Considering the given probability distributions, 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, only distribution D has a sum of 1, hence it is the only valid distribution.
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Answer:
Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Step-by-step explanation:
The answer above is correct.
write the numerical expression for each statement
An expression is defined as a set of numbers, variables, and mathematical operations. The sum of three and the square root of a number is expressed as 3 + √x.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Let the unknown number be represented by x.
1.) The sum of three and the square root of a number.
3 + √x
2.) Nine less than a number cubed.
x³ - 9
3.) The quotient of a number and 7.
x ÷ 7
4.) Four times a quantity plus five.
4x + 5
Hence, The sum of three and the square root of a number is expressed as 3 + √x.
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The fit line equation is Y = -2.61x +152.51, where x is variable 1 and Y is variable 2. According to the equation, what is the expected value of Y when x-value is 45?
The expected value of y when x is equals to 45 in the equation is 35.06
How to find variable from an equation?The equation is given as follows;
y = -2.61x + 152.51
where
x = variable 1y = variable 2Therefore,
when
x = 45
y = -2.61x + 152.51
y = -2.61(45) + 152.51
y = - 117.45 + 152.51
y = 35.06
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solve this trigonometry question too, please by an easy method.
Answer:
proof given below
Step-by-step explanation:
Combine the fractions by making the denominators the same:
[tex]\dfrac{\sin \theta}{1+ \cos \theta}+\dfrac{1+ \cos \theta}{ \sin \theta}[/tex]
[tex]=\dfrac{\sin \theta}{1+ \cos \theta} \cdot \dfrac{\sin \theta}{\sin \theta}+\dfrac{1+ \cos \theta}{ \sin \theta} \cdot \dfrac{1+ \cos \theta}{1+ \cos \theta}[/tex]
[tex]=\dfrac{\sin \theta(\sin \theta)}{\sin \theta(1+ \cos \theta)}+\dfrac{(1+ \cos \theta)(1+ \cos \theta)}{\sin \theta(1+ \cos \theta)}[/tex]
[tex]= \dfrac{\sin^2 \theta}{\sin \theta(1+ \cos \theta)} +\dfrac{1+2 \cos \theta + \cos^2 \theta}{\sin \theta(1+ \cos \theta)}[/tex]
[tex]= \dfrac{\sin^2 \theta+ \cos^2 \theta+1+2 \cos \theta }{\sin \theta(1+ \cos \theta)}[/tex]
Use the trigonometric identity [tex]\sin^2 \theta + \cos^2 \theta=1[/tex] :
[tex]= \dfrac{1+1+2 \cos \theta}{\sin \theta(1+ \cos \theta)}[/tex]
[tex]= \dfrac{2+2 \cos \theta}{\sin \theta(1+ \cos \theta)}[/tex]
Factor out 2 from the numerator:
[tex]= \dfrac{2(1+ \cos \theta)}{\sin \theta(1+ \cos \theta)}[/tex]
Cancel the common factor:
[tex]= \dfrac{2}{\sin \theta}[/tex]
[tex]\textsf{Use the identity} \quad\csc \theta=\dfrac{1}{\sin \theta}:[/tex]
[tex]=2 \csc \theta[/tex]
Hence proved.
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Step-by-step explanation:
please mark me as brainlest
Given: ABCD is a parallelogram and AC bisects BD.
Prove: AB is congruent to BC.
Let's see
In ∆ABE and ∆CBE
BE=BE(Common side)AE=EC[Diagonals of a parallelogram bisect each other]<AEB=<BEC[90°]So by
SAS congruence the triangles are congruent
AB=BC
ProvedFact:-
It's already given AC is perpendicular to BD
It means diagonals are perpendicular to each otherAccording to general property of rhombus this parallelogram is also a rhombus.
So sides are equal hence AB =BC
Please help me thank youuu
Answer:
(c) -3.8, 3
Step-by-step explanation:
The solutions to the equation f(x) = g(x) are the values of x where the function values are equal. These are the x-coordinates of the points where the graphs of y=f(x) and y=g(x) intersect each other.
Points of intersectionThe points where the graphs cross can be estimated to be ...
