Answer:
289560
Step-by-step explanation:
A bag contains 3 gold marbles, 5 silver marbles, and 26 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
The expected value if you play this game will be -$0.205.
Let the number of gold, silver, and black marbles be P1, P2, and P3, respectively.
Given, The bag contains,
Number of gold marbles (P1) = 3
Number of silver marbles (P2) = 5
Number of black marbles (P3) = 26
Also given,
The winning value if a gold marble is selected = $3
The winning value if a silver marble is selected = $2
The losing value if a black marble is selected = $1
Probability = Expected value/ Sum of the total number of events
Probability of picking a gold marble,
P1 = 3/ (3+ 5+ 26)
= 3/34.
Probability of picking a silver marble,
P2 = 5/ (3+ 5+ 26)
= 5/34.
Probability of picking a black marble,
P3 = 26/ (3+ 5+ 26)
= 26/34.
The expected value if you play the game will be,
Value = ($3) P1 + ($2) P2 + (-$1) P3
= ($9/34) + ($10/34) - ($26/34)
= - ($7/34)
= -$ 0.205
Thus, you will face a loss of 0.205 cents.
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Order the steps to show how to solve the system of equations using substitution.
y=6x+1
7x – 2y= –1
Answer: The correct answer is x=−1/5 and y=−1/5
Step-by-step explanation:
Solve the System by substitution:
y=6x+1 and 7x−2y=−1
Solve y=6x+1 for y:
y=6x+1
Substitute 6x+1 for y in 7x−2y=−1:
7x−2y=−1
7x−2(6x+1)=−1
−5x−2=−1 (Simplify both sides)
−5x−2+2=−1+2 (Add 2 to both sides)
−5x=1
−5x/−5 = 1/−5 (Divide both sides by -5)
x=−1/5
Substitute −1/5 for x in y=6x+1:
y=6x+1
y=6(−1/5)+1
y=−1/5 (Simplify both sides)
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Considering the following statements, what is X → Z? X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle. Y → Z: If a shape is a triangle, then it has three sides. Question 4 options: A) X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides. B) X → Z: If a shape has three sides, then it's a triangle. C) X → Z: If a shape has three sides, then the sum of the interior angles of the shape is 180°. D) X → Z: If the sum of the interior angles of a shape isn't 180°, then it doesn't have three sides.
The correct statement that is a combination of both conditional statements is; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
How to interpret conditional statements?
A triangle is defined as a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.
We are given the conditional statements as;
X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle.
Y → Z: If a shape is a triangle, then it has three sides.
Now, transitive property states that “if two quantities are equal to a third quantity, then we can say that all the quantities are equal to each other”.
Thus, applying transitive property to our given statements we can say that; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
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Calculating Loan Risk
Cass is reviewing historical data about loans the financial institution gave out to see how credit score was linked to defaulting. In the past, the financial institution gave loans only to those with a credit score of 501 or above.
Answer:
Loan analysis is an evaluation method that determines if loans are made on feasible terms and if potential borrowers can and are willing to pay back the loan. It checks the eligibility of the potential borrower against the criteria set forth for lending. Loan analysis helps in assessing the skills and financial knowledge of the borrower to ...
Am I correct? Did I do this right?
Answer:
Step-by-step explanation:
Yes, you did it right.
Exercise 4.3
1. Given f=x^2 y; the change in for the total differential of fis given by df = Pdx+Qdy.
Find P, Q at x=1 and y=-1
(Ans: P= -2; Q=1)
Question one
By using the concept of differentiation, it can be calculated that
value of P is -2 and value of Q is 1
What is differentiation?
Differentiation is the process where the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus
Here differentiation is used
f(x) = [tex]x^2y[/tex]
[tex]df = 2xydx+x^2dy[/tex]
Here P = 2xy, Q = [tex]x^2[/tex]
At x = 1, y = -1
P = 2(1)(-1) = -2
Q = [tex](-1)^2[/tex] = 1
So value of P is -2 and value of Q is 1
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3
8
13
24
53
123
213
Answer:
321 is the next number that comes in the calculator.
