Considering the given probability distribution, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.,The sum of all probabilities is of 1.In this problem:
For distribution A, the sum is of 1.2, hence it is not valid.For distribution B, the sum is of 1.2, hence it is not valid.For distribution C, the sum is of 0.9, hence it is not valid.For distribution D, the sum is of 1, hence it is valid.More can be learned about probability distributions at https://brainly.com/question/23670007
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If f(x) = 2x² + 3 and g(x)=x2-7, find (f- g)(x).
Step-by-step explanation:
arithmetic operations with functions just means to do these operations with the function expressions. and the result is the resulting function.
so,
(f - g)(x) = f(x) - g(x) = (2x² + 3) - (x² - 7) =
= 2x² + 3 - x² + 7 = x² + 10
Write a formula for the following:
The amount in an account at the end of a year, if simple interest is paid at
the rate of 16%, and the account contains d dollars at the beginning of the year.
Answer:
A = 1.16d
Step-by-step explanation:
Multiplying by 1 + the percentage value is equivalent to adding the percentage.
Please HELP!!!!!
The domain (input values) of the cosine function is:
A. angle measures less than 2π radians.
B. angle measures between 0 and π radians.
C. angle measures less than 90°.
D. all negative and positive angle measures.
SUBMIT
Answer: D. all negative and positive angle measures.
Which the most accurate statement about progress monitoring?
a. Progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in.
b. Incorporating children's individual differences into lesson planning is not necessary since the curriculum includes all the skills children need to learn in the order they need to learn them.
c. Progress monitoring is about administering formal assessments at the beginning and end of the year.
The most accurate statement about progress monitoring is progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in. Option A
What is progress monitoring?
Progress monitoring can be defined as a standard process of evaluating or checking progress toward a performance target on the basis of level of improvement from frequent assessment of a skill.
Thus, the most accurate statement about progress monitoring is progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in. Option A
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Complete the equation of this circle:
(x − [?])²+(y - [ ])²=[ ]
Answer:
(x-{-2})^2+(y-{4})^2={36}
Equation:
x^2+y^2=r^2
r=radius
Blank following x/y is flipped center(of circle) coordinate for x/y
Formulate the quadratic function that contains the points (-2,1), (0,1) and (1,4).
Answer:
Step-by-step explanation:
The expression √5x is equivalent to the expression x√5.
O A. True
OB. False
Answer: False
Step-by-step explanation:
[tex]\sqrt{5x}=\sqrt{x} \sqrt{5} \neq x\sqrt{5}[/tex]
Volume of a cone 27cm 13 cm
The volume of the cone is 4775.94 cu.cm
What is a cone ?A cone is a three dimensional shape which has a circular base and then tapers down to a point called as Vertex.
It is given that the cone has
Height = 27 cm
Radius = 13 cm
The volume of the cone is given by
V = (1/3)πr²h
Volume = (1/3) * 3.14 * (13)² * 27
Volume = 4775.94 cu.cm
Therefore the volume of the cone is 4775.94 cu.cm
The complete question is
Find the volume of the cone of height = 27 cm and radius is 27 cm.
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A couple decides that sophia will drive the first 3/5 of a trip and toby the last 2/5. the entire trip is 500 miles long. how far will sophia drive?
The miles Sophia drove is 60 miles
The distance Sophia drove is represented in fractions.
What is a Fraction?A number is expressed as a quotient where a numerator is divided by a denominator. In a simple fraction, both are integers.
A fraction consists of a numerator and a denominator. An example of a fraction is 1/2 where 1 is the numerator and 2 is the denominator.
In order to determine the miles Sophia drove, the total distance of the trip would be multiplied by the fraction of the time Sophia drove.
Miles Sophia drove = 3/5 x 100
= 60 miles
So sophia drove 60 miles in 500 miles.
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When graphing the function f(x)=x^2-81/x^2-11x 18 on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?
An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.
We have been given a rational function:
[tex]f(x)=\frac{x^{2} -81}{x^{2} -11x+18}[/tex]
And we are required to determine an appropriate viewing rectangle for the graphing calculator.
Hence, An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.
For the given function, an appropriate viewing rectangle will be [-20,20,2] by [-20,20,2].
This function, when graphed using a graphing calculator on the said viewing rectangle, it appears as attached.
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Cube A and cube B are similar solids. The volume of cube A is 27 cubic inches, and the volume of cube B is 125 cubic inches. How many times larger is the base area of cube B than the base area of cube A? A small cube labeled cube A has points K, L, M, and N on the top face and O, P, Q, and R on the bottom face. A large cube labeled cube B has points A, B, C, and D on the top face and E, F, G, and H on the bottom face. A. B. C. D.
The area of the base of cube B is 25/9 times larger than the area of the base of cube A.
