The following are solutions to the inequalities;
7. c < 7
8. h < -4
9. r ≤ 55
What is an Inequality?Inequality is a relationship between two expressions or values that are not equal to each other. Lack of balance results in inequality.
In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs.
7. 8c - 21 < 35
8c < 35 +21
8c < 56
c < 7
8. -6h + 17 > 41
-6h > 41 - 17
-6h > 24
h < 24/-6
h < -4
9. r/5 - 2 ≤ 9
Multiplying through by 5
r - 10 ≤ 45
r ≤ 45 + 10
r ≤ 55
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A recreation center is offering special prices on its pool passes and gym memberships for the summer. On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships. Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership. She paid $72.
1. Write a system of equations that represents the relationships between pool passes, gym memberships, and the cost.
2. Find the price of a pool pass and the price of a gym membership by solving the system algebraically. Explain or show your reasoning.
1. The system of equations is given as follows:
2x + y = 48.2x + y = 72.2. The system of equations has no solutions.
How to obtain the amounts?The amounts are obtained solving a system of equations, for which the variables are given as follows:
Variable x: cost of a pool pass.Variable y: cost of a gym membership.On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships, hence:
4x + 2y = 96.
2x + y = 48.
Later that day, an individual bought a pool pass for herself, a pool pass for a friend, and 1 gym membership, hence, spending $72, hence:
2x + y = 72.
The system of equations has no solutions, as the linear functions have the same slope but different intercepts.
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if a quick bread recipe yields 6 cups of batter and a muffin requires 1/4 cup of batter, how many muffins will the quick bread recipe yield?
The number of muffins that the quick bread recipe will yield is given as follows:
24 muffins.
How to obtain the number of muffins that the quick bread recipe will yield?The number of muffins that the quick bread recipe will yield is obtained applying the proportions in the context of this problem.
We have that:
Quick break yields 6 cups of batter.A muffin requires 1/4 of a cup of batter.Hence the number of muffins that the quick bread recipe will yield is calculated as follows:
6/(1/4) = 6 x 4 = 24 muffins.
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add 1/3 and 2/5 1/3 + 2/5 = 5/15 + blank = blank
The sum of the fractions 1/3 and 2/5 is 11/15.
How can we add two fractional numbers?
For the addition of fractions with the same denominator, we just add the numerators of two fractions, keeping the denominator common. We can then simplify the fraction to the lowest form.
For the addition of fractions with different denominators, we first find the LCM of the denominators and rationalise them. Then we add the numerators and simplify the fraction.
Following the above rules, we can add 1/3 and 2/5.
Now they have different denominators.
LCM of 3 and 5 is 15.
So we rationalise them.
[tex]\frac{1*5}{3*5} +\frac{2*3}{5*3} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}[/tex]
Therefore the sum of the given fractions is 11/15.
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What is the equation for the graph below.
The equation of the straight line will be -
y = x - 4.
What is the general formula of a straight line?The general formula of a straight line will be -
y = mx + c
Given is a graph of straight line as shown in the image.
We can write the equation as -
y = mx + c
Now, we can write the slope as -
m = (0 + 4)(4 - 0) = 4/4 = 1
{m} = 1
{y} - intercept = - 4
{c} = - 4
We can write the equation as -
y = x - 4
Therefore, the equation of the straight line will be -
y = x - 4.
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describe and correct the error in indentifying a parallelogram.
Sides [tex]\overline{JM}[/tex] and [tex]\overline{KL}[/tex] are not given to be parallel.
Determine the domain of the function h(x)=9x/x(x2-49).
The domain of the function h(x)=9x/x(x²-49) is (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).
In math the term called the domain of a function is the set of its possible inputs which is the set of input values where for which the function is defined.
Here we have know the function is h(x)=9x/x(x²-49)
And we need to find the domain of the function.
Here we know that this function is defined for values where the denominator is not equal to zero.
Which is written as,
=> x(x²-49) ≠ 0
When we elaborate the equation based on the difference between the two squares property, it can be written as,
=> x(x + 7)(x - 7) ≠ 0
Based on this we have identified that the value of x must not be
=> x ≠ -7, 7, 0
Then the domain of the function is written as,
=> (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).