What are some points on a graph of the equation y=-1/3x-1
A few points (co-ordinates) for the given equations are :
(1,-1/2),(-1,1/4),(0,1),,(2,-1/4)
What are the points on the graph called?These points are called Coordinates, where the horizontal line denotes the x-axis and the verticle line is the y-axis.
Each point is identified by both x and y coordinates. A point's x-coordinate is a value that indicates how far the point is from the horizontal or x-axis origin.
According to the given information:y denotes the distance of the point on the vertical line from the origin
x denotes the distance of the point on the horizontal line from the origin
In the given equation y=-1/3x-1
We can substitute x with any integer (i.e any number among the positive or negative numbers)
Putting, x=1 in the given equation we get
y=-1/(3x1)-1
⇒ y=-1/3-1
⇒y=-1/2
Thus the coordinate when x=1 is (1,-1/2)
Similarly by putting x=0, 1, 2, -1 ;we get the following co-ordinates respectively
(0,1), (1,-1/2), (2,-1/4),(-1,1/4)
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14.4.3 Quiz: Stretching and Compressing Functions
Question 2 of 10
Suppose f(x) = x². What is the graph of g(x)=f(x)?
If f(x) = x², the graph of g(x) = f(x) is x².
What is a Graph of a function?
The graph of a function f is the set of all points in the plane of the form (x, f(x)).
How to find the graph of a function:
You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.
We are given the function; f(x) = x²
Also, we want to find the graph of g(x) = f(x)
From the above, it means that we put x in place of x for function f(x) to get the function g(x).
so, g(x) = f(x)
g(x) = (x)²
Hence the graph of g(x) = f(x) is x².
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5. Simplify the complex fraction. a.-2/7
1 1/3
The simplification of the complex fraction is found as 11/14.
Define complex fraction/mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that. Step 1: Multiply the mixed fraction's denominator by the whole number component.Step 2: Increase the product from Step 1 by the numerator.Step 3: In the numerator/denominator form, write the improper fraction using the total from Step 2.For the given question, the expression is-
-2/7 + 1 1/3
To convert mixed fraction 1 1/3 i improper fraction, multiply 3 with 1 and add 1.
1 1/3 = 1 x 3 + 1 /3
1 1/3 = 4/3 Put in main equation.
-2/7 + 4/3
Simplify the expression.
= -2 x 3 + 4 x 7/ (7 x 4)
= -6 + 28 / 28
= 22/28
Divide both with 2
= 11/14
Thus, the simplification of the complex fraction is found as 11/14.
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The correct question is
Simplify the complex fraction.
-2/7 + 1 1/3
A bus ticket used to cost $2.50
Today, 1 bus ticket costs $2.75
The increase in cost is?
The percent increase is?
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The valid equations are written below. Then the correct options are C, D, and E.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The sum of the two interior angles is equal to the exterior angle of the third angle.
The sum of the supplementary angle will be 180°.
From the diagram, the equations are written as,
m∠5 + m∠6 = 180° (Supplementary angle)
m∠2 + m∠3 = m∠6 (Exterior angle)
m∠2 + m∠3 + m∠5 = 180° (Angle sum of triangle)
Then the correct options are C, D, and E.
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The complete question is attached below.
What is the slope of this line
Answer: Slope is 0
Step-by-step explanation
the graph's points doesn't change its value on the y - values but the x values change by 1 meaning the slope is 0/1 meaning there is no slope
Please help please and thank you..
The value of x for the triangle by the mid point theorem is obtained as 5.
What is defined as the mid-point theorem?The line segment of a triangle connecting the midpoint in two the triangle's sides is thought to be parallel to that third side and also half the length of the third side, according to the midpoint theorem. A location that is at, close, or equally far both from ends of a line segment is referred to as the midpoint. To put it another way, the midpoint is indeed the place in a fact where the beginning and the conclusion meet.For the given diagram in the question.
As, the sides of the triangle is divided in equal parts.
By the mid -point theorem-
(1/2)24 = x + 7
12 = x + 7
x = 12 - 7
x = 5
Thus, the value of x for the triangle by the mid point theorem is obtained as 5.
