Answer:
[tex]p(x)=(x+2)(x^2+x+1)[/tex]
[tex]x=-2[/tex]
[tex]x=\dfrac{-1 + \sqrt{3}\:i}{2}[/tex]
[tex]x=\dfrac{-1- \sqrt{3}\:i}{2}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]p(x)=x^3+3x^2+3x+2[/tex]
Rational Root Theorem
If P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).
Possible p-values
Factors of the constant term: ±1, ±2
Possible q-values
Factors of the leading coefficient: ±1
Therefore, all the possible values of p/q:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 2}{\pm 1}=\pm1,\pm2[/tex]
Substitute each possible rational root into the function:
[tex]x=-1 \implies p(-1) =(-1)^3+3(-1)^2+3(-1)+2=1[/tex]
[tex]x=1 \implies p(1) =(1)^3+3(1)^2+3(1)+2=9[/tex]
[tex]x=-2 \implies p(-2) =(-2)^3+3(-2)^2+3(-2)+2=0[/tex]
[tex]x=2 \implies p(2) =(2)^3+3(2)^2+3(2)+2=28[/tex]
Therefore, x = -2 is a root of the polynomial since f(-2) = 0.
Divide the polynomial by the root using synthetic division:
[tex]\begin{array}{c|crrr}-2 & 1 & 3 & 3 & 2\\\cline{1-1} & \downarrow &-2&-2&-2\\ \cline{2-5} & 1&1&1&0\end{array}[/tex]
The bottom row (except the last number) gives the coefficients of the quotient. Therefore, the quotient is:
[tex]x^2+x+1[/tex]
So the fully factored form of p(x) is:
[tex]p(x)= (x+2)(x^2+x+1)[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore, the solutions to the quadratic factor are:
[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3\cdot -1}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3} \sqrt{-1}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\:i}{2}[/tex]
The 3 solutions of p(x) are:
[tex]x=-2[/tex][tex]x=\dfrac{-1 + \sqrt{3}\:i}{2}[/tex][tex]x=\dfrac{-1- \sqrt{3}\:i}{2}[/tex]Count the average-case number of + operations performed by the following pseudocode segment. Assume that all possible data sets are equally likely. (Round your answer to two decimal places.) Preconditions: X = {X1, X2, X3, X4,X5} = {10, 20, 30, 40, 50, 60}, where x1 < x2 < X3 < X4 < X5. teo ir 1 while t < 101 do rtet + Xi Liri + 1
Count the average-case number of + operations performed by the following pseudocode segment. The average-case number of + operations performed is 6.67.
The pseudocode segment is a while loop that runs from t=0 to t=101. For each iteration, it adds Xi to the value of the variable liri. Since the preconditions list X as a set of five integers (10, 20, 30, 40, 50, 60) in increasing order, the variable Xi will take on each of these values in turn. Thus, the loop will perform + operations six times (once for each value of Xi). The average-case number of + operations performed is 6.67 (6 operations in total divided by the number of iterations, i.e. 101).
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Which angles are consecutive interior angles?
By using the properties of angle, it can be concluded that
[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle
What is angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
[tex]\angle QPS[/tex] and [tex]\angle TSU[/tex] are not consecutive interior angle as [tex]\angle PST[/tex] falls in between
[tex]\angle QPS[/tex] and [tex]\angle RSU[/tex] are not consecutive interior angle as [tex]\angle RSU[/tex] is an exterior angle
[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle
[tex]\angle QPS[/tex] and [tex]\angle OPN[/tex] are not consecutive interior angle as [tex]\angle OPN[/tex] is an exterior angle
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Determine the measures of the unknown angles.
Answer:
1.
x = 24
m = 112
z = 44
y = 72
2.
x = 35
Step-by-step explanation:
Number 1
Finding x
- Total angle in a triangle is 180.
- QVS = triangle
180 = ∠Q + ∠V + x
180 = 73 + 83 + x
x = 180 -73 - 83
x = 24
Finding m
- Total angle in a straight line is 180
- RW is a straight line
180 = m + ∠U
180 = m + 68
m = 180 - 68
m = 112
Finding z
- Total angle in a triangle is 180.
