The probability of rolling the dies and getting greater than 4 will be [tex]\dfrac{2}{6}[/tex].
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Given that the 6-sided die is rolled, the probability of getting a number greater than 4 will be calculated as,
Sample space = {1, 2, 3, 4, 5, 6} = 6
Favourable outcomes = {5,6} = 2
[tex]\rm Probability = \dfrac{Favourable \ events}{Sample\ space}[/tex]
[tex]\rm Probability = \dfrac{2}{6}[/tex]
Therefore, the probability will be [tex]\dfrac{2}{6}[/tex].
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The average salary of 36 employee was 4650 and the sample standard deviation was 165. Find the 90% confidence interval for the population mean salary. Select one: a. 4650 + 53.90 b. 4650 + 70.84 c. 4650 + 67.05 d. 4650 + 63.97 e. 4650 + 55.83 f. 4650 + 45.24 g. 4650 + 46.48 h. 4650 + 74.91
The 90% confidence interval for the population mean salary is 4650 + 45.24. The correct answer is option f.
To find the 90% confidence interval for the population mean salary, we need to use the formula:
CI = x ± z(s/√n)
Where:
- CI = confidence interval
- x = sample mean
- z = z-score for the desired confidence level
- s = sample standard deviation
- n = sample size
Plugging in the given values, we get:
CI = 4650 ± 1.645(165/√36)
CI = 4650 ± 1.645(165/6)
CI = 4650 ± 1.645(27.5)
CI = 4650 ± 45.2375
CI = 4650 ± 45.24
Therefore, the 90% confidence interval for the population mean salary is 4650 ± 45.24 or (4604.7625, 4695.2375).
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2.9. A computer program has produced the following out- put for a hypothesis-testing problem:
Difference in sample means: 2.35
Degrees of freedom: 18
Standard error of the difference in sample means: ?
Test statistic: to = 2.01
P-value: 0.0298
(a) What is the missing value for the standard error?
(b) Is this a two-sided or a one-sided test?
(c) If a = 0.05, what are your conclusions?
(d) Find a 90% two-sided CI on the difference in means.
(a) The standard error is 1.17. (b) IT is a two-sided test. (c) If a = 0.05, it can be concluded that we can reject the null hypothesis and accept the alternative hypothesis. (d) A 90% two-sided CI on the difference in means is (0.33, 4.37).
(a) The missing value for the standard error of the difference in sample means can be calculated using the formula:
Standard error = (Difference in sample means) / (Test statistic) = 2.35 / 2.01 = 1.17
(b) This is a two-sided test because the P-value is given for a two-sided test. If it were a one-sided test, the P-value would be half of the given value, or 0.0149.
(c) If a = 0.05, we can conclude that the difference in sample means is statistically significant because the P-value (0.0298) is less than a (0.05). This means that we can reject the null hypothesis and accept the alternative hypothesis that there is a difference in the means.
(d) A 90% two-sided CI on the difference in means can be calculated using the formula:
CI = (Difference in sample means) ± (t-value) × (Standard error)
The t-value for a 90% two-sided CI with 18 degrees of freedom is 1.734. So the CI is:
CI = 2.35 ± 1.734 × 1.17 = (0.33, 4.37)
Therefore, the 90% two-sided CI on the difference in means is (0.33, 4.37).
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Find an angle in each quadrant with a common reference angle with 12°, from 0°≤θ<360°
Answer: the first quadrant : 12° i the second quadrant : 168° i
the third quadrant : -168° i the forth quadrant : 348°.
Step-by-step explanation:
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Mandla, a farmer, wants to buy a new tractor. The tractor costs R160 000 excluding VAT He can pay a deposit of R20 000. He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 % a. What will his instalment be? b. How much interest will he pay? c. How much will he pay in total for the tractor over 60 months?
a) Amount financed is, R164,000
b) Total interest over 60 months is, R98,400
c) The farmer would pay a total of R262,400 after 60 months.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
The tractor costs R160 000 excluding VAT
And, He can pay a deposit of R20 000.
