Given:
The table of values.
To find:
The rate of change.
Solution:
From the given table it is clear that the rate of change is constant and function passes through two points (-1,5) and (2,-4). So, the rate of change is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{-4-5}{2-(-1)}[/tex]
[tex]m=\dfrac{-9}{2+1}[/tex]
[tex]m=\dfrac{-9}{3}[/tex]
[tex]m=-3[/tex]
So, the rate of change is -3.
Therefore, the correct option is C.
Jasmine spent $2.03 buying party favors for her birthday party. She bought less than ten
identical favors. How much was each one and how many did she buy?
BE SURE YOU ANSWER BOTH QUESTIONS!!
Hint: Each favor costs the same amount
Given the total spent on buying favors = 2.03 $
Let the number of favors she bought = x
let the amount of each favor = y
She bought favors for less than 10 be
x < 10
The amount she spent can be written as
x * y = 2.03
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Determine whether function for the situation would have a discrete or continuous graph.
20. The cost of a given number of handbags
19. Amount of juice in a jug over time.
21. Area of a field based on length 22. Tires in a number of cars.
The cost of a given number of handbags - Discrete
Amount of juice in a jug over time - Continuous
Area of a field based on length - Continuous
Tires in a number of cars -Discrete
A discrete function as its name suggests has distinct or separate values against one value. That is, one at a time values are in a discrete function. So its domain and image sets will have discrete values.
A continuous function has continuous values within intervals. Its domain will be intervals having a continuous range and images will also be in a continuous range.
We need to check if the following will have a discrete or a continuous graph:
1. The cost of a given number of handbags.
This is a discrete function as the cost and number of handbags will have discrete values. So it will have a discrete graph.
2. Amount of juice in a jug over time
This is a continuous function. The variables here are the amount of juice and time in which time, clearly, is a continuous variable. So it will have continuous values in an interval. So the amount of juice can also be measured continuously. So the graph will be continuous.
3. Area of a field based on length
Here the length can take continuous values in an interval. So the area can also be measured continuously giving a continuous graph here.
4. Tires in a number of cars.
Number of tires and number of cars both will take only discrete values. So it can only give a discrete graph.
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3 different two-digit numbers are selected and multiplied together. the probability that the product is even is where are relatively prime. what is
Probability of an even number product as requested = 7/10 = .7 = 70%
The probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4), and 3 odd digits, (1,3,5).
Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 even digits = 1*1 = 1. there are thus 6+1 = 7 distinct 2 digit products that result in even numbers from among 10 possible 2 digit products.
Probability of an even number product as requested = 7/10 = .7 = 70%
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which one of the following pairs of numbers contains like fractions ?
A. 6/7 and 60/79
B.4/8 and 12/16
C. 1/2 and 3/2
D. 5/4 and 4/5
Answer:
C
Step-by-step explanation:
the mean time that a certain model of light bulb will last is hours, with a standard deviation equal to hours.
The mean time that a certain model of light bulb will last is hours is 900 hours and the required percentage of bulbs is 2.5%
Here,
x is the time that a certain bulb will last.
(in houses.
μ=900 hours;
σ=1200 hours.
The standardized value for a light bulbs lasts 1100 hours, is,
z=x-μ/σ
z=1100-900/100=2
We know, for a bell-shaped distance, Approximately,
68% of the data falls within M-uσ;
By rule (ii), here,
95% of the data falls within (μ-2σ,u+2σ)
(900-2x100,900+2x100)
(700,1100)
So (100-95=5%) falls outside of (700,1100)
Since, the distance is symmetric (i.e. bell-shaped); we find the percentage of bulbs that is expected lo lase longer than 1100 hours, is
5/2% =2.5%
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.What does the standard deviation means?Image result for standard deviationA standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.To learn more about standard deviation visit:
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25 POINTS AND BRAINLIEST
NO EXPLANATION NEEDED JUST ANSWER
Answer: 13
Step-by-step explanation:
Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 3 : 2 She needs to make 40 litres of punch for a party. How much of each ingredient does she need?
Fruit juice = litres
Lemonade = litres [4]
Answer:
Fruit Juice = 24 litres
Lemonade = 16 litres
Step-by-step explanation:
So, the ratio: [tex]3:2[/tex] really just means: "for every every 3 litres of fruit punch, there is 2 litres of lemonade.
