Answer:
Step-by-step explanation:
think that there are 15 ways ... call the boxes A, B, and C.
You could put all four b***s into either box A, or box B, or box C ---> 3 ways.
You could put three ball into one box and the other ball into another box:
-- 3 into A, 1 into B, 0 into C; or 3 into A, 0 into B, 1 into C; or 1 into A, 3 into B, 0 into C; or 1 into A, 0 into B, 3 into C; or 0 into A, 3 into B, 1 into C; or 0 into A, 1 into B, 3 into C ---> 6 ways
You could put two balls into one box and the other two balls into another box:
-- 2 into A, 2 into B, 0 into C; or 2 into A, 0 into B, 2 into C; or 0 into A, 2 into B, 2 into C ---> 3 ways.
You could put two b***s into one box and one ball into each of the other two boxes:
-- There are three boxes that could get the two b***s ---> 3 ways
Total: 3 + 6 + 3 + 3 = 15 ways.
Statistics and
Probability
Jonathan earned the following
scores on his math tests:
82, 79, 85, 100, 46, 92, 88
What is his mean test score?
Write a linear function f with the values f(0) =10 and f(6) =34.
Answer:
f(x) = 4x + 10
Step-by-step explanation:
The given information is in the form f(x) = y.
f(0) = 10 means if x is 0, y is 10. This is the point (0,10)
Likewise, f(6) = 34
means when x is 6, y is 34. That is the point (6,34).
Slope is y-y / x-x
34-10 / 6-0
is 24/6.
The slope is 4.
The y-intercept is where x is 0, that is 10.
y=mx+b is slope-intercept form. Fill in the slope, 4 for m and the y-intercept, 10, for b.
y = 4x + 10
but they also asked to call it f, so for function notation, use f(x) instead of y.
f(x) = 4x + 10
How was the Greeks and mathematics related
Greek mathematicians, who were first influenced by the Egyptians, would go on to produce innovations like Pythagoras' theory of right-angled triangles and, by concentrating on the abstract, bring accuracy and clarity to venerable mathematical conundrums.
How related Greeks and mathematics?Modern mathematics was created as a result of the contributions made by the ancient Greeks to the subject. The Greeks generally concentrated on geometry in an effort to describe shapes using numbers. This emphasis produced a number of quite important discoveries, many of which are still applicable to the mathematics we practice today.Miletus, a city of Ionia in Asia Minor and the cradle of Greek philosophy, mathematics, and science, was the location of the greatest Egyptian and Babylonian influence.Modern mathematics was created as a result of the contributions made by the ancient Greeks to the subject. The Greeks generally concentrated on geometry in an effort to describe shapes using numbers.To learn more about Greeks and mathematics refer to:
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The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45.
The actual roots ordered from least to greatest are
and
.
The actual roots ordered from least to greatest is -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45
What are rational roots?Rational roots are roots of a quadratic equation which can be expressed as a ratio or are elements of rational numbers.
How to the actual roots ordered from least to greatest?Since we have that the possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45.
We list the actual roots as follows
+1, -1, +3, -3, +5, -5, +9, -9, +15, - 15, +45 and -45
Since we require the actual roots from least to greatest knowing that the largest negative number is the least and tha largest positive number is the greatest, rearranging, we have
-45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45
So, the actual roots are -45, - 15, -9, - 5, - 3, - 1, +1, +3, +5, +9, +15, and +45
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Below are different equations, determine whether each equation is quadratic or not quadratic.
Write your answer on the space provided.
1x-5x+3=0
2.2s + 3t = -7
3,8k-3 = 12
4,9²-25=0
5.4m² + 4m + 1 = 0
Answer: calculate these equations
Step-by-step explanation: if you have times the square of the expression following b plus b times that same expression not squared plus c equal to 0, you have an equation that is quadratic in form. If we substitute what is in the ( ) with a variable like t, then the original equation will become a quadratic equation.
a chemist makes 100 L of a 76% -acid solution using 52%-acid solution and an 82% - acid solution. how many liter each solution does the chemist need.
For each solution, the chemist needs 80 liters of 82% solution and 20 liters of 52% solution.