(-3.8, 6.5) and (3, -6)
The x-coordinates of these points are the solutions to the equation:
x = -3.8, 3
The end of month balances of college students is listed in the following chart. 25 37 43 55 57 68 72 74 87 123 125 127 141 149 185 203 215 234 234 252 279 302 303 321 327 350 358 404 425 440 489 489 503 521 608 703 712 758 863 900 Your first interval has a frequency of 14 and a total of 40, what is the value of the Relative Frequency Distribution
The value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.
In a Relative Frequency Distribution, we list how often a data value appears and scale it using the total frequency.
The sum of Relative Frequencies adds to 1.
In the question, we are informed that the first interval has a frequency of 14.
This implies that the data appears 14 times in the first interval.
Also, we are told that the total frequency is 40.
Thus, the relative frequency can be calculated as the ratio of the frequency of the interval to the total frequency.
Therefore, Relative frequency = 14/40 = 0.35.
Thus, the value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.
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Is -(3x + 5)^2 a perfect trinomial? Why or why not?
The given equation-(3x + 5)^2 is not a perfect trinomial because it is not obtained through the multiplication of a binomial.
What is a perfect trinomial?A perfect square trinomial is takes the algebraic expression form ax^2 +bx + c, where the square root of the first term and the third term is the equation to the second term.
Given that:
-(3x + 5)^2
Open brackets
= - (9x +30x + 55)
Multiply through by (-)
= -9x^2 - 30x - 55
Therefore, we can conclude that the given equation-(3x + 5)^2 is not a perfect trinomial because it is not obtained through the multiplication of a binomial. i.e. the multiplication of the square root of the first and the third term did not result in the 2nd term.
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Find the value of each variable in the diagram given that a ∥ b.
Answer:
v = 130
w = 30
x = 100
y = 25
z = 30
Step-by-step explanation:
I don't know how to solve this at all, i just need some help on how to figure it out. Thanks!
Answer:
[tex]\sf \dfrac{3}{{z-3} }[/tex]
Explanation:
[tex]\Longrightarrow \sf \dfrac{1}{z} \div \dfrac{z-3}{3z}[/tex]
apply the theorem when [tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex] then [tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]
[tex]\Longrightarrow \sf \dfrac{1}{z} \times \dfrac{3z}{z-3}[/tex]
Join the fractions
[tex]\Longrightarrow \sf \dfrac{3z}{z({z-3)} }[/tex]
Cancel out common factor z
[tex]\Longrightarrow \sf \dfrac{3}{{z-3} }[/tex]
The answer is : [tex]\boxed {\frac{3}{z-3}}[/tex]
Remember that dividing fractions is the same as multiplying the 1st fraction by the reciprocal of the other.
[tex]\mathsf {\frac{1}{z} \div \frac{z-3}{3z}}[/tex]
[tex]\mathsf {\frac{1}{z} \times \frac{3z}{z - 3}}[/tex]
[tex]\mathsf {\frac{3}{z-3}}[/tex]
anybody can help me im stuck U_U
Graph (b) represents the data provided that option (b) would be the correct choice.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have the data shown in the table.
The equation of the line M = 3n represents the data provided,
After plotting all the points on the coordinate plane.
We will get a graph that represents the data.
Thus, graph (b) represents the data provided the option (b) would be the correct choice.
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what multiplication expression could the area model above represent?
A: 8.3 x 19
B: 8.3 x 1.9
C: 83 x 19
D: 8.03 X 19
Question 1
1 pts
You borrow money to purchase a car. You secure a 5 year loan for $15,000 with an annual percentage
rate of 5%. How much will your monthly payments be?
Answer:
$283.07
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
PMT = monthly paymentP = loan amounti = monthly interest rate (in decimal form)n = term of the loan (in months)Given:
P = 15000i = 5% / 12 = 0.05 / 12n = 5 years = 60 monthsSubstitute the given values into the formula and solve for PMT:
[tex]\implies \sf PMT=\dfrac{15000\left(\frac{0.05}{12}\right)\left(1+\frac{0.05}{12}\right)^{60}}{\left(1+\frac{0.05}{12}\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=283.0685047...[/tex]
Therefore, the monthly payments will be $283.07.
How to put a starting pay of $500 with 100% increase every month on a graph.
This is the graph I need to use
Answer:
if boo ygdv
Step-by-step explanation:
f bi igfcnkyf f jurf
20points
please come help me
Please Help fast!!!!! I'll give 30 pts.!
