a) Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in question.
Hence answer provided.
b) As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.
True. Because the t distribution resembles the normal distribution when the degrees of freedom are high.
c) The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations have different standard deviations.
False - Because the non-pooled t-test can be used to compare the means of the two populations when the assumption of equal variances is true.
d) The standard error is the standard deviation of the sampling distribution and is calculated by dividing the sample standard deviation by the square root of the sample size.
False - Because the standard error, which is determined as the sample standard deviation divided by the square root of the sample size, is a measure of the variability of the sample mean.
a) Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in question.
b) Given statement : As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.
The given statement is true.
Because, When the degrees of freedom are large, the t distribution approaches the standard normal distribution.
c) Given statement: The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations share the same standard deviation.
The given statement is true.
Because, When the assumption of equal variances is met, the non-pooled t-test can be used to compare the means of the two populations.
d) Given statement: The standard error is not always equal to the sample standard deviation.
The given statement false.
Because, The standard error is a measure of the variability of the sample mean, and it is calculated as the sample standard deviation divided by the square root of the sample size.
The sample standard deviation is a measure of the variability within the sample itself.
The standard error tends to be smaller than the sample standard deviation because it accounts for the effect of the sample size on the variability of the sample mean.
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A rhombus has a diagonals of 6 inches and 8 inches. what is the perimeter and the area of the rhombus?
the perimeter of the rhombus is 20 inches, and the area is 24 square inches.
How to solve the question?
To find the perimeter of a rhombus, we need to know the length of one side. Fortunately, we can use the properties of a rhombus to find the length of the sides. A rhombus has two pairs of equal-length sides, so we can use the Pythagorean theorem to find the length of each side.
Let's label the diagonals of the rhombus as d1 and d2. The diagonals of a rhombus bisect each other at right angles, so we can draw a right triangle with half of each diagonal as the legs and a side of the rhombus as the hypotenuse. Using the Pythagorean theorem, we can find the length of the sides:
(1/2)d1 = 3 inches
(1/2)d2 = 4 inches
Side length = √((1/2)d1² + (1/2)d2²) = √(9 + 16) = 5 inches
Now that we know the length of the sides, we can find the perimeter:
Perimeter = 4 x side length = 4 x 5 = 20 inches
To find the area of the rhombus, we can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
Area = (6 x 8) / 2 = 24 square inches
So the perimeter of the rhombus is 20 inches, and the area is 24 square inches.
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Where will the parabola intersect the line? What equation did you solve to find the intersection? Question content area bottom
Part 1 Use the equation to find the intersection.
The parabola will intersect the line at____enter your response here.
From the graph of the parabola, line, and the given values we found out that the parabola will intersect the line at coordinates ([tex]2\sqrt{14}[/tex],7).
What is a parabola and how do we obtain the equations of the same?A parabola is a type of curve that can be described as a symmetrical U-shape. The generalized equation of a parabola is [tex]y=ax^{2} +bx+c[/tex], where a, b, and c are constant values.This equation represents a vertical parabola with its vertex at the point [tex](-b/2a, c - b^2/4a)[/tex] and an axis of symmetry that is parallel to the y-axis.This equation represents a parabola that opens to the right or left, with its vertex at the point [tex](c - b^2/4a, -b/2a)[/tex] and an axis of symmetry that is parallel to the x-axis. The specific coefficients in the equation depend on the particular characteristics of the parabola, such as its vertex, axis of symmetry, and whether it opens up or down or left or right.As the parabola is originating from the origin and opens at the y-axis, hence:
Equation of parabola = [tex]x^{2} =4ay[/tex] {where a =2} .....................(1)Equation of the line=[tex]y-7=0[/tex].............................................(2)From equation 2 we obtain y=7 and will put this value in 1.After computing the above values in 1 we get: [tex]x^{2} =4*2*7\\x=\sqrt{4*2*7}\\ x=2\sqrt{14}[/tex] and y=7So the coordinates at which the parabola intersects the line is [tex](2\sqrt{14} ,7)[/tex]To know more about the parabola visit:
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Which of the following are examples of rational numbers? Select all that apply.