Here, He decides to buy the tractor on hire purchase over 60 months at a simple interest rate of 10 %
Hence, We get;
Total price with VAT = R160,000 + 15% of R160,000
= R184,000
Hence, We get;
Amount financed = Total price - Deposit
= R184,000 - R20,000
= R164,000
Thus, Total interest over 60 months = R164,000 x 10% x 5
= R98,400
Here, Total payment = Amount financed + Total interest
= R164,000 + R98,400
= R262,400
Therefore, The farmer would pay a total of R262,400 after 60 months.
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How many real solutions are there to the equation 2(x-1)^(2)(2x+3)(x+5)^(3)=.001?
There are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]
To find the real solutions, we can use the zero product property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. In this case, we can set each of the factors equal to zero and solve for x:
[tex]2(x-1)^(2)=02x+3=0(x+5)^(3)=0[/tex]
Solving each of these equations gives us the following solutions:
[tex]x=1x=-3/2x=-5[/tex]
However, we need to check each of these solutions to see if they satisfy the original equation. Plugging each solution back into the equation gives us:
[tex]2(1-1)^(2)(2(1)+3)(1+5)^(3)=.0012(-3/2-1)^(2)(2(-3/2)+3)(-3/2+5)^(3)=.0012(-5-1)^(2)(2(-5)+3)(-5+5)^(3)=.001[/tex]
The first and third solutions do not satisfy the equation, but the second solution does. Therefore, there are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]
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Peter mows 7 lawns in 11 hours. If he continues at the same rate, how many lawns will Peter mow in 55 hours?
If Peter mows 7 lawns in 11 hours, then the number of lawns Peter can mow in 55 hours is 35.
How many lawns can he mow?The first step is to determine how many lawns Peter can mow in 1 hour. To do this, divide 7 by 11.
Division is the process of determining the quotient of two or more numbers. It entails putting a number into equal groups using another number.
Number of lawns that Peter can mow in 1 hour = 7 / 11To determine the number of lawns that can be mowed in 55 hours, multiply the fraction derived in the previous step by 55.
Multiplication is the process of determining the product of two or more numbers.
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Let \( f(x)=6 x-5 \) and \( g(x)=x^{2}-6 x+3 \). \[ \begin{array}{l} (f \circ g)(x)= \\ (g \circ f)(x)= \end{array} \] Question Help: \( \square \) Message instructor
et \( f(x)=\frac{1}{x-5} \) and
The composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).
Given functions are \( f(x)=6x−5 \) and \( g(x)=x^2−6x+3 \). Let's find the composition of functions below:\((f\circ g)(x)\)First, we need to substitute \( g(x) \) in place of \( x \) in \( f(x) \). Hence,\( (f\circ g)(x) = f(g(x)) \)\( f(g(x)) = 6g(x) - 5 \)Substitute \( g(x) \) in the above equation,\( (f\circ g)(x) = 6(x^2-6x+3) - 5 \)\( (f\circ g)(x) = 6x^2 - 36x + 13 \)\((g\circ f)(x)\)First, we need to substitute \( f(x) \) in place of \( x \) in \( g(x) \). Hence,\( (g\circ f)(x) = g(f(x)) \)We are given that \( f(x)=6x−5 \) , substitute this in the above equation,\( (g\circ f)(x) = g(6x-5) \)Substitute this in the function \( g(x) \),\( (g\circ f)(x) = (6x-5)^2 - 6(6x-5) + 3 \)\( (g\circ f)(x) = 36x^2 - 72x + 29 \)Hence, the composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).
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Help as much anything is appreciated!
Due to length restrictions, we kindly invite to read the explanation to see the lenghts of each 30-60-90 right triangles.