Or in other words, every 3 litres of fruit punch, the entire mixture of both fruit punch and lemonade will be 5 litres, since there is 3 litres and 2 litres.
So dividing the 40 litres, by this 5 litres, we get 8. So we know there will be "8" of 3 litres of fruit punch, and "8" of 2 litres of lemonade.
Thus there will be 24 litres of fruit punch, and 16 litres of lemonade.
A group of workers can plant at a rate of 34 acres per day.
How many acres can they plant in 2 days?
Answer:
68 acres per day
Step-by-step explanation:
34 acres per day × 2 days = x
34 × 2 = x
x = 68 acres per day
Hope this helps!
Answer:
68 acres
Step-by-step explanation:
34 acres= 1 day
x=2 days
x=68 acres
they can plant 68 in 2 days
Three fair 6-sided dice are thrown. What is the probability that the three numbers
rolled are three consecutive numbers, in some order?
The probability that the 3 outcome of numbers obtained are three consecutive numbers is 1/9.
What is defined as the probability?The probability of an event occurring is calculated by dividing the amount of favourable outcomes by total number of possible outcomes.
Now, as per the given question;
The first number must be either 1, 2, 3, or 4, with a probability; 4/6 = 2/3. The second number must be one higher, which occurs with a probability of 1/6. The third number must then be one greater than the second, which occurs with a probability of 1/6. Therefore the answer to the question about the order; (2/3)×(1/6)×(1/6) = 2/108.To address your point, if the three numbers seem to be different, there are 3! = 6 different orders in which they could have been placed.
As a result, the solution to the question;
= (2/3)×(1/6)×(1/6)×6
= (2/3)(1/6)
= 1/9.
Therefore, the probability of getting the three consecutive number is 1/9.
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a body’s weight varies inversely with the square of its distance from the center of the earth; if a chicken weighs 12 pounds when it is 5,000 miles from the earth’s center, how much will the chicken weigh when it is 10,000 miles from the earth’s center ?
The chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
There are two types of proportions.
1) Direct Proportion - shows the direct relationship between two quantities. It can be represented by the equation y = kx. As one quantity increases, the other quantity also increase.
2) Inverse Proportion - describes the indirect relationship between two quantities. It can be represented by the equation y = k/x. As one quantity increases, the other quantity decreases.
According to the problem, a body’s weight varies inversely with the square of its distance from the center of the earth.
y = k/x
let y = a body's weight
x = square of its distance from the center of the earth
Solving for the proportionality constant, k.
y = k/x
12 = k / (5000^2)
k = 12 x 25, 000, 000
k = 300, 000, 000
The equation for the relationship in the problem can now be represented by:
y = 300,000,000/x
where
y = a body's weight
x = square of its distance from the center of the earth
Evaluating the new equation where x = square of 10,000:
y = 300,000,000/x
y = 300,000,00/(100,000,000)
y = 3
Hence, the chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
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in a small library there are 5 nonfiction books for every 9 fiction book there are 130 nonfiction book
The number of fiction books in the library are 324, as found by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given: There are 5 non-fiction books for every 9 fiction books. Total 130 non-fiction books are there in the library.
To find: number of fiction books.
Finding: By unitary method, For every 5 non-fiction books, there are 9 fiction books.
For every 1 non-fiction book, there are 9/5 fiction books.
For every 130 non-fiction books, there are 9/5 × 130 = 324 fiction books.
Hence, The number of fiction books in the library are 324, as found by unitary method.
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(COMPLETE QUESTION:in a small library there are 5 nonfiction books for every 9 fiction book there are 130 nonfiction book. How many fiction books are there in the library?)
Number 4, please help
Hi there!
From the given conditions:
[tex]1→1 ⟹1 \times 1 = 1[/tex]
[tex]5→7⟹ 5 \times 7 = 35[/tex]
[tex]8→11 ⟹8 \times 11 = 88[/tex]
[tex]9→4 ⟹9 \times 4 = 36[/tex]
[tex]10 →2 ⟹10 \times 2 = 20[/tex]
Sum = 180, no. of customers = 25
[tex]average = \frac{sum}{