√4+√16
√5 +√36
√9+√24
2* √4
√49 • √81
3√12
The rational numbers in the list of options are √4+√16, 2* √4 and √49 • √81
The examples of rational numbers among the given options are:
2√4: √4 is equal to 2, so 2√4 = 2*2 = 4, which is a rational number.√49 • √81: √49 is equal to 7 and √81 is equal to 9, so √49 • √81 = 7 • 9 = 63, which is a rational number.√4+√16: √4 is equal to 2 and √16 is equal to 4, so √4+√16 = 2 + 4 = 6, which is a rational number.The other options are not rational numbers:
√5+√36: √5 is an irrational number, so √5+√36 is not a rational number.√9+√24: √24 is an irrational number, so √9+√24 is not a rational number.3√12: √12 is equal to 2√3, so 3√12 = 3 • 2√3 = 6√3, which is not a rational number.Read more about rational numbers at
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Choose a Strategy. Ms. Jimenez earns $27,000 per year. She is paid weekly. She puts 8% of her salary in a retirement fund. How much money goes into this fund each week?
After answering the presented question, we may conclude that expressions As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
We need to do the following to figure out how much money Ms. Jimenez puts into her retirement fund each week:
Ms. Jimenez's yearly retirement fund contribution is calculated as follows:
8% of $27,000 = annual retirement fund contribution
= 0.08 x $27,000
= $2,160
To calculate the weekly retirement fund contribution, divide the yearly payment by the number of weeks in the year:
Contribution to a retirement fund on a weekly basis = Annual contribution to a retirement fund divided by the number of weeks in a year
= $2,160 / 52
≈ $41.54
As a result, Ms. Jimenez contributes roughly $41.54 to her retirement fund each week.
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A rectangle is 5√7+2√3 meters long and 6√7-3√3 meters wide.
a. Find the perimeter of the rectangle in simplest form.
b. Find the area of the rectanglè in simplest form
The a. Perimeter = 22√7 - 2√3 meters. The Area = 4√12 - 3√7 square meters
How to Find the Area and Perimeter of a Rectangle?Area = length * width
Perimeter = 2(length + width)
Given the following:
Length of the rectangle = 5√7 + 2√3 meters
Width of the rectangle = 6√7 - 3√3 meters
a. Perimeter = 2(5√7 + 2√3) + 2(6√7 - 3√3)
10√7 + 4√3 + 12√7 - 6√3
22√7 - 2√3 meters
b. Area = (5√7 + 2√3)(6√7 - 3√3)
= 5√7(6√7 - 3√3) + 2√3(6√7 - 3√3)
= 210 - 15√21 + 12√21 - 18
= 192 - 3√7
= 4√12 - 3√7 square meters
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4. Find the area of the shaded region. 5 ft 9 ft 3 ft 4 ft A. 36 ft² B. 38 ft² C. 39 ft² D. 40 ft²
Due before 8:30
Answer:
C. 39 ft²
Step-by-step explanation:
Area of the outer rectangle which includes the white triangle
= length x width
= 5 x 9
= 45 ft²
Area of the white triangle
= 1/2 x base x height
= 1/2 x 4 x 3
= 6 ft²
Area of shaded region
= Area of rectangle - Area of triangle
= 45 - 6
= 39 ft²
The proportion of scores in a standard Normal Distribution that are greater than 1.25 is closest to...a) .1056b) .1151c) .1600d) .8849e) .8944
The proportion of scores in a standard Normal Distribution that are greater than 1.25 is closest to a. a is 0.1056.
The proportion of scores in a standard Normal Distribution that are greater than 1.25 is:
[tex]P(Z > 1.25) = 1 - P(Z < 1.25)[/tex]
Using a standard normal distribution table or a calculator.
The area to the left of 1.25 is 0.8944, so:
[tex]P(Z > 1.25) = 1 - P(Z < 1.25) = 1 - 0.8944 = 0.1056[/tex]
The closest answer choice is (a) 0.1056.
The percentage of scores in a normal distribution with a standard deviation larger than 1.25 is:
either a calculator or a normal distribution standard table.
