The probability that you first choose a green marble and then a blue marble is, P(green then blue) = 1/5.
What is probability?
Simply put, probability measures how likely something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Given:
A bag contains 2 blue, 1 red, and 3 green marbles.
So, the total marbles are 2 + 1 + 3 = 6
The probability of selecting a green marble is:
P(Green) = 3/6
Now, there are 5 marbles left.
The probability of selecting a blue marble is:
P(Blue) = 2/5
The required probability is:
P = 3/6 * 2/5 = 6/30 = 1/5
Hence, the probability that you first choose a green marble and then a blue marble is, P(green then blue) = 1/5.
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Ariana has 6 posters she wants to hang on the wall. How many different ways
can the posters be arranged in a row?
HELP DUE TODAY THE 16TH OF DEC
Simplify fraction with 8 minus 4 times 3 in the numerator and the cube root of 8 plus 5 in the denominator.
twelve sevenths
negative twelve sevenths
four sevenths
negative four sevenths
PLEASE HELP ASAP!!!!
Answer:
statements 2 and 3 are true
Step-by-step explanation:
using the rule of exponents
[tex]a^{0}[/tex] = 1
then
1 [tex]a^{0}[/tex]≠ a ← lie
2 [tex]x^{0}[/tex] = 1 ← true
3 [tex]5^{0}[/tex] = 1 ← true
[tex]3(x+7)=7x-48[/tex] I can't solve this question can you help me please !!!
Therefore the value of x from the given equation comes out to be 13.5
What is equation?A statement proving the equality of two mathematical expressions is known as an equation. The equal sign (=) is used to represent an equation between two mathematical expressions. Anything that contains the equal sign is an equation, to put it simply. Examples of equations include x=7, 2x+5=7, etc.
Here,
The equation given is 3(x+2)=7x-48
thus we find the value of x from the given equation
=> 3(x+2)=7x-48
=> 3x+6=7x-48
=> 7x-48-3x-6=0
=> 4x-54=0
=> 4x=54
=> x=54/4
=> x=13.5
Therefore the value of x from the given equation comes out to be 13.5
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A line has a slope of 3 and passes through the point (1, 1). What is its equation in
slope-intercept form?
Answer:
y = 3x - 2
Step-by-step explanation:
Slope intercept form is y= mx+b
m being the slope
and b being the y intercept
we have the slope, but we need to find the y intercept. first, plot (1,1) you can use a sheet of graph paper, demos or just a little grid on scrap paper. then you want to create another point on your graph using the slope, in this case 3 would be 3/1 so you go from your plotted point 3 units down, then 1 unit to the left. keep on plotting points until you identify your y intercept, where a plotted point goes through y axis. this is -2, which will be B in the equation.
HELP LIKE WHAT ELSE DO I DO???? IT WONT LET ME PROOVE THAT LINES BA AND CD ARE PARALLEL
The triangles ABC and CDA are congruent by SAS criteria.
What are the criteria for congruent triangles?Two triangles are said to be congruent when all of their corresponding sides and angles are equal. For this relation between two triangles, there are many criteria such as SSS, SAS, ASA and RHS.
Given that,
In quadrilateral ABCD, AD = BC and AD ║BC.
Now, the given relation ΔABC ≅ ΔCDA can be proved as follows,
In ΔABC and ΔCDA, it is found as,
AC = AC (Common sides)
AD = BC (Given data)
And, ∠ACB = ∠DAC (Interior angles between parallel lines AD and BC)
Thus, ΔABC ≅ ΔCDA by SAS congruence criteria.
Hence, the given relation ΔABC ≅ ΔCDA is proved by SAS criteria.
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What is an algebraic expression for 16 more than the product of 43 and a number?
