Answer: y = -3x^2 + 24x - 45
Step-by-step explanation:
To find the equation of the parabola with a vertex of (4, 3) and passing through points (2, -9) and (5, 0), we can use the vertex form of a parabolic equation:
y = a(x - h)^2 + k
Here, (h, k) is the vertex of the parabola. So, we have:
y = a(x - 4)^2 + 3
Now, we need to find the value of 'a' using the two points (2, -9) and (5, 0).
First, let's plug in the point (2, -9):
-9 = a(2 - 4)^2 + 3
-9 = a(-2)^2 + 3
-9 = 4a + 3
Subtract 3 from both sides:
-12 = 4a
Now, divide both sides by 4:
a = -3
Now that we have the value of 'a', we can plug it back into the equation:
y = -3(x - 4)^2 + 3
This is the equation of the parabola in vertex form. To convert it to standard form, we can expand the equation:
y = -3(x^2 - 8x + 16) + 3
y = -3x^2 + 24x - 48 + 3
Now, combine the constants:
y = -3x^2 + 24x - 45
This is the equation of the parabola in standard form.
Look at the system of equations below. Which of these statements must be true? Check ALL that applies.
y= -2x+5
y= -2x+3
The statements are:
1.) The lines intersect at one point
2.) The equations represent parallel lines
3.) The equations represent the same line
4.) The solution to the system will have no solution
5.) The solution to the system will have infinitely many solutions
6.) The system is inconsistent
7.) The system is consistent
8.) The system is independent
9.) The system is dependent
what is m∠S?
I cant figure it out at all
The measure of the angle S of the cyclic quadrilateral QRST is 96 degrees.
We know that the sum of opposite angles of a cyclic quadrilateral is equal to 2 right angles that is 180 degrees.
Here QRST is a cyclic quadrilateral and angle Q and angle S are the opposite angles of this cyclic quadrilateral.
Given that angle Q = x + 51
angle S = x + 63
According to condition then the sum of the angle Q and angle S must be 180 degrees.
x + 51 + x + 63 = 180
2x + 114 = 180
2x = 180 - 114 = 66
x = 66/2 = 33
So the value of angle S = x + 63 = 33 + 63 = 96 degrees.
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Select the correct answer. Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get? A. 4^2 − 3^3 B. 3^3 + 4^2 C. 4 − 3^3 D. 3^3 − 4^2 E. 3^2 − 4^3
Out of the given options, the total quantity of jelly beans that Alia got is D. 3³ − 4²
Jelly beans received by Alia = 4²
Jelly beans received by Kelly = 3³
Quantity refers to the amount or number of something. In the given question, the quantity can be described by the total number of jelly beans received by both the girls.
Calculating the jelly beans Kelly gets -
= 3³ = 3 x 3 x 3
= 27 jelly beans.
Calculating the jelly beans Alia gets -
= 4² = 4 x 4
= 16
Thus, these are fewer beans than Kelly.
Calculating the number of jelly beans that Alia gets is:
= Total jelly beans with Kelly - Total jelly beans with Alia
= 27 - 16
= 11
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In spring 2017, data was collected from a random selection of sta 2023 students. one of the questions asked how many hours they had exercised in the past 24 hours. for the 39 randomly selected upperclassmen, the sample mean was 0.76 and sample standard deviation was 0.75. for the 35 randomly selected underclassmen, the sample mean was 0.60 and the sample standard deviation was 0.73. what is the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen?
Point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.
Explain the process to calculate point estimate of the difference in the population mean?To calculate point estimate of the difference in the population mean exercised between underclassmen and upperclassmen we use the difference between the sample means:
point estimate = x1 - x2
where x1 is the sample mean for the upperclassmen and x2 is the sample mean for the underclassmen.
Substituting the given values, we get:
point estimate = 0.76 - 0.60
point estimate = 0.16
Therefore, the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.
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A prism has a perimeter of 9 a Height of 6 and a base of 7.8 what is the lateral and surface area
The lateral and total surface area of the prism for the given dimensions is equal to 54 square units and 69.6 square units respectively.
