Answers
On solving the provided question, we can say that - in the linear equation y = 1/2x + 5, slope, m = 1/2
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here,
in the linear equation =>
y = +1/2x + 5
on comparing with y = mx +c
slope, m = 1/2
and, c= +5
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Related Questions
2. Solve for x. Show your work.
45x 4 = 642x+12
Answers
The value of x for the equation 4(5x - 4) = 64( 2x + 12) is x = -7.25
What is equation ?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
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.
4(5x - 4) = 64(2x + 12)
20x - 16 = 128x + 768
20x - 128x = 768 + 16
-108x = 784
x = -7.25
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Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 5 on them.
(a) What is the expected value of the number shown when we draw a single slip of paper?
(b) What is the expected value of the number shown if we add one additional 3 to the bag?
(c) What is the expected value of the number shown if we add two additional 3's (instead of just one) to the bag?
Answers
The expected values for each experiment are:
A) 3.4
B) 3.36
C) 3.33
How to get the expected values?If we have an experiment with the outcomes:
{x₁, x₂, ..., xₙ}
Each one with the correspondent probability:
{p₁, p₂, ..., pₙ}
Then the expected value of that experiment will be:
EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ
A) in this case we have 10 slips of paper, 8 of them with the number 3, and 2 of them with the number 5.
So the outcomes are:
{3, 5}
The probabilities are:
{8/10, 2/10}
Then the expected value is:
EV = 3*(8/10) + 5*(2/10) = 3.4
B) If we add another slip of paper with a number 3 on it, the new probabilities are:
{9/11, 2/11}
Then the new expected value is:
EV = 3*(9/11) + 5*(2/11) = 3.36
C) Finally, if we add 2 slips of paper with the number 3, now we will have a total of 12 slips of paper, then the new probabilities are:
{10/12, 2/12}
So the new expected value is:
EV = 3*(10/12) + 5*(2/12) = 3.33
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1: What number must be multiplied by (5x + 6) to result in the expression 20x + 24?
2: On the first day of a road trip, you drive x miles.
On Day 2, you drive 10 more than twice the miles driven on Day 1.
On Day 3, you drive 100 miles less than Day 1.
Write an expression to represent the miles driven on each day of the road trip, then write a final simplified expression representing the total miles driven in three days.
a) Day 1:
b) Day 2:
c) Day 3:
d) Final simplified expression to represent total miles driven in three days:
e) Look at your expression for c) Day 3: "100 miles less than Day 1." Describe a real-word situation to explain why order matters when writing this expression.
Answers
1. The number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is 4.
2. An expression representing the miles driven on each day of the road trip and a final simplified expression of the total drives in three days are as follows:
a) Day 1: x
b) Day 2: 2x + 10
c) Day 3: x - 100
d) Final simplified expression to represent total miles driven in three days: 4x + 10 - 100.
e) A real-world situation in which order matters when writing the expression x - 100 is that the value of x is supposed to be more than the value of 100.
What is a mathematical expression?A mathematical expression is the combination of constants, numbers, mathematical operators, and variables without the equation sign (=).
Literarily, a mathematical expression is like a phrase in the English language because it does not make complete sense without the equation sign.
1) Multiplication:
(20x + 24) ÷ (5x + 6) = 4
Check:
4(5x + 6) = 20x + 24
2) Road Trip Expressions:
Day one driving distance = x miles
Day two driving distance = 2x + 10
Day three driving distance = x - 100
Total distance = x + 2x + 10 + x - 100
= 4x + 10 - 100
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Round 0.25773438 to the nearest hundredth
Answers
Answer:
The answer is 0.26.
I wish you luck on your assignments.
Answer: 0.26
Step-by-step explanation:
1. The hundredths place is two digits from the decimal point
2. Look at the thousandths place and if it is larger or equal to 5 then we round up, otherwise we round down and the hundredths digit remains the same
3. 7 is larger than 5 therefore the hundredths place digit of 5 rounds to a 6
4. Our final answer is 0.26
**You should not need to round on this problem, no %'s decimals only**
At Houston Community College 60% of the students who take English will pass. Of those who pass English, 70% will also pass Accounting. Of those that do not pass English, 45% will still pass accounting.