How to resolve a 30-60-90 right triangle
In this problem we find six cases of 30-60-90 right triangles, that is, right triangles whose inner angles have the following measures: 30°, 60°, 90°. The length of sides can be found by the following relationships:
The leg adjacent to 60° is 1 / 2 times the hypotenuse.The leg adjacent to 30° is √3 / 2 times the hypotenuse.The leg adjacent 30° is √3 times the leg adjacent to 60°.Now we proceed to determine the missing length:
Case 1:
PV = 4 / (1 / 2)
PV = 8
VT = √3 · 4
VT = 4√3
Case 2:
PT = 2 / √3
PT = 2√3 / 3
PV = 2 / (√3 / 2)
PV = 4√3 / 3
Case 3:
PT = (1 / 2) · 3
PT = 3 / 2
VT = 3√3 / 2
Case 4:
PT = 7 / √3
PT = 7√3 / 3
PV = 7 / (√3 / 2)
PV = 14√3 / 3
Case 5:
VT = √3 · (1 / 2)
VT = √3 / 2
PV = (1 / 2) / (1 / 2)
PV = 1
Case 6:
PV = 100
PT = 50
VT = 50√3
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3.04 Unit 3 Test
Question 1: Identify the zeros in the given graph.
(the one where its curved pointing downwards)
Question 1: Options:
{-3,-1,1}
{-3,-1,4,1}
{-3,1}
{-3,-4,1}
Question 2: Identify the roots in the given graph.
(the one where its curved pointing upwards)
Question 2: Options:
{-2, -8,4}
{0,-8}
{-8}
{-2, 4}
Question 3: what are the solutions to x^2 + 10x = 24
Question 3: Options:
{0,-12,2}
{-12,2}
{2}
{-12}
Question 4: identify all solutions to x^2 + 18x = 4x - 49
Question 4: Options:
{-7,0,-7}
{-7}
{-7,7}
{-10,7}
Question 5: Identify the zeros of x^2 - 9x = 0
Question 5: Options:
{9}
{-9}
{-9,9}
{0,9}
Question 6: identify the roots of 4x^2 - 24 = 20x
Question 6: Options:
{-1,6}
{-1}
{6}
{-1,0.6}
Question 7: Which equations have solutions of -2 and 3?
Question 7: Options:
y = x^2 + x - 6
y = x^2 - x - 6
y = x^2 + 5x + 6
y = x^2 - 5x + 6
The zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.
What are zeroes of graph?The solutions to the equation p(x) = 0, where p(x) stands for the polynomial, are the zeros of a polynomial. If we plot this polynomial as y = p, we can see that these are the values of x where y = 0. (x). In other words, these are the x-intercepts of the graph.
The polynomial's zeros can be found by locating the locations where its graph contacts or crosses the x-axis.
When f(x) = 0, or when the graph's y-coordinate is equal to 0, the zeroes of the graph are determined.
From the graph we see that, at y = 0 we have the values of x as:
1. x = -3 and x = 1
Hence, the zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.
2. Roots of the graph are - x = - 2 and x = 4, {-2, 4}
3. solutions to x² + 10x = 24,
x² + 10x - 24 = 0
x² + 12x - 2x - 24
x(x + 12) -2 (x + 12)
(x - 2) (x + 12)
x = 2 or x = -12
{-12,2}
4. solutions to x² + 18x = 4x - 49
x² + 14x + 49
x² + 7x + 7x + 49
x(x + 7) + 7 (x + 7)
(x + 7)(x + 7)
x = -7
{-7}
5. zeros of x² - 9x = 0
x(x - 9) = 0
Either x = 0 or x = 9,
{0,9}
6. roots of 4x² - 24 = 20x
4x² - 20x - 24 = 0
x² - 5x - 6 = 0
x² -6x + x - 6 = 0
x(x - 6) + 1(x - 6) = 0
(x + 1) (x - 6)
x = -1 and x = 6
{-1,6}
7. correct option is y = x² - x - 6
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okay i will answer it for you yes
Aplumber is fixing a pipe with a an interior diameter of 0.63 inches. He buys a replacement piece that must fit inside the old pipe. He uses plumbing tape that will fill 0.15 inches of the space between the two pieces of pipe. The new pipe much be 0.1 inches smaller than the old pipe and tape, so that it can fit inside.