Perimeter of the prism = 9 units
Height of the prism = 6 units
Base area of the prism = 7.8 units
The lateral area of a prism is the sum of the areas of all its lateral faces,
And the surface area is the sum of the areas of all its faces.
Lateral area of the prism = perimeter × height
Substitute the values we have,
⇒ Lateral area of the prism = 9 × 6
⇒ Lateral area of the prism = 54 square units.
Total surface area of the prism
= perimeter × height + 2 × Base area
Substitute the values we have,
⇒Total surface area of the prism
= 9 × 6 + 2 × 7.8
= 54 + 15.6
= 69.6 square units.
Therefore, the lateral surface area and total surface area of the prism are 54 square units and 69.6 square units respectively.
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The above question is incomplete, the complete question is:
A prism has a perimeter of 9 ,a Height of 6 and a base area of 7.8 what is the lateral and total surface area of the prism.
Can someone help me, please!!!
The length of the base, x is b) 2.90.
Let's call the length of the hypotenuse "h" and the length of the base "x". We can use trigonometry to set up an equation relating these three lengths.
Since we know that the triangle is right-angled, we can use the trigonometric function "sine" to relate the angle between the perpendicular and the hypotenuse to the sides of the triangle:
sin(71) = 4/h
Multiplying both sides by h, we get:
h * sin(71) = 4
Next, we can use the Pythagorean theorem to relate the length of the hypotenuse to the length of the base:
[tex]h^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]
Substituting the first equation into the second equation, we get:
[tex](hsin(71))^{2}[/tex] = [tex]x^{2}[/tex] + [tex]4^{2}[/tex]
Simplifying and solving for x, we get:
x = [tex]\sqrt{(hsin(71))^{2}-4^{2} }[/tex]
Using a calculator, we can evaluate this expression and find that x is approximately equal to 2.90.
Therefore, the answer is (b) 2.90.
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find the coterminal angle of -36 that is between 0 and 360
The coterminal angle of -36° that is between 0° and 360° are -396° and 324°.
We need to find the coterminal angle of -36° that is between 0° and 360°.
We find one negative angle and one positive that is coterminal with angle =θ=-36°
The coterminal of a given angle for one full rotation can be solved by: θ±360°n
Note that n is the number of rotations.
positive n means counterclockwise rotation
negative n means clockwise rotation
In order to find one negative angle that is coterminal with the given angle, we subtract 360° and apply one full rotation counterclockwise (n=1)
θ-360°n
When n=1
Now, -36°-360°(1)
= -396°
Hence, one negative angle that is coterminal with the given angle is -396°.
In order to find one positive angle that is coterminal with the given angle, we subtract 360° and apply one full rotation clockwise (n=-1)
θ+360°n
When n=1
Now, -36°+360°(1)
= 324°
Therefore, the coterminal angle of -36° that is between 0° and 360° are -396° and 324°.
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Please do this asap, last question on the packet!!
Answer: c
Step-by-step explanation:
Write the Equation
= 5.5x + 6.2y + 4.3x + 8.3z + 1.6z - 5.1y
Re-arrange them
= 5.5x + 4.3x + 6.2y - 5.1y + 8.3z + 1.6z
Add them
= 9.8x + 0.1y + 9.9z
Find the area of the composite figure, the figure consist of a square and a half circle
Step-by-step explanation:
A. Circle = πr²
A. half circle = 1/2 πr²
A. Rectangle = w × l
we know that
w = d = 8 ft
r = 1/2 d
= 1/2 × 8
= 4 ft
l = 10 ft
π = 3.14
Total area = A. Circle + A. rectangle
= 1/2 πr² + w × l
= (1/2 × 3.14 × (4)²) + 8 × 10
= (1/2 × 3.14 × 16) + 80
= 3.14 × 8 + 80
= 25.12 + 80
= 105.12 ft
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Yames had $43. On his birthday, he received $25. Write and solve an equation to find how much money Yames has now. Show work
Step-by-step explanation:
43+25 which is the addition of the two numbers which is 68
What is the interquartile range of the data 10 12 28 59 61 67 89 93
The interquartile range (IQR) is found by subtracting Q1 from Q3.
First, find the median.