0.8944 is the region to the left of 1.25, so:
The nearest possible response is (a) 0.1056.
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continuation. to investigate the believability of my results (dr eh), a student conducted a separate interview (secretly and randomly) on 60 students and construct a 95% confidence interval using the similar approach. suppose that this interview also discover 75% of students favor a difficult final exam. what can you say about this 95% confidence interval based 60 students?
With the probability that 75% of students favor a difficult final exam, the 95% confidence interval based 60 students for sample proportion is ( 0.64, 0.86).
We have to investigate the believability of my results.
Sample size, n = 60
Confidence nterval = 95%
Sample proportion for students who favour the difficulty of exam, [tex] \hat p[/tex] = 75% = 0.75
We have to determine 95% confidence interval based 60 students. Using the confidence interval formula or sample proportion, [tex]CI = \hat p ± z^* \sqrt{\frac{\hat p ( 1 - \hat p )}{n}}[/tex]
Now, using the Z-distribution table, the value z- score for 95% of confidence interval is equals to 1.96.
Substitute all known values in above formula, [tex]= 0.75 ± 1.96 \sqrt{ \frac{ 0.75( 1- 0.75)}{60}}[/tex]
= 0.75 ± 0.11
= ( 0.64, 0.86)
Hence, required value of interval is ( 0.64, 0.86), i.e., 0.64 < p < 0.86.
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HELP I GOT AN F IN MATH AND MY MOMMA AINT GONNA LIKE IT WHEN SHE FINDS OUT
The quadratic equation y = x²-6x+5 is minimum because the coefficient of x² is positive.
x = [tex]\frac{-b}{2a}[/tex], but a = 1 and b = -6
therefore x = [tex]\frac{-(-6)}{2(1)}[/tex] = 3
By plugging the value in the quadratic equation above, then we have
y = (3)² - 6(3) + 5 = -4 = -4
Note that y is the y-value of the vertex.
How to determine the minimum/maximum of a functionTo determine whether the function y = x^2 - 6x + 5 has a maximum or minimum value, we can use the vertex formula, which gives the x-coordinate of the vertex of a quadratic function as -b/2a.
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Please help me I can also offer a commission too
The average rate of change of each function on the interval 2 ≤ x ≤ 6 is given as follows:
f(x): -1.25.g(x): -0.715.How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
For the function f(x), we have that:
When x = 2, y = 7.When x = 6, y = 2.Hence the rate is given as follows:
r = (2 - 7)/(6 - 2)
r = -5/4
r = -1.25.
For the function g(x), we have that:
When x = 2, y = 2(-5/7) - 6 = -7.43.When x = 6, y = 6(-5/7) - 6 = -10.29.Hence the rate is given as follows:
r = (-10.29 - (-7.43))/(6 - 2)
r = -0.715
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explain each step in the process of finding the area of a circle given the circumfrence
Answer:
Divide the circumference by [tex]2\pi[/tex]Square the remaining numberMultiply the resulting value by [tex]\pi[/tex]Step-by-step explanation:
Recall that the formula for the circumference of a circle is:
[tex]2\pi r[/tex]
Also recall that the formula for the area of a circle is:
[tex]\pi r^2[/tex]
Both formulas use the radius; one squares it, while the other doubles it.
Let's start by turning the formula for the circumference of a circle into the formula for the area of a circle. We start off with:
[tex]2\pi r[/tex]
We want to square the radius, but we can't do that without squaring everything else, too, so let's get rid of the other terms.
Divide the circumference by [tex]2\pi[/tex]:
[tex]2\pi r\\\frac{2\pi r}{2\pi } =\\r[/tex]
Now, we can square r:
[tex]r\\r^2[/tex]
Now, all we have to do is multiply by pi:
[tex]r^2\\\pi r^2[/tex]
We now have the area.
Let's look back at out steps.
First, we divided the circumference by [tex]2\pi[/tex].
Next, we squared the number we had left (the radius).
Finally, we multiplied by [tex]\pi[/tex].