What is the largest interior diameter pipe he can buy that will still fit inside the old pipe?
Answer____inch
Explain how you found your answer.
Answer:
0.68 inches
Step-by-step explanation:
The interior diameter of the old pipe is 0.63 inches, and the plumbing tape will fill 0.15 inches of the space between the old pipe and the new pipe. Therefore, the total diameter that the new pipe must fit inside is:
0.63 inches + 0.15 inches = 0.78 inches
The new pipe must be 0.1 inches smaller than this diameter to ensure a proper fit. Therefore, the diameter of the new pipe should be:
0.78 inches - 0.1 inches = 0.68 inches
So, the new pipe must have an interior diameter of 0.68 inches to fit correctly inside the old pipe with the plumbing tape.
For f(x)=6x+8 and g(x)= 5x, find the following composite functions and state the domain of each (a) fog (b) gof (c) fof (d) gog (a) (fog)(x) = _____ (Simplify your answer.)
The composite functions and their domains are:
(a) (fog)(x) = 30x + 8, domain: all real numbers
(b) (gof)(x) = 30x + 40, domain: all real numbers
(c) (fof)(x) = 36x + 56, domain: all real numbers
(d) (gog)(x) = 25x, domain: all real numbers
The composite functions are formed by substituting one function into another. We can find the composite functions for f(x)=6x+8 and g(x)=5x by following these steps:
(a) (fog)(x) = f(g(x)) = f(5x) = 6(5x) + 8 = 30x + 8
The domain of (fog)(x) is the set of all real numbers, since there are no restrictions on the values of x.
(b) (gof)(x) = g(f(x)) = g(6x+8) = 5(6x+8) = 30x + 40
The domain of (gof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
(c) (fof)(x) = f(f(x)) = f(6x+8) = 6(6x+8) + 8 = 36x + 56
The domain of (fof)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
(d) (gog)(x) = g(g(x)) = g(5x) = 5(5x) = 25x
The domain of (gog)(x) is also the set of all real numbers, since there are no restrictions on the values of x.
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PLEASE HELP!!
Steve gets 4 points for every correct answer and looses 1 point for every wrong answer. If he answered 30 questions and scored 20 points, write a system of equations.
Answer:
Option B.
Step-by-step explanation:
Let r represent right questions and w represent wrong questions
Total number of questions can be written as:
r + w = 30
We can multiply the question type by the number of points and set it to equal to the total points:
4r - 1w = 20
Thus, our two equations match with Option B best.
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HELP PLS PLS PLS PLS
DUE TOMORROW AND WORTH 50 POINTS AND I GIVE THE BRAINLESS!!
PLS STRESSING TIMES
Answer: 1,068 and wil
Step-by-step explanation:
.Write an equation for the graph that passes through (0,4) and (5,19).
We can use the two-point form to find the equation of the line passing through the two given points:
y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
where (x1, y1) = (0, 4) and (x2, y2) = (5, 19).
Substituting the values, we get:
y - 4 = ((19 - 4)/(5 - 0))(x - 0)
Simplifying the equation, we get:
y - 4 = (15/5)x
y - 4 = 3x
Adding 4 to both sides, we get:
y = 3x + 4
Therefore, the equation of the line passing through the points (0, 4) and (5, 19) is y = 3x + 4.
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a) find slope
19-4/5-0 = 15/5 = 3
plug into equation
y = 3x + b
plug in coordinate pair to solve for b
4 = 3(0) + b
4 = 0 + b
b = 4
y = 3x + b
Angle Q measures 30 degrees. If angle Q is rotated 45 degrees, what is the measure of angle Q'?
Substituting Q = 30 degrees, we get:
Q' = 30 degrees + 45 degrees
Q' = 75 degrees
Therefore, the measure of angle Q' is 75 degrees.