10, 12, 28, 59, 61, 67, 89, 93
12, 28, 59, 61, 67, 89
28, 59, 61, 67
59, 61
median = 60
Second, separate the data set at the median and find the median of each of those sections (do not include the median number we just found).
data set one = 10, 12, 28, 59
median of data set one = 20 (a.k.a. Q1)
data set two = 61, 67, 89, 93
median of data set two = 78 (a.k.a. Q3)
Third, subtract Q1 from Q3 to get the IQR.
Q3 - Q1 = IQR
78 - 20 = 58
Answer: 58
Hope this helps!
Answer:
Interquartile Range: 58
Step-by-step explanation:
25th Percentile: 20
50th Percentile: 60
75th Percentile: 78
Interquartile Range: 58
a confidence interval for the population mean number of us states americans have visited was found to be 11.4 to 12.5. find the best point estimate of this confidence interval.
The best point estimate of the confidence interval is the midpoint or the mean of the interval.
The confidence interval is a range of values that we are confident contains the true population mean.
However, to get a single estimate of the population mean, we use the midpoint of the interval as the point estimate.
This is because the midpoint represents the most likely value of the population mean based on the sample data.
Therefore, the best point estimate for this confidence interval would be the average of the two endpoints:
(11.4 + 12.5) / 2 = 11.95
Hence, the best point estimate for the confidence interval 11.4 to 12.5 is 11.95, which represents the most likely value of the population mean based on the sample data.
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a) Work out the bearing of A from B.
b) Work out the bearing of B from A.
(Hint: bearings are written with three digits.)
N
A
293°
67°
113°
Z+
N
B
247°
Not drawn accurately
Answer:
247° and 067°
Step-by-step explanation:
the bearing of one point to another is the measure of the angle from the north point N at one point in a clockwise direction to the other point.
(a)
bearing of B from A = 247° ( from N at B clockwise to A )
(b)
bearing of B from A = 067° ( from N at A clockwise to B )
if a given graph that shows one of the x-intercepts is (-3 0) and the vertext is (0,-9) what is the quadratic equation in standard form?
The quadratic equation can be written as y = x² - 9.
To find the quadratic equation in standard form, we need to use the vertex form of the quadratic equation, which is given by:
y = a(x - h)² + k
where (h, k) is the vertex and a is a constant that determines the shape of the parabola.
We know that the vertex is (0, -9), so we can substitute these values into the equation:
y = a(x - 0)² - 9
Simplifying this equation, we get:
y = ax² - 9
Now, we need to find the value of a. We know that one of the x-intercepts is (-3, 0), which means that the parabola intersects the x-axis at x = -3. This tells us that (-3, 0) is a solution of the equation, so we can substitute these values into the equation and solve for a:
0 = a(-3)² - 9
0 = 9a - 9
9 = 9a
a = 1
Therefore, the quadratic equation in standard form is:
y = x² - 9
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For the past three years, Derek has grown 1 inches each year. How many total inches has he grown in the past three years?
5/12, inch
3 3/4 inches
3, 1/4 inches
1 3/4 inches
The total inches Derek has grown in the past three years is 3 inches.
None of the given options is correct.
Given information:
For the previous three years, Derek has become an inch taller every year.
This means that we can add up those three inches to find his total growth over the three-year period.
Thus, 1 + 1 + 1 equals 3 inches.
Derek has therefore gained 3 inches in total over the last three years.
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13 A number sequence starts 1 2 4
Emma says that the next term is 7
(a) Explain why Emma may be correct.
Emma may be correct because the addition of 1, 2 and 4 gives 7
Explaining why Emma may be correct.From the question, we have the following parameters that can be used in our computation:
Sequence: 1 2 4
Emma says that the next term is 7
This statement may be true because the addition of 1, 2 and 4 gives 7
i.e. next term = 1 + 2 + 4
Evaluate
next term = 7
Hence, Emma is right
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Question 1(Multiple Choice Worth 2 points)
(Scale Factor MC)
A triangle with a perimeter of 24 meters was created from a triangle with a perimeter of 3 meters using a scale factor. What is the scale factor?
8:1
28:1
32:1
72:1
The scale factor of the triangle is 4:1.
