The required, two expressions are not equivalent, and Pat's claim is false.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.
Here,
a) To show that Pat is wrong, we can substitute p = 3 into both expressions and compare the results:
4 - (p + p + p) = 4 - (3 + 3 + 3) = 4 - 9 = -5
4 - p + p + p = 4 - 3 + 3 + 3 = 7
Since the two expressions have different values when p = 3, Pat's claim is false.
b) Simplifying each expression algebraically, we have:
4 - (p + p + p) = 4 - 3p
4 - p + p + p = 4 + p
Therefore, the two expressions are not equivalent, and Pat's claim is false.
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1/8 an integer or not
Answer: no
Step-by-step explanation: an integer is a number that is not a fraction or a decimal
Answer:
nope
Step-by-step explanation:
it's a decimal, so by definition, it's not an integer.
What is the standard deviation for the following dataset?
18 22 39 48 77 89
The standard deviation for the dataset is 28.89.
What is the standard deviation?
When we measure diversity in a data set, it is called standard deviation. We have to calculate the variance first. The square root of variance gives the standard deviation. The formula to calculate standard deviation is:
s= [tex]\sqrt{\frac{(x1-xm)^{2} + (x2-xm)^{2} +........+ (xn-xm)^{2} }{n-1} }[/tex]
First, we will calculate the mean of the data, xm
[tex]xm=\frac{18+22+39+48+77+89}{6}[/tex]
[tex]=48.83[/tex]
Then, we will calculate the following:
[tex](x1-xm)^{2}=(18-48.83)^{2} \\\\(x2-xm)^{2}=(22-48.83)^{2} \\\\(x3-xm)^{2}=(39-48.83)^{2} \\\\(x4-xm)^{2}=(48-48.83)^{2} \\\\(x5-xm)^{2}=(77-48.83)^{2} \\\\(x6-xm)^{2}=(89-48.83)^{2} \\[/tex]
The summation comes out to be 4174.83.
Therefore, the standard deviation becomes = [tex]\sqrt{\frac{4174.83}{5} }[/tex]
=28.89
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Among 350 randomly selected drivers in the 20−24 age bracket, 3 were in a car crash in the last year. If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car crash during the next year? Is it unlikely for a driver in that age bracket to be involved in a car crash during a year? Is the resulting value high enough to be of concern to those in the 20−24 age bracket? Consider an event to be "unlikely" if its probability is less than or equal to 0.05.
Question content area bottom
Part 1
The probability that a randomly selected person in the 20−24 age bracket will be in a car crash this year is approximately enter your response here.
(Type an integer or decimal rounded to the nearest thousandth as needed.)
The probability that a randomly selected driver in the 20-24 age bracket will be in a car crash during the next year is 0.86%.
It is unlikely for a driver in that age bracket to be involved in a car crash during a year
The resulting probability of 0.0086 is relatively low.
How to find the probabilityThe approximate probability can be calculated by dividing the number of drivers who were in a car crash in the last year by the total number of drivers in the 20-24 age bracket:
Probability = Number of drivers in a car crash / Total number of drivers in the age bracket
Probability = 3/350
Probability ≈ 0.0086
Part 2
Since the probability is less than 0.05, it is unlikely for a driver in that age bracket to be involved in a car crash during a year.
Part 3
While any car accident can be a concern, the resulting probability of 0.0086 is relatively low.
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Colleen has 6 eggs, one of which is hard-boiled while the rest are raw. Colleen can't remember which of the eggs are raw. Which of the following statements is true? If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5. The probability of Colleen selecting the hard-boiled egg on her first try is 1/5. If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/6. The probability of Colleen selecting a raw egg on her first try is 1/6.
Answer: If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5, and the probability of Colleen selecting the hard-boiled egg on her first try is 1/6.
To see why, let's consider the possible scenarios:
Colleen selects the hard-boiled egg on her first try. There is only 1 hard-boiled egg out of the 6, so the probability of this happening is 1/6.
Colleen selects a raw egg on her first try. There are 5 raw eggs out of the 6, so the probability of this happening is 5/6. After she cracks open the raw egg, there will be 4 raw eggs and 1 hard-boiled egg left. So the probability of selecting the hard-boiled egg on her second pick is 1/5.
Therefore, the statement "If Colleen selected one egg, cracked it open and found out it was raw, the probability of selecting the hard-boiled egg on her second pick is 1/5, and the probability of Colleen selecting the hard-boiled egg on her first try is 1/6" is true.
Step-by-step explanation:
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 54 months and a standard deviation of 11 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 21 and 32 months?
