Answer: Based on the information provided, we can use the proportion of blue m&ms found in the sample (82 out of some larger total number of m&ms) to estimate the total number of m&ms in the entire bag.
If we let x be the total number of m&ms in the bag, we can set up the proportion:
82/x = blue m&ms / total m&ms
To solve for x, we can cross-multiply and divide by 82:
x = 82 * total m&ms / blue m&ms
x = 82 * 1
x ≈ 82
Therefore, based on the sample, we expect there to be approximately 82 m&ms in the entire bag, rounded to the nearest whole m&m.
It's worth noting that this is an estimation, and the actual number of m&ms in the bag may be different.
Step-by-step explanation:
Find the equation of the line containing the point
P(1, 2)
and parallel to the graph of
5x + y = −2.
Answer:
y = -5x + 7
Step-by-step explanation:
Parallel lines on a graph have the same slopes/gradients.
m1=m2
First you want to rewrite the equation of the graph given. So put the 5x to the other side and you will have:
y = -5x -2
This means that the equation that we need must have the gradient -5 (bc it is m in y=mx+c)
The equation will be y = -5x + c
However we must still find c aka the y intercept.
Sub the point we are given (1,2) into the equation
We will have:
2 = -5(1) + c
2 = -5 + c
7 = c
Now that we know c, we know what the equation of the line is. Just sub it in (without 1 and 2)
y = -5x + 7
Which expression is equivalent to 250h² - 100h?
O 50h(5h - 2)
○ 50(5h - 2)
○ 50h (5h+2)
50(5h+2)
Answer:
50h(5h - 2)
Step-by-step explanation:
Open up all the parenthesis on each answer
only the first one is correct
Answer:
50h(5h-2)
Step-by-step explanation:
Solution given
250h² - 100h
50*5*h*h-50*2*h
taking common
50*h(5*h-2)
50h(5h-2)
here taking common and keeping remaining on bracket
50h(5h-2)
State if the two triangles are congruent. If they are, state how
you know.
Explanation:
ASA = angle side angle
The marked side is between the marked angles.
The markings on the angles tell us which angles pair up to be congruent. The tickmark on the sides tell us the sides are congruent.
AAS is similar to ASA, but with AAS the marked side isn't between the marked angles.
We cannot use SAS since we don't know anything about another pair of sides.
-11x-14x-26=-25-25x-1
What kind of equation is it
Answer:
Linear equation with one variable
Step-by-step explanation:
Here, that one variable is x.
- 11x - 14x - 26 = - 25 - 25x - 1
- 25x - 26 = - 25x - 25 - 1
- 25x - 26 = - 25x - 26
Multiply - 1 on both sides,
25x + 26 = 25x + 26
This equation has infinite solutions.
Where value you substitute in place of x, you will the same answer on the both the sides.
I need to know the 10th term?
to find a given term, substitute the corresponding value of n into the ninth term formula. For example, if the ninth term is 3n + 2, the 10th term of the sequence can be found by substituting n = 10 into the ninth term. 3 x 10 + 2 = 32 and so, the tenth term of the sequence is 32.
To find the nth term of an arithmetic sequence, use the following formula:
[tex]an = a + (n - 1)d[/tex]
an(nth term) = a(first term) + (n(term you are looking for) - 1) * d(common difference)
Solve for the solution to a system of equations using the following matrices and Cramer’s rule. Show your work.
A= [2 1] X= [5 1] Y= [2 5]
[1 3] [5 3] [1 5]
I know each x_i (i = 1, 2, ..., n) is a random variable based on the sample size n obtained. Therefore, [tex]\frac{}{X}[/tex] is a random variable since it would be a different (random) value for each new sample size of n collected. How would I further elaborate on this explanation to answer the question in the screenshot?
The sample mean can be classified as a random variable because it is calculated from the sample which is built as random.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
Hence the sample mean is obtained as the sum of all observations of the sample divided by the sample size.
As the observations of the sample are taken at random, the sum of these observations will be a random variable, and so will the sample mean.
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Given the figure below shows a regular hexagon, ABCDEF
What is the measure of each interior angle?
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.