The given equation shows a proportional relationship betweenthe variables r and s. Which expression is equivalent to 6r. R=10/3s
The equivalent expression for 6r in terms of s is 20s, which we obtain by substituting the value of r from the given equation and simplifying.
The given equation, r = (10/3)s, shows that there is a proportional relationship between the variables r and s. This means that when one variable changes, the other variable changes in direct proportion to it. In other words, if we increase r by a certain factor, s will increase by the same factor, and vice versa.
To find an expression that is equivalent to 6r, we can substitute the value of r from the given equation and simplify.
r = (10/3)s (given equation)
6r = 6(10/3)s (substitute 6r for r in the equation)
6r = 20s (simplify by multiplying 6 and 10/3)
Therefore, the expression that is equivalent to 6r in terms of s is 20s. This means that if we know the value of s, we can use this expression to find the value of 6r in a proportional relationship. For example, if s = 2, then 6r = 20s = 20(2) = 40.
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A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years given by 1.272+/-0.570. Assume that the conditions for inference for the slope of the regression equation are met. Which of the following is the correct interpretation of the interval?
It can be concluded that we are 95 percent confident that the mean increase in the weight of a black bear for each one year increase in the age of the bear is between 7.0 and 18.4 pounds.
What is mean?
In statistics, the mean is one of the measures of central tendency which is nothing but simple average, apart from the mode and median. Mean is the average of the given set of values. Mean denotes the equal distribution of values for a given set of data.
A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years given by 1.272 ±0.570.
From the given data it is clear that the 95 confidence interval given by 1.272±0.570, or (0.702,1.842)
[ 1.272-0.570 = 0.702 and 1.272+0.570= 1.842]
It estimates the relationship between weight in tens of pounds and age in years. So the given data makes us 95 percent confident that the mean increase in the weight of a black bear must be in between 7.02 and 18.42 pounds and it is for each one-year increase in the age of the bear.
Hence, it can be concluded that we are 95 percent confident that the mean increase in the weight of a black bear for each one year increase in the age of the bear is between 7.0 and 18.4 pounds.
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Alvin's new bag of 50 marbles of different
designs spilled in his backpack. On the way
home from school, he randomly selects one
marble from the backpack, records the
result, puts the marble back in the bag,
and selects again. Here are his results:
jasper, galaxy, cat's-eye, rainbow,
galaxy, sunburst, galaxy, cat's-eye,
sunburst, jasper
Based on the data, estimate how many of
the marbles in Alvin's backpack are galaxy
marbles.
If necessary, round your answer to the
nearest whole number.
Answer: 7
Step-by-step explanation:
i did it a weird way
Given that ZQRP = (2x + 20) and ZPSQ = 30°, find the value of x.
The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.
We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.
If angles QRP and PSQ are supplementary, their sum is 180°:
(2x + 20)° + 30° = 180°
Now, we can solve for x:
2x + 50 = 180
Subtract 50 from both sides:
2x = 130
Divide by 2:
x = 65
2. Find the volume. Show work, and round to 2 decimal places
*triangle based prism*
answer
as we all know volume is equal to length times width times height therefore to get you answer you have to multiply all the three giving measurements the answer that you get you are supposed to round it to the nearest to decimal places when you say around it off to the nearest two decimal places it means that they need to be too this two numbers after the coma
HELP PLEASE I NEED THIS DONE ASAP
Answer:5
Step-by-step explanation:
it would be 5 because
Solve for A and B using special right triangles
Answer:
a = 10
b = 5
Step-by-step explanation:
A 30-60-90 triangle is a right triangle where the interior angles measure 30°, 60° and 90° and the sides are in the ratio 1 : √3 : 2.
The formula for the ratio of the sides is x : x√3 : 2x where:
x = the shortest side opposite the 30° angle.x√3 = the side opposite the 60° angle.2x = the longest side (hypotenuse) opposite the right angle.From inspection of the given triangle, the measure of the side opposite the 30° angle is "b", the side opposite the 60° angle is 5√3, and the hypotenuse is "a". Therefore:
x = bx√3 = 5√3 2x = aIf x√3 = 5√3, then x = 5. Therefore:
b = x = 5a = 2x = 10The lengths of the three sides are given for several right triangles. For each, write an equation that expresses the relationship between the lengths of the three sides.
