The initial force between the two charges is given by:
[tex]F=k\frac{q_{1} q_{2} }{d^2}[/tex]
where k is Coulomb's constant, q1 and q2 are the two charges, and d is their separation. Let's analyze now the other situations:
1. F
In this case, q1 is halved, q2 is doubled, but the distance between the charges remains d.
So, we have:
q'₁=q₁/2
q'₂=2q₂
d'=d
So, the new force is:
[tex]F'=k\frac{q'_{1}q'_{2} }{d^2} \\\\F'=k\frac{(\frac{q_{1} }{2})(\frac{q_{2} }{2}) }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{d^2} =F[/tex]
So the force has not changed.
2. F/4
In this case, q1 and q2 are unchanged. The distance between the charges is doubled to 2d.
So, we have:
q'₁=q₁
q'₂=q₂
d'=2d
So, the new force is:
[tex]\\F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{q_{1}q_{2} }{2d^2} \\\\F'=\frac{1}{4} k\frac{q_{1}q_{2} }{d^2} \\\\F'=\frac{F}{4}[/tex]
So the force has decreased by a factor of 4.
3. 6F
In this case, q1 is doubled and q2 is tripled. The distance between the charges remains d.
So, we have:
q'₁=2q₁
q'₂=3q₂
d'=d
So, the new force is:
[tex]F'=k\frac{q'_{1} q'_{2} }{d^2} \\\\F'=k\frac{2q_{1}3q_{2} }{d^2}\\ \\F'=6k\frac{q_{1}q_{2} }{d^2} =6F[/tex]
So the force has increased by a factor of 6.
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Answer:
1. F
2. F/4
3. 6F
an education researcher gathers data about freshman students in an economics course. she collects the number of hours that students study and the number of questions they missed (got wrong) on exams. the regression results were:
On solving the provided question we can say that the linear regression results were: = 9.23 X [tex]10^{-3}[/tex]
what is linear regression?When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.
an education researcher gathers data about freshman students in an economics course.
he collects the number of hours that students study and the number of questions they missed (got wrong) on exams
the linear regression results were: = 9.23 X [tex]10^{-3}[/tex]
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If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, which of the following probabilities is not correct?
a. P(x ≥ 1) =.1587
b. P(x < 2) =.9772
c. P(x = 0) =.50
d. P(x ≤ 1) =.8413
If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.
The probability of all the events in a sample space adds up to 1.
Thus, If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.
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is it possible for a data set to have no mode? group of answer choices yes, if two observations occur twice. no, unless there is an odd number of observations no, if the data set is nonempty, there is always a mode yes, if there are no observations that occur more than once.
Yes, it is possible for a data set to have no mode.
A mode is the most common value in a data set, so if there are no observations that occur more than once, the data set would have no mode. For example, a data set of the numbers {1, 2, 3, 4, 5} would have no mode because none of the numbers appear more than once.
Additionally, a dataset can also have multiple modes, or a bimodal distribution, which means that there are two or more observations that occur with the same highest frequency. A dataset can have a multimodal distribution as well if it has more than two modes.
In summary, a dataset can have no mode if no observations occur more than once, or have multiple/multimodal modes if more than one observations occur with the same highest frequency.
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The twenty-four students who earned A Honor Roll at Harmony School were twelve less than three times the number of students who earned B Honor Roll. How many students earned B Honor Roll?
Answer:
12 students earned B Honor Roll
Step-by-step explanation:
Let A be the number of students who earned A Honor Roll and B the number who earned B.
We are told that A = 24,
and that A = 3B-12 [ . . .were twelve less than three times the number of students who earned B Honor Roll]
Since we know the value of A (24) use the second equation to find B:
A = 3B-12
24 = 3B-12
3B = 36
B = 12
CHECK:
Is 24 12 less than three times B(12)?
24 = 3*12 - 12?
24 = 36 - 12?
24 = 24
YES
Find the area of the SHADED figure. Pictures are not drawn to scale. Round answers to the nearest tenth.
The area of the shaded portion of the figure is 272 units squared.
How to find area of a figure?The figure above is a triangle inside a trapezium. The area of the shaded portion can be found when we subtract the area of the triangle from the area of the trapezium.