Therefore , the solution of the given problem of percentage comes out to be 11.31% of the vehicles in use are between 21 and 32 months old.
Describe percentages.In statistics, a percentage is a figure or a figure that is expressed as a fraction of 100. Furthermore, "pct.," "pct," as well as "pc," are rarely used. However, it is commonly denoted by the "%" sign. There are no dimensions; the percentage total is flat. Percentages are essentially numbers because their numerator is 100. To indicate that a number is a percentage, the percent sign (%) or the phrase "percent" must appear before the number.
Here,
This rule states that for a normal distribution, which is presumed here because of the bell-shaped curve:
The data is within yet another standard deviation of the median for 68% of the time.
The data is within 2 standard deviations of the median for 95% of the time.
The data is now within three standard deviations of the mean in 99.7% of the cases.
As a result, z1 = (21 - 54) / 11 = 3 and z2 = (32 - 54) / 11 = 2
The numbers -3 and -2 represent the number of standard deviations that each figure is from the mean.
determine what percentage of the data lies in between two values:
P(-3 ≤ Z ≤ -2) = 0.1359 - 0.0228 = 0.1131
According to this, 11.31% of the vehicles in use are between 21 and 32 months old.
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sebastian is creating a rectangular garden in his backyard. the length is 11 feet. the perimeter of the garden must at least be 56 feet and no more than 76 feet. what is the width of the garden must at least be?
The garden must be at least 17 feet wide.
Let's use w to represent the garden's breadth.
The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width.
Assuming that the length is 11 feet, the expression for the perimeter can be written as follows:
P = 2(11) + 2w = 22 + 2w
The perimeter is stated to be at least 56 feet and not to exceed 76 feet. Hence, we can create the inequality shown below:
56 ≤ 22 + 2w ≤ 76
When we take 22 out of every aspect of the inequality, we get:
34 ≤ 2w ≤ 54
By multiplying every aspect of the inequality by 2, we obtain:
17 ≤ w ≤ 27
Thus, the garden must be at least 17 feet wide.
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Use synthetic division to evaluate for the indicated x value.
--x³-2; f (5)
f (5)
=
We can write the function f(x) = (- x³ - 2) at {x} = 5 as -
f(5) = - 127.
What is expression?An expression is a term made up of both constants and variables.
Given is the function as -
f(x) = - x³ - 2
We can write f(5) as -
f(5) = - (5)³ - 2
f(5) = - 125 - 2
f(5) = - 127
Therefore, we can write the function f(x) = (- x³ - 2) at {x} = 5 as -
f(5) = - 127.
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Create an equivalent expression for 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six.
Answer:
Step-by-step explanationuuh soo I don’t understand this app:
Use matrices A, B, C, and D. Find each scalar product, sum, or difference.
A-2B
We can write the equivalent value of the matrix {A - 2B} as -
[9 2]
[2 6]
[3 -10]
What are matrices?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
Given are the matrices as given in the equation.
We can write the elements for {A - 2B} as -
A{ 1 } = 3 + 6 = 9
A{ 2 } = 4 - 2 = 2
A{ 3 } = 6 - 4 = 2
A{ 4 } = - 2 + 8 = 6
A{ 5 } = 1 + 2 = 3
A{ 6 } = - 10
So, we can write the matrix as -
A - 2B =
[9 2]
[2 6]
[3 -10]
Therefore, we can write the equivalent value of the matrix {A - 2B} as -
[9 2]
[2 6]
[3 -10]
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Determine the total number of eggs in 7 dozen eggs
Answer:
Seven dozen eggs would equal a total of 84 eggs
Step-by-step explanation:
Answer:
84 eggs
Step-by-step explanation:
1 dozen of eggs = 12 eggs
Then :
1 dozen -------- 12 eggs
7 dozen ------- x eggs
x = (7 x 12) / 1 = 84 eggs
Which conic section does the equation below describe? (x - 3)^2)/10 - (y + 5)^2)/9 = 4
Answer:
The given equation is of the form:
((x - h)^2)/a^2 - ((y - k)^2)/b^2 = 1
Comparing it with the given equation:
((x - 3)^2)/10 - ((y + 5)^2)/9 = 4
We can rewrite the equation in the standard form by dividing both sides by 4, then adding (y+5)^2/9 to both sides:
((x - 3)^2)/40 - ((y + 5)^2)/36 = 1
Now, we can see that the equation is in the standard form of a hyperbola. The center of the hyperbola is (3, -5), the distance between the center and each vertex is sqrt(10) in the x-direction and sqrt(9) in the y-direction, and the hyperbola opens to the left and right.