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The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Jelly Belly Candy Company is testing two machines that use different technologies to fill three pound bags of jelly beans. The file Bags contains a sample of data on the weights of bags (in pounds) filled by each machine. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a level of significance. What is your conclusion
Variability in a production process is a crucial indicator of the process's quality. A significant variance frequently represents a chance to improve the process by figuring out how to lower the variance.
It will be stated as, what machine 1's mean is.
[tex]x1= \frac{2.95+3.16+3.2+3.45+...+3.35+3.12}{25} =3.3284[/tex]
Thus, machine 1's average is 3.3284.
Following that, we'll provide the variance of machine 1.
[tex]s21= \frac{∑(x−¯x1)^{2} }{n−1 } \\ = \frac{(2.95−3.3284)2+(3.16−3.3284)2+...+(3.12−3.3284)^{2} }{24} =0.0489[/tex]
So machine 1 has a variance of 0.0489.
I'll provide the machine 2 mean as,
[tex]x2= \frac{3.22+3.38+3.30+...+3.33}{22} =3.27[/tex]
Therefore, machine 1's mean value is 3.2782.
Following that, the variance of machine 2 will be given as.
[tex]s22= \frac{∑(x−¯x2) ^{2} }{n−1} \\ [/tex]
[tex]\frac{(3.22−3.2782)2+(3.38−3.2782)2+(3.30−3.2782)2+...+(3.33−3.2782)^{2} }{21} \\ =0.0059[/tex]
Thus, machine 2's variance is 0.0059.
Here are the proposed hypotheses:
[tex]H0:σ21=σ22 \\ H1:σ21>σ22[/tex]
To verify the theory, the F-test will be applied. The test statistic is as follows:
[tex]TS= \frac{s21}{s22} × \frac{σ22}{σ21} \\ =0.04890.0059=8.29[/tex]
As will be used to calculate the p-value.
P(F24,21>8.29)=1−0.99999=0.00001.
The null hypothesis will be rejected because the p-value is less than the level of significance of 5%. This indicates that machine 1 offers a greater opportunity for quality improvements.
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After class, Mrs. Sandoval picked up several pieces of paper containing students' work from
I WILL GIVE BRAILEIST
After class, Mrs. Sandoval picked up several pieces of paper containing students' work from the floor and Mrs Sandoval probably picked up the pieces of paper because she wanted to properly dispose of them.
The second reason for her act is she may have also wanted to make sure that students' work was not lost or damaged.
A thing is an action when it is carried out, not just thought about or said. A person might do anything from blink to invade a nation. Agere, a Latin verb that means "to do," is where action originates.
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Vicky has 12 clear crystals in her collection. She has c more colored crystals than clear ones. Write an expression that shows the number of colored crystals Vicky has in her collection.
Answer:
Step-by-step explanation:
y= 12+c
The supervisor gave each of her 25 students 3 pieces of construction paper.
she had 2 pieces left over.
The supervisor started with _______ pieces of construction paper.
(be careful! This problem is done like a CHECK for a division problem.)
Answer:
The supervisor started with ___77____ pieces of construction paper.
Step-by-step explanation:
Each student received 3 pieces of construction paper.
There are 25 students.
25 × 3 = 75
The students received 75 pieces altogether.
She had 2 pieces left.
75 + 2 = 77
She started with 77 pieces.
The supervisor started with ___77____ pieces of construction paper.
Which phrase represents this expression?
7 × 4 + 3
Responses
3 more than the product of 7 and 4
the product of 7 and the sum of 4 and 3
the product of 7 and the difference of 4 and 3
3 less than the product of 7 and 4
Answer:
The Answer is 49
Step-by-step explanation:
4+3 =7 and 7 x 7 = 49
hope this helps
Question 5 of 10
Whitney's steel house is located in the country. If her building property
insurance is $603. 50 per year, how much is her house worth?
Annual Premium per $100 of coverage
Brick
Steel
Mixed
Wood
Area
Building Contents Building Contents Building Contents Building Contents
rating
City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76
Suburb 0. 45 0. 52 0. 56 0. 63
0. 74 0. 83 0. 85
Rural 0. 6
0. 69 0. 71
0. 89
0. 91 1
1. 02
0. 72
0. 8
O A. $17,350
The correct answer is B. $60,350.00. To calculate the value of Whitney's steel house, you need to multiply the annual premium per $100 of coverage ($0.43) by the annual property insurance premium ($603.50) and then divide that by 100. This works out to $60,350.00.
To determine the annual premium per $100 of coverage, you need to look at the table provided in the question. Since Whitney's steel house is located in the country, the annual premium per $100 of coverage is $0.43. Multiplying this by the annual property insurance premium of $603.50 gives you the total value of the house, which is $60,350.00. To summarize, the value of Whitney's steel house can be calculated by multiplying the annual premium per $100 of coverage by the annual property insurance premium and then dividing that by 100. In this case, the value of the house is $60,350.00.
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Question 5 of 10 Whitney's steel house is located in the country. If her building property insurance is $603. 50 per year, how much is her house worth? Annual Premium per $100 of coverage Brick Steel Mixed Wood Area Building Contents rating City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76 Suburb 0. 45 0. 52 0. 56 0. 63 0. 74 0. 83 0. 85 Rural 0. 6 0. 69 0. 71 0. 89 0. 91 1 1. 02 0. 72 0. 8 O A. $17,350.00 B. $60,350.00 C. $171,050.00 D. $603.50
1 Area: 54 cm² 7 cm 6 cm 10 cm
what is x
The length of x for the given shape is 3 cm.
What is the area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Given the shape, and area of the figure is 54 cm²,
the figure is of L shape,
which consist of two rectangles,
the dimensions of the first rectangle are 6 cm by 7 cm
and dimensions of the second rectangle are x cm by 4 cm (reducing 6 from 10)
Area of shape = sum of the area of both rectangles
Area of shape = 6*7 + x*4
54 = 42 + 4x
4x = 54 - 42
x = 12/4
x = 3 cm
Hence the value of x is 3 cm.
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The length of a rectangle is 6 inches more than its width. The area of the rectangle is 16 inches. Which quadratic equation could you use to find the dimensions of the rectangle?
The quadratic equation we use to find the dimensions of the rectangle is w^2 + 6w - 16 = 0
What is Quadratic equation?
The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax^2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients.
What is Rectangle?
A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equal sides.
Let W be the width of rectangle.
then, length of the rectangle is W + 6 .
and the Area, A = 16 inches^2
And the area of recatngle is A = L x W
Hence, A = (W+6)W
So, 16 = W^2 + 6W
Hence the quadratic equation whichuse to find the dimensions of the rectangle is ;
W^2 + 6W - 16 = 0
By the quadratic formula we have
[tex]w = \frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]w = \frac{-6 \pm \sqrt{6^{2}-4*1*(-16) } }{2*1}[/tex]
[tex]w = \frac{-6 \pm \sqrt{36 + 64} }{2}[/tex]
[tex]w = \frac{-6 \pm 10 }{2}[/tex]'
Hence, we take width as a positive because width never be negative .
so,the value of width is ;
w = 2
and length o rectangle is ;
l = w + 6 = 2 + 6 = 8
l = 8
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IIn the figure, m∠POR = 170° and m∠ROQ = 52°. If m∠POQ = x, which equation could be used to solve for x? A. X + 170° = 52° B. X + 52° + 170° = 180° C. X + 52° = 170° D. X = 170° + 52°n the figure, m∠POR = 170° and m∠ROQ = 52°. If m∠POQ = x, which equation could be used to solve for x? A. X + 170° = 52° B. X + 52° + 170° = 180° C. X + 52° = 170° D. X = 170° + 52°
Option C is correct - X + 52 = 170.
Angle
A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Straight line
A line is a geometry object characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.
According to the question,
∠POR = 170°
∠ROQ = 52°
∠POQ = x,
it is clear by the question,
on the basis of figure attached with this solution,
two angles together make the third angle,
so,
first angle is 52 degree
second angle is x degree,
∠ROQ + ∠POQ =∠POR
x + 52 = 170
so the answer is x + 52 = 170.
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you roll a fair six-sided die with the hopes of rolling a 5 or a 6. these two events are because they have no sample points in common. a. complements b. mutually exclusive events c. posterior events d. independent events
you roll a fair six-sided die with the hopes of rolling a 5 or a 6. these two events are because they have no sample points in common mutually exclusive events
Hence, option (b) is the correct choice.
Two occurrences are mutually exclusive or disjoint in logic and probability theory if they cannot occur at the same time. The set of outcomes of a single coin toss, which can result in either heads or tails but not both, is a good example.
Events that are mutually exclusive do not occur at the same time. For example, when a coin is tossed, the outcome will be either head or tail, but we cannot obtain both. Such occurrences are also known as disjunct events since they do not occur at the same time.
Events that are mutually incompatible cannot occur at the same moment. Right and left hand turns, even and odd numbers on a dice, winning and losing a game, or running and walking are all examples.
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Convert each equation from slope-form to standard form
The conversion of the equation from slope-form to standard form is -2x + y = -3.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be represented or modeled by using this linear equation:
y = mx + c
Where:
m represents the slope.c represents the y-intercept.x and y are the data points.Generally speaking, the standard form of a linear function is given by this mathematical expression:
Ax + By = C
Where:
A, B, and C represents a numerical value (number).
Rewriting the given linear function in standard form, we have the following:
-2x + y = -3.
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Meredith orders three items from an online retailer. the first item will arrive with equal likelihood in one of the first through third days of feburuary. the second will arrive with equal likelihood in one of the second through fourth days of february, and the third will arrive with equal likelihood in one of the third through fifth days of february. if at most one item can be delivered in a given day, what is the probability that the first time is not the first to be delivered?
is it 0.4???
The probability that the first item is not the first to be delivered is 0.6667
How to determine the probabilityLet's call the events that the first, second, and third items arrive on the first day of February A, B, and C, respectively.
The probability that the first item arrives on the first day of February is 1/3.The probability that the second item arrives on the first day of February is 1/3,The probability that the third item arrives on the first day of February is 0.Therefore, the probability that one of the other two items arrives first is
1/3 + 1/3 = 2/3.
The probability that the first item is not the first to be delivered is
1 - 2/3 = 1/3
Evaluate
1 - 2/3 = 0.6667
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Which of the following is the product of the rational expressions shown
below?
222
²-1
2x²
OA. ²-2-20
OB.
O C.
O D.
3x
x-1
2x²
x²-1
2x²
x²-9x-20
The product of the rational expressions shown is equal to: B. 2x/(x² - 1).
What is a rational expression?In Mathematics, a rational expression simply refers to a type of expression which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:
NumeratorDenominatorIn this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;
Product of numerator = 2 × x
Product of numerator = 2x
For the denominator, we have the following:
Product of denominator = (x + 1) × (x - 1)
Product of denominator = x² - x + x - 1
Product of denominator = x² - 1
Therefor, the product of the rational expressions is given by 2x/(x² - 1).
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En un restaurante se compra 12 bandejas de huevo en 78,000 cuánto cuestan 18 bandejas
El valor de las 18 bandejas es un total de $117.000
$78,000 for 12 bandejas
18 bands:
Bandeja 1:
We must first determine the price of one bandeja in order to determine the price of 18 bandejas.
solo divide 78 ÷ 12 que te dará 6.5 después multiplicas 6.5 × 18 que te dará:117
así que la respuesta es 117 pesos
entonces...
78.000÷12= 6.500
Now we have the price for 18 bandejas.
First, split $78.000 by 12 to determine the cost of each bandeja of eggs.
The result is $6.500, which you will multiply by 18 to determine their cost. This gives us a result or answer of $117.000.
RPTA: The cost of 18 bandejas is $117,000
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What is the
Use that same equation y = 50/3x + 350 to calculate
how much money Beth will have after 21 months.
Form
Using the equation y = 50x/3 + 350, Beth will have $700 after 21 months.
We have to determine how much money Beth will have after 21 months.
The equation is:
y = 50x/3 + 350
The value of x = 21.
Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variables is an expression when it implies that equations in the variable share the same value.
Putting the value of x in equation y = 50x/3 + 350
y = (50×21)/3 + 350
y = 50 × 7 + 350
Simplify
y = 350 + 350
y = 700
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Question 4 (1 point)
What is the Greatest Common Factor between -6x12y and -3xy?
W
The GCF is
Blank 1:
Question 5 (4 points)
Can you explain how too
The Greatest Common Factor(GSF) of -6x12y and -3xy is 3xy.
To find the greatest common factor (GCF) between two numbers or expressions, we need to identify the highest power of each common factor that divides both numbers or expressions.
In this case, we are trying to find the GCF between -6x12y and -3xy.
The prime factorization of the first expression is -6x12y = -2 * 3 * x * 2 * 2 * 3 * y
And, the prime factorization of the second expression is -3xy = -3 * x * y. The common factors between these two expressions are 3, x, and y.
Since, we are finding the greatest common divisor, we neglect the minus sign to obtain the largest value possible.
We can see that both expressions share a factor of 3, x, and y.
Since the GCF is the highest power of each common factor that divides both expressions, in this case, the GCF of -6x12y and -3xy is 3xy.
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claim sizes are 100, 1200, 1800, 2000, 3000 and 5000. the true probabilities are 0.5, 0.2, 0.1, 0.1, 0.05, 0.05, respectively. determine the coefficient of variations, skewness and kurtosis of the observations.
The coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.
A coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial. It is usually a number, but sometimes may be replaced by a letter in an expression. For example, in the expression: ax2 + bx + c, x is the variable and 'a' and 'b' are the coefficients.
coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable and written next to it. The variables which do not have a number with them are assumed to be having 1 as their coefficient.
Let [tex]$x$[/tex] denote the claim sizes
[tex]& x= \begin{cases}100 & ; p=0.05 \\200 & ; p=0.2 \\300 & ; p=0.5 \\400 & ; p=0.2 \\500 & ; p=0.05\end{cases}[/tex]
[tex]& \mu_1^{\prime}=\varepsilon(x)=\sum x^0 p(x=x)=300 \\\\& \mu_2{ }^{\prime}=\sum x^2 p(x)=98000 \\\\& \mu_3^{\prime}=\sum x^3 p(x)=342 \times 10^5 \\[/tex]
[tex]& \mu_4^{\prime}=\sum x^4 p(x)=1.262 \times 10^{10} \\\\& \mu_2=\mu_2^{\prime}-\left(\mu_1^{\prime}\right)^2=8000 \\\\& \mu_3=\mu_3^{\prime}-3 \mu_2^{\prime} \\\\\mu_1^{\prime}+2\left(\mu_1^{\prime}\right)^3=0 \\\\& \mu_4=\mu_4^{\prime}-4 \mu_3^{\prime} \mu_1^{\prime}+6[/tex]
[tex]\mu_2^{\prime} \mu_1^{\prime 2}-3 \mu_1^{\prime 4} \\& \mu_4=2 \times 10^8 \\\\& \beta_1=\frac{\mu_3{ }^2}{\mu_2^3}=0 \quad \Rightarrow y_1=0 \\\\& \beta_2=\frac{\mu_4}{\mu_2{ }^2}=\frac{2 \times 10^8}{64 \times 10^6}=3.125\\ \\& y_2=\beta_2-3=0.125 \\[/tex]
Therefore, coefficient of skewness is 0 and coefficient of Kurtosis is 0.125.
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Multiply the complex numbers below and simply your answer. Show work.
(3i-2)(51-6)
Step-by-step explanation:
(3i-51)*(2-6)
(-48) (-4)
192
What is the length of segment DF?
A teacher pops 4 bags of popcorn
for the class party. There are 10
students in the class. What part of a
bag of popcorn will each student
receive?
The required part of a bag of popcorn will each student receive is 2/5.
What is Part of something?Use "part" when a part of the whole lacks significance on its own; use "a part" when a part of the whole has meaning when combined with other meaningful parts of the same total. For instance, this object is a part of my collection even if my leg is a part of my body.
According to question:We have,
4 bags of popcorn for the party and There are 10 students in the class.
Part of popcorn bag each student receive.
Part of popcorn = 4/10 = 2/5
Thus, 2/5 part of bag each student receive.
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So each student will receive 0.4 bags of popcorn or 4/10 which is 2/5 of a bag of popcorn.
What part of a bag of popcorn will each student receive?Each student will receive 0.4 bags of popcorn or 4/10 which is 2/5 of a bag of popcorn.There are 4 bags of popcorn and 10 students in the class. To find how much of a bag of popcorn each student will receive, you can divide the total number of bags of popcorn by the number of students.4 bags of popcorn / 10 students = 0.4 bags of popcorn per.So each student will receive 0.4 bags of popcorn or 4/10 which is 2/5 of a bag of popcorn.To learn more about probability refer:
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PLEASE HELPP,TEST QUESTION LIMITED TIME!!
Question- Given circle C with center (3, 4) and radius of 10, and circle D with center (0,1) and radius of 2, what sequence of transformations should be used to prove circle C is similar to circle D by mapping C onto D? Show all work and explain your reasoning.
Answer: it’s A
Step-by-step explanation:
HELP ME NEED HELLBSNHDJD
Answer:
Step-by-step explanation:
Find the probabilty of obtaining exactly two 2's in five rolls of a fair die.
Answer:
[tex]\rm{ \dfrac{1250}{7776}\; or\; 0.16075\\\\}[/tex]
Step-by-step explanation:
This probability can be determined using combinatorics. The number of ways a sample of size r can be obtained from a larger set of n items is given by the formula
[tex]C(n,r) = \dfrac{n!}{( r! (n - r)! )}[/tex]
We pronounce C(n, r) as n choose r
We are rolling the die five times. So n = 5
On each roll a 2 can appear or not
We need two 2's . This is our r
The number of ways two 2's can appear is given by 5 choose 2
[tex]C(5,2)\\\\= \dfrac{5!}{( 2! (5 - 2)! )}\\\\= \dfrac{5!}{2! \times 3! }\\\\[/tex]
5! is the factorial of 5, 2! is the factorial of 2 and 3! is the factorial of 3
5! = 5 x 3 x 3 x 2 x1
3! = 3 x 2 x 1
2! = 2 x1
[tex]C(5,2) = \dfrac{5\times 4 \times 3 \times 2 \times 1}{((2 \times 1) \times (3 \times 2 \times 1)}\\\\= 10\\[/tex]
You need not go through this laborious process to find 5 choose 2 there are calculators available
So two 2's can appear 10 times.
The probability of getting a 2 on one roll is 1/6 and the probability of not getting a 2 on a single roll is 1-1/6 = 5/6
This works out to a binomial probability which can be computed by the formula
P(x) = C(n, x) pˣqⁿ⁻ˣ
Where x is the number of times the desired outcome succeeds and n the total number of trials
Here x = 2, n = 5, C(5, 2) = 10
[tex]\rm{So\:P(two\:2s\:on\:5\:throws)\: = 10 \cdot \left(\dfrac{1}{6}\right)^2\cdot \left(\dfrac{5}{6}\right)^3\\\\[/tex]
[tex]{= \dfrac{10 \cdot 1\cdot 125}{{6^5}} = \dfrac{1250}{7776} = 0.16075\\\\[/tex]
a large tire manufacturing company has claimed that its top line tire will last more than 80,000 miles. if a consumer group wished to test this claim, the research hypothesis would be:
The research hypothesis would be Ha : μ > 80,000.
The research hypothesis for a consumer group testing the claim that a large tire manufacturing company's top line tire will last more than 80,000 miles would be: "The large tire manufacturing company's top line tire will last more than 80,000 miles."
Ha : μ > 80,000
A research hypothesis for a consumer group testing the claim that a large tire manufacturing company's top line tire will average more than 80,000 miles would be Ha : μ > 80,000 miles. The "Ha" stands for the alternative hypothesis, which states that the population mean (μ) of the tire's mileage is greater than 80,000 miles. This hypothesis is chosen because it represents the claim made by the tire manufacturing company and it is what the consumer group is trying to test against the null hypothesis (H0) which is the opposite of the claim, in this case, H0 : μ <= 80,000 miles.
So, the research hypothesis would be Ha : μ > 80,000.
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