What is Percent?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.A% is a number that has neither dimensions nor a defined unit of measurement.So, a chemist intends to create a 76% acid solution in 100 liters.
He will create it by combining an acid solution that is 52% with an acid solution that is 82%.
Let, x = amount of the 82% solution.Given that the sum is 100 liters.(100-x) equals the quantity of 52% solution needed.Now, calculate as follows:
0.82x + 0.52(100-x) = 0.76(100) (100)
0.82x + 52 - 0.52x = 76;0.82x - 0.52x = 76- 52;0.3x = 24x = 24;x = 80 liters of 82% solution and,100 - 80 = 20 liters of 52% solutions.Hence, for each solution, the chemist needs 80 liters of 82% solution and 20 liters of 52% solution.
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last year at a certain high school, 10 students sought the nomination for president of the student body. in how many ways could the voters (student body) rank their first 5 choices? a) 5 b) 50 c) 30,240 d) 3,628,800 e) 252 f) none of the above.
The number of ways voters could rank their first 5 choices out of 10 is 30240.
Given,
Number of students sought the nomination for president of the student body = 10 students
We have to find the number of ways voters could rank their first 5 choices.
Permutation;
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Here we have to use permutation formula;-
ⁿPr = n! / (n - r)!
Here,
n is the number of students = 10
r is the choices = 5
Then,
ⁿPr = n! / (n - r)!
¹⁰P₅ = 10! / (10 - 5)!
¹⁰P₅ = 10! / 5!
¹⁰P₅ = 10 x 9 x 8 x 7 x 6
¹⁰P₅ = 30240
That is,
The number of ways voters could rank their first 5 choices out of 10 is 30240.
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Identify the two x-values where the expression is undefined: *
x²+6x-27/x^2-81
-81
9
3
-3
81
The value of x are, x = 9, x = -9.
What is undefined expression?
A mathematical expression that consists of a number of variables and arithmetic operations but has no known solution is referred to as an undefined expression. Any expression that has the symbol ∞ in any part of its expression or that has zero in the denominator is regarded as being undefined.
When the denominator is zero, a rational expression cannot be defined. Set the denominator equal to zero and solve the ensuing equation to get the values that render a rational expression undefined.
So, to find the x - values set denominator equal to zero.
[tex]x^2 - 81 = 0\\x^2 = 81\\x = \sqrt{81}[/tex]
x = ± 9
Therefore, the value of x are, x = 9, x = -9.
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Three children split a land inheritance in the ratio of 2:4:5. The land is made up of 2,750 acres. The one with the largest parcel of land from the inheritance decides to sell that parcel for $600 an acre. How much money does this person make on the sale of his share of the inheritance?
Using the properties of ratio we calculate that the largest land inheritance was sold at $825000 .
The ratio in which the land is divided is 2:3:5
Let the common ratio be x .
Hence the land is divided which has a combined area of 2750 acres.
Now, 2x+3x+5x = 2750
or, 10x = 2750
or, x = 275
Now the person with the highest inheritance will be having land:
= 5× 275
= 1375 acres
Cost of the land at $600 per acre
= 600 × 1375
= $825000
therefore the cost of the land is $825000
A ratio can therefore be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value represented by this fraction.
Ratios of counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of two numbers is a dimensionless number when they are measured using the same unit, which happens frequently.
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1/2 years = how many months??
Answer:
6 months.
Step-by-step explanation:
estimate by rounding
496.1+212.4+301=
Dan uses the equation g left parenthesis x right parenthesis equals 5 x plus 50 to model the balance of his savings account after saving for x weeks. What is the value and meaning of g left parenthesis 60 right parenthesisblank in the context of the problem?
The value is 350.
From the question, we have
Dan uses the equation g(x)=5x+50 to model the balance of his savings account after saving for x weeks.
g(x)=5x+50
substituting the value x = 60, we get
g(60)=5*60+50
=300+50
=350
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Carmen has taken out a loan for $800 to buy a car. She plans to pay back the loan at a rate of $40 per month. Ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month.
How long will it take Ramona to pay back her loan?
a.
25 months
b.
20 months
c.
15 months
d.