What exactly does a degree angle mean?Acute angles are those that range in degree from 0 to 90. Obtuse angles (90°–180°) are those that fall within this range. • A right angle is one with an angle of 90 degrees (= 90°).
If angle Q measures 30 degrees and is rotated 45 degrees, we can find the measure of the new angle Q' as follows:
Q' = Q + 45 degrees
Substituting Q = 30 degrees, we get:
Q' = 30 degrees + 45 degrees
Simplifying, we get:
Q' = 75 degrees
Therefore, the measure of angle Q' is 75 degrees.
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Adding rational expressions with different Subtract. (5)/(2)-(1)/(2d) Simplify your answer as much as possible.
The simplified rational expression of (5)/(2)-(1)/(2d) is (5d-2)/(2d).
To add rational expressions with different denominators, we first need to find a common denominator. In this case, the common denominator is 2d.
Once we have the common denominator, we can multiply each fraction by a factor that will give us the common denominator. For the first fraction, we need to multiply by d in the numerator and denominator. For the second fraction, we need to multiply by 2 in the numerator and denominator.
After multiplying, we can combine the numerators and keep the common denominator.
So, the steps to simplify (5)/(2)-(1)/(2d) are as follows:
1. Find the common denominator: 2d
2. Multiply the first fraction by d/d: (5d)/(2d)
3. Multiply the second fraction by 2/2: (2)/(2d)
4. Combine the numerators and keep the common denominator: (5d-2)/(2d)
5. Simplify the numerator: (5d-2)/(2d)
Therefore, the simplified rational expression is (5d-2)/(2d).
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ASAP A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 7, 1 comma 9, 2 comma 5, 3 comma 6, 3 comma 7, 5 comma 7, 6 comma 5, 7 comma 3, 9 comma 1, and 10 comma 1
Which two points would a line of fit go through to best fit the data?
(3, 6) and (7, 3)
(3, 7) and (9, 1)
(1, 9) and (10, 1)
(1, 7) and (2, 5)
(1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.
What is Scatter Plot ?
A scatter plot is a graph that shows the relationship between two sets of data. Each dot on the plot represents a single data point, and the position of the dot corresponds to the values of the two variables being plotted.
In this specific scatter plot, we have 10 data points represented by dots. To find the two points that a line of best fit would go through, we want to look for a pattern or trend in the data. Ideally, the line of best fit should pass as close as possible to all of the data points, but this is not always possible.
One common method for finding the line of best fit is to choose two points that seem to be close to the middle of the data and that the line passes through. This is because we want the line to be a good representation of the overall trend in the data.
Looking at the scatter plot provided, we can see that there is a general trend of the data points sloping downward from left to right. If we draw a line that passes through the points (3, 7) and (9, 1), we can see that it closely follows the trend of the data points. Therefore, these are the two points that a line of best fit would go through to best fit the data.
Therefore, (1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.
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PLEASE I NEED URGENT HELP!!!!
The value of the fractions will be:
a. 1/3 + 1/4 = 7/12
b. 1/3 + 2/7 = 13/21
c. 1/2 + 2/9 = 13/18
d. 3/4 + 1/5 = 19/20
e. 1/3 + 4/9 = 7/9
f. 1/6 + 3/4 = 11/12
How to calculate the value of the fractionA fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
The value of the fractions will be:
a. 1/3 + 1/4
= 4/12 + 3/12
= 7/12
b. 1/3 + 2/7
= 7/21 + 6/21
= 13/21
c. 1/2 + 2/9
= 9/18 + 4/18
= 13/18
d. 3/4 + 1/5
= 15/20 + 4/20
= 19/20
e. 1/3 + 4/9 = 7/9
f. 1/6 + 3/4 = 11/12
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Write the solution set in interval notion for 9t+27 <4t-18. Solve the inequality
The solution set of inequality " for 9t+27 <4t-18" in interval notation is (-∞, -9).