How many times larger is the base area of cube B than the base area of cube A?Because the cubes are similar, then we know that the dimensions of cube B are a dilation of scale factor K of the dimensions of cube A.
Then, the volume of cube B is K³ times the volume of cube A.
The area of any face of cube B is K² times the area of any face of cube A
From this we can write:
125 in³ = K³*27in³
(125/27) = K³
If we apply the cubic root in both sides, we get:
∛(125/27) = K = 5/3
Then the relation between the areas is equal to:
K² = (5/3)^2 = 25/9
The area of the base of cube B is 25/9 times larger than the area of the base of cube A.
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Answer:
25/9
Step-by-step explanation:
I Just Took the Test.
What is the length of DE ?
Answer:
option D. DE = 11
Step-by-step explanation:
The line DF is equivalent in length to the blue line,
(x + 7) + 7 = 4x + 2
Solve:
x + 14 = 4x + 2
subtract 14 from both sided to get x alone,
x + 14 - 14 = 4x + 2 - 14
x = 4x - 12
subtract 4x from both sided,
x - 4x = 4x - 4x - 12
-3x = -12
divided both sides by -3,
-3x / 3 = -12 / -3
x = 4
Plug in x into DE equation:
x + 7: (4) + 7 = 11
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Gabrielle is 15years older than mik. The sum of their ages is 103.what is mik age?
Answer:
Mikhail is 44 years old.
Step-by-step explanation:
Set both Gabrielle and Mikhail's age to a variable.
Gabrielle is x, Mikhail is also x.
Now create an equation using the variables with the sum.
Age1 + Age2 + 15 = 103
x + x + 15 = 103
Now we solve.
1. Combine like terms
2x + 15 = 103
2. Make all the numbers on one side of the equation, and the variables of the other, so subtract.
2x + 15 - 15 = 103 - 15
2x = 88
3. Simplify further by dividing.
x = 44
Mikhail is 44 years old.
Check your work:
44 + (x + 15) = 103
x + 15 = 59
x = 44
Answer:
Step-by-step explanation:
Let Gabrielle's age be x.
The age of the milk will be x - 15.
x + (x - 15) = 103.
2x - 15 = 103
2x = 118
x = 59
The milk's age = x - 15 = 59 - 15 = 44.
What percent of 5280 feet is 880 yards
Answer:16.67
Step-by-step explanation:
880 of 5280 can be written as:
880
5280
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
880
5280
×
100
100
= (
880 × 100
5280
) ×
1
100
=
16.67
100
Therefore, the answer is 16.67%
If you are using a calculator, simply enter 880÷5280×100 which will give you 16.67 as the answer.
What is the definition of yield to maturity?
Review Later
The return the investor gets from the income component of a bond as a percent of it's current price
The overall return the investor makes as a percent of a bond's par value
The overall return the investor makes if they purchase a bond today and hold to maturity
The return the investor gets from the income component of a bond as a percent of it's par value
The yield to maturity best defined by the option c. The overall return the investor makes if they purchase a bond today and hold to maturity.
It is the total return of rate that will have been incomed by a bond when it makes all liability payments and repays the principal amount.
Since, as per the definition of yield to maturity, investor would get the original price of bond plus and the rate of interest that finalized (at the time of bond purchase) when the maturity period will over.
Thus, the overall return the investor makes if they purchase a bond today and hold to maturity. Best describes yield to maturity.
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help me please i need help
Answer:
B
Step-by-step explanation:
[tex](f-g)(x)=4x^2+5x-3-(4x^3-3x^2+5)\\\\=-4x^3+7x^2+5x-8[/tex]
Hence B is correct.
what’s the slope of the line
Answer:
90
Step-by-step explanation:
slope
Answer:
formula is equal to rice run is equal to y 2 -y 1 X2 minus X1
G(X) IS A TRANSFORMATION OF F(X) WHAT IS G(X) IN TERMS OF F(X)
This is a very simple transformation problem and can be solved by observation. The correct answer is Option D where g(x) = f(x-3) + 6. See the attached graph for the full question.
What is a transformation?
In mathematics, transformation is the process of converting one figure, expression, or function into another of equivalent value.
What is the explanation for the above problem?Note that on an x-axis, moving past zero to the left gets you into the negative, and vice versa.
On the y-axis moving upwards past zero gets you into the positive.
Recall that g(x) is a transformation of f(x). This means that the original image is f(x).
Notice that F(x) is transformed three degree beyond 0 on the -axis and 6 degrees beyond zero on the y-axis. Hence the correct equation is:
g(x) = f(x-3) + 6.
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Find the measure of an interior angle of a regular nonagon (9-sided polygon).