Use the information in this table(in the attachment) to help you answer the questions. Remember, you have a budget of $20,000 for the car.
1. What add-on options do you want in your car?
Sun-roof, and Keyless entry
2. Write an inequality to model purchasing a car from Dealership A with the desired add-on options and staying within your budget. Use x to represent the base price of the car. (Assume that only the base price of the car is taxed to simplify the problem.)
3. Solve for x. Explain in words what the solution to the inequality means.
4. Graph the possible base price values that are included in the solution. Please upload an image of your graph.
5. Complete 2–4 for Dealership B using the same add-on options.
Will you buy from Dealership A or from Dealership B? Why?
The best buy is from dealership B because dealership B has a lesser base price
The add-on optionsFor the purpose of this exercise, the add-on options to select are:
SunroofKeyless entryDealership AThe total amount of the add-on options is:
Total = $500 + $1500
Total = $2000
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 17248.44
Divide both sides by (1 + 6.75%)
x ≤ 16157.79
The solution means that the base price of the car cannot exceed $16157.78 for dealership A
The graph of the possible base price
See attachment
Dealership BThe total amount of the add-on options is:
Total = $750 + $1000
Total = $1750
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 16725.28
Divide both sides by (1 + 6.75%)
x ≤ 15667.71
The solution means that the base price of the car cannot exceed $15667.71 for dealership B
The graph of the possible base price
See attachment
Where to buy fromBuy from dealership B because dealership B has a lesser base price
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help me please i dont understand
Answer:
22
Step-by-step explanation:
The line where it says 2cm, extend that line to the top. You know have 2 triangles, call the one on the left A and the one on the right B
area of recntangle = bh
Rect A:
b = 5
h = 4 - 2
h = 2
bh = 5 x 2
bh = 10
Rect B:
b = 3
h = 4
bh = 4 X 3
bh = 12
Total = 10 + 12
Total = 22
write an exponential function that includes the following given pair of points.
(1,5) and (2,25)
Answer:
[tex]y=5^x[/tex]
Step-by-step explanation:
[tex]y=a*b^x\\(1,5)=5=a*b^1 \implies(1)\\(2,25)=25=a*b^2\implies(2)\\(2)\div(1)=\frac{25}{5} =\frac{a*b^2}{a*b^1} \\5=b[/tex]
[tex](1)=5=a*5\implies a=1 y=5^x\implies y=5^x[/tex]
question on the image
Answer:
475.2
Step-by-step explanation:
682 is 1.55 of the original amount so 1.55x=682
682/1.55=440
440*1.08=475.2
Complete the statements about simplifying this expression: (xy^3/yz^2)(z^3/y^2x^2)
Hence, the variable y can be entirely eliminated using by applying the identity property of elimination
the numerator of the rational expression in the simplest form is z
the denominator of the rational expression in the simplest form is x
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?we have,
[tex](\frac{xy^3}{yz^2} )(\frac{z^3}{y^2x^2} )[/tex]
on simplifying,
we get. [tex]\frac{z}{x}[/tex]
Hence, the variable y can be entirely eliminated using by applying the identity property of elimination
the numerator of the rational expression in the simplest form is z
the denominator of the rational expression in the simplest form is x
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For f(x) = 4x + 1 and g(x) = x² – 5, find (f+ g)(x).
Answer:
x^2 + 4x -4
Step-by-step explanation:
Simply combine all the like terms by adding:
x^2 + 0x - 5
0x^2 + 4x +1
_____________
x^2 + 4x - 4
Construct the graph of the equation given. Categorize this graph a horizontal or vertical line. Label the intercept as well as the axis on the graph.
x = -2.5
The linear function x = -2.5 is plotted on the graph attached with an x intercept at (-2.5, 0)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A linear equation is in the form:
y = mx + b
Where m is the slope and b is the y intercept.
The linear function x = -2.5 is plotted on the graph attached with an x intercept at (-2.5, 0)
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A(n) _______ appears behind selected text. dotted line double-arrow point blue line shaded background
A (n) Shaded background Appears behind selected text so option. 4) Is correct.
What is shading background?
Shading background is process, When selecting a particular text there behind the text a shad will form which shows the number of texts selected
Thus, shaded background appears behind selected text
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Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
mABX = °
The measures of GX = 13
The measures of [tex]\angle ABX=22^0[/tex]
EX = 4z + 1 and XF = 2z + 7
Take EX and XF equal time each other and then solve for z and then you will get GX because EX = XF = GX are congruent.