Answers
a) Probability of student passed in English and Accounting [tex]= \frac{21}{50}[/tex]
b) Probability of Number of Student passed Accounting [tex]=\frac{3}{5}[/tex]
c) Given that student passed Accounting. Probability that they passed English = [tex]\frac{9}{125}[/tex]
What is Probability?The ratio of favorable outcomes to all possible outcomes of an event is known as the probability.
Here let us assume the Total Number of students is 100.
Students who passes in English = 60% of total number of students
= [tex]60*100/100=60[/tex]
Students who passes in English = 60.
Out of 60 students , 70% of 60 pass in Accounting = [tex]70/100*60=42[/tex]
So Student who passed in both English and Accounting = 42.
Also Number of student that do not passed in English = 100 - 60 = 40.
Out of these 40 students , 45% passes in Accounting = [tex]45/100*40=18[/tex]
So Number of student pass in Accounting but not in English = 18.
Total Number of student pass in Accounting = 42 + 18 = 60.
A) Number of student passed in English and Accounting = 42
Total Number of student = 100
Probability of student passed in English and Accounting= [tex]\frac{42}{100} = \frac{21}{50}[/tex]
B) Total Number of Student passed Accounting = 60
Total Number of student = 100
Probability of Number of Student passed Accounting = [tex]\frac{60}{100} = \frac{3}{5}[/tex]
C) Probability that student passed Accounting = 60/100.
Probability that student passed English = 60/100.
Given that student passed Accounting. Probability that they passed
English = [tex]\frac{60}{100} * \frac{60}{100} = \frac{3600}{10000} = \frac{9}{125}[/tex]
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what is the slope of the table below? 3/8 15/12 9/10 0/7
Answers
The slope of the table shown in the image attached below is equal to: D. 1/3.
How to calculate the slope of the given table?Mathematically, the slope of the given table can be calculated by using the following mathematical expression;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided in the table, we have the following data points:
Points on x-axis = (-2, 2).
Points on y-axis = (-4, -2).
Substituting the given points into the slope formula, we have;
Slope, m = (12 - 8)/(15 - 3)
Slope, m = 4/12
Slope, m = 1/3
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A company is producing picture frames as well as the glass for the front of the frames. The amount of wood required
for the frame is represented by the function W/(x), and the amount of glass is represented by the function G(x). The
frames have lengths represented by the function f(x) and widths represented by g(x).
X
2
3
4
5
W(x)=2[(f+g)(x)]
14
24
34
44
G(x) = (f-g)(x)
6
27
60
105
Which statement describes the combined functions W(x) and G(x)?
O The amount of glass required has a constant rate of change, but the amount of wood does not.
O The amount of wood required has a constant rate of change, but the amount of glass does not.
O Both the amount of wood required and the amount of glass required have a constant rate of change.
ONeither the amount of wood required nor the amount of glass required has a constant rate of change.
Answers
Answer:The combined functions W(x) and G(x) represent the amount of wood and glass required to produce a picture frame. Based on the information provided,
W(x)= 2[(f+g)(x)] and G(x) = (f-g)(x)
By looking at the values of the given table, it can be observed that the rate of change in the amount of glass required (G(x)) is not constant, it increases as x increases.
On the other hand, the rate of change in the amount of wood required (W(x)) is not constant as well, it increases as x increases too.
It's not mentioned any information about constant rate of change for f and g.
Therefore, the correct statement that describes the combined functions W(x) and G(x) is: "Neither the amount of wood required nor the amount of glass required has a constant rate of change."
It's important to mention that the problem provided does not have a unique solution, because the values for f and g are not defined so it's not possible to infer their behaviour over time.
It is only possible to infer the behaviour of the functions W(x) and G(x) given the information provided, and it is clear that the rate of change for both functions does not remain constant, but it increases as x increases.
Step-by-step explanation:
Keshawn is organizing textbooks on his bookshelf. He has a Spanish textbook, a biology textbook, a history textbook, and a writing textbook. How many different ways can he line the textbooks up on his bookshelf?
Answers
Answer: four textbooks
Step-by-step explanation:
A company tests a new battery for an electric car. The distance the car travels, d km, and the charge left in the battery, C%, are measured. Some measurements are shown in the table. Find the C-axis intercept of the line. Pls help I would really appreciate it!
Answers
Based on the measurements shown in the table, the C-axis intercept of the line is equal to 100.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, exponential function, polynomial function, quadratic function, etc., generally occur at the point where the value of "x" is equal to zero (x = 0).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a linear function, exponential function, polynomial function, quadratic function, etc., crosses the x-coordinate and the value of "y" is equal to zero (y = 0).