A: 16 − 43y
B: 43y(16)
C: 43y − 16
D: 43y + 16
The algebraic expression that can be represented by the statement is 43y + 16
How to make a algebraic expression that can be represented by the statement?From the question, we have the following statement that can be used in our computation:
16 more than the product of 43 and a number
Represent the variable with y
So, we have the following representation
16 more than the product of 43 and y
Express the product as an actual product
So, we have the following representation
16 more than 43y
more than as used here means addition
So, we have
43y + 16
Hence, the expression is (d) 43y + 16
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Answer: 43y + 16
Step-by-step explanation:
i did the test
A company uses a new machine and an old machine to print booklets. Each
machine prints booklets at a constant rate. The graph and the equation represent the relationships between x, the number of minutes the machines print, and y, the number of booklets printed.
The company uses both machines to print a total of 1,250 booklets. Both
machines start printing at the same time. During printing, the old machine breaks down and stops printing. The new machine continues printing for an additional 14 minutes and completes the order
What is the total number of minutes the new machine prints? Show or explain all
your work. Write your answer and your work below.
By solving a linear equation, it can be calculated that
Time for which new machine prints = 64 minutes
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
For the new machine
The line passes through (0, 0) and (6, 75)
Slope = [tex]\frac{75 - 0}{6-0}[/tex] = 12.5
Equation of line for new machine
y - 0 = 12.5(x - 0)
y = 12.5x
Equation of line for old machine
y = 9x
Now,
During the 14 minutes, the number of pages printed = 12.50 [tex]\times[/tex] 14 = 175
Number of pages printed earlier = 1250 - 175 = 1050
By the problem,
12x + 9x = 1050
21x = 1050
x = [tex]\frac{1050}{21}[/tex]
x = 50
Time for which new machine prints = 50 + 14 = 64 minutes
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if a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?
The given statistic is said to be an "unbiased estimator". In this statistic, the mean is equal to the true value of the estimated parameter.
What is an unbiased estimator?In a statistic, if the mean is equal to the estimated parameter, then that statistic is said to be an unbiased estimator. It is used to estimate a population parameter.
Calculation:Consider a statistic.
"A statistic describes a portion of the target population".
"A parameter describes the whole population".
In a statistic, the mean of the sampling distribution is equal to the true value of the estimated parameter.
I.e., μ = E(x)
So, that statistic is said to be an unbiased estimator.
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What are the values of x and y in the figure?
Hello please perform indicated operation this with steps
(x+4)^2(x-2)
We can expand the given expression:
(x + 4)²*(x - 2)
To get the equivalent one:
x³ + 6x² - 32
How to perform the operation?Here we want to expand the given expression, which is:
(x + 4)²*(x - 2)
First remember the rule:
(a + b)² = a² + 2ab + b²
So we can rewrite the first factor as:
(x + 4)² = x² + 2*4*x + 4²
= x² + 8x + 16
Replacing that in our expression we get:
(x² + 8x + 16)*(x - 2)
Now we can expand that to get:
x²*x + x²*(-2) + (8x)*x + 8x*(-2) + 16*x + 16*(-2)
= x³ - 2x² + 8x² - 16x + 16x - 32
= x³ + 6x² - 32
That is the expression expanded.
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Help me please before my assignment is due
Greta's current age is m + n years.
What is an expression?An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
In other words, algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation
Therefore, let's convert the word's expression to an algebraic expression.
Greta was m years old n years ago. Her age now is as follows:
n years ago Greta was m years old. This simply means n years ago Greta was m years old. Her current age will be the sum of her current age and the number of years ago.
Therefore,
(m + n) years
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Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135. What was the total of his sales for that week?
The total of his sales for that week is $49,500.
Given :
Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135.
Let x be the total sales.
2135 = 2.5 % * 50000 + 3 % (x - 50000 )
= 2.5 * 50000 / 100 + 3/100 ( x - 50000 )
1235 = 2.5 * 500 + 0.03x - 0.03 * 50000
1235 = 1250 + 0.03x - 1500
0.03x = 1235 - 1250 + 1500
0.03x = -15 + 1500
0.03x = 1485
multiply by 100 on both sides
0.03x * 100 = 1485 * 100
3x = 148500
x = $49500
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Solve for x. 6 + |4x - 1| > 10 Graph the solution on the number line.