To solve the inequality 9t + 27 < 4t - 18, we need to isolate the variable t on one side of the inequality. Here are the steps:
1. Subtract 4t from both sides: 9t - 4t + 27 < -18
2. Simplify: 5t + 27 < -18
3. Subtract 27 from both sides: 5t < -45
4. Divide both sides by 5: t < -9
Now we can write the solution set in interval notation: (-∞, -9)
So the solution set is all values of t that are less than -9.
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The lengths of the bases are 62 inches and 6 feet. The perpendicular distance between the bases of a trapezoid is 5 feet. What is the area of a trapezoid in square inches?
The area of the trapezoid is 335 square inches.
What is Trapezoid ?
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The distance between the bases is called the height or altitude of the trapezoid.
First, we need to convert the lengths of the bases and the perpendicular distance to the same units. Let's convert 6 feet to inches:
6 feet = 6 x 12 inches = 72 inches
Now we can calculate the area of the trapezoid using the formula:
Area = (a + b) * h / 2
where a and b are the lengths of the bases and h is the perpendicular distance between them.
Substituting the given values, we get:
Area = (62 + 72) * 5 / 2
Area = 134 * 5 / 2
Area = 670 / 2
Area = 335 square inches
Therefore, the area of the trapezoid is 335 square inches.
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Find the determinant of the triangular matrix.−37−605700−3
Determinant of the given triangular matrix is 105.
What is determinant of a matrix?The determinant of a matrix is a number that represents the volume or area of the matrix. It is calculated by using a formula that involves the entries of the matrix, and is used in solving linear equations and in proving theorems in linear algebra.
The determinant of a triangular matrix can be found by multiplying the elements on the main diagonal. In this case, the main diagonal elements are -3, 5, and -7.
So, the determinant of the triangular matrix is:
-3 * 5 * -7 = 105
Therefore, the determinant of the triangular matrix is 105.
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Given the graph of the quadratic function, determine the features.
For the given quadratic function the features are:
Domain: (-∞, ∞): Range :[-1, ∞)Vertex: (-3, -1)Explain about the quadratic function?A parabola, a U-shaped curve, is the shape of a quadratic function's graph.
The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of a quadratic function, is where the parabola will open up.There are three characteristics that all quadratic functions share:
A quadratic function's graph is always a parabola with an end behaviour that is either upward or downward; its domain will be all real numbers; and its vertex is really the lowest point once the parabola opens upwards.Thus, for the given quadratic function the features are:
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A line passes through the points (2, −2) and (3, −9). Write its equation in slope-intercept
form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
An equation in slope-intercept form is y = -7x + 12.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (2, -2), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - (-2) = (-9 - (-2))/(3 - 2)(x - 2)
y + 2 = (-9 + 2)/(3 - 2)(x - 2)
y = -7x + 14 - 2
y = -7x + 12
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Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below:
x 1 2
p(x) 0.04 0.05
(a) What is P(x = 4)? P(x = 4) = (b) What is P(x4)? P(x4) = (c) What is the probability that the selected student is taking at most five courses? P(at most 5 courses) = (d) What is the probability that the selected student is taking at least five courses? more than five courses? P(at least 5 courses) = P(more than 5 courses) = (e) Calculate P(3x6) and P(3 < x < 6). P(3x6) = P(3 < x < 6) =
a)0
b)0.09
c)0.09
d)0
e)P(3x6) = 0.09 P(3 < x < 6) = 0
A) P(x = 4) = 0
B) P(x4) = 0.09
C) P(at most 5 courses) = 0.09
D) P(at least 5 courses) = 0 P(more than 5 courses) = 0
E) P(3x6) = 0.09 P(3 < x < 6) = 0
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Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3) and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)." What is the scale factor of the dilation that maps Triangle ABC onto triangle XYZ. ((PLS HELP ITS DUE TOMORROW))
The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
What is scale factor?A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
here, we have,
given that,
Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3)
and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)."
now, we now that,
distance formula:
d=√(x2−x1)^2+(y2−y1)^2
so, we get,
length of AB = 3√2
and, length of XY = 3
so, scale factor = AB/XY
=3√2/3
=√2
Hence, The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
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Carys calculates the total amount E, in dollars, theat she earns for working h hours using the equation E=10h. How many dollars does she earn per hour?