We have,
The ratio of the perimeters of two similar triangles is equal to the ratio of their corresponding sides.
Let's call the scale factor "k", and the length of one side of the original triangle "x".
Then, the length of the corresponding side in the new triangle is kx.
The problem tells us that the perimeters of the two triangles are in the ratio 24:3, or 8:1.
Therefore, we have:
24/3 = (kx + kx + x)/(x + x + x)
Simplifying the left side of the equation, we get:
8 = 2k
Dividing both sides by 2, we get:
k = 4
Therefore,
The scale factor is 4:1.
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The probability is 0.45 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In eight traffic fatalities, fine the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a.exactly three; =________ at least three; =_______ at most three =__________ b. between two and four, inclusive c. find and interpet the mean of the random variable Y d. obtain the stand deviation of y
Regarding resolving the given issue, we have P(Y<=3) = 0.3909 (rounded to four decimal places)
What is probability?The likelihood that an event will occur or that a proposition is true is determined by a field of mathematics known as probability theory. An event's probability is expressed as a number between 0 and 1, where 1 indicates certainty and roughly 0 indicates how likely it is that the event will occur. A probability is a numerical expression of the likelihood or potentiality of a given event. Probabilities can alternatively be stated as integers between 0 and 1, percentages between 0% and 100%, or as percentages between 0% and 100%. the fraction of times that all equally probable alternatives occur compared to all potential outcomes.
This issue has the parameters n=8 (the number of trials) and p=0.45 (the chance of success in each trial). It is a binomial distribution problem.
The likelihood that Y=3 is:
[tex]P(Y=3) = (8 choose 3) * 0.45^3 * (1-0.45)^(8-3) = 0.3113[/tex]
The probability that Y is at least 3 is:
[tex]P(Y > =3) = P(Y=3) + P(Y=4) + P(Y=5) + P(Y=6) + P(Y=7) + P(Y=8)[/tex]
[tex]P(Y > =3) = (8 choose 3) * 0.45^3 * (1-0.45)^(8-3) + (8 choose 4) * 0.45^4 * (1-0.45)^(8-4) + (8 choose 5) * 0.45^5 * (1-0.45)^(8-5) + (8 choose 6) * 0.45^6 * (1-0.45)^(8-6) + (8 choose 7) * 0.45^7 * (1-0.45)^(8-7) + (8 choose 8) * 0.45^8 * (1-0.45)^(8-8)[/tex]
P(Y>=3) = 0.5626 (rounded to four decimal places)
The probability that Y is at most 3 is:
[tex]P(Y < =3) = P(Y=0) + P(Y=1) + P(Y=2) + P(Y=3)\\P(Y < =3) = (8 choose 0) * 0.45^0 * (1-0.45)^(8-0) + (8 choose 1) * 0.45^1 * (1-0.45)^(8-1) + (8 choose 2) * 0.45^2 * (1-0.45)^(8-2) + (8 choose 3) * 0.45^3 * (1-0.45)^(8-3)[/tex]
P(Y<=3) = 0.3909 (rounded to four decimal places)
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Find the surface area of the prism.
Therefore, the surface area of the prism is 453.5 square meters.
What is surface area?Surface area is the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces, surfaces, or sides of the object. Surface area is measured in square units, such as square inches, square feet, or square meters, depending on the units used to measure the object's dimensions. Surface area is an important concept in geometry and is used in many real-world applications, such as calculating the amount of paint needed to cover a surface or the amount of material required to build a structure.
Here,
To find the surface area of the prism, we need to find the area of all six faces and then add them together. The prism has two congruent rectangular faces (front and back) and four trapezoidal faces (top, bottom, left, and right).
The area of the rectangular faces is:
20 m × 4 m = 80 m² (each face)
The area of the trapezoidal faces can be found using the formula for the area of a trapezoid:
Area = (a + b) × h / 2
where a and b are the lengths of the parallel sides, h is the height, and the slanting height is used to calculate the height.