Therefore,
area of the shaded portion = area of the trapezium - area of the triangle
area of the triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × 18 × 16
area of the triangle = 288 / 2
area of the triangle = 144 units²
area of the trapezium = 1 / 2 (a + b)h
where
a and b are the top and baseh = height of the trapeziumTherefore,
area of the trapezium = 1 / 2 (18 + 34)16
area of the trapezium = 1 / 2 (52)16
area of the trapezium = 832 / 2
area of the trapezium = 416 unit²
Therefore,
area of the shaded portion = 416 - 144
area of the shaded portion = 272 units²
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Pick two or fewer different digits from the set {1, 3, 6, 7} and arrange them to form a number. How many prime numbers can we create in this manner
We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.
Given that,
The number is either 1-digit or 2-digit.
In the case of 1-digit, the only 1-digit primes are 3 and 7, for a total of 2 primes.
In the case of 2-digit, We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield 12-4=8 prime numbers.
Thus, We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.
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Can someone help me??!!!
Please
For given function f(x) the y in the graph are f(2) = 4,f(0) = 3 ,f(-6) = -6 and f(4) = 5
What is function?A function is described as a relationship between a set of inputs, each of which has a single output. The simplest definition of a function is an association between inputs where each input is connected to a single, unique output. There is a codomain or range for each function. A function is frequently referred to as f(x), where x is the input.
Here,
In the given graph
when x = 2
y = 4
and x = 0
y = 3
Put it in slope formula
=> m =y2 - y1 / x2 -x1
=> m =1/2
m = 1/2
Now we can just put them into slope formula
y - y₁ = m(x - x₁)
y - 4 = 1/2(x - 2)
y = 1/2(x) -1 + 4
y = 1/2(x) + 3
Now we can just put them into slope formula
y - y₁ = m(x - x₁)
y - 3 = 1/2(x - 0)
y = 1/2(x) + 3
Thus, the function for given f(x) is solved
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does it make sense that the number of cats falling frm the 5th floor would be greater than those of the 4th
Yes, it makes sense that the number of cats falling from 5th floor would be greater since the terminal velocity of the cat would be greater at higher altitudes.
What is velocity?The pace at which an object's location changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
What is altitude?A distance measurement between a reference datum and a point or object, typically in the vertical or "up" direction, is known as altitude, height, or depth.
The terminal velocity of the cat would be greater at higher altitudes; hence cats have higher risk of falling from heights.
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peters school runs a rugby team. over their first 10 games they scored a mean of 17 points per game. after their 11th game the mean had reduced to 16 points per game. how many points were scored in the 11th game?
6 points were scored in the 11th game.
What is mean ?Mean is the arithmetic average of a set of given numbers. Therefore the mean in math is often referred to as simply the average.
The mean is the total number of points scored divided by the number of games.
So if the mean is 17 points per game for the first 10 games, the total number of points scored in the first 10 games is 17 * 10 = 170.
Similarly,
if the mean is 16 points per game after the 11th game, the total number of points scored in the first 11 games is 16 * 11 = 176.
To find the number of points scored in the 11th game
we can subtract the total number of points scored in the first 10 games from the total number of points scored in the first 11 games:
176 - 170 = 6
Therefore, 6 points were scored in the 11th game.
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How to turn a number into a fraction
Answer:
1. Write the number as the numerator of the fraction.
2. Write 1 as the denominator of the fraction.
Step-by-step explanation:
Example-
To turn the number 3 into a fraction, write 3 as the numerator and 1 as the denominator. The resulting fraction is 3/1.
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Determina los primeros cuatro términos de la sucesión: -n2 -2n +3
The sequence of numbers for the expression -n² - 2n + 3 is
0, -5, -12, -21, and -32.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
-n² - 2n + 3
The sequence of numbers for n = 1, 2, 3, 4, 5 are:
n = 1,
-1 - 2 + 3
= -3 + 3
= 0
n = 2,
-4 - 4 + 3
= -8 + 3
= -5
n = 3,
-9 - 6 + 3
= -15 + 3
= -12
n = 4,
-4² - 2 x 4 + 3
= -16 - 8 + 3
= -21
n = 5,
-25 - 10 + 3
= -35 + 3
= -32
Thus,
The sequence of numbers is 0, -5, -12, -21, and -32.
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How many solutions exist for the given equation?
1/2(x+ 12) = 4x-1
zero
one
two
O infinitely many
0.5x + 6 = 4x - 1
3.5x = 7
x = 2
Only one solution exists for the given equation.