13>10 is the answer on the number line.
What exactly is a graph solution?A system of linear equations has a solution, which is the quantity that makes all of the equations true. This is the intersection of the two graphs for two variables and two equations. The two variables in the two equations will have a solution at these coordinates.When x=6, x will remain 6 regardless of what y is. Therefore, simply draw a vertical straight line through (6, 0), parallel to the y axis, and extend it on both sides. The finished graph is there.Explanation:
x.6 + 4x -1 > 10
6.6 = 4.6 - 1
36 = 24 - 1
36 - 23 = 13>10.
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13>10 is the answer on the number line.
What exactly is a graph solution?A system of linear equations has a solution, which is the quantity that makes all of the equations true. This is the intersection of the two graphs for two variables and two equations. The two variables in the two equations will have a solution at these coordinates.
When x=6, x will remain 6 regardless of what y is. Therefore, simply draw a vertical straight line through (6, 0), parallel to the y axis, and extend it on both sides. The finished graph is there.
x.6 + 4x -1 > 10
6.6 = 4.6 - 1
36 = 24 - 1
36 - 23 = 13>10.
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Jack is running on a treadmill at a speed of 7. 2 miles per hour a slim y equals total distance and x equals number of hours
Need help pls important!!!!!!!!
Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
Speed of him=7.2 miles/hour
Let y be the total distance and x be the number of hours,
speed=distance/time
7.2=y/x
y=7.2x
The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.
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convert 5 centimeters into yards rounded to nearest hundredth
Answer:
.05 yd
Step-by-step explanation:
5/91.44=.05468066
If 9^x / 9^3 = 9^5 what is x
Answer:
since , 9^x / 9^3 = 9^5
and since there is a law for exponents that says if the bases of the exponent are equal and divided by each other we subtract the exponents
, so 9^x-3 = 9^5
then x-3 =5 , therefore the final answer will be X= 8 .
Simplify each ratio. Make sure to convert the units when needed
1,320 feet: 1 mile (Hint: There are 5,280 feet in one mile.)
The simplification of the ratio 1320 feet : 1 mile will be 1:4
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. The term ratio is a straight borrowing from the Latin word ratio. In Latin, ratio could imply everything from "reason" to "calculation" to "proportion," and it was this last meaning that was used to create the mathematical and English ratios.
Given taht we need to simplify the ratio 1320 feet : 1 mile
For simplifying ratios we need to convert the terms in same units
and we know that 1 mile = 5280 feet
So,
1320 feet : 1 mile can be written as 1320 feet : 5280 feet
The simplification wil be 1:4
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The Scooter Company's total profit function is represented by -2x²+250x-2000.
Total profit of a company is the difference between total revenue and total cost.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Company earns a total revenue that can be determined by the function R(x) = 400x - 2x²
Each scooter cost $150 to produce, and the company has a fixed cost of $2,000.
Variable cost = Cost of each scooter × Number of scooter sold
Total cost = fixed cost + variable cost
= 2000 + (150×x)
Cost, C(x) = 2000 + 150x
Revenue, R(x) = 400x - 2x²
Total profit = Revenue - Cost
= 400x-2x²-(2000 + 150x)
= 400x-2x²-2000-150x
= -2x²+250x-2000
Therefore, the Scooter Company's total profit function is represented by -2x²+250x-2000.
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A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
Given that,
461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students. Sales of tickets totaled $1624.
We have to find the system of equations to model.
We know that,
We get,
a + s = 461
s = 461 -a
The student tickets sold = s × 3 = 3 × (461-a)
The adult tix sold = 4 a
Summed they total 1624
We get system of equations as
s = 461-a
3 (461-a) + 4a = 1624
1383 -3a +4a = 1624
a = 241
Then
s = 461 -a = 220
Therefore, The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
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Molly wants to put a triangular fence around her garden. Use the diagram below to answer the questions.
Molly would need 43 feet of fencing to fence the triangular area.
What is Pythagorean theorem?
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).