Hint: (n-2)180
x=[?] degrees
The measure of an interior angle of a regular nonagon (9-sided polygon) is 140°
How to determine the angle
The formula for sum of interior angles of a polygon is given as;
= ( n -2) × 180
Recall that a nonagon has nine sides, so , n = 9
Substitute the value into the formula
= ( 9 -2) × 180
= 7× 180
= 1260°
Since the sum of the angles = 1260°
One of the angles = 1260/ 9 = 140°
Therefore, the measure of an interior angle of a regular nonagon (9-sided polygon) is 140°
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Brad has the option of using three types of tables in his bagel shop: square tables with a side length of 39 inches rectangular tables 23 inches wide and 71 inches long round (circular) tables with a diameter of 48 inches. Which type of table has the largest area?
The type of table that has the largest area is circular table
How to find area of figures?area of a square = l²
where
l = lengthTherefore,
area of the square table = 39² = 1521 inches²
area of a rectangle = lw
where
l = lengthw = widthTherefore,
area of the rectangular table = 23 × 71 = 1633 inches²
area of a circle = πr²
where
r = radiusTherefore,
area of a circular table = π × (48 / 2)² = 576π = 1808.64 inches²
Therefore, the table that has the largest area is the circular table.
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Express the number as a ratio of integers.
0.16 = 0.16161616...
0.16 = 0.16161616... as a ratio of integers is 16 : 99
How to express as a ratio?The equation is given as:
0.16 = 0.16161616...
The above is a non-terminating decimal.
It can be represented as:
a/b - 1
Where
a = 16
b = 100
So, we have:
16/100 - 1
Evaluate the difference
16/99
Express as ratio
16 : 99
Hence, 0.16 = 0.16161616... as a ratio of integers is 16 : 99
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A normal population has a mean of 20.0 and a standard deviation of 4.0.
a. Compute the z value associated with 25.0.
b. What proportion of the population is between 20.0 and 25.0?
c. What proportion of the population is less than 18.0?
Calculations:
Normal pop has mean of 20.0
standard deviation = 4.0
XNN(20.0, 4.0)
a).
[tex]z=\frac{x-h}{z}[/tex]
[tex]=\frac{25-20}{4.0} =\frac{5}{4} =1.25[/tex]
Z = 1.25
b).
The proportion between 20 and 25 is P(20 <x<25.0)
[tex]=p(\frac{20-20}{4} < z < \frac{25-0}{4} )[/tex]
[tex]=P(0 < z < 1.25)[/tex]
[tex]=P(Z < 1.25)-P(z < 0)[/tex]
[tex]=0.8944-0.5000[/tex]
P(20 < x < 25)=0.3944
c).
The proportion value is less than 18 when
[tex]P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}[/tex]
[tex]=P(z < \frac{-2}{4})[/tex]
[tex]=P(z < -0.5)[/tex]
P(x<18) = 0.3085
Use the function below to find F(4)
Answer:
A 256/3
Step-by-step explanation:
1/3 * 4^4 =
1/3 * (4*4*4*4) =
1/3 * 256 = 256/3
Answer:
A = 256/3
Step-by-step explanation:
F(x) = 1/3 × 4ˣ = 4ˣ/3
F(4) = 4⁴/3 = 256/3
the graph below shows the quadratic function of f and the table below shows the quadratic function of g -1 0.75 2 2.75 3 2.75
The correct information based on the equation is that the functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
How to illustrate the information?From the graph of f(x):
⇒ Axis of symmetry will be at x = 2
⇒ The maximum value of f(x) = 4
From the table of g(x):
⇒ Axis of symmetry will be at x = 2
⇒ The maximum value of g(x) = 3
The graph is attached.
The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
Here is the other part of the question:
Which statement is true?
The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.
The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.
The functions f and g have different axes of symmetry and different maximum values.
The functions f and g have the same axis of symmetry and the same maximum values.
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2) Which statement about the radius of a circle is true?
A. The radius is the boundary of a
circle.
B. The radius is the distance around a portion of a circle's boundary.
C. The length of a radius is always the same for a given circle.
D. The radius is a line segment passing through a circle's center, with endpoints on the boundary.
Answer:
C.
Step-by-step explanation:
The boundary of a circle is the circle itself.
The radius of a circle is a segment from the center of the circle to any point of the circle.
In a circle, every radius has the same length.
Answer: C.
David and Lacey are 2000 feet apart on a coastline. They each look at the same boat in the water. The angle between the coastline and the line from David to the boat is 70%. The line between the coastline
and the line from Lacey to the boat is 32.
Part A: How far is the boat from David?
Part B: How far is the boat from Lacey?
Part C: If David moved so that his distance from the boat is 1200 feet, what would the angle be between the coast and his view of the boat?