In this scenario, the C-axis intercept of the line simply refers to x-intercept. Therefore, we can reasonably infer and logically deduce that the C-axis intercept of the line (x-intercept) is equal to 100 while the d-axis intercept of the line (y-intercept) is equal to 200.
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b) The completed construction of a regular hexagon is shown below. Explain why ACF is a 30º-60º-90º triangle. (10 points)
Answers
[tex] \div 7841562130. = 98[/tex]
Answer:
123459c
Step-by-step explanation:
round
Estthe product silve using an area model and the standard algorithm 1.7x55=
Answers
The expression 1.7 x 5.5 can be an area model of the rectangle where the length is 1.7 and the width is 5.5
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The expression 1.7 x 55 is an area model.
Area of rectangle = length x width
Now,
Length = 1.7
Width = 55
Area = 1.7 x 5.5
Thus,
The expression 1.7 x 5.5 can be an area model.
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find the value of x !
Answers
Answer:
x = 7
Step-by-step explanation:
You want to know the value of x when the base of a triangle measures 5x+35, and its midsegment measures 35.
MidsegmentThe base of the triangle is twice the length of the midsegment, so you have ...
5x +35 = 2(35)
5x = 35 . . . . . . . . . . subtract 35
x = 7 . . . . . . . . . . divide by 5
__
Additional comment
The midsegment joins the midpoints of the sides of the triangle.
In more formal terms, the smaller triangle is similar to the larger one with a scale factor of 1/2. That means the parallel segments are related by that scale factor of 1/2: (1/2)(5x +35) = 35.
13. Communicate and Justify During a chemistry experiment, Julian
records how the temperature changes over time using ordered
pairs (time in minutes, temperature in °C).
(0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100)
a. Which variable is the independent variable?
The dependent variable? Explain in need answerssss
Answers
Julian uses ordered pairs to record the temperature variations over time during a chemistry experiment (time in minutes, temperature in °C). (0, 15), (5, 20), (10, 50), (15, 80), (20, 100), (25, 100) (25, 100).
What do you meant by depend and independent variable ?It is the cause that is the independent variable. Its worth is unrelated to other study variables. The effect serves as the dependent variable. The independent variable's modifications determine its value. It is a thing that is dependent on other things. The amount of study you did, how much sleep you had the night before the test, or even how hungry you were when you took it.
Could all affect your test result, which makes it a dependent variable. The dependent variable is impacted by the independent variable. For instance, your exam results are influenced by how much sleep you get (an independent variable) (dependent variable). This is understandable, but Ex. How much sleep you get depends on your test results.
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Combine the like terms
-n + (-4) - (-4n) + 6
Answers
the simplest form of the given expression is 3n+2.
What is polynomials?
Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
-n + (-4) - (-4n) + 6
= -n + (-4) + 4n + 6
= 3n -4 +6
= 3n+2
Hence the simplest form of the given expression is 3n+2.
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Six bottles of water cost £2.10. How much does one bottle of water cost?
Answers
Explanation
1. Set up the proportion 6/2.10 = 1/x to find the cost of one bottle.
2. Cross multiply. 2.10(1) = 6x —> 2.10 = 6x
3. Divide by 6 on both sides to get the variable by itself. 2.10/6 = 6x/6 —> 0.35 = x
1. The sum of two angles is 85°, one angle is five more than the measure of the other angle. Write the equation that represents this scenario and find the measure of each angle. Be sure to show your
work.
Answers
On solving the provided question, we can say that - by equation angles will be, x + 5x = 85 => 6x = 85 => x = 14.1666666667
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
let one angle be = x
other angle be 5x
then, x + 5x = 85
6x = 85
x = 14.1666666667
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A system of linear equations with an infinite number of solutions is a(n) __________ system.
Answers
A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
When a system of linear equations consists of an infinite number of solutions then this equation should be dependent and consistent as well, and this system is said to be a system of equivalent equations.
Thus, A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
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Write three to five sentences explaining which levels of production provide Alonzo’s Cycling with the maximum profit
Answers
The data provided in the table implies that Alonzo's Cycling should produce five or six bikes if it wants to maximize its profits.
What is profit maximization?Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.