Answer:
one
Step-by-step explanation
For a polynomial function, the number of solutions, or zeros, is generally equivalent to the highest degree. For example, a cubic function (e.g. [tex]x^3+2x^2[/tex]) has 3 real zeros (x=-2, x=0, and x=0) and a quadratic (e.g. [tex]x^2-1[/tex]) has 2 real zeros (x=-1 and x=1).
For your problem, [tex]\frac{1}{2} (x+12)=4x-1[/tex], the highest degree is 1 since this is a linear function. To prove there is only one solution, let's bring all the terms to one side, simplify, and solve for x.
Distribute the 1/2 --> [tex]\frac{1}{2} x+6=4x-1[/tex]Subtract 4x from both sides --> [tex]\frac{1}{2}x+6-4x=-1[/tex]Subtract 6 from both sides --> [tex]\frac{1}{2} x-4x=-7[/tex]Combine 1/2x and -4x --> [tex]-3.5x=-7[/tex]Divide both sides by -3.5 --> [tex]x=2[/tex]There only one solution to the equation as shown above and as can be seen in step 4, the x is only to the first degree ([tex]x=x^1[/tex]) which indicates that there is only one solution, 2.
Which number gives the same result if it is multiplied by 999/998 or if any number is added to it?
Please give me the answer with an explanation!
Thanks in advance!
Answer:
The number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
The property of a number being unchanged after being multiplied by a fraction and a constant is called an "Identity element". The identity element for multiplication is 1 and for addition is 0.
When any number is multiplied by 1, it stays the same. So, if we multiply any number by 999/998, which is equivalent to multiplying by 1, it stays the same.
Similarly, when any number is added to zero, it stays the same. So, if we add any number to 0, it stays the same.
Therefore, the only number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).
An ant crawling along the floor follows a semi-circular path, going halfway around the circumference of a circle of radius R.
The distance traveled and the displacement of the ant are, respectively,
πR and πR
2R and πR
πR and 2R
πR and zero
none of these
The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.
The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.
So, the option c is most suitable option.
Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.
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The time to manufacture a pair of headphones on each assembly line is 1/3 hour. if there are 24 assembly lines and they operate 8 hours a day, how many pairs of headphones can be manufactured in a day?
you get brainliest if you answer!!!!!! i need this right now! +15 points
The number of pais of headphones that can be manufactured in a day = 576
Given that the time to manufacture a pair of headphones on each assembly line is 1/3 hour.
By unitary method the number of pairs of headphones can be manufactured in an hour :
1 ÷ (1/3)
= 1/ (1/3)
= 3
So, 3 pairs of headphones can be manufactured in an hour.
We need to determine the number of pairs of headphones that can be manufactured in a day.
Since we can operate assemply line 8 hours a day.
By unitary method the number of pairs of headphones can be manufactured in 8 hours:
3 × 8 = 24
And there are such 24 assembly lines.
So, the number of pais of headphones that can be manufactured in a day:
24 × 24 = 576
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using one or more coins, how many different amounts of money can be made from a collection of coins that consists two pennies, one nickel and one dime?
Answer:
We can use the following steps to determine the different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime:
Step 1: List out all the different combinations of coins that can be used to make the different amounts of money.
Two pennies
One penny and one nickel
One penny and one dime
Two pennies and one nickel
Two pennies and one dime
One nickel and one dime
Two pennies, one nickel, and one dime
Step 2: Calculate the value of each combination of coins.
Two pennies = $0.02
One penny and one nickel = $0.06
One penny and one dime = $0.11
Two pennies and one nickel = $0.07
Two pennies and one dime = $0.12
One nickel and one dime = $0.15
Two pennies, one nickel, and one dime = $0.17
Step 3: Write down the total amount of money that can be made from each combination.
Final Answer: There are 7 different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime, they are $0.02, $0.06, $0.11, $0.07, $0.12, $0.15, and $0.17
The power of 10 is the ________________ of places we move the decimal point to get the first factor. For any number greater than ______, the power of 10 in scientific notation will be (positive or negative?).
First_______ Power of_____
Example: Let’s look at the mass of Earth in kilograms.
What power?____
Numbers can also be converted from scientific notation to standard notation.
Look at the number 6.51 × 108 . The power of 10 denotes the ________________ of places the ________________ ________________ has to move. The power of 10 in this number is positive, so we move the decimal point to the (left or right?) 8 places.
The number 6.51 × 108 written in standard notation is ______________________.
Answer:
Step-by-step explanation:
The power of 10 is the exponent of places we move the decimal point to get the first factor. For any number greater than 1, the power of 10 in scientific notation will be positive.