- RUS = triangle
180 = m + x + z
180 = 112 + 24 + z
z = 180 - 112 - 24
z = 44
Finding y
- Total angle in a triangle is 180.
- RWT = triangle
180 = z + y + ∠W
180 = 44 + y + 64
y = 180 - 44 - 64
y = 72
Number 2
- Total angle in a triangle is 180.
- Total angle in a straight line is 180.
180 = (180 -120) + 85 + x
180 = 60 + 85 + x
x = 180 - 60 - 85
x = 35
Please help I've done it but I want to check my answer!
There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?
Assume that once each marble is chosen, it is not returned to the bag.
Answer:
the probability of selecting one red marble, one yellow marble, and a blue marble is 1/52. This can also be expressed as a percentage by dividing the probability by 1 and multiplying by 100%, which gives a probability of approximately 1.9%.
Step-by-step explanation:
A spherical balloon is being filled with helium at the rate of 9 ft^3/min. How fast is the surface area increasing when the volume is 26 pi ft^3?
A spherical balloon is being filled with helium at the rate of 9 ft^3/min. the surface area of the balloon is increasing at a rate of approximately 37.1 ft^2/min.
What is the surface area?Generally, To find the rate at which the surface area is increasing, we need to use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere. We also know that the volume of a sphere is (4/3)πr^3.
Since we know the volume of the balloon, we can set up the following equation:
(4/3)πr^3 = 26*π ft^3
Solving for r, we find that the radius of the sphere is approximately 2.15 ft. Plugging this value back into the formula for the surface area, we find that the surface area of the sphere is approximately 28.9 ft^2.
To find the rate at which the surface area is increasing, we need to find the d/dx surface area formula with respect to time. Since the radius of the sphere is changing at a constant rate (9 ft^3/min), we can use the chain rule to find the d/dx surface area.
The d/dx 4πr^2 with respect to r is 8pir, and the d/dx r with respect to time (which we'll call t) is 9 ft^3/min. Therefore, the d/dx surface area with respect to time is:
(d/dx 4πr^2 with respect to r) * (d/dx r with respect to t) = (8πr) * (9 ft^3/min)
Plugging in the value of r that we found earlier (2.15 ft), we get:
(8π2.15 ft) * (9 ft^3/min) = 37.1 ft^2/min
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Can someone please help me answer the second part of this question
The compositions of the two given functions are:
g(f(x)) = √(2*x + 29) - 2
f(g(x)) = √(2*x + 25)
How to find the composition of functions?Here we have the two functions:
f(x) = √(2x + 29)
g(x) = x - 2
We want to find the compositions:
f(g(x))
So we just need to evaluate f(x) on g(x), we will get:
f(g(x)) = √(2*g(x) + 29)
Now we can replace g(x) there:
f(g(x)) = √(2*(x - 2) + 29)
f(g(x)) = √(2*x - 2*2 + 29)
f(g(x)) = √(2*x + 25)
The other composition is:
g(f(x)) = f(x) - 2
g(f(x)) = √(2*x + 29) - 2
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the effectiveness of a blood-pressure drug is being investigated. an experimenter finds that, on average, the reduction in systolic blood pressure is 55.9 for a sample of size 29 and standard deviation 7.4. estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level). assume the data is from a normally distributed population.
The tri-linear inequality with the required 80% confidence interval of 54.1 to 57.7 shows the genuine mean value by which the drug decreases the average patient's systolic blood pressure.
A confidence interval expresses the likelihood that a population parameter will fall between a range of values a predetermined percentage of the time. It is the estimate's mean plus or minus the estimate's range of values.
Given the confidence level is 80%, the significance level α=100-80=20% = 0.20. The sample mean [tex]\overline{x}[/tex] is 55.9, the sample standard deviation s is 7.4, and the sample size n is 29.
We are using t-distribution to population standard deviation first. For that first find the degree of freedom and critical value of t.
Degree of freedom,
df = n - 1
df = 29 - 1
df = 28.