This is because the sixth bike is the point at which the marginal revenue matches the marginal cost. The company will make $90 in profit with the sale of its fifth or sixth bike each day. After that, the profit begins to fall with each sale.
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A right triangle with coordinates A (-2,5), B (-2, 9) and C (4,5) is first rotated 90 degrees clockwise and then
translated 1 unit left and 2 units down to form triangle A'B'C'. What is the measure of angle B'A'C', in
degrees, in the resulting figure?
Answers
Answer:
90 degree
Step-by-step explanation:
since the angle BAC is 90 degree, no matter the triangle is rotated, or translated , the angld of the triangle do nit change.
To illustrated this, see attached pages.
Evaluate the expressions 56 with a variable of -1
Answers
Answer:
The expression 56 with a variable of -1 is not well defined. The term 56 is a constant number, and the variable of -1 is also a constant. Therefore there is nothing to evaluate.
Step-by-step explanation:
If you want to evaluate the expression 56*(-1) it would give -56 as output because -1 is a scalar and multiplying with a scalar will change the sign of the constant 56 but it won't change its value.
In other words, to evaluate an expression, it needs to have a mathematical operation or function, operands, and/or variables that can be replaced with values or expressions. Without any operation, there's nothing to evaluate.
cesar is making a solution for his chenistry class. he puts 3/4 gram sodium chloride and 1/3 gram potassium chloride on the scale. what is the combined mass of the compounds?
Answers
The combined mass of the compounds is 13/12 grams
How to determine the combined mass of the compounds?From the question, we have the following parameters that can be used in our computation:
3/4 gram sodium chloride and 1/3 gram potassium chloride
The combined mass of the compounds is then calculated as
Combined mass = sodium chloride + potassium chloride
Substitute the known values in the above equation, so, we have the following representation
Combined mass = 3/4 + 1/3
Evaluate the sum
Combined mass = 13/12
Hence, the combines mass is 13/12 grams
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You can perform 6 push-ups in 16 seconds. Write and
graph an equation that represents the relationship between
time and the number of push-ups. At this rate, how many
pushups can you perform in 2 minutes?
Answers
Answer:
320 pushups
Step-by-step explanation:
16/6= 8/3
8/3*120=32
The label on Masao's breakfast cereal said that
one serving of cereal provides 85 milligrams (mg) of
potassium, which is 2% of the recommended daily
amount. What is the total recommended daily
amount of potassium?
Nutrition Facts
Serving Size: 1 cup (47g)
Servings Per Container: About 7
Amount Per Serving
Calories
Calories from Fat
Total Fat 1g
Saturated Fat Og
Trons Fat og
Polyunsaturated Fat 0.5g
Monounsaturated Fat 0.5g
Cholesterol Omg
Sodium 190mg
Potassium 85mg
Total Carbohydrate 40g
Dietary Fiber 1g
Sugars 8g
Protein 3g
Cereal With Milk
180
2:30
20
10
% Daily Value
2%
0%
0%
8%
2%
13%
4%
2%
0%
|
0%
11%
8%
15%
4%
STAR
22
Find the unit rate: 406 miles to 14.5 gallons of gas.
Find the unit rate: 423 miles to 18 gallons of gas.
The grocery store charges $3.99 for a case of 24
bottles of water. What is the unit price?
Paul is shopping for laundry detergent. At the grocery
store, the liquid detergent is priced at $14.99 for 64
loads of laundry and the same brand of powder
detergent is priced at $15.99 for 80 loads. Which is
the better buy, the liquid, or the powder
Answers
Therefore , the solution of the given problem of percentage comes out to be 4250 mg, or 4.25 g and the percentage increase is 50%.
A percentage is what?A% is a number that can be expressed as a decimal or a fraction and indicates what proportion of 100 it is. Put 100 in the denominator and the percentage amount in the numerator to turn a percentage into a fraction.
Here,
This "Nutritional Facts" table indicates that 85 mg of potassium, or 2% of the daily recommended value, corresponds to the row "Potassium".
By using the unitary method, (85/2) mg of potassium will represent 1% of the daily required intake.
As a result, 4250 mg of potassium, or 100% of the daily allowance, will be required: (85/2 * 100).
The entire quantity of potassium that is advised for daily consumption is 4250 mg, or 4.25 g.
(New value) − (Initial value) / (Initial value) = percent change. * 100%.
Here,
Initial value: $1.50 (the 1995 fare).