For the top and bottom faces, the parallel sides are 5 m and 20 m, and the height is 4.47 m. So, the area of each face is:
(5 m + 20 m) × 4.47 m / 2 = 56.75 m² (each face)
For the left and right faces, the parallel sides are 4 m and 5 m, and the height is 20 m. So, the area of each face is:
(4 m + 5 m) × 20 m / 2 = 90 m² (each face)
Now, we can add up the areas of all six faces to get the total surface area:
Total surface area = 2 × 80 m² + 2 × 56.75 m² + 2 × 90 m²
Total surface area = 160 m² + 113.5 m² + 180 m²
Total surface area = 453.5 m²
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I NEED HELP ON THIS ASAP!!!!
Answer:
Step-by-step explanation:
the answers is Ax + By + C = 0 y = mx + c y − y1= m(x − x1) m = Δy/Δx = (y2 − y1)/(x2 − x1)
Based on the table, which statement is true?
A. About 40% of the students prefer Chocolate.
B. About 30% of the students prefer Mint.
C. About 20% of the students prefer Orange.
D. About 50% of the students prefer Orange.
The Ratio of student that prefer mint was 30%
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
From the table:
Total number of students = 34 + 38 + 35 + 27 + 36 + 35 = 205 students
Students that prefer chocolate = 34 + 38 = 72 students
Ratio of student that prefer chocolate = 72/205 * 100% = 35%
Students that prefer mint = 35 + 27 = 62 students
Ratio of student that prefer mint = 62/205 * 100% = 30%
Students that prefer orange = 36+ 35 = 71 students
Ratio of student that prefer orange = 71/205 * 100% = 35%
The Ratio of student that prefer mint was 30%
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I’m so confused can someone please help me?
Answer:
[tex]3 \sqrt{49 {b}^{3}d } = 3 \sqrt{49} \sqrt{ {b}^{2} } \sqrt{bd} [/tex]
[tex]3 \times 7 |b| \sqrt{bd} = 21 |b| \sqrt{bd} [/tex]
If this does not work, try
[tex]21b \sqrt{bd} [/tex]
on the interval determine which angles are not in the domain of the given functions. what angles are not in the domain of the tangent function on the given interval? given in order from least to greatest.
In the interval [0, 2π), the cosine function is equal to zero at θ = π/2 and 3π/2. As a result, the domain of the tangent function on this interval does not include these angles.
So the angles that are NOT in the domain of the tangent function on the interval [0, 2π) are:
π/2 (90 degrees)
3π/2 (270 degrees)
The tangent function is a trigonometric function that describes the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. Specifically, it is defined as the ratio of the sine of an angle to the cosine of that angle.
The tangent function is denoted by the symbol "tan" and is typically used in mathematics and physics to solve problems involving angles and triangles. It is one of the six basic trigonometric functions, along with sine, cosine, cosecant, secant, and cotangent. The value of the tangent function ranges from negative infinity to positive infinity, and it has periodicity of 180 degrees. The tangent function is undefined at certain angles, such as 90 degrees and 270 degrees, where the adjacent side is equal to zero.
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Complete Question: -
On the interval [0,2π) determine which angles are not in the domain of the tangent function, f(θ)=tan(θ)
What angles are NOT in the domain of the tangent function on the given interval?
If a 12-year-old boy is 1/3 as old as his father, how old will the father be when his son is 24?
If a boy having age as 12 years is "1/3" as old as his father, then his father will be 72 years when his son is 24.
We know that, the 12-year-old boy is 1/3 as old as his father,
So, we write an equation to express this relationship:
⇒ 12 = (1/3)F, where F = age of father.
On simplifying,
We get,
⇒ 36 = F,
So, the father's current-age is = 36 years old.
We have to find how the age of father when his son is 24.
So, 24 = (1/3)F,
On simplifying,
We get,
⇒ 72 = F
Therefore, father will be 72 years old when his son is 24.
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What number does point A represent?
In the figure of the number line A represent
7.4What is a number line?A number line is a horizontal representation of number parts with equal intervals
The numbers in a number line is arranged to be increasing from left to right , hence drawing a number line will have the smaller values to the left of the bigger values
Examining the figure shows that there are 5 divisions before on each interval and the numbers from 7 are
7.2
7.4
7.6
7.8
A occupies 7.4
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Three functions are shown in the table. x f(x) g(x) h(x) 1 512 18 65 2 128 16 33 3 32 14 17 4 8 12 9 5 2 10 5 Part A: Which of the functions represents an exponential function? What is the common ratio of that function? Explain. Part B: What is the average rate of change for the function h(x) over the interval 2 ≤ x ≤ 4? Show your work or explain how you found your answer.