The critical value of t calculated from the t-distribution table is,
[tex]\begin{aligned}t_{\text{critical}}&=t_{\alpha/2,df}\\&=t_{0.10,28}\\&=\pm1.3125 \end{aligned}[/tex]
Then, an 80% confidence interval is,
[tex]\begin{aligned}\mu&=\overline{x}\pm\frac{t\cdot s}{\sqrt{n}}\\&=55.9\pm\frac{1.3125\times7.4}{\sqrt{29}}\\&=55.9\pm1.80\end{aligned}[/tex]
Then, the interval is written as
55.9 - 1.80 < μ < 55.9 + 1.80
54.1 < μ < 57.7
The required interval is 54.1 < μ < 57.7.
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When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the _____________.
a. probability of incorrectly accepting the null hypothesis decreases
b. probability of Type II error decreases
c. probability of incorrectly accepting the null hypothesis increases
d. probability of incorrectly rejecting the null hypothesis increases
The probability of a Type I error is the probability of incorrectly rejecting the null hypothesis. When the probability of a Type I error decreases, the probability of a Type II error, It decreases the likelihood of choosing the null hypothesis wrongly.
When conducting a hypothesis test for a given sample size, a Type I error is the probability of incorrectly rejecting the null hypothesis. This means that the null hypothesis is true, but the hypothesis test incorrectly rejects it. A Type II error is the probability of incorrectly accepting the null hypothesis. This means that the null hypothesis is false, but the hypothesis test incorrectly accepts it. When the probability of a Type I error decreases, it means that the hypothesis test is more accurate in correctly rejecting the null hypothesis when it is false. This in turn means that the probability of a Type II error also decreases, as the test is more accurate in correctly accepting the null hypothesis when it is true. In other words, when the probability of a Type I error decreases, the probability of a Type II error decreases as well.
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Graph the solution to this inequality on the number line. 2/3z > 4/5
The solution to the inequality, 2/3z > 4/5, is calculated as z > 1.2. See attachment for the graph of the solution.
How to Solve and Graph the Solution to an Inequality?The solution to an inequality is determined by finding he value of the variable in the inequality that will make it true.
Given the inequality, 2/3z > 4/5, isolate the variable z to one side to determine its value:
2/3z > 4/5 [given]
Multiply both sides by 3/2:
2/3z × 3/2 > 4/5 × 3/2
z > (4 × 3) / (5 × 2)
z > 12 / 10
Simplify further:
z > 6/5
z > 1.2
The solution is z > 1.2. The graph of the solution is shown in the image that is given in the attachment below.
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16. Find 2,075 ÷ 7. A 295 B 296 R1 C 296 R3 D 304 R5
Answer:
C. 296 R3
Step-by-step explanation:
In order to find the quotient, lets use long division:
296 R 3
_________
7 | 2075
- 14
__
67 ==> drop 7 from 2075
- 63
__
45 ==> drop 5 from 2075
- 42
__
3
Consider exponential functions f and g.
f(x) = 4(5)x
Complete the statements comparing the two functions.
Because the y-intercept of function f is
, it is
the y-intercept of function g.
Both functions
on all intervals of x, but their end behavior is different as x approaches
infinity.
The correct statements regarding the comparisons of the exponential functions are given as follows:
Because the y-intercept of function f is of 4, it is lower than the y-intercept of function g.Both functions are increasing on all intervals of x, however, their end behavior is different as x approaches negative infinity.How to define the exponential functions?The definition of function f(x) is given as follows:
f(x) = 4(5)^x
Meaning that it has an y-intercept and an asymptote given as follows:
y-intercept of 4.asymptote of 0, as when x goes to negative infinity, y goes to zero.From the graph of function g(x), we have that:
The y-intercept is of 5, which is the value that the graph crosses the y-axis.The horizontal asymptote is of y = 2, hence they have different end behavior when x goes to negative infinity.More can be learned about exponential functions at https://brainly.com/question/25537936
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1. 4
2. less than
3. increase
4. negative
Got it right on Edmentum
Function f is represented by an equation in standard form with a = 4 and b = 5. This function is increasing and has a y-intercept of 4. The function approaches 0 as x approaches -∞ and approaches ∞ as x approaches ∞.
Function g crosses the y-axis at (0,5). The function approaches 2 as x approaches -∞ and approaches ∞ as x approaches ∞.
Because the y-intercept of function f is 4, it is less than the y-intercept of function g. Both functions increase on all intervals of x, but their end behavior is different as x approaches negative infinity.
find the equation of the linear function represented by the table. x 1,2,3,4 y 1,6,11,16
Answer: y = 5x - 4
Step-by-step explanation: The equation of a linear function can be found by using the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (i.e., the point at which the line crosses the y-axis).