First Non-zero Power of 10
Example: Let’s look at the mass of Earth in kilograms.
What power? 9
Numbers can also be converted from scientific notation to standard notation.
Look at the number 6.51 × 108 . The power of 10 denotes the number of places the decimal point has to move. The power of 10 in this number is positive, so we move the decimal point to the right 8 places.
The number 6.51 × 108 written in standard notation is 651000000.
jackie says that the constant of proportionality in the equation is 0.25 is jackie correct
Yes, Jackie is correct as the equation x = 0.25y could be written as x = ky which means x ∝ y. thus, 0.25 is a constant of proportionality.
What is a constant of proportionality?The ratio between two proportional quantities has a constant value, which is known as the constant of proportionality. When either their ratio or their product produces a constant, two varying quantities are said to be in a proportional relationship. The Direct Variation and Inverse Variation types of proportion between the two given quantities determine the proportionality constant's value.
When two variables are directly or indirectly proportional to one another, their relationship can be expressed as y = kx or y = k/x, where k specifies how the two variables are related to one another. The proportionality constant, k, stands for this.
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Full question
Jackie was given a proportion x = 0.25y. Jackie says that the constant of proportionality in the equation is 0.25 is Jackie correct.
help me please with this work
Step-by-step explanation:
we know
[tex]y = mx + c[/tex]
Answer:
y-intercept: -3
slope: 4
equation: y=4x-3
Step-by-step explanation:
To find the y-intercept, it shows in the table of value that when x is 0, y is -3 so y-intercept = -3. To find the slope, find the first differences which is 4.
How do you list angles and sides in order from smallest to largest?
Listing of the angles and the sides in the order of smallest to largest is given by :
Side opposite to obtuse angle > Side opposite to acute angle and
side opposite to right angle > side opposite to acute angle.
As given in the question,
In the given triangle,
Ordering of the angles and sides from smallest to largest.
As per the property of the triangle:
Side opposite to the greatest angle is the largest side of the given triangle.
If the given triangle is obtuse angle triangle,
Then other two angles are acute.
Compare all the angles and sides arrange in ascending order.
Side opposite to obtuse angle > Side opposite to acute angle
In the right angled triangle,
Other two angles are acute.
Same compare and write in ascending order.
side opposite to right angle > side opposite to acute angle
Therefore, the sides and angles can be written in smallest to largest order by comparison and is given by:
Side opposite to obtuse angle > Side opposite to acute angle and
side opposite to right angle > side opposite to acute angle.
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URGENT WORTH 20 POINTS!!!
A polynomial f and a factor of f are given. Factor the polynomial completely using long division. Show work.
The polynomial x⁵ - 4x³ + x² - 4 will have a remainder of -8 when divided by x² - x + 1 and the result can be written in the form (x³ + x² - 4x + 4) - 8/(x² - x + 1).
How to divide the polynomialUsing the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder
We shall divide the polynomial x⁵ - 4x³ + x² - 4 by x² - x + 1 as follows;
x⁵ divided by x² equals x³
x² - x + 1 multiplied by x³ equals x⁵ - x⁴ + x³
subtract x⁵ - x⁴ + x³ from x⁵ - 4x³ + x² - 4 will result to x⁴ - 5x³ + x² - 4
x⁴ divided by x² equals x²
x² - x + 1 multiplied by x² equals x⁴ - x³ + x²
subtract x⁴ - x³ + x² from x⁴ - 5x³ + x² - 4 will result to -4x³ - 4
-4x³ divided by x² equals -4x
x² - x + 1 multiplied by -4x equals -4x³ + 4x² - 4x
subtract 4x³ + 4x² - 4x from -4x³ - 4 will result to 4x² - 4x - 4
4x² divided by x² equals 4
x² - x + 1 multiplied by 4 equals 4x² - 4x - 4
subtract 4x² - 4x - 4 from 4x² - 4x - 4 will result to a remainder of -8.
Therefore, the polynomial x⁵ - 4x³ + x² - 4 divided by x² - x + 1 gives a quotient x³ + x² - 4x + 4 and a remainder of -8 and can be written as (x³ + x² - 4x + 4) - 8/(x² - x + 1).
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GIVING 74 POINTS ALL!!! ANSWER THIS ASAP! GIVING 74 POINTS! GIVING 74 POINTS. MATH QUESTION!!!!!! How many 6 digit numbers are in the form 225A7B such that the number is divisible by 36? I also have other problem. How many numbers are in the form AB554433221100 such that the number is divisible by 11?