10 months
Answer:
Carmen will have her loan paid back in 20 months
a course catalog for the open university of earth lists classes via a sequence of three numbers (chosen from 0 to 9) followed by three letters in english (chosen from a to z). how many courses can be given unique catalog numbers? choose the best answer.
17576000 courses can be given unique catalog numbers.
There are three numbers and three English letters.
Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is = 10
So the total number to choose three numbers = 10*10*10 = 1000
Each of letters can be chosen from A to Z.
Number of choice for the each letter = 26
So, the outcomes of letter combination = 26*26*26 = 17576
Hence the total possible catalog numbers = 1000*17576 = 17576000
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Can anyone write the equation of the graph?
The absolute equation in the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we can see that the lines on the graph has a sharp v-shape
Graphs that have this form are absolute value graphs
The general form of an absolute value equation is expressed as
y = |x - h| + k
From the above form, we have
Vertex = (h, k)
By definition, the vertex of a function is either the maximum point or the minimum point
On the given graph, the minimum point is (3, 5)
So, we have the following representation
(h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the above equation
So, we have:
y = |x - 3| + 5
Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5
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Solve for x.
2/x^2−4 − 1/x+2 = 3/x−2
In regards to the question above, the solution for the equation is x=-2(1+2x)/x^2-4.
What is the equation known as?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Equations come in two varieties: identities and conditional equations.
How to solve this:
2/x^2-4 -1/x+2=3/x-2
collecting like terms
2/x^2-4 -1/x+2 -3/x-2=0
Divides through by:
x^2-42 -1(x-2) -3(x+2)/x^2-4=0
Remove bracket: 2-x+2-3x-6/x^2-4
Lastly, collecting like terms:
2+2-6-x-3x/x^2-4-2-4x/x^2-4
=-2(1+2x)/x^2-4
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Karen buys a pack of 8 bottles of water.
The pack costs £1.25
Karen sells all 8 bottles of water for 50p each
Work out Karen's percentage profit.
The percentage of the profit gain by karen on a pack of 8 bottles is 220%.
Karen buys a pack of bottles of water. = 8
Karen sells all 8 bottles of water for rupees = 50p each
= 50p/100 each
= 0.5 rupees
Total rupees for 8 bottles = 8 x 0.5 = 4
The pack costs = 1.25
Profit % = (Profit / C.P.) × 100
Profit = SP - CP
= 4 - 1.25
= 2.75
then using these values in equation we get :
profit = [tex]\frac{4 - 1.25}{1.25} * 100[/tex]
profit = (2.75/1.25 )x 100
profit = 2.2 x 100 = 220
profit = 220%
The percentage of the profit gain by karen on a pack of 8 bottles is 220%.
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what is 4/7 divided 5
Answer:
[tex]\dfrac{4}{35}[/tex]
Step-by-step explanation:
Dividing a number is the same thing as multiplying by its reciprocal. So:
[tex]\dfrac{4}{7} \div 5 = \dfrac{4}{7} \cdot \dfrac{1}{5}[/tex]
Finally, simplify by multiplying out the numerators and the denominators.
[tex]\dfrac{4}{7} \cdot \dfrac{1}{5} = \dfrac{4 \cdot 1}{7 \cdot 5} = \dfrac{4}{35}[/tex]
Answer:
4/7 divided by 5 is 4/35
Step-by-step explanation:
Step 1: Convert 5 into an improper fraction
A. 5 = 5/1
Step 2: Divide 4/7 by the reciprocal of 5/1
B. 4/7 ÷ 1/5 = 4/35
estelle's cornfield is divided into 666 regions. she wants to know if a new pesticide is as effective as the pesticide that she currently uses. she randomly assigns each of the 666 regions to either the new or current pesticide for a month, and she'll compare the effectiveness of the pesticides. what type of experiment design is this?
This is completely Randomized experiment design .
Randomized block design is an experiment design in which the experimental units are categorized into groups, which are called blocks.
In the given question, we see that Estelle's cornfield is divided into 666 regions. She is curious about whether a new pesticide is effective because she uses pesticides and assigns each of the 666 regions at random.Now, the experiment units, i.e., 666, are not split into groups before random assignment. The entire region is randomly assigned to a pesticide. A randomised block design assigns some of each block to different treatment and control groups.