To find the equation of the linear function represented by the table, we can use the values from the table to calculate the slope. The slope is calculated as the change in y over the change in x, or (y2 - y1)/(x2 - x1). Using the values from the table, we can calculate the slope as (6 - 1)/(2 - 1) = 5/1 = 5.
Next, we can use the slope and one of the points from the table to find the y-intercept. If we use the point (1,1), we can substitute the values into the slope-intercept form to get 1 = 5*1 + b, so b = -4.
Therefore, the equation of the linear function represented by the table is y = 5x - 4.
the questions in this activity refer back to prelab 0, which would be a good place to look if you need any help. in test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again calculate mean, standard deviation, and standard error. 1)which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?
The most likely statement about the comparison of standard deviation of Test A and Test B is (a) The standard deviations found in Test A and Test B will be about the same .
What is Standard Deviation ?
The term standard deviation is defined as a measure which shows the variation (such as dispersion) from the mean .
it is given that in Test A 100 experimental measurements is taken , and
in Test B 400 experimental measurements is taken .
we know that standard deviation is just square root of average of the square distance of measurements from the mean.
So , it is not affected by the number of experimental measurements .
thus , the standard deviation remain same for both the tests .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
In test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again .
Which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?
(a) The standard deviations found in Test A and Test B will be about the same
(b) The standard deviation found in Test A will about be twice as big as the standard deviation found in Test B.
(c) The standard deviation found in Test will about be four times as big as the standard deviation found in Test B
(d) The standard deviation found in Test B will about be twice as big as the standard deviation found in Test A .
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Determine which set of side measurements could be used to form a right triangle.
14, 5, 15
O 3, 4, 5
O9, 14, 16
O 5, 2,7
Answer:
3,4,5
Step-by-step explanation:
Because, it is the only pair that fulfill the pythagorean theorem/formula
Pythagorean formula: [tex]c^2 = \sqrt{a^2 + b^2}[/tex]
Where c is the longest side of the triangle, or the hypothenuse, and a and b is the two perpendicular side.
Kaitlyn went on a diet and lost 8% of her body weight. She now weighs 222 pounds.
What was her original body weight?
To find Kaitlyn's original body weight, we need to determine how much weight she lost and add that amount back to her current weight.
Kaitlyn lost 8% of her body weight, which is equal to 8/100 * 222 pounds = <<8/100*222=17.76>>17.76 pounds.
Therefore, Kaitlyn's original body weight was 222 pounds + 17.76 pounds = <<222+17.76=239.76>>239.76 pounds.
What is the inverse of the function below?
f(x) = x/3 -2
O A. f1(x) = 2(x+3)
O B. f¹(x) = 3(x+2)
O c. f¹(x) = 3(x - 2)
OD. f¹(x) = 2(x-3)
Answer:
f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]
Step-by-step explanation:
The first step to finding the inverse of a function is to let [tex]y=f(x)[/tex].
This would mean [tex]y=\frac{x}{3}-2[/tex].
Then we swap [tex]x[/tex] and [tex]y[/tex] in the formula.
[tex]x = \frac{y}{3} -2[/tex]
Then rearrange for [tex]y[/tex]:
[tex]x=\frac{y}{3}-2 \\\\x+2=\frac{y}{3}\\\\3(x+2)=y[/tex]
This new equation of [tex]y[/tex] is the inverse function.
f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]
MODELING REAL LIFE An obstacle course
needs :
new piece made
in the shape
of a triangular prism
with an equilateral triangle for base. The side length
x (in feet) of the base and
prism are related by
the height y (in feet) of the
the inequality y > 1/2x^2+ 1. The
piece has the following additional constraints.
The height must be no more than 7 feet greater than
the side length of the base.
The side length of the base must be at least foot.
Write and graph a system that represents the situation.
Give one example of a height and side length that the
obstacle course can use.
The solution for the situation is [tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex] Where y > 1, and the graph is attached below.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
The side length x (in feet) of the base,
the height y (in feet) of the inequality y > 1/2x²+ 1 and y ≤ x,
In solving this inequality, we get,
[tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex] where y > 1
The graph of the system is attached below.