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which is the correct answer ????
A certain number is multiplied by 7, and 4 is taken from the product. Finally, the difference is divided by 9, resulting in 5. Find the initial number.
Alex house is 15 blocks from school. Carlene lives 7 blocks from Alex's house. Which equation represents the location of Carlene's house in relation to the school?
|x+7|=15
|x-7|=15
|x+15|=7
|x-15|=7
Answer:
Answer is b
Step-by-step explanation:
Because
|x-7|=15--->x=15+7, x=22Use the number line to plot –3, 1, and 3.
Which statements are true
Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1
The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.
The correct statements regarding the number line are given as follows:
1 < 3.–3 < 1.How to plot an integer number on the number line?Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.
These numbers are plotted marking a symbol such as a X or a circle on the number line.
The number line is increasing, so the negative numbers appear before the positive numbers.
This means that if a number a is to the left another number b, the number a is less than b, hence:
1 < 3–3 < 1.As the order in which the numbers appear is given as follows:
-3, 1 and 3.
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The formula is у= 6х - 5 Determine the value of x, if y=7
Answer:
x=2
Step-by-step explanation:
You can put the equation as 7=6x-5
Move equation
12=6x
Divide
x=2
From their locations in the diagram, what are two possible values for n and m? The letters n and m represent two unknown numbers.
The possible values for n and m are:
m = √5 and n = 7/5
In this question, we have been given the locations of numbers n and m.
From their locations in the diagram, we need to find the possible values for n and m.
From the location of n we can say that the value of n is a rational number but not an integer.
We know that rational numbers are of the form p/q where p, q are integers with q ≠ 0
And the value of m is an irrational number.
So, the possible value of n am m:
m = √5 and n = 7/5
Therefore, the possible values for n and m are:
m = √5 and n = 7/5
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Add.
−1 4/5 + (−1/4) + (−1/5)
The required simplified value of the given expression is given as -13/20.
Given that,
An expression is given, −1 4/5 + (−1/4) + (−1/5) we have to determine the sum of the expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
= -1 4/5 + (-1/4) + (-1/5)
= -1/5 -1/4 -1/5
= -2/5 -1/4
= -13/20
Thus, the required simplified value of the given expression is given as -13/20.
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About 53% of adults in the US have traveled with a commercial airline. A random sample of 400 adults was selected
and whether they have traveled with a commercial airline was recorded.
Calculate the standard deviation of the sampling distribution of
O 0.00062
O 0.00086
* 0.00125
O 0.02495
B
M
B
1
■
▬
T
U
Done
♥
The standard deviation of the sampling distribution is 0.01767.
What is a standard deviation?Standard deviation is a measure of the amount of variability or spreads in a set of data.
It is calculated as the square root of the variance and is often denoted by the symbol σ (sigma) for a population and s for a sample.
We have,
Given that the sample size is sufficiently large (n=400) and the population proportion is known, we can use the formula for the standard deviation of the sampling distribution of the sample proportion, which is:
[tex]\sigma_{\hat{p}} = \sqrt((p (1 - p)) / n)[/tex]
where p is the population proportion and n is the sample size.
In this case,
p = 0.53 (as given in the problem) and n = 400.
Substituting these values into the formula, we get:
[tex]\sigma_{\hat{p}} = \sqrt((0.53 (1 - 0.53)) / 400)\\\sigma_{\hat{p}} = \sqrt((0.53 0.47) / 400)\\\sigma_{\hat{p}} = \sqrt(0.0003121)\\\sigma_{\hat{p}} = 0.01767[/tex]
(rounded to five decimal places)
Therefore,
The standard deviation of the sampling distribution is 0.01767.
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A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1600 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week?
If the fuel efficiencies of each of the cars that week is 20 gallons of gas and 25 gallons of gas.
