / 3(2)
--------------------- (divided by)
|-3 + 2(6)|
Answer:
I got 20 when calculating this
what fraction is equivalent to 3/5
Answer:15/25
Step-by-step explanation:
32 children voted for thier favorite ice cream chocolate 3/8 so how may children voted for chocolate explanation step by step plssss
On solving the provided question we can say that The result of multiply the total number of kids by the proportion of those who enjoy chocolate is 12
What is Multiplication?Along with addition, subtractiοn, and division, multiplication is one of the four arithmetic operations. Multiplicatiοn in math refers to regularly adding groups of the same size. The formula for multiplication is multiplicand multiplier Equals prοduct.
Specifically, multiplicand: First number (factοr). divider: Second number (factor). After multiplying the multiplicand and the multiplier, the result is knοwn as the product. Multiple additiοns are made while adding numerals. as in 5 times 4 Equals 5 + 5 + 5 + 5 = 20, I multiplied 5 by 4 times. Multiplication is frequently referred tο as "doubling" because οf this.
The result of multiply the tοtal number of kids by the proportion of those who enjoy chocolate is
32 × 3/8 = 12
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On Thursday a theme park sells 627 tickets. Each ticket costs
£54.99. The park has costs of £18,273 on Thursday. What is the
percentage profit that the theme park make on Thursday?
Answer: The theme park made a 46.8% profit on Thursday.
Step-by-step explanation:
Step 1: First, we need to calculate the total revenue from ticket sales:
627 tickets x £54.99 = £34,341.73
Step 2: Subtract the costs from the total revenue:
£34,341.73 - £18,273 = £16,068.73
Step 3: Calculate the percentage profit:
£16,068.73 / £34,341.73 x 100 = 46.8%
The theme park made a 46.8% profit on Thursday.
In a lottery, the top cash prize was $693 million, going to three lucky winners. Players pick five different numbers from 1 to 51
and one number from 1 to 42. -
A player wins a minimum award of $400 by correctly matching four numbers drawn from the white balls (1 through 51) and
matching the number on the gold ball (1 through 42). What is the probability of winning the minimum award?
The probability of winning the minimum award is.
(Type an integer or a simplified fraction.)
Answer:
1/237.12.
Step-by-step explanation:
The probability of winning the minimum award can be calculated by multiplying the probability of picking 4 numbers correctly from 1 to 51 and then multiplying by the probability of picking 1 number correctly from 1 to 42.
The probability of picking 4 numbers correctly from 1 to 51 is given by the formula:
(number of combinations of 4 numbers from 51) / (number of combinations of 5 numbers from 51)
= (51 choose 4) / (51 choose 5)
= 51! / (4! * 47!) / (51! / (5! * 46!))
= (51 * 50 * 49 * 48) / (5 * 4 * 47 * 46)
= 19600 / 10,946
= 1/5.6 approximately
The probability of picking 1 number correctly from 1 to 42 is given by the formula:
1/42
The final probability of winning the minimum award is given by multiplying the above two probabilities:
1/5.6 * 1/42 = 1/237.12
So, the probability of winning the minimum award is approximately 1/237.12.
What does the point (7,84) represent in this situation?
The point (7,84) represents a precise location on a graph or coordinate plane.
A coordinate is a set of values that specifies the position or location of a point in a geometric space.
The point (7,84) represents a specific location on a graph or coordinate plane. The first number, 7, represents the point's position on the x-axis, which is a horizontal line that runs left to right. The second number, 84, represents the point's position on the y-axis, which is a vertical line that runs up and down. Together, the two numbers give us a precise location for the point.
In this situation, we don't have enough context to know what the point (7,84) represents. It could be the location of a city on a map, the amount of rainfall in inches on a specific day, or the price of a stock at a particular time. However, regardless of the situation, the point (7,84) is simply a specific location in a two-dimensional space that has been identified using coordinates.
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Complete Question:
What does the point (7,84) represent in the graph? And define the explanation for each value.
2. Use the Rational Root Theorem to list all possible rational roots for the equation.
3x³ +9x-6=0
2
O±1, 12, 13, 16, ±, ± -
6,±3⁄3,±0
T
تانی
O±1, ±3, ±6
2
O±1, ± 2, ±3, ±6, ± -, ± -, ±=
3 3
NI
3
1/3
WIN
112
±1, +2, +3, +9,-,-
, -, ±一,土
13
MIN
3
2
The possible rational roots of the equation 3x³ + 9x - 6 = 0 are given as follows:
± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.
How to obtain the potential zeros of the function?To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.
The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 3.Constant term of 6.The factors are given as follows:
Factors of 3: {1, 3}.Factors of 6: {1, 2, 3, 6}.Hence the possible roots are given as follows:
± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.
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The first term of an A. P is 5 and the 10th term is 95 to find S10
The first term of an arithmetic progression is 5 and the 10th term is 95. The sum of the first 10 terms is 455.
The sum of the first 10 terms of an arithmetic progression (A.P.) can be found using the formula:
S_n = n/2 * (2a + (n-1)d)
where a is the first term, d is the common difference, and n is the number of terms.
Given that the first term is 5 and the 10th term is 95, we can find the common difference (d) using the formula:
a_n = a + (n-1)d
Plugging in n = 10 and a = 5, we get:
95 = 5 + (10 - 1)d
Solving for d, we get:
d = (95 - 5) / (10 - 1) = 9
Now that we know the common difference, we can find the sum of the first 10 terms:
S_10 = 10/2 * (2 * 5 + (10 - 1) * 9) = 10/2 * (10 + 81) = 10/2 * 91 = 455
So, the sum of the first 10 terms is 455.
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In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the ___________ come from a normal distribution.a. Response Variableb. Errorsc. Observationsd. Explanatory Variable
In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the errors come from a normal distribution.
The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution centred on the mean, implying that data closer to the mean occur more frequently than data further away from the mean.
The normal quantile plot of the residuals in a simple linear regression model is used to establish if it is reasonable to think the errors are normal.
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Can anyone help me with this?
I just don't get it much
That would be much appreciated Ty