The solution is:
(a)f(x), Common Ratio = 1/4
(b) -12
Explanation:
Part A
From the functions on the table, the function that represents an exponential function is f(x).
The common ratio of f(x) is derived below:
512 × 1/4 = 128
128 × 1/4 = 32
32× 1/4 = 8
8 × 1/4 = 2
The common ratio is 1/4.
Part B
We want to find the average rate of change for the function h(x) over the interval 2 ≤ x ≤ 4.
From the table:
• When x=4, h(x)=9: h(4) = 9
• When x=2, h(x)=33: h(2) = 33
The average rate of change = 9 - 33 /2
= -12
The average rate of change for h(x) over the interval 2 ≤ x ≤ 4 is -12.
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When converting 8 fluid ounces to pints, will the number of pints be greater than
or less than 8?
After converting 8 fluid ounces to pints, the number of pints will be greater than 8.
To convert fluid ounces to pints, we need to use the conversion factor of 1 pint equals 16 fluid ounces. So, to convert 8 fluid ounces to pints, we can divide 8 by 16.
8 fluid ounces / 16 fluid ounces per pint = 0.5 pints
Therefore, 8 fluid ounces is equal to 0.5 pints.
We can see that the number of pints is less than 8. This is because 8 fluid ounces is only half of a pint, since there are 16 fluid ounces in one pint. When we divide 8 by 16, we get 0.5, which means that 8 fluid ounces is equivalent to half of a pint.
The conversion factors when making conversions between units. In this case, we used the conversion factor of 16 fluid ounces per pint to convert from fluid ounces to pints. By using this conversion factor, we were able to determine that 8 fluid ounces is equivalent to 0.5 pints.
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if the hypothesis test yields a t statistic 5.42 and a p-value of 0.0001, will you reject the null hypothesis or fail to reject the null hypothesis?
We reject the null hypothesis since the p-value of 0.0001 is less than the significance level of 0.05, indicating a significant difference between the sample mean and the hypothesized population mean.
If the hypothesis test yields a t-statistic of 5.42 and a p-value of 0.0001, this indicates that the probability of observing a test statistic as extreme or more extreme than 5.42, assuming the null hypothesis is true, is 0.0001.
This p-value is very small, and if we use a typical significance level of 0.05, we would reject the null hypothesis because the p-value is less than the significance level.
Therefore, we can conclude that we reject the null hypothesis and accept the alternative hypothesis, which suggests that there is a significant difference between the sample mean and the hypothesized population mean.
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18. Find the area of the triangle.
Answer:
Area = 30
Step-by-step explanation:
Okay, to find the area of this triangle, you have to use the formula [tex]\frac{bh}{2}=A[/tex]. In this case, we are given the height (if we were given the slant height, we could not solve this problem very quickly, so you HAVE to use the regular size.)
Okay, now we substitute in values.
[tex]\frac{bh}{2}=A\\\\\frac{(6)(10)}{2}=A\\\\\frac{60}{2}=A\\\\30=A[/tex]
So, A = 30 is our final answer.
The detailed reason we cannot use slant height is that if you have any line and then put it on a slant, the size would have to be different. For example, if you have support beams on a building going up and down, if you wanted to make one of them slanted, the length of it would have to increase for it to touch the ground appropriately.
Therefore, we cannot use the slant height because it would be longer than the actual height of the triangle.
Identify the transformations of the graph of f(x) = x³ that produce the graph of the given function g(x). Then graph g(x) on the same coordinate plane as the graph of f(x) by applying the transformations to the reference points (-1,-1),(0,0), and (1,1).
g(x) = x³ + 2
Reference
Points
(-1,-1)
(0,0)
(1,1)
First Transformation Second Transformations?
Step-by-step explanation:
The graph is shifted UP 2 units:
