The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.
The linear functionLinear function: y = 3x + 1
x y
3 10
5 16
7 22
9 28
The linear function is positive, which means that the airplane's altitude is increasing as it moves towards the right on the graph. In context, this means that the airplane is ascending as it moves away from the observer towards the rainbow.
The system of equations created by the two functions is:
y = -x^2 + 19
y = 3x + 1
By substituting y in the second equation with the first equation, we get:
-x^2 + 19 = 3x + 1
Solving for x, we get:
x = -2 or x = 5
Substituting these values of x back into either of the equations, we get the corresponding values of y:
(-2, 7) and (5, 16)
These two solutions represent the points of intersection between the rainbow and the airplane's trajectory.
The domain of the rainbow is all real numbers, while the range is y ≤ 19. In context, this means that the rainbow can appear at any point in the observer's field of view, but its highest point is at y = 19.
All of the values in the domain and range make sense in this situation since they are within the physical limits of the observer's perception.
The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.
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What is the distance between points (4, -2) and (4,4) on a coordinate plane
Answer:
The distance between points (4, -2) and (4,4) on a coordinate plane is 6 units. This is because the two points lie on the same vertical line, where the x-coordinate remains constant at 4. To find the distance between them, we simply need to subtract their y-coordinates: 4 - (-2) = 6. Therefore, the distance between the two points is 6 units.
You are going to have a birthday party and serve pizza. You plan to order pepperoni pizza that costs $8 each and sausage pizza that costs $6 each. You need 100 pizzas and have $740 to spend, how many of each type of pizza can you buy?
Therefore , the solution of the given problem of unitary method comes out to be you can purchase 30 sausage and 70 pepperoni pizzas to serve at your birthday party.
Define unitary method.To complete the assignment, make use of the tried-and-true fundamental technique, the actual variables, and any insightful knowledge you gain from the general and detailed questions. In response, customers might be given another opportunity to sample the products. We will miss out on substantial expression gains in programming comprehension if these changes don't take place.
Here,
Let's use "p" for the quantity of pepperoni pizzas and "s" for the quantity of sausage pizzas. Finding p and s values that meet the requirements is necessary.
In light of the information provided:
One pepperoni pizza costs $8.
One sausage pizza costs $6.
100 pizzas are required.
Budget total: $740
To reflect the stated conditions, we can construct the following system of equations:
=> p + s = 100 (1)
=> 8p + 6s = 740 (2)
=> 8p + 8s = 800 (3)
=> 8p + 6s - (8p + 8s) = 740 - 800
=> -2s = -60
=> s = (-60)/(-2)
=> s = 30
=> p + 30 = 100
=> p = 100 - 30
=> p = 70
With a $740 budget, you can purchase 30 sausage and 70 pepperoni pizzas to serve at your birthday party.
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Find the missing side
Please help
Answer:
The answer is D. 4(sqrt(5))
Step-by-step explanation:
To find this we use the Pythagorean Theorem a^2+b^=c^2
So making 4 = to a, and 8 = to, and x = to, we do
4^2+8^2= 80
Then we take the square root of 80 to find the missing side, which is equal to 4(sqrt(5)
Good luck!
Which of the following equations will produce the graph shown below? A. x²/20 + y²/20 = 1 B. 20x² - 20y² = 400 C. 6x² + 6y² = 144 D. 5x² + 5y² = 80
An equation that will produce the graph shown above include the following: D. 5x² + 5y² = 80.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Based on the information provided above, we have the following parameters:
Radius, r = √16 = √80/5
Center, (h, k) = (0, 0).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 0)² = (√80/5)²
5x² + 5y² = 80.
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You paid $6.99 for a shirt that was 70% off; what was the original price of the shirt?
Answer:
$23.30
Step-by-step explanation:
We Know
You paid $6.99
The shirt was 70% off
$6.99 = 30%
What was the original price of the shirt?
We Take
(6.99 ÷ 30) x 100 = $23.30
So, the original price is $23.30
In a company, 80% of the workers are women. If people work for the company who aren't women , how many workers are there in all?