Answer: number 1: 0.1111 and number 2: 1.0909
Step-by-step explanation: I hope I did this right
[tex]-\sqrt{16y^4}[/tex] if y<0
Answer:
-4y²
Step-by-step explanation:
You want to simplify the expression -√(16y⁴), given that y < 0.
Square rootThe square root can be simplified by removing squares from under the radical.
[tex]-\sqrt{16y^4}=-\sqrt{(4y^2)^2}=\boxed{-4y^2}[/tex]
The sign of y is irrelevant.
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a circumfrence of 10. it has an arc of the length 9/2. what is the central angle of the arc,in degrees/
The central angle of the arc in degrees is 162 degrees.
How to find the central angle ?The circumference of the circle is 10 units. The length of the arc is 9 / 2 units. The central angle can be calculated as follows;
We can find the central angle by comparing it to the length of the arc.
Therefore, we know the circle has a circumference of 10. We also know a circle is 360°. The length of the arc is given as 9 / 2 units(4.5 units).
To determine the degrees of the central angle, we have to set up a ratio and set the unknown angle as x.
Hence,
length of the arc / circumference = angle of the arc / angle of the circle
4.5 / 10 = x / 360
cross multiply
360 × 4.5 = 10x
1620 = 10x
divide both sides by 10
x = 1620 / 10
x = 162 degrees
Hence,
central angle = 162 degrees.
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The graphs of y=-4x and y=-4x+2 are shown. Use the drop down menus to complete the statements. The ratios of y/z are the same for the graph of
Answer:
y = -4x
Step-by-step explanation:
When equations are in the form
y = mx the slope m (is y/x)
a bag contains red marbles and blue marbles. zuri randomly removes marbles from the bag, one at a time and without replacement, and stops when she has removed all the red marbles from the bag. what is the expected value of the number of marbles zuri removes from the bag?
The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles.
The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red and blue marbles. This is because the expected value of an event is the sum of the probability of each outcome multiplied by the associated outcome. Since Zuri is randomly removing marbles from the bag, one at a time and without replacement, the probability of each outcome (red or blue) is equal. Therefore, the expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles. This is because each marble has an equal chance of being removed and, therefore, each marble has the same expected value.
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The lengths of two sides of a triangle are 7 cm and 17 cm. Identify the range of possible lengths for the third side.
The range possible length of the third side of the triangle is greater than 11.
How to find the third side of a triangle?The lengths of two sides of a triangle are 7 cm and 17 cm. The range of the possible length for the third side can be calculated as follows:
The triangle inequality theorem simply states that the sum of any two sides in a triangle must be greater than the length of the third side of the triangle.
Using triangle inequality theorem, if a, b and c are the sides of the triangle. Hence,
a + b > c
a + c > b
b + c > a
Hence,
7 + 17 > c
7 + c > 17
17 + c > 7
Therefore, using 7 + c > 17, c should be greater than 11.
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Please answer these questions for 100 POINTS!
Answer:
Step-by-step explanation:
true true false
$73 is what percent of $125
Answer:
58.4%
Step-by-step explanation:
several different types of cheese are produced in the shape of a wheel. because of the differences in consistency of these different types of cheese, there is variation in the amount of cheese in the wheel. cam embert wishes to determine if there is a significant difference, at the 5% level, between gouda cheese and brie cheese. she randomly samples 18 wheels of gouda and finds the mean is 1.3 pounds with a standard deviation of 0.31 pound and 13 wheels of brie and finds a mean of 0.95 pounds and a standard deviation of 0.26 pound. is the difference between the weights of the two cheeses significant at the 0.05 level of significa
There is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.
What is standard deviations?Standard deviation is a measure of how spread out a set of numbers is from the mean. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. In other words, it is a measure of how much the values in a dataset differ from the mean, or average, value. Standard deviation is a useful tool for understanding the distribution of data and can be used to identify outliers and compare data sets.
To answer this question, we must use a two-tailed hypothesis test, where the null hypothesis is that there is no difference between the two cheeses. The alternative hypothesis is that there is a significant difference between the two cheeses.
Using the sample data provided, we are able to calculate the test statistic, which in this case is 2.02. This can be compared to the critical value from the t-distribution table, which is 1.711 for a 5% level of significance and 31 degrees of freedom.
Since the test statistic is larger than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.
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