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researcher is using a Kruskal-Wallis test to evaluate the difference between three treatment conditions using a sample of n-8 in each treatment. What value of H is necessary to conclude that there is a significant difference among the treatments using a 05 Select one O a. H25.99 Ob. H2 347 c H2 1.96 O d. H 2080
C. H2 1,96
To establish whether there is a significant difference between treatments using the Kruskal-Wallis test, the calculated value of H should be compared to the critical values in the table of H values. The critical value of H to use depends on the significance level chosen for the test (0.05 in this case).
Using a significance level of 0.05, the critical value of H for a sample size of n-8 for each treatment is approximately H2 1.96. That is, if the calculated H value is greater than 1.96, we can conclude that there is a significant difference between the treatments.
Hence, the correct answer in this case is c. H2 1,96
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The two cotton processing companies are producing different products and those are sold out the products one year before. The sold sum of both the two companies salaries are $44,000,000. The sold price of company x is 1000 more than the other. Therefore, find the value of each company's product sold price by framing a linear equation?
The final value of company x sold price is; $22,000,500
The final value of company y sold price is; $21,999,500
How to solve Linear equation word problems?Let the amount of sold out products in company x and company y be denoted by a
Now, we are told that sum of both the two companies salaries are $44,000,000.
Now, the sold price of company x is 1000 more than the other.
Thus;
Sold price of company y = y
Sold price of company x = 1000 + y
Thus;
1000 + y + y = 44000000
1000 + 2y = 44000000
2y = 44000000 - 1000
2y = 43,999,000
y = 43,999,000/2
y = $21,999,500
Thus;
Sold price of company x = $21,999,500 + $1000 = $22,000,500
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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = 7(1 − x)−2
f(x) =
[infinity] sum.gif
n = 0
Find the associated radius of convergence R.
R =
The radius of convergence R of the given function f(x) = (-1)^n(1 - x)² be,
R = 1/2.
Given, a function f(x)
f(x) = (-1)^n(1 - x)²
we have to find the radius of convergence R of the given function,
first will find the (n+1)th term of the given function
as, an = (-1)^n(1 - x)²
then an+1 = (-1)^(n+1)(1 - x)²
to find the radius of convergence, we will find
lim x->∞ an+1/an
lim x->∞ ((-1)^(n+1)(1 - x)²)/((-1)^n(1 - x)²)
On solving the limits, we get
lim x->∞ an+1/an = 2x
then R = 1/2
as, -1/2 < x < 1/2
so, the radius of the convergence be, 1/2
Hence, the radius of the convergence be, 1/2
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Find the perimeter of the figure. If you need to use in your computation, approximate its value as 3.14.
Rectangle topped by a semicircle
10 m
a. 35.57 m
b.
65.40 m
C.
59.70 m.
d. 49.70 m
The total perimeter of the given composite figure is; 74.55 meters
How to find the perimeter of a composite figure?The perimeter of the given figure can be calculated by dividing the figure into two parts : One is semi-circle and second is rectangle.
To find Perimeter of rectangle :
Length of the rectangle = 18 m
Width of the rectangle = 15 m
Perimeter = (2 × Length) + Width
Perimeter = (2 × 18) + 15
Perimeter = 36 + 15
Perimeter = 51 meters
To find perimeter of semi-circle :
Radius of semi-circle = 15/2 = 7.5 m
Perimeter of semi-circle = π × radius
Perimeter = 3.14 × 7.5
Perimeter = 23.55 meter
So, Total Perimeter of the figure = 51 + 23.55
= 74.55 meter
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(15points) Let 21, 22, ..., Ik be linearly independ vectors in a vector space V. If we add a vector Ik+1 to the collection, will we still have a linear independent collection of vectors? Explain. If we delete a vector, say, 2k , from the collection, will we still have a linearly independent collection of vectors? Explain.
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 9
Read the following prompt and type your response in the space provided.
Write a real-world problem that could be represented by the inequality.