The theoretical probability is 25%, and the experimental probability is 27.5%.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.If two events A and B occur on a single performance of an experiment, this is called the intersection or joint probability of A and B, denoted as P(A ∩ B).Given is that There are 10 brown, 10 black, 10 green and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Thee given table is -
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
The probability of pulling out a gold ball will be -
P{gold} = 11/40 = 0.275 = 0.275 x 100 = 27.5%
P{gold} = 27.5%
Therefore, the theoretical probability is 25%, and the experimental probability is 27.5%.
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Factorise fully 20xy - 54
Plss answer
The factorisation of 20xy - 54 can be expressed as 2( 10xy - 27 ).
What is factorisation?The concept here is the factorisation . The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.
We were given, 20xy - 54, we can see that that factor of 2 is common for both 20xy and 54.
Then we can factorize as 2( 10xy - 27 ).
2( 10xy - 27 )
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Multiply Both Equations to Eliminate a Variable
5.x - 3y = 6
2x + 5y = -10
The value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.
The given equations are:
5x - 3y = 6, and
2x + 5y = -10
Isolate the value of x in the following equation:
5x - 3y = 6
5x = 6 + 3y
x = (6 + 3y)/5
Substitute the value of x as follows:
2x + 5y = -10
(2) (6 + 3y)/5 + 5y = -10
12 + 15y + 25y = -50
40y = -50 -12
40y = -62
y = -62/40
Substitute the value of y to find the value of x:
2x + 5(-62/40) = -10
16x - 62 = -80
16x = -80 + 62
16x = -18
x = -18/16
Hence, the value of x and y obtained when multiplying equations to eliminate variable is y = -62/40 and x = -18/16.
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a six sided dice is rolled 4 times, How many outcomes are there of rolling a 6 exactly 2 times?
The outcome that are there when a six sided dice is rolled four times is 2
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The p space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.
The sample space of getting a 6 from a die is 1. A die has six sides and are labelled 1-6
The outcome of 4 times is is 4
Therefore for two rolls, it will be 4/2 = 2
Therefore the outcome to get 6 exactly two times is 2.
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determine whether the statement below is true or false. justify the answer. the solution set of the linear system whose augmented matrix is is the same as the solution set of the equation .
This is a True statement that both the matrix equation and the augmented matrix translate into the same system of linear equations.
What are Linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
A rectangular matrix is a grouping of numbers into rows and columns. Systems of equations can be solved using matrices. But first, we need to understand how to use matrices to represent systems.
An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system. As a result, it is clear that augmented matrices provide a convenient approach to express systems of equations.
Therefore it is true that the solution set of the equation's equation is the same as the solution set of the linear system whose augmented matrix is.
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2/ ((s+1)(s+2) (0.5s+1)) inverse laplace
s3+5s2+8s+4
Step-by-step explanation:
Answer:
(1-e^(-2t))*u(t) - (1-e^(-t))*u(t)
Where u(t) is the step function
Step-by-step explanation:
use partial fraction decomposition. This involves expressing the rational function as the sum of simpler fractions, each with a pole at a different point in the complex plane. Once we have done this, we can use the formula for the inverse Laplace transform of a simple pole to find the inverse Laplace transform of the original function.
Which table shows a proportional relationship between X and Y?
K12
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
What is a ratio?If the ratios of two or more numbers or variables are equal to one another, they are said to be in proportion.
The answer to the query is
8; 10, 12; 14, given x
y : 5, 7, 9, 11
Ratios between various x and y values are not comparable.
( 8 /5)
≠ (10 / 7)
≠ (12 /9)
≠(14 /11)
We get to the conclusion that x and y have no proportional relationship.
Hence, Option(1) is the correct answer.
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
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4. Is 3 in the domain of the function ? Why or why not?
The domain of the function f(x) = √(x - 5) is x ≥ 5, thus, x = 3 is not in the domain.
Is 3 on the domain of the function?Remember that for a function y = f(x), we define the domain as the set of the possible inputs.
Here we have the square root function:
f(x) = √(x - 5)
Remember that the argument of a square root needs to be zero or larger, then the domain of the given function is:
x - 5 ≥ 0
Solving for x:
x ≥ 5
The domain is the set of values equal to or larger than 5, thus, the value 3 is not in the domain.