New value equals $2.25 for the 2008 fare.
Therefore,
percentage variation
= [(2.25 - 1.50) / 1.50] .50] * 100%
= (0.75 / 1.50) * 100%
= 0.5 * 100%
= 50%.
Positive indications of the transition point to an increase in fare.
The percentage increase is therefore 50%.
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Bismah is building 5 raised garden beds in a community garden. Each raised
garden bed will need 1 7/8 bags of soil. How many bags of soil will Bismah need for
8
all 5 raised garden beds?
5 5/8bags of soil
9 3/8 bags of soil
9 5/8 bags of soil
8 7/8 bags of soil
5 3/8 bags of soil
Answers
The fraction of soil bags Will needs in total for all 5 raised garden beds is 9 3/8.
What is community?In mathematics, community is the study of how objects interact and relate to each other. It focuses on analyzing the relationships between elements and understanding how they interact to form each other. Also explore how changes in one element affect other elements. Community in mathematics is also about recognizing patterns, finding solutions, and exploring the impact of change. It is an integral part of mathematics and is used in many areas of study such as algebra, geometry, and calculus. This can be calculated by multiplying the number of raised beds (5) by the amount of soil required per raised bed.
(1 7/8 bag).
5 x 1 7/8
= 9 3/8 bags
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two numbers have a sum of 33. if one of the numbers is -37 , what is the other number?
Answers
Answer:
70
Step-by-step explanation:
Well -37 plus 70 would give you 33, so therefore 70 is the answer. You can also check your answer by subtracting -37 from 33 which would give you 70.
multiply the following binomials
(x+3)(x-4)
(s-2)(2s+4)
Answers
Step-by-step explanation:
x²-4x+3x-12
x²-x-12.
2s²+4s-4s-8
2s²-8
n x (5 + 3) = (6 x 5) + (6 x 3) write the missing number.
Answers
Answer:
6 is the missing number
Step-by-step explanation:
Solve what is inside of the parenthesis, then evaluate.
N x (8) = (30) + (18)
8N = 48
Solve for N.
N = 48/8
N = 6
In the School of ICT, one person in 80, on average, has blood of type O. If 200 student blood donors are taken at random, find an approximation to the probability that they include at least five persons having blood of type O. How many student donors must be taken at random in order that the probability of including at least one student donor of type O shall be 0.9 or more
Answers
The probability that they include at least five persons having blood of type O is given as follows:
0.1075 = 10.75%.
The number of donors needed so that the probability of including at least one student donor of type O shall be 0.9 or more is of 184 donors.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of the parameters for this problem are given as follows:
n = 200, p = 1/80 = 0.0125.
The probability of less than five is given as follows:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Using a binomial distribution calculator, these probabilities are given as follows:
P(X = 0) = 0.0808. P(X = 1) = 0.2046.P(X = 2) = 0.2576.P(X = 3) = 0.2153.P(X = 4) = 0.1342.Hence the probability of less than five successes is given as follows:
P(X < 5) = 0.0808 + 0.2046 + 0.2576 + 0.2153 + 0.1342 = 0.8925.
Hence the probability of at least five is given as follows:
P(X >= 5) = 1 - P(X < 5) = 1 - 0.8925 = 0.1075.
The probability of at least one is given as follows:
P(X >= 1) = 1 - P(X = 0)
P(X >= 1) = 1 - (1 - 0.0125)^n.
This probability is of 0.9 when:
1 - (1 - 0.0125)^n = 0.9
(0.9875)^n = 0.1
log((0.9875)^n) = log(0.1)
nlog(0.9875) = log(0.1)
n = log(0.1)/log(0.9875)
n = 183.1.
Rounding up, at least 184 donors must be surveyed.
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Beth poured 1/2 of the juice from a 5-liter bottle while serving guests at a party. How much juice, in liters, is still left in the bottle?
Answers
Answer:
2.5 litres
Step-by-step explanation:
EXAMPLE 3.1.30. Let R be the relation on Z defined by ïRy ⇒ x − y is divisible by 3. Then R is an equivalence relation on Z. Find [0], [1], [2], [4], [-1]
Answers
equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0
What is slope?A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).
equation is -
y = 2x - 5
since these are parallel to each other,
slope, m= 2
now the equation is -
( y - y1 ) = m( x - x1 )
y - 7 = 2 (x-8)
2x - y - 1 = 0
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