Answer:
She earns 10 dollars per hour.
Step-by-step explanation:
They substituted h for the amount of hours, since it is unknown. And you can see 10 is multiplied with h. So that is how much she earns an hour.
Please help me! I’ve been sick and out of school so I don’t understand.. thanks! :)
Answer:
Step-by-step explanation: So first, you're gonna distribute the 4/5 to the b and the -5, by doing that u will get 3.2=4/5b - 4. Then you're gonna cancel out the -4 by adding it on both sides - 3.2+4=4/5b, you get 7.2=4/5b. Multiply by the reciprocal of 4/5 which is 5/4 on both sides. 7.2 x 5/4 = b. you get 9 = b
What is the value of x
in the rational equation x5=618
The required, value of x in the rational equation x⁵=618 is approximately 4.951.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
To solve for x in the rational equation x^5 = 618, we need to isolate x on one side of the equation.
Taking the fifth root of both sides, we get:
[tex]x = 618^{1/5}[/tex]
The approximate value of the fifth root of 618 is approximately 4.951.
Therefore, the value of x is approximately 4.951.
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Precalculus Project 2 1) In multiplying two real numbers, we are familiar with the "Zero-Product Property from both Intermediate and College Algebra. Recall that this says that if you have two numbers and y such that the product xy = 0, then either x = 0 or y=0 or they are both zero. This is not true for matrices. In other words, given matrices A and B. A could be a nonzero matrix and B could be a nonzero matrix and you would still obtain AB=0. Let A = [-12 4]
[ 15 -5]
Construct a 2 x 2 matrix B such that AB is the zero matrix.
"Use two different nonzero columns for B. *Clearly show your multiplication that gets your zero matrix.
AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.
When multiplying two matrices, we use the dot product of the rows of the first matrix and the columns of the second matrix to obtain the entries of the resulting matrix. In order for the product of two matrices to be the zero matrix, the dot product of each row of the first matrix with each column of the second matrix must be zero.
Let's construct a 2 x 2 matrix B such that AB is the zero matrix. We can use two different nonzero columns for B to obtain the zero matrix. Let's start with the first column of B:
B = [b1 b3]
[b2 b4]
We need to find values for b1, b2, b3, and b4 such that the dot product of each row of A with each column of B is zero. Let's start with the first row of A and the first column of B:
-12b1 + 4b2 = 0
We can rearrange this equation to solve for b2 in terms of b1:
b2 = 3b1
Now let's look at the second row of A and the first column of B:
15b1 - 5b2 = 0
Substituting the value of b2 from the first equation gives us:
15b1 - 5(3b1) = 0
Simplifying gives us:
0 = 0
This equation is always true, so we can choose any value for b1 and find the corresponding value for b2. Let's choose b1 = 1:
b2 = 3(1) = 3
Now let's look at the first row of A and the second column of B:
-12b3 + 4b4 = 0
We can rearrange this equation to solve for b4 in terms of b3:
b4 = 3b3
Now let's look at the second row of A and the second column of B:
15b3 - 5b4 = 0
Substituting the value of b4 from the first equation gives us:
15b3 - 5(3b3) = 0
Simplifying gives us:
0 = 0
This equation is always true, so we can choose any value for b3 and find the corresponding value for b4. Let's choose b3 = 2:
b4 = 3(2) = 6
Now we have the values for all of the entries of B:
B = [1 2]
[3 6]
Let's check our work by multiplying A and B:
AB = [-12 4] [1 2]
[ 15 -5] [3 6]
= [(-12)(1) + (4)(3) (-12)(2) + (4)(6)]
[(15)(1) + (-5)(3) (15)(2) + (-5)(6)]
= [0 0]
[0 0]
So AB is indeed the zero matrix, and we have found a 2 x 2 matrix B such that AB is the zero matrix.
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