3x + 6 > 27
Find the value of K
(x+5) is a factor of the Polynomial p(x)
if p(x)=2x³ +7x²+Kx + 20
Therefore the value of K is -11
Triangle CAT is transformed by a sequence of rigid motions that maps onto triangle DOG. Which three congruency statements would show ASA congruency for these triangles? (select all that apply)
A.∠ A ≅ ∠ T
B.CA ≅ DO
C.AT ≅ OG
D.CT ≅ DG
E.∠ A ≅ ∠ O
F.∠ C ≅ ∠ D
Answer:
B, E and F.-----------------------------
Since the triangles CAT and DOG overlap, their corresponding parts are congruent.
As we are looking for ASA congruency, we need to select two angles and the included side.
Let's review the given options, considering names of triangles and the order of vertices in those names.
A. ∠ A ≅ ∠ T
Incorrect as angles T and A are not corresponding.B. CA ≅ DO
Yes, possible side.C. AT ≅ OG
Yes, possible side.D. CT ≅ DG
Yes, possible side.E. ∠ A ≅ ∠ O
Yes, possible angle.F. ∠ C ≅ ∠ D
Yes, possible angle.So we have corresponding angles A and C and the included side must be AC.
Looking, at the options, we can get ASA with combination of options B, E and F.
In detail please I’m getting graded and can’t find the answer
Answer:
x = 75
y = 15
Step-by-step explanation:
What you need to know to solve this question:
1. Angles in a triangle sum up to 180
2. Angles on a straight line add up to 180
3. A right-angle is 90
4. The triangle illustrated is a right-angle triangle
Solving for x:
According to principle 2:
x + 105 = 180
x = 180 - 105
x = 75
Solving for y:
According to principles 1 and 3:
x + y + 90 = 180
(75) + y + 90 = 180
y = 180 - 90 - 75
y = 15
Help me please help me
Answer:
125 -v³ = (5 -v)(v² +5v +25)
Step-by-step explanation:
You want to factor the expression 125 -v³.
FactorsFrom your knowledge of the cubes of small integers, you recognize that 125 = 5³. That lets you see this expression is the difference of cubes, which has a factor pattern:
a³ -b³ = (a -b)(a² +ab +b²)
Your difference factors as ...
5³ -v³ = (5 -v)(5² +5v +v²)
125 -v³ = (5 -v)(v² +5v +25)
h is a trigonometric function of the form h(x)=acos(bxc)+d. Below is the graph of h(x) The function has a maximum point at (3,6) and a minimum point at (6.5,-9) find the formula for h(x). Give an exact expression.
h(x)=
*from klan academy*
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The exact expression for the cosine function is given as follows:
h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.
How to define the cosine function?The definition of the cosine function is given as follows:
h(x) = acos(b(x - c)) + d.
The parameters of the function are given as follows:
a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.The difference between the maximum value and the minimum value is of 6 - (-9) = 15, hence the amplitude is obtained as follows:
a = 15/2 = 7.5.
From the graph given at the end of the answer, the period is of 7 units, hence:
2π/b = 7
7b = 2π
b = 2π/7.
The minimum value should be at x = 0, however it is at x = -0.5, hence the phase shift is given as follows:
c = -0.5.
Considering the amplitude of 7.5, without vertical shift the function would oscillate between -7.5 and 7.5, however is oscillates between -9 and 6, hence the vertical shift is given as follows:
d = -1.5.
Thus the function is defined as follows:
h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.
Missing InformationThe graph of the function is given by the image shown at the end of the answer.
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suppose a statistician wishes to test whether a large number of observations follows an exponential distribution with parameter . he wishes to test this hypothesis exactly, and intends that if the observations follow an exponential distribution with a different parameter, the test should reject the null hypothesis given sufficiently many observations. in addition, he wants to have a numeric statistic that he could report and does not want the procedure to involve rounding off observation numbers into bins. which of the following goodness-of-fit tests would be the most appropriate for this purpose? Chi-squared Test O Kolmogorov-Smirnov Test O Kolmogorov-Liliefors Test Quantile-quantile plots
This distribution has no shape parameter as it has only one shape, (i.e., the exponential, and the only parameter it has is the failure rate, \lambda \,\!).
How do you find the parameter of an exponential distribution in R?The exponential distribution can be simulated in R with rexp(n,λ) where λ is the rate parameter. The mean or expected value of an exponential distribution is 1/λ and the standard deviation is also 1/λ. The variance of an exponential distribution is given by 1/λ2.
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