5,2.2360679775,5.47722557505
On solving the provided question we can say that As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle.
what is Pythagorean theorem?The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.
The supplied figures reflect the lengths of the three sides of a right triangle, with the hypotenuse (the side opposite the right angle) being 5.47722557505, and the other two sides being 2.2360679775 and 5.
The sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, according to the Pythagorean theorem. In this situation, we can write:
2.2360679775² + 5² = 5.47722557505²
When we simplify and solve for one of the variables, we get:
5² = 5.47722557505² - 2.2360679775²
25 = 24.9999999999971
As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle. We could round the data to approach the sides of a right triangle, but it would not get accurate solutions.
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Kyle who is a lifeguard is roping off a rectangular swimming area of 70 m. He uses the beach as one side.
Determine the minimum length, to 2 decimal places, of rope needed.
If he uses the beach as one side. the minimum length, to 2 decimal places, of rope needed is: 70 meters of rope.
What is the minimum length?Let's assume that the length of the swimming area is L and the width is W. The perimeter of the swimming area will be the length of the rope that Kyle needs to rope off the area.
From the problem, we know that one side of the swimming area is the beach, so we have:
L + W + L = 70
Simplifying this equation, we get:
2L + W = 70
To find the minimum length of rope needed, we need to minimize the perimeter of the swimming area. We can use the above equation to express W in terms of L:
W = 70 - 2L
Substituting this expression for W into the formula for the perimeter, we get:
P = L + W + L
= 2L + (70 - 2L)
= 70
So the perimeter of the swimming area is fixed at 70 m, regardless of the values of L and W. Therefore, the minimum length of rope needed to rope off the area is simply the perimeter of the swimming area, which is 70 meters.
Therefore, Kyle needs a minimum of 70 meters of rope.
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What is the most common type of employee benefit?
O retirement
O disability insurance
O life insurance
O healthcare
Answer:
life insurance is the most common type of employee benefit
The time $t$t (in seconds) it takes a dropped object to fall h$h$h feet is given by t is equal to square root of h over 16 end root$t=\sqrt{\frac{h}{16}}$t=√
h
16 .
A building of height 55 feet.
a. Estimate how long it takes an earring to hit the ground when it falls from the roof of the building. Round your answer to the nearest hundredth.
about ____ seconds
b. Estimate how much sooner the earring hits the ground when it is dropped from two stories (22 feet) below the roof. Round your answer to the nearest hundredth.
about seconds
You are playing a game where a quarter is tossed 4 times. What is the probability that the quarter lands on tails exactly one time?
PLEASE ANSWER FAST!
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 6
Spade 4
Club 7
Diamond 3
Determine the experimental probability of drawing a spade.
0.15
0.20
0.40
0.45
The experimental probability of drawing a spade is 0.2
How to determine the experimental probability?When we perform an experiment N times, and we got a given outcome K times, the experimental probability of said outcome is given by the quotient:
P = K/N
Here the experiment is performed:
N = 6 + 4 + 7 + 3 = 20 times
And a spade is drawn 4 times, then the experimental probability is:
P = 4/20 = 1/5 = 0.20
The correct option is the second one.
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Simplify. (3/4)^2= ?
Answer:
9/16.
Step-by-step explanation:
To simplify (3/4)^2, we simply need to square the numerator (3) and the denominator (4) separately, and then simplify the result:
(3/4)^2 = (3^2)/(4^2) = 9/16
Therefore, (3/4)^2 simplifies to 9/16.