So , this is a completely randomized block design.
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Find the two solutions to the equation
(x − 10) (x + 7) = 0
Answer:
x = - 7 , x = 10
Step-by-step explanation:
(x - 10)(x + 7) = 0
equate each factor to zero and solve for x
x - 10 = 0 ⇒ x = 10
x + 7 = 0 ⇒ x = - 7
easy analyzing (due in 20 minutes)
Answer: f = 12m
Step-by-step explanation:
Starting at mile 5 we notice it's 60. But now at mile 7, we notice its 84. This means that we increase by 12 for each mile. Ergo, the answer should be f = 12m.
Help asap please
I don’t underddd
Given that X is directly proportional to y2. if x=4 units and y=3 units ,then find the value of y when x= 3 units
Answer:
y = 2.60 (to 3sf)
Step-by-step explanation:
Since x is directly proportional to y², then x = ky², where k is a constant.
When x = 4, y = 3,
4 = k(3)²
4 = 9k
9k = 4
∴[tex]k =\frac{4}{9}[/tex]
∴ When x = 3,
[tex]\frac{4}{9}y^{2} = 3[/tex]
∴y = 2.60 (to 3sf)
(Irrational Numbers MC)
Approximate -17 √√60 to the nearest tenth.
O-9.3
-7.7
7.7
9.3
Question 6(Multiple Choice Worth 2 points)
(Multiplying and Dividing with Scientific Notation MC)
The value of the square root of 60 subtracted from 17 is D. 9.3
How to illustrate the informationIt's important to note that a square root simply means the number that you can multiply by itself in order to get the original number.
In this case, the information given regarding the numbers is illustrate below:
= 17 - ✓60
= 17 - 7.7
= 9.3
Therefore, the value is.9.3
The correct option is D.
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What is the period for the contangent function?
complete the statement using angle R + angle A + angle T =
The complete statement will be;
⇒ angle R + angle A + angle T = 180°
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle RAT is shown in figure.
Now,
We know that;
The sum of all interior angles in a triangle is 180 degree.
Hence, In ΔRAT;
⇒ ∠R + ∠A + ∠T = 180°
Thus, The complete statement will be;
⇒ angle R + angle A + angle T = 180°
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The area of a square foot ball field is
16900cm². calculate the length of the field.
AREA OF A SQUARE= LENGTH* LENGTH
16900= L²
TAKE THE SQUARE ROOTS OF BOTH SIDES
√16900 =√L²
L= 130
THEREFORE THE LENGTH OF THE FIELD IS 130cm.
the probability distribution of all possible values of the sample mean is called the . select one: a. central probability distribution b. standard error c. sampling distribution of the sample mean d. random variation
The probability distribution of all possible values of the sample mean is called the sampling distribution of the mean.
What is meant by the sampling distribution of the mean?
An accurate probability distribution of a statistic is known as a sampling distribution, and it is created by repeatedly sampling a certain population. It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.Why is sampling essential and what does it mean?
Sampling is the process of choosing a portion of the general population or a subset of social phenomena to be investigated. The primary goal of sampling is to make assumptions about the larger group based on data collected from the smaller group. The selection of a representative sample is the primary means of achieving this.Learn more about Probability
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3y - x - (4x - 5y)/10 - 7y+2x/4
A spinner with 9 equal sections is numbered 1 through 9. The probability of spinning a 3 is 1/9. What is the probability of not spinning a 3 is what
The probability of not spinning a 3 is 8/9
How to determine the probability that the number 3 is not spun?From the question, the given parameters are:
Number of sections = 9
Sections = Number 1 to 9
The probability of spinning a 3 = 1/9
The above probability can be represented as
P(3) = 1/3
The probability that the number 3 is not spun is the complement of the probability of spinning a 3
This is calculated as
P(3) + P(Not 3) = 1
Substitute the known values in the above equation So, we have the following equation
1/9 + P(Not 3) = 1
Evaluate the like terms
P(not 3) = 8/9
Hence, the probability is 8/9
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