By using the given distances and directions, we have;
Part A: 1083.5 feet
Part B: 1921.37 feet
Part C: 58.05°
How can the distances and directions be calculated?The distance between David and Lacey = 2000 feet
David's angle to the boat = 70°
Lacey's angle to the boat = 32°
Part A
The distance of the boat from David is found as follows;
Imaginary lines drawn from the boat to David and then to Lacey form a triangle.
In the triangle, let A = 70°
B = 32°
Therefore by the sum of angles in a triangle, we have;
C = 180° - (70° + 32°) = 78°
By using sine rule we have;
[tex] \frac{a}{sin(A)} = \frac{b}{sin( B )} = \frac{c}{sin(C)}[/tex]
David's distance from the boat, b, is therefore;
[tex] \frac{b}{sin( 32 )} = \frac{2000}{sin(78)}[/tex]
The angle subtended by the coastline, C, is therefore;
[tex] b = \frac{2000}{sin(78)} \times sin( 32 ) = 1083.5 [/tex]
David's distance from the boat is 1083.5 feetPart B
The distance between the boat and Lacey is found as follows;
[tex] \mathbf{ \frac{a}{sin( 70)} }= \frac{2000}{sin(78)}[/tex]
[tex] a = \frac{2000}{sin(78)} \times sin( 70 ) = 1921.37 [/tex]
Lacey's distance from the boat is 1921.37 feetPart C
When b = 1200 feet, we have;
Finding the vertical distance of the boat from the coastline, we have;
1083.5 × sin(70) = 1018.17
We have;
[tex] \frac{1200}{sin(90)} = \frac{1018.17}{sin( B' )} [/tex]
[tex] {sin( B' )} = \frac{sin(90)}{1200} \times 1018.17 [/tex]
The angle between the coastline and his view to the boat, B', is therefore;
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PLEASE I NEED THIS ASAP PLEASE
The correct option is the second one:
i) right, right, left.ii) Undefined.What can we say about the calculation?We know that:
x > 0z > 0y < 0We have the operation:
x - y + (-z)
Notice that because y is negative, then -y is positive.
Because z is positive, -z is negative.
Then we have:
positive + positive + negative
Or, in the number line:
right, right, left.
Second question:
Can we conclude the sign of the outcome?
No, we can't, the sign will depend on the values of x, y, and z.
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Answer:The correct option is the second one:i) right, right, left.ii) Undefined.
Step-by-step explanation:
Prove: The product of the slopes of lines AC and BC is -1.
Given that the AC and BC are perpendicular, their slopes are the negative inverse of each other which gives that the product of the slopes of AC and BC is -1
How can the prove that the product of the slopes is -1 be found?The completed proof is presented as follows;
The slope of AC or GC is GF/FC by definition of slope. The slope of BC or CE is DE/CD by definition of slope.
<FCD = <FCG + <GCE + <ECD by angle addition property <FCD = 180° by the definition of a straight angle, and <GCE = 90° by definition of perpendicular lines. So by substitution property of equality 180° = <FCG + 90° + <ECD. Therefore 90° - <FCG = <ECD, by the subtraction property of equality . We also know that 180° = <FCG + 90° + <CGF by the triangle sum theorem and by the subtraction property of equality 90° - <FCG = <CGF, therefore <ECD = <CGF by the substitution property of equality. Then <ECD ≈ <CGF by the definition of congruent angles. <GFC ≈ <CDE because all right angles are congruent. So by AA ∆GFC ~ ∆CDE. Since the ratio of corresponding sides of similar triangles are equal then GF/CD = FC/DE or GF•DE = CD•FC by cross product. Finally, by the division property of equality GF/FC = CD/DE. We can multiply both sides using the slope of using the multiplication property of equality to get GF/FC × -DE/CD = CD/DE × -DE/CD. Simplify so that GF/FC × -DE/CD = -1. This shows that the product of the slopes of AC and BC is -1.
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Unknown to a medical researcher, 6 out of 25 patients have a heart problem that will result in death if they receive the test drug. 8 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that exactly 6 patients will die? Express your answer as a fraction or a decimal number rounded to four decimal places.
Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that exactly 6 patients will die.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of the parameters for this problem are:
N = 25, k = 6, n = 8.
The probability that exactly 6 patients will die is P(X = 6), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 6) = h(6,25,8,6) = \frac{C_{6,6}C_{19,2}}{C_{25,8}} = 0.0002[/tex]
0.0002 = 0.02% probability that exactly 6 patients will die.
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The price of a CD decreased from $18 to$12 . What is the percent of decrease? 6% 25% 33% 60%
A percentage is a way to describe a part of a whole. The percetage decrease in the price of CD is 33.33%.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The price of the CD decreases from $18 to $12. Therefore, the percentage decrease is,
Percentage Decrease = ($18-$12)/$18 × 100% = 33.33%
Hence, the percetage decrease in the price of CD is 33.33%.
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