There are a total of 2000 workers in all in the company
How many workers are there in all?From the question, we have the following parameters that can be used in our computation:
Women percentage = 80%
People not women = 400
Using the above as a guide, we have the following:
People not women percentage = 1 - 80%
Evaluate
People not women percentage = 20%
So, we have
People not women = People not women percentage * Total
substitute the known values in the above equation, so, we have the following representation
20% * Total = 400
Divide
Total = 2000
Hence. there are 2000 people in the company
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I am struggling if you have done this assignment before don't hesitate to send the whole thing
The values of x, y and z are given as follows:
x = 10.7.y = 12.3.z = 21.8.What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The bases for the triangle in this problem are given as follows:
6 and 19.
Hence the segment x is obtained as follows:
x² = 6 x 19
x = sqrt(6 x 19)
x = 10.68.
Applying the Pythagorean Theorem, the value of y is given as follows:
y² = 6² + 10.68²
y = sqrt(6² + 10.68²)
y = 12.25.
The value of z is given as follows:
z² = 10.68² + 19²
z = sqrt(10.68² + 19²)
z = 21.8.
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If you look up the definition of absolute in the dictionary, you’ll find several definitions. All of them reference totality, completeness, and having no limitations or dependence on anything else. The definition of the absolute value of a number is its magnitude, or distance, from zero. How do these two definitions connect?
A relationship between two definitions can be seen through the idea of magnitude or distance.
How do these two definitions connect?Finding an absolute value of a number requires us to inspect the difference between that figure and zero on a number line; this amount is always positive regardless of whether the initial number was negative or positive. To illustrate, the absolute value of -5 is 5 since there is only five units separating it from zero.
The absolute value primarily entails a totality- recognizing the entirety of someone's peculiarity independent of their direction. It serves as a method of measuring the scope or size of a number without any external parameters or assessment.
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Find the interest
earned:
$9,900 for 24 months
at 7.8% annual simple
interest
To find the simple interest earned on an investment, we use the formula:
I = P * r * t
Where:
I = simple interest earned
P = principal amount invested
r = annual interest rate (as a decimal)
t = time period of investment (in years)
In this case, we have:
P = $9,900
r = 7.8% = 0.078 (since the rate is given as an annual rate, we need to divide by 100 to get the decimal equivalent)
t = 24 months / 12 months/year = 2 years
Substituting these values into the formula, we get:
I = 9,900 * 0.078 * 2
= $1,545.60
Therefore, the simple interest earned on the investment is $1,545.60.
50 points. use rotation tool in top right to flip upright.
Answer:
(a) 56%
(b) 28%
Step-by-step explanation:
Hope this helps! :)
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the 6 months before the exercise program began and in the 6 months following the exercise program. Following are the results.
Employee Before After
1 8 7
2 7 3
3 8 2
4 8 4
5 6 5
6 7 10
7 6 4
8 8 9
At the 0.050 significance level, can he conclude that the number of absences has declined?
a. Compute the test statistic.
b. Compute the p-value.
The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073.
How to solve the question?
To determine whether the fitness program has had a significant effect on reducing employee absenteeism, we need to conduct a hypothesis test.
Null hypothesis: The average number of absences before and after the fitness program are the same.
Alternative hypothesis: The average number of absences after the fitness program is less than before the program.
To test this hypothesis, we can use a one-tailed paired t-test with a significance level of 0.05. We will calculate the difference between the number of absences before and after the program for each employee, and then compute the mean and standard deviation of the differences. The t-test statistic will then be calculated as the mean difference divided by the standard deviation of the differences, multiplied by the square root of the sample size.
Using the given data, we calculate the differences and obtain the following results:
Employee Before After Difference (d) d²
1 8 7 -1 1
2 7 3 -4 16
3 8 2 -6 36
4 8 4 -4 16
5 6 5 -1 1
6 7 10 3 9
7 6 4 -2 4
8 8 9 1 1
Mean difference (d-bar) = -1.25
Standard deviation of differences (s) = 3.27
Sample size (n) = 8
The t-test statistic can now be calculated as:
t = (d-bar / (s / √(n))) = (-1.25 / (3.27 / √(8))) = -1.63
The degrees of freedom for the t-test is n-1 = 7, which can be used to obtain the p-value from a t-table or calculator. Using a one-tailed test with a significance level of 0.05 and 7 degrees of freedom, the critical t-value is -1.895.
Since our calculated t-value (-1.63) is greater than the critical t-value (-1.895), we fail to reject the null hypothesis. In other words, we do not have sufficient evidence to conclude that the fitness program has resulted in a significant reduction in employee absenteeism.
The p-value can also be calculated using a t-distribution table or a statistical software package. Using a two-tailed test with 7 degrees of freedom and a significance level of 0.05, we obtain a p-value of 0.073. Since this p-value is greater than the significance level, we again fail to reject the null hypothesis.
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125 pounds decreased by 4%
Answer:
Step-by-step explanation:
125 pounds decreased by 4% it would be 120 because 4% of 125 is 5, so you subtract 5 from 125 and then you get 120.
Owen receives $10 and puts it into his saving account. He adds $0.50 to the account each day for a number of day, d, after that. He writes the expression 10+ 0.5(d-1) to find the amount of money in his account after d days. Which statement about his expression is true?
The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.
What does the expression 10+0.5(d−1) represent in Owen's savings account?The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.
By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.
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El m.c.m y m.c.d de 15 21 y 63
NO LINKS!! URGENT HELP PLEASE!!!!
If x < 0 and y > 0, determine the sign of the real number.
Answer:
(a) The product xy is negative because one of the factors (x) is negative and the other factor (y) is positive. Therefore, the sign of xy is negative.
(b) The expression x^2y is also negative because x^2 is positive (the square of any real number is positive) and y is positive, so their product is positive. But since x is negative, the overall product is negative.
(c) The expression x/y + x can be written as (x/x)y + x, which simplifies to y + x. Since y is positive and x is negative, the sum y + x could be either positive or negative, depending on which absolute value is greater. If |y| > |x|, then y + x is positive. If |x| > |y|, then y + x is negative.
(d) The expression y-x is positive because y is greater than x and y is positive while x is negative. So the difference y-x is positive.
The frequency table represents the fraction of an hour
Rita spends writing in her journal each night. Represent
this data in the line plot.
16. What fraction of an hour did Rita spend most days
writing?
17. What is the difference between the greatest amount
of time spend writing and the least?
A line plot that represents the data is shown in the image attached below.
A fraction of an hour which Rita spend most days writing is 3/4.
The difference between the greatest amount of time spend writing and the least is 3/4.
What is a line plot?In Mathematics and Statistics, a line plot is a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.
Additionally, we can logically deduce that the mode of the data set is equal to 3/4 (the fraction of an hour Rita spend most days writing) because it has the highest frequency of 5.
Difference = greatest amount of time - least amount of time
Difference = 1 - 1/4
Difference = 3/4.
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Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
(b) How much does Jack receive the following Christmas?
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
a) Jill receives £45
b) Jack receives £20 the following Christmas
c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.
Explain the term years
Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.
According to the given information
(a) Let's first find the total ratio of their ages:
1 + 3 = 4
So Jack's share will be:
1/4 x £60 = £15
And Jill's share will be:
3/4 x £60 = £45
Therefore, Jill receives £45.
(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:
2/6 x £60 = £20
So Jack receives £20.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:
1/4 x £60 = £25
Multiplying both sides by 4/60, we get:
x = 5/4
So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.
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answer is c please help its about limit
Using limits the value of k is c √2
What is the limit of a function?The limit of a function is the valuer the function tends to as the dependent variable tends to a particular value.
Given that the limit lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1, we desirte to find the value of k.
So, we proceed as follows
lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1
Factorizing out √2x, we have that
lim n → ∞ [x√(x + 1)[1 - √(2x√(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [x√(x + 1)√(2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
Also, factorizing out √x, we have that
lim n → ∞ [x√x√(1 + 1/√x)√2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [x√x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1
Factorizing x² from the denominator, we have that
lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/x²(7/x² - 6/x + k) = - 1
lim n → ∞ [√2√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7/x² - 6/x + k) = - 1
Now substituting x = ∞ into the equation, we have that
[√2√(1 + 1/√∞)[1/√(2∞ - √(1 + 3/√(2∞)]/(7/∞² - 6/∞ + k) = - 1
[√2√(1 + 0)[0 - √(1 + 0]/(0 - 0 + k) = - 1
[√2√(1)[- √1]/k = - 1
[√2(1)[- 1]/k = - 1
-√2/k = - 1
k = -√2/-1
k = √2
So, the value of k is c √2
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3 tons of bark cost $23,640.00. What is the price per pound?
pls help me
2 ¿Qué figura tiene exactamente 2 ejes de simetría? F G H J K
The figure given that has exactly two lines of symmetry is C. Rectangle.
How many lines of symmetry does a rectangle have ?A rectangle has two lines of symmetry.
A line of symmetry is a line that divides a shape into two equal parts that are mirror images of each other. In a rectangle, the two lines of symmetry run through the center of the rectangle, dividing it into two congruent halves. These lines of symmetry are perpendicular to each other and bisect both pairs of opposite sides of the rectangle.
Therefore, a rectangle has two lines of symmetry, one horizontal and one vertical, which make it a symmetrical shape.
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Mr. Hernandez has a high-speed printer that can produce 32 pages per minute.
Write an equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y.
y =
An equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y is y = 32x
The equation that shows the relationship between the print time in minutes, x, and the number of pages printed, y, can be obtained using the following formula:
y = r * x
where r represents the rate of printing in pages per minute, which in this case is 32 pages per minute.
Therefore, the equation becomes:
y = 32x
This equation states that the number of pages printed, y, is directly proportional to the print time in minutes, x, at a rate of 32 pages per minute.
For example, if Mr. Hernandez wants to print 128 pages, we can use the equation to find out how long it will take him:
128 = 32x
x = 128/32
x = 4
Therefore, it will take Mr. Hernandez 4 minutes to print 128 pages on his high-speed printer.
In summary, the equation y = 32x represents the relationship between the print time in minutes, x, and the number of pages printed, y, when using a high-speed printer that can produce 32 pages per minute.
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Barry buys a plot of land that measures 1/4 acre. He divides the plot into 3 equal pieces
The calculated area of each piece is 1/12 acre
Calculating the area of each pieceIf Barry buys a plot of land that measures 1/4 acre, then the total area of the land is 1/4 acre.
If he divides the land into 3 equal pieces, then each piece will have 1/3 of the total area.
So the area of each piece will be:
Area of each piece = (1/3) x (1/4) acre
Multiplying the fractions, we get:
Area of each piece = 1/12 acre
Therefore, each piece of land will have an area of 1/12 acre.
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a) Calculate the scale factor from shape A to shape B. b) Find the value of t. Give each answer as an integer or as a fraction in its simplest form.
Answer:
a) The scale factor is [tex]\frac{4}{5}[/tex]
b) [tex]t=5\frac{3}{5}[/tex]
Step-by-step explanation:
The scale factor from shape A to shape B is the value that is multiplied by the side measures of shape A to arrive at the side measures of shape B.
In other words, 5 times a certain value is 4, 15 times a certain value is 12. and 7 times a certain value is t.
Let's start by calling our "certain value" k.
[tex]5k=4=\\k=\frac{4}{5}[/tex]
Let's check 15 to make sure k is 4/5, like so:
[tex]15(\frac{4}{5})=\\\frac{60}{5} =\\12[/tex]
Since 15 times 4/5 is twelve, our initial answer was correct.
So, the scale factor, or k, is 4/5.
Following this logic, we know that 7 multiplied by the scale factor is equal to t.
Let's set up an equation and solve for t:
[tex]7(\frac{4}{5} )=t=\\\frac{28}{5} =t=\\5\frac{3}{5} =t[/tex]
So, [tex]t=5\frac{3}{5}[/tex]
at first, only 1/3 of the students who were going on the band trip were on the bus. after 21 students got on the bus 4/5 of the students who were going on the trip were on the bus. how many students were going on the band trip
The total number of students going on the band trip is 45.
how many students were going on the band trip?Let's denote the total number of students going on the band trip as "x". According to the given information:
Initially, only 1/3 of the students were on the bus, which means (1/3)x students were on the bus.