EX = XF
What is congruent?
Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
4z + 1 = 2z + 7
2z = 6
z = 3
As, EX = XF = GX
EX = 4(3) + 1
EX = 13
Therefore, GX = 13 ------ ( EX = XF = GX )
To find the angle ABX, divide the angle ABC by 2 you will get
[tex]\angle ABX=22^0[/tex]
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Answer: 13, 22°
Step-by-step explanation: Trust Me!
Answer is correct on Edge. Good Luck! :)
GX = 13
mABX = 22 °
How many points? Help me please:)
Answer:
187 Points
Step-by-step explanation:
Total ratio units = 17 + 14 = 31 units
Total they scored = 341 points
Therefore total units = 31 = 341 points
31 units = 341 points
1 unit = (341/31) points
1 unit = 11 points
Nina scored 17 units of the total points
17 units = (17 x 11) points
= 187 points
Polygon LMNOP was transformed to create polygon L'M'N'O'P'.2 pentagons have identical side lengths and angle measures. The points are labeled with the same letters.
Which angle corresponds to AngleN?
Angle
Angle
Angle
Angle
The Angle that would correspond to Angle N after the transformation is; Angle N'
How to Interpret Transformations?
A polygon is defined as a two-dimensional geometric figure that has a finite number of sides. The sides of a polygon are made of straight line segments connected to each other end to end. Thus, the line segments of a polygon are called sides or edges.
In the transformation of LMNOP to create polygon L'M'N'O'P', we have that;
L corresponds to L'
M corresponds to M'
N corresponds to N'
O corresponds to O'
P corresponds to P'
Thus, we can conclude that Angle N would correspond to Angle N'
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the complete transformation is Rk, where k is the line with equation
The complete transformation is Rk, where k is the line with equation x = 2
How to complete the transformation?The complete question is added as an attachment
From the attached graph, we can see that the triangle and its image have a common vertex at C.
This means that the triangle is reflected across a vertical line that passes through point C.
The coordinate of C is:
C = (2, -2)
The vertical line passes through the x-coordinate.
So, we have:
x = 2
Hence, the complete statement is:
The complete transformation is Rk, where k is the line with equation x = 2
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1. The scale on a map reads 3 inches = 25 miles.
If two cities are 7.5 inches apart on the map,
find their actual distance.
A. 54.5 miles
B. 57.5 miles
C. 59.5 miles
D. 62.5 miles
Answer:
D. 62.5
Step-by-step explanation:
2 ways
1.
7.5 ÷ 3 = 2.5
25 times 2.5 = 62.5
2.
3/7.5 = 25/x
3x = 187.5
187.5 ÷ 3 = 62.5
The actual distance for a length on a map is 62.5. so correct option is D.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Given The scale on a map reads 3 inches = 25 miles.
If two cities are 7.5 inches apart on the map,
Find the actual distance for a length on a map.
Let x be the actual distance
7.5 ÷ 3 = 2.5
25 times 2.5 = 62.5
Thus,
3/7.5 = 25/x
3x = 187.5
187.5 ÷ 3 = 62.5
Therefore, the actual distance for a length on a map is 62.5.
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The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral is 90° counterclockwise rotation about point A followed by the reflection across y axis and a translation 20 units down.
What is transformation?It should be noted that a transformation simply illustrates the change in shape.
In this case, the sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral is 90° counterclockwise rotation about point A.
This will then be followed by the reflection across y axis and a translation 20 units down.
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Lewis is planning a cycling holiday.
a) He decides to cycle for 6 hours each day.
He thinks he can cycle at an average speed of 12 miles per hour.
How far would Lewis cycle each day?
miles
Answer:
72 miles/day
Step-by-step explanation:
12 m/hr * 6 hr / day = 72 mi/day
Mr. Jenkins was arranging chairs for a school awards assembly. Each row contained 15 chairs. If there were 21 rows. how many chairs had to be arranged?
Answer:
315 chairs
Step-by-step explanation:
This question can instill your quick calculation skills which can be very useful when it comes to event planning.
1 row of chairs = 15 chairs
21 rows of chairs = 15 x 21
= 315 chairs.