How many times 9 goes into 22
Does this represent a function yes no because
We can conclude that the set of points {(−9,0),(−4,5),(0,9),(4,5),(9,0)} does not represent a function.
What is functions ?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are commonly denoted using functional notation, where the function name is followed by its input, such as f(x) or g(t).
According to given information:To determine if the set of points {(−9,0),(−4,5),(0,9),(4,5),(9,0)} represents a function, we need to check if for every x-coordinate there is only one corresponding y-coordinate.
We can start by graphing the set of points:
From the graph, we can see that for x = -4 and x = 4, there are two different y-coordinates, which means that the set of points does not represent a function.
Therefore, we can conclude that the set of points {(−9,0),(−4,5),(0,9),(4,5),(9,0)} does not represent a function.
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What number has the same
value as I2 tens?
For questions 4-6, calculate the simple interest and the amount after the specified period of time.
4. $328.00 invested at 5% for 3 years.
4. Interest:
5. $635.85 invested at 7% for 6 months.
6. $175.01 invested at 8% for 90 days.
Amount:
5. Interest:
Amount:
6. Interest:
Amount:
Step-by-step explanation:
328×5×3÷100
100÷5=20
20÷2=10
328÷2=164
Lily has read 3/4 of her book. Sophie has read 2/6 of her book. Which girl has read more of her book?
Answer: Lily
Step-by-step explanation:
3/4 is larger than 2/6
Answer: Lily
Step-by-step explanation: 3/4 > 2/6
3/4 = 0.75
2/6= 0.33
compare the two decimal places, 0.75 > 0.33
is my answer correct?
If f(x) = 2/3x^2 + 8x, what is the value of f(6)?
Answer:198
Step-by-step explanation:
15+15+15+!5
f(6)=72
Explanation:
to evaluate f(6) substitute x = 6 into f(x)
f(6)=2/3×(6x6x6x6x6x6)+(8×6)
=2/3×36+48
24+48=72
72 is your answer
Determine if it is Exponential growth or decay. Use the information below to plug in the numbers to the formula. f(x)=a(1+or-r)^x
initial value: 2,000
growth rate: 6%
The exponential function is an exponential growth.
Is it an exponential growth or decay?The general exponential function is:
f(x) = a*(b)^x
Where a is the initial value and b is the base, if:
b > 1 then it is a growth.
0 < b < 1 then it is a decay.
In this case, b = 1 + r
Where r is the growth rate, in this case is 6%, writting it as a decimal we get:
b = 1 + 6%/100% = 1.06
It is larger than 1, so this is a growth.
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If 6% of a number is 10, find 3% of that number.
Answer:
1.8
Step-by-step explanation:
6 is 10% of 60, which means 3% of 60 is 1.8.
Kelly had
27 points in a game.
On her next 4 turns, she
won 5 points, gained 8
points, lost 7 points, and
then lost 2 points. What is
her score now?
Answer:
46
Step-by-step explanation:
27+4*5+8-7-2=
27+20+8-7-2=
47+8-7-2=
55-7-2=
48-2=
46
please help me with this question
Answer:
it's C
All the graphs except C crosses the x axis at the roots but C doesn't
Which graph is the result of reflecting f(x) =1/4 (8)x across the y-axis and then across the x-axis?
Answer:
Answer on pic
Step-by-step explanation:
#CarryOnLearning
If 55% of a number is 121 and 75% of the same number is 165, find 20% of that number.
Answer:
20% of the number is 44.0.
Step-by-step explanation:
Let's say the number is "x".
We can start by setting up two equations based on the given information:
0.55x = 121
0.75x = 165
We can solve for x by dividing both sides of each equation by the coefficient of x:
x = 121/0.55 ≈ 220.0
x = 165/0.75 = 220.0
Now that we know the value of x, we can find 20% of it by multiplying it by 0.20:
0.20 * 220.0 = 44.0
Therefore, 20% of the number is 44.0.
PLEASE HELP ITS DUE TONIGHT I DONT KNOW HOW TO DO IT
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
-4.8y-2(6.35y +4.65)
Answer:
Expanding the expression, we have:
-4.8y - 2(6.35y + 4.65)
= -4.8y - 12.7y - 9.3 (distributing the -2)
= -17.5y - 9.3
Step-by-step explanation:
The graph shows the total cost c of buying one large bucket of popcorn and d large drinks. Write an equation from the graph that could be used to find the total cost c if you buy one large bucket of popcorn and d large drinks.