Answer:
0.5625
Step-by-step explanation:
(3/4)²
9/16
0.5625
can someone help me w this
Find a possible solution to the equation cos(x+2)=sin(3x)
A.
x=0. 5 degrees
B.
x=1 degree
C.
x=22 degrees
D.
x=44 degrees
A possible solution to the equation cos(x+2)=sin(3x) is x = 22 degrees
The correct answer is an option (C)
Consider a trigonometric equation,
cos(x+2) = sin(3x)
For value x = 0.5 degrees,
cos(x + 2) = cos(2.5)
= 0.999
and sin(3x) = sin(1.5)
= 0.026
For x = 1 degree,
cos(x + 2) = cos(3)
=0.9986
sin(3x) = sin(3)
= 0.052
For x = 22 degrees
cos(x + 2) = cos(24)
= 0.913
sin(3x) = sin(66)
= 0.913
for x = 44 degrees,
cos(x + 2) = cos(46)
= 0.69
sin(3x) = sin(132)
= 0.743
Therefore, the solution to an equation cos(x+2) = sin(3x) is x = 22 degrees
The correct answer is an option (C)
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h(x)= 6/x-h+k
Oh no! He seems to be missing some parts though. He was "robbed" of his asymptotes!
Luckily, he can remember what they were:
1. This functions vertical asymptote was x = 4.
2. This functions horizontal asymptote was y = -15.
Please recreate this function with those identifying features! Please make sure it looks like the function at the beginning of this problem.
At a function x = 4 has a vertical asymptote and at y = -15 has a horizontal asymptote.
What are asymptotes?The general form of a function is x= a and y = b.
f(x) = (kx + m) / (x - a) + b
k and m are constants.
We require a factor of (x - 4) in the denominator to get a vertical asymptote at x = 4. It is necessary for the fraction to approach -15 when x approaches positive or negative infinity in order to obtain a horizontal asymptote at y = -15.
One potential function that meets these specifications is:
H(x) = 6/(x - 4) - 15 + k
where k is a constant that establishes the function's vertical shift (i.e., its value at x = 0).
By entering a point on the graph, such as the x-intercept (where y = 0), the value of k can be determined:
0 = 6/(x - 4) - 15 + k
15 - k = 6/(x - 4)
x - 4 = 6/(15 - k)
x = 6/(15 - k) + 4
We may enter this value of x into the original equation to find k since y = 0 at the x-intercept:
0 = 6/((6/(15 - k) + 4) - 4) - 15 + k
0 = 6/(6/(15 - k)) - 15 + k
0 = 15 - k - 15 + k
The x-intercept and asymptotes are unaffected by the value of k, and any value of k will result in a function with the same asymptotes. K does, however, have an impact on the function's vertical shift.
We can select a value for k and then search for a specific function that has the specified asymptotes.
For instance, if we select k = 0, we obtain:
H(x) = 6/(x - 4) - 15
This function has the same shape as the original function H(x) presented in the problem and asymptotes at x = 4 and y = -15, respectively.
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Write down the size of angle ABC. Give a reason for your answer.
Answer:
∠ ABC = 90°
Step-by-step explanation:
∠ ABC is the angle on the circle subtended by the diameter AC
it is the angle in a semicircle and is 90°
Find all the values of k for which the equation 2x^2+x+4k has (a) two real solutions, (b) one real solution, and (c) no real solutions.
the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.
How to solve the question?
The given equation is 2x² + x + 4k.
(a) For the equation to have two real solutions, the discriminant b² - 4ac must be positive.
Therefore, for this equation, b² - 4ac > 0
=> 1 - 4(2)(4k) > 0
=> 1 - 32k > 0
=> k < 1/32
Hence, all values of k less than 1/32 will give the equation 2x² + x + 4k two real solutions.
(b) For the equation to have one real solution, the discriminant b² - 4ac must be zero.
Therefore, for this equation, b² - 4ac = 0
=> 1 - 4(2)(4k) = 0
=> 1 - 32k = 0
=> k = 1/32
Hence, only the value of k equal to 1/32 will give the equation 2x² + x + 4k one real solution.
(c) For the equation to have no real solutions, the discriminant b² - 4ac must be negative.
Therefore, for this equation, b² - 4ac < 0
=> 1 - 4(2)(4k) < 0
=> 1 - 32k < 0
=> k > 1/32
Hence, all values of k greater than 1/32 will give the equation 2x² + x + 4k no real solutions.
In conclusion, the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.
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