After 21 students got on the bus, the number of students on the bus increased to 4/5 of the total number of students going on the trip, which is (4/5)x students.
We can create an equation based on this information:
(1/3)x + 21 = (4/5)x
To solve for "x", we can follow these steps:
Subtract (1/3)x from both sides of the equation to isolate the "x" term on one side:
(1/3)x + 21 - (1/3)x = (4/5)x - (1/3)x
21 = (7/15)x
Multiply both sides of the equation by 15/7 to eliminate the fraction:
(15/7) * 21 = (15/7) * (7/15)x
45 = x
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Can someone help me with this problem please? :(
Answer:
y =- [tex]\frac{3}{4}[/tex] x + 1
Step-by-step explanation:
This is a linear equation: y = mx + b
First, you are going to find the y-intercept, b, which in this case is 1.In order to find the slope just use the [tex]\frac{rise}{run}[/tex] method, which in this problem it goes down 3 and 4 to the right.Directions: Compute the number of board feet of lumber with the following dimensions.
1. 4"x 8"x 12"
2. 3"x 2"x 10"
3. 2" x 4" x 12"
4. 2" x 2" x 8"
5. 4" x 4" x 10"
Answer:
4.) 32 answer
Step-by-step explanation:
2×2 is 4
4× 8 is 32
I NEED HELP WITH “describe linear and nonlinear function” look at the pic please PLEASE HELP ASAP!! EXTRA POINTS
Answer: #1
Step-by-step explanation:
In situation number one, the equation for the garden's area would be [tex]x^2[/tex] which is nonlinear. The other questions map to linear equations in the form [tex]y = mx + b[/tex]
Answer:
Linear relationship always produces a straight line and are without exponential.
2.the height, y, of a 6-foot tree that grows 0.2 feet per month for x months
3.the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days
4. the total miles, y, traveled by a car going 62 miles per hour in x hours
Step-by-step explanation:
Hope this helps! =D
Compare and contrast the direct write-off method and the allowance method for bad debts.
At a minimum, please consider the following in your answer:
When is the expense for uncollected accounts receivable recognized under each method?
Why is the direct write-off method not considered to follow generally accepted accounting
The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.
How do we explain?When an account is found to be uncollectible, the direct write-off method records the expense for uncollected accounts receivable. This approach involves simply writing off the uncollectible account as a bad debt expense and deducting the outstanding quantity from the accounts receivable total.
Despite being quite easy to understand and basic, this method does not adhere to generally accepted accounting principles (GAAP) because it does not match expenses to the time period during which income was generated.
In contrast, the allowance approach establishes an allowance for doubtful accounts contra-asset account and estimates the amount of uncollectible accounts before recognizing the expense for uncollected accounts receivable.
This allowance account is used to lower the balance of accounts receivable to the anticipated amount of collection. Instead of when the account is found to be uncollectible, the expense is recognized at the time the estimate is made. Because it matches the expense to the time period in which the revenue was received, this method is thought to be more accurate than the direct write-off method.
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What inequality matches this graph?
A} x > 1
B} x ≥ 1
C} x < 1
D} x ≤ 1
Answer:
x<1
Step-by-step explanation:
looking at the graph, the x values are 0,-1,-2,-3,-4,-5.
therefore, all the values of x are below 1.
x<1 is the suitable inequality that matches the graph.
A six sided dice is rolled. What is the probability of rolling a number greater than 2?
The probability of rolling a number greater than 2 is 2/3
Calculating the probability of rolling a number greater than 2?From the question, we have the following parameters that can be used in our computation:
Rolling a number cube once
Using the above as a guide, we have the following:
Sample space, S = {1, 2, 3, 4, 5, 6}
In the above sample space, we have
Outcomes greater than 2 = {3, 4, 5, 6}
So, we have
P(greater than 2) = n(Outcomes greater than 2)/n(Sample space)
Substitute the known values in the above equation, so, we have the following representation
P(greater than 2) = 4/6
When evaluated, we have
P(greater than 2) = 2/3
Hence, the probability is 2/3
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