The equation of the line that represents the total cost is c = 4d + 8 and the total cost when 1 drink is bought is $ 12.
The slope-intercept form:The slope-intercept form of a line has used to form a linear equation in two variables. It is called the slope-intercept form because it gives us two pieces of information about the line its slope and y-intercept.
The slope-intercept form of a line is given by the equation:
y = mx + bwhere:
m is the slope of the line
b is the y-intercept of the line
Here we have
The graph shows the total cost c of buying one large bucket of popcorn and d large drinks.
From the graph, the line passes through points (0, 8) and (1, 12)
Hence, slope of the line (m) = [(y₂ - y₁) / (x₂ - x₁) ]
= [(12 - 8) / (1 - 0) ] = [4 / 1] = 4
Let y = mx + c be the lines
=> y = 4x + c
Since the line passes through (0, 8)
=> 8 = 4(0) + c
=> c = 8
Hence, the required equation is y = 4x + 8
From the data,
The y-axis represents the total cost 'c' and the x-axis represents the number of drinks 'd'
=> Total cost c = 4d + 8
Hence,
The equation of the line that represents the total cost is c = 4d + 8
If we bought 1 large drink
=> c = 4(1) + 8 = 12
Therefore,
The equation of the line that represents the total cost is c = 4d + 8 and the total cost when 1 drink is bought is $ 12.
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Tell how many polygons can be formed by each set of points
The number of polygons that can be formed are
(0, 1) and (2, 3): Zero polygon(4, 5), (6, 7), and (8, 9): One polygon (triangle)(3, 5) and the x-axis: One polygon (triangle)How to determine the number of polygonsPoints (0, 1) and (2, 3)
The set of points (0, 1) and (2, 3) cannot form a polygon as they are collinear (i.e., lie on the same straight line) and do not enclose an area.
Points (4, 5), (6, 7), and (8, 9)
These are three different points.
Because a triangle has three sides, one triangle can be formed by the set of points (4,5), (6,7), and (8,9). i.e. One polygon
Points (3, 5) and the x-axis.
One polygon can be formed by the set of points (3,5) and the x-axis: a triangle with vertices at (3,5), (0,0), and (6,0).
How to determine the areas and the perimetersPolygon (4)
This is a rectangle with the dimension:
6 units by 5 units
So, we have
Perimeter = 2 * (6 + 5) = 22 units
Area = 6 * 5 = 30 squared units
Polygon (5)
This is a composite figure with the following dimensions:
Square of 4 units
Rectangle: 6 units by 2 units
So, we have
Perimeter = 4 * 4 + 2 * (6 + 2) = 32 units
Area = 4 * 4 + 6 * 2 = 28 squared units
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In the given figure, ABC is a right angled triangle. Find sina, cosa, tana, sintheta, costheta and tantheta.
Got all the values of alpha but how can I get the values of theta?
The exact values of the trigonometric functions associated with the geometric system are:
sin α = √161 / 15, cos α = 8 / 15, tan α = √161 / 8, sin θ = 8 / 15, cos θ = √161 / 15, tan θ = 8 / √161
How to determine the exact values of trigonometric functionsIn this problem we find a geometric system formed by two similar right triangles. Two triangles are similar if both have congruent internal angles and sides are not congruent though proportional. Then, we find the following relationships:
∠ B ≅ ∠ E
ED = √(EC² - DC²)
And the exact trigonometric functions are listed below:
sin α = DE / EC
cos α = DC / EC
tan α = DE / DC
sin θ = DC / EC
cos θ = DE / EC
tan θ = DC / DE
If we know that DC = 8 cm and EC = 15 cm, then the exact values of the trigonometric functions are:
DE = √[(15 cm)² - (8 cm)²]
DE = √161
sin α = √161 / 15
cos α = 8 / 15
tan α = √161 / 8
sin θ = 8 / 15
cos θ = √161 / 15
tan θ = 8 / √161
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During an experiment, the temperature of a mixture changes from 12.25°F to 15.6°F.
What is the percent of increase in the temperature of the mixture?
(ROUND TO NEAREST
HUNDREDTH )
Answer:
The percentage increase is 21.4% increase
Given Data
Initial temperature = 12 1/4°F = 49/4 = 12.25°F
Final Temperature = 15 3/5°F = 78/5 = 15.6°F
We know that the expression for percentage increase is given as
Percent Increase = Increase/Final *100
Percent Increase = 15.6-12.25/15.6 *100
Percent Increase = 3.35/15.6 *100
Percent Increase = 0.214 *100
Percent Increase = 21.4%
Hence there is a 21.4% increase
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