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Resolve the vector combinations below:
a. 45 m S and 35 m S
b. 15 m N and 60 m S
c. 5 m S, 10 m E, and 7m W
a. 45 m S and 35 m S: This vector combination resolves to 10 m S.
b. 15 m N and 60 m S: This vector combination resolves to 45 m S.
c. 5 m S, 10 m E, and 7m W: This vector combination resolves to 8 m E.
What is the vector?Vectors can be added, subtracted, and multiplied by scalars (numbers) to create new vectors. In physics, vectors are used to represent quantities such as velocity, force, and acceleration.
They can also be used in other fields such as engineering, computer graphics, and economics. Vectors can be represented in different ways, such as in Cartesian coordinates (x, y, z) or polar coordinates (magnitude, angle).
a. The vector combination of 45 m S and 35 m S is 10 m S. This is because the vectors are pointing in the same direction (south) and the magnitude of the resultant vector is the sum of the magnitudes of the individual vectors.
b. The vector combination of 15 m N and 60 m S is 45 m S. This is because the vectors are pointing in opposite directions (north and south) and the magnitude of the resultant vector is the difference of the magnitudes of the individual vectors.
c. The vector combination of 5 m S, 10 m E, and 7 m W is 8 m E. This is because the vectors are pointing in different directions (south, east, and west) and the magnitude of the resultant vector is found using the Pythagorean theorem.
The east and west vectors can be viewed as the legs of a right triangle, with the resultant vector being the hypotenuse. The magnitude of the resultant vector is the square root of the sum of the squares of the individual vectors.
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Which of the following are square properties? Choose ALL that apply.
Diagonals are congruent.
Exactly one pair of parallel sides.
Four right angles.
Diagonals are perpendicular.
The sum of the measures of angle P and angle Q is 100⁰.
• The measure of angle P is (3x - 15)°.
• The measure of angle Q is 25°.
What is the value of x? (7.11C, SS, RC3)
Answer:
x = 30
Step-by-step explanation:
You are given an angle and the sum of that angle with another that is (3x-15)°, and you want the value of x.
EquationThe sum of the two angles is given as 100°.
P +Q = 100°
(3x -15)° +25° = 100° . . . . . . use the given values for angles and sum
3x = 90 . . . . . . . . . . . . divide by ° and subtract 10
x = 30 . . . . . . . . . divide by 3
The value of x is 30.
According to an article on The Guardian website, a British woman born in 2003 has probability 0.27 of living at least 100 years. Five high school friends all happen to be females born in 2003.Assuming that the survival of each one is independent of the others, what is the probability that at least one of them lives to be 100 years old?
The probability that at least one of the five female high school friends born in 2003 lives to be 100 years old is 0.054 or 5.4%.
What is the probability?Probability refers to the chance, odds, or likelihood that an expected outcome occurs when there are many possible outcomes.
Probability is a fractional value, lying between one and zero when the expected event is not 100% certain or uncertain.
Probability is computed as the quotient or ratio that results from dividing the expected value by the total weight.
The chance of British women born in 2003 living at least 100 years according to The Guardian website = 0.27
The probability that at least one of five female high school friends born in 2003 lives to be 100 years old = 0.27 x 1/5
= 0.054
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Find the domain of F(x)=8/x
Since divisions by zero is ill-defined, the domain for F(x)=8/x includes any real integers other than x=0. F(xdomain )'s is therefore (-infinity, 0) U (0, +infinity).
The definition of domainDescribe domain. The term "domain," which is unique to the internet, can apply to both the structure of the internet and the organization of a company's network resources. A domain is typically a sphere of information or a governing region.
What characteristics define a domain?A function's domain is the set of all potential inputs. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
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A cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches. What is the surface area of the vase? Use the formula SA= B+ Ph, since the vase has a bottom but no top. Use 3.14 for TT and round to the nearest tenth of a square inch.
Answer: To find the surface area of the cylindrical vase, we can use the formula:
SA = B + Ph
Where B is the area of the base (the circular top of the vase), P is the perimeter of the circular top of the vase, and h is the height of the vase.
We know that the diameter of the vase is 4.3 inches and the height of the vase is 11 inches. To find the radius of the base, we can divide the diameter by 2:
r = 4.3 inches / 2 = 2.15 inches
The area of the base is given by πr², so:
B = πr² = π * 2.15² = 14.65 square inches
To find the perimeter of the circular top we can use 2πr:
P = 2πr = 2 * 3.14 * 2.15 = 13.64 inches
Now we can substitute these values into the formula:
SA = B + Ph = 14.65 + 13.64 * 11 = 260.04 square inches
Rounded to the nearest tenth, the surface area of the vase is 260.0 square inches.
Step-by-step explanation:
What is the greatest number that evenly divides the sum of any three consecutive whole numbers
The greatest number that evenly divides the sum of any three consecutive whole numbers is three.
What is an Integer?
This is referred to as a whole number that can be positive, negative, or zero and we should note that it doesn't a fractional number and examples include 0, 2, -3 etc.
The product of any three consecutive integers is always divisible by 3 and the addition of any 3 consecutive numbers together it will always equal a multiple of 3 which is therefore the reason why it was chosen as the correct choice.
An example is n+2 is an integer, 3(n+2) is divisible by 3 in this scenario hence 3 is the correct choice.
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(Show your work please) Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.Rewrite in simplest rational exponent form square root x times 4 square root x
By applying the exponential properties, it can be concluded that the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
Exponential is a repeated multiplication method with the same number, which is notated in the form aⁿ, where a is called the base and n is the exponent or power.
Some properties of exponent:
[tex]a^{x}[/tex] x [tex]a^{y}[/tex] = [tex]a^{x+y}[/tex]
[tex]a^{x}[/tex] : [tex]a^{y}[/tex] = [tex]a^{x-y}[/tex]
[tex](a^{x}) ^{y}[/tex] = [tex]a^{xy}[/tex]
[tex](\frac{a}{b} )^{x}[/tex] = [tex]\frac{a^{x} }{b^{x} }[/tex]
a⁰ = 1
a⁻ˣ = 1 / aˣ
In mathematics, a radical is described as [tex]\sqrt[n]{x}[/tex], where n is a positive integer ≥ 1 and x is a real number. Then n is called the index of the radical, x is the radicand, and the symbol √ is the radical.
The radical can be written as a rational exponent as follows:
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex] or [tex]\sqrt[n]{x^{m} } = x^{\frac{m}{n} }[/tex]
From the problem, we can denote the expression as follows:
square root of x = √x
the fourth root of x = ⁴√x
The product of the two expressions will be:
(√x) x (⁴√x) = [tex]x^{\frac{1}{2}}[/tex] x [tex]x^{\frac{1}{4} }[/tex]
= [tex]x^{\frac{3}{4} }[/tex]
Thus the simplest rational exponent is [tex]x^{\frac{3}{4} }[/tex]
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P (n), given below, is the price in dollars for n grams of vitamins. P(n)=0.5n+6.4 Complete the following statements. Let P¹ be the inverse function of P. Take x to be an output of the function P. That is, x=P (n) and n=P-¹(x). (a) Which statement best describes P-¹(x)? The reciprocal of the price (in dollars) for x grams of vitamins. The amount of vitamins (in grams) for a price of x dollars. The price (in dollars) for x grams of vitamins. The ratio of the price (in dollars) to the number of grams, x. -1 (b) P(x) = - 1 (c) P (9.2) = log 010 X log No solution 0=0 Ś
The number of vitamins (in grams) for a price of x dollars. Then the correct option is B. The inverse function is P⁻¹(x) = (x - 6.4) / 0.50. And at x = 9.2, the value P⁻¹(x) will be 5.4 grams.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The function is given below.
P(n) = 0.50n + 6.4
The inverse of the function P(n) is given as,
x = 0.50P⁻¹(x) + 6.4
P⁻¹(x) = (x - 6.4) / 0.50
At x = 9.2, then we have
P⁻¹(9.2) = (9.2 - 6.4) / 0.50
P⁻¹(9.2) = 5.6 grams
The number of vitamins (in grams) for a price of x dollars.
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Complete the table of ordered pairs for the linear equation y=3x-11
NO LINKS!!
43. For the following functions, state whether they are growth or decay, then determine each function's growth/decay rate. (NOT MULTIPLE CHOICE)
a. f(x) = 0.3(1.6)^x
b. g(x) = 0.8^0.5x - 7
c. h(x) = 3(-5)^x
d. f(x) = e^(-0.45x) + 4
Answer:
a) Exponential growth function: 60%
b) Exponential decay function: 20%
c) Neither
d) Exponential decay function: 45%
Step-by-step explanation:
[tex]\textsf{Exponential Growth}: \quad y=a(1+r)^x[/tex]
[tex]\textsf{Exponential Decay}: \quad y=a(1-r)^x[/tex]
where:
a = initial value (the amount before measuring growth or decay)r = growth/decay rate (in decimal form)Part aGiven function:
[tex]f(x) = 0.3(1.6)^x[/tex]
The function is an exponential growth function and the growth rate is:
[tex]1+r=1.6 \implies r= 0.6 = 60\%[/tex]
Part bGiven function:
[tex]g(x) = 0.8^{0.5x} - 7[/tex]
The function is an exponential decay function and the decay rate is:
[tex]1-r=0.8 \implies r=0.2=20\%[/tex]
Part cGiven function:
[tex]h(x) = 3(-5)^x[/tex]
This is neither an exponential growth or decay function as exponential functions cannot have negative bases.
Part dNatural base exponential function
[tex]y=ae^{rx}[/tex]
If a > 0 and r > 0, the function is an exponential growth function.
If a > 0 and r < 0, the function is an exponential decay function.
Given function:
[tex]f(x) = e^{-0.45x} + 4[/tex]
As a = 1 > 0 and r = -0.45 < 0, the function is exponential decay function and the decay rate is:
[tex]r=-0.45=45\%[/tex]
which of the following are true of quantitative research and quantitative researchers? (select all that apply.)
The correct statement about quantitative research is:
It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
We know that the quantitative research is nothing but the process of collecting and analyzing numerical data.
It is used to find the patterns, make predictions, test the relationships, and generalize results to given populations.
Whereas the qualitative research involves collecting and analyzing non-numerical data.
Quantitative research is mostly used in the natural sciences and social sciences.
It collects data using sampling methods, or by sending out online surveys/ polls, and questionnaires.
It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
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The complete question is:
Which of the following is true of quantitative research?
1) It enables researchers and clients to get closer to their customers and potential customers than does qualitative research.
2) It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
3) It is most often used with exploratory research designs.
4) It usually involves collecting detailed data from relatively small samples by asking questions or observing behavior.
5) It is superior for studying topics that involve complex psychological motivations not easily reduced to survey formats and quantitative analyses.
which of the following tables best shows the expected values in the f2 generation for a chi-square goodness-of-fit test for a model of independent assortment?
The chi-square goodness-of-fit test requires a comparison of the observed values with their expected values in the f2 generation.
Option A. Observed Values | Expected Values; this is the best choice for this comparison.The chi-square goodness-of-fit testThe chi-square goodness-of-fit test is used to determine how well observed values fit a model of independent assortment. The test requires a comparison of the observed values with their expected values in the f2 generation.
Option A is the best choice for this comparison, as it provides a direct comparison of the observed and expected values. This comparison allows for an assessment of the goodness-of-fit of the model, as any differences between the observed and expected values can be attributed to the model's performance.
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NO LINKS!!!!
Please help me with #4
Answer:
C) To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.
Step-by-step explanation:
Two triangles are said to be similar if:
corresponding angles are the same size, andcorresponding sides are in the same ratio.As there are three interior angles in a triangle, and the sum of the interior angles is always 180°, we need to know the measure of at least 2 angles in each triangle to determine if they are similar. The known angles don't have to be corresponding angles, as we can calculate the third angle and then compare all three angles to determine if the triangles are similar.
With regards to the sides of a triangle, it is not enough to know the measure of 2 sides to determine if they are similar. We would need to know at least one interior angle in this case.