How to find the efficiencies?Let x represent the gallons consumed by car 1
Let y represent gallons consumed by car 2
Formulate an equation:
30x+40y = 1600 equation 1
x+y = 45 equation 2
Substituting equation 2 into equation 1,
30x+40(45-x) = 1600
30x+ 1800-40x = 1600
-10x+1800 = 1600
-10x = -200
Divide both side by -10x
x = -200/-10
x = 20
Substitute value of x into equation 2
x+y = 45
20+y = 45
y = 25
Hence,
Car 1 consumes 20 gallons of gas and Car 2 consumes 25 gallons of gas.
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Assume that a hat contains four bills: a $1, a $5, a $10,
and a $20 bill. Two bills are to be selected at random with
replacement. Find the probability that both bills are $20 if
the first selected is a $20 bill?
The probability that both bills are $20 if the first selected is
a $20 bill is
(Simplify your answer. Type an integer or a fraction.)
The probability that both bills are $20 if the first selected is a $20 bill is 1/16.
What is probability ?The probability formula is as defined as the possibility of any event to happen which comes to be equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event to occur P (E) =
[tex]\frac{Number of favourable outcomes}{ Total number of outcomes }[/tex]
Hat contains four bills: a $1, a $5, a $10, and a $20 bill.
Probability(P1) of Getting $20 bill in 1st selection = 1/4 ;
After Replacement,
Probability(P2) of Getting $20 bill in 2nd selection = 1/4 ;
So, the probability that both bills are $20 if the first selected is
a $20 bill = 1/4 * 1/4 = 1/16,
Hence we get 1/16 as the probability of getting both bills of $20.
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Lena took out a $9000 loan for 7 months and was charged simple interest. The total interest she paid on the loan was $336.
The loan given has a rate of 0.53%
Simple InterestSimple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.
The formula of simple interest is given as;
S.I = P(1 + RT)
S.I = Simple interestP = principalR = rateT = timeSubstituting the values into the formula;
(9000 + 336) = 9000(1 + r * 7)
9336 = 9000 + 63000r
Collecting like terms
336 = 63000r
r = 0.0053
r = 0.0053 * 100
r = 0.53%
The rate on the loan is 0.53%
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Select the correct answer from each drop-down menu. Using the image below, select the best answer from each pull-down to complete the statements. The measure of ∠FED is ? °. ∠CBD and ∠ ? are complementary angles. Please help. thank you
The value of ∠FED is 120° and ∠CBD is complementary to ∠FDE
What are complementary angles?Complementary angles are two angles that sum up to 90°
For example 60° and 30° are complementary.
Either angle is called the complement of the other angle.
∠FED, ∠FDE and ∠DFE are in a triangle.
so,
∠FED + ∠FDE + ∠DFE = 180°
16x - 8 + 2x + 9 + 35 = 180 ( sum of angles in a triangle)
18x +36 = 180
18x = 180 - 36
18x = 144
x = 144/18
x = 8
so ∠FED = 16x - 8
Substitute x = 8 into the equation above we have
16(8) - 8 = 128 - 8 = 120°
∠FDE = 2x + 9
∠FDE = 2(8) + 9 = 25°
∠BED = 6x + 12
∠BED = 6(8) + 12
∠BED = 48 + 12
∠BED = 60°
∠CBD = -2x + 81
∠CBD = -2(8) + 81
∠CBD = 65°
so since ∠CBD = 65° and 90 - 65 = 25°
∠CBD is complementary to ∠FDE
In conclusion, ∠FED is 120° and ∠CBD is complementary to ∠FDE
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Please help
A T-shirt company can produce and sell x T-shirts per day. The total cost C (in dollars) for producing x T-shirts is
C = 1,780 + 7x,
and the total revenue R (in dollars) is
R = 14x.
Find the profit (in dollars) obtained by selling 275 T-shirts per day.
Answer:
$145
Step-by-step explanation:
The revenue - the cost is the profit.
14x - (1708 + 7x) Distribute what is in the parentheses by -1
14x -1(1780) -1(7x) Simplify
14x - 1780 -7x Combine like tersm
7x - 1780 Plug in 275 for x
7(275) - 1780
1925 - 1780
145
Simplify these expressions
a) ххххххуху
b) 2 xx x x x 3 xyxyxy
-10b+3 ≤-37
Compound inequalities
I want the answer please please