According to the given question:
We can see that the area is in the form of a right-angled triangle. Since only two sides of the triangle is given, we could utilize Pythagoras theorem to our advantage to find out the third side.
In Δ ABC
AB² (base) + AC² (perpendicular) = BC² (hypotenuse)
Substituting the values of AB as 10 feet and BC as 18 feet
AC²= BC²- AB ²
∴AC²= 224
∴AC= 14.96 cm
Amount of fence required by molly would equal perimeter of the area.
⇒The perimeter of the area would equal AB+BC+AC
⇒Summing up the values of AB, AC and BC
Perimeter= 10+14.96+18= 42.96 feet which is about 43 feet
Hence, Molly would require 43 feet of fencing.
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Write ONE equivalent ratio for the following: 6 : 4
THANK YOU AND HELP I’m VERY CONFUSED
Answer:
The first one is the answer
Below are the steps to solve an equation:
Step 1: x 5+2=5
Step 2: x - 5] 5-2
Step 3: x 5 = 3
Which of the following is a correct next step to solve the equation? (1 point)
Ox+5=-3
O-x-5-3
Ox-5--3
Ox+5=3
The length of my outdoor volleyball net is 6 m plus half its own length. How long is the net?
Answer:
12 meters
Step-by-step explanation:
The length of the volleyball net is "L"
6 + 1/2 L = L <======this is given , solve for L
6 = 1/2 L
L = 12 Meters
classify the polynomial 2x^3-5+9x^2
The category of the polynomial 2x³ - 5 + 9x² is a trinomial
How to determine the category of the expression?From the question, we have the following expression that can be used in our computation:
2x^3-5+9x^2
Rewrite this expression properly
So, we have the following representation
2x³ - 5 + 9x²
This expression can be further rewritten as
2x³ + 9x² - 5
The degree of a polynomial is the highest power of the polynomial
In this case, the degree of the above polynomial is 3
As a general rule, a trinomial is any polynomial that has a degree of 3
Hence, the expression is a trinomial
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Describe a set of data in which it would be most appropriate to use the mode as the measure of central tendency.
Answer:
It would be most appropriate to use the mode for categorical data, such as favorite ice cream flavor. This is because you can't use mean or median for flavors such as chocolate or vanilla, so mode would make the most sense there.
Whats the scale factor of triangle PQR to triangle STU.
PR =8 SU=12
RQ=6 UT=9
QP=10 TS=15
The scale factor of triangle PQR to triangle STU is 3/2
How to find the scale factor of the two trianglesScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
Taking a point of reference say PR and SU
PR = 8
SU = 12
let the scale factor be r such that
8 * r = 12
r = 12 / 8
r = 3/2
checking with other sides
PR to UT
6 * 2/3 = 9 correct
QP to TS
10 * 3/2 = 15 correct
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Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Eliana and her friend Greta are each baking apple pies and tarts for a bake sale, using the
same recipes. Eliana baked 2 apple pies and 6 apple tarts, using a total of 38 apples. Greta
made 2 apple pies and 8 apple tarts, which used 46 apples. How many apples does each
dessert require?
An apple pie uses
Submit
apples and an apple tart requires
C
zoom
apples.
O
An apple pie requires 7 apples and an apple tart requires 4 apples
How to write a system of equations to describe a situation?To set up this problem, we can let p represent the number of apples needed for one pie and t represents the number of apples needed for one tart.
We can then set up the following system of equations to represent the information given in the problem:
2p + 6t = 38
2p + 8t = 46
To solve this system, we can subtract the first equation from the second to eliminate the p terms:
2p + 8t - 2p - 6t = 46 - 38
2t = 8
t = 4
Substituting this value back into the first equation, we get:
2p + 6(4) = 38
2p = 14
p = 7
Thus, an apple pie requires 7 apples and an apple tart requires 4 apples.
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Example An investor Saved #120,000 For 7 years in a bank which pays interest of 11½% per annum Calculate the a. Interest which accrued b balance if # 25,000 was withdrawn from the account (N 28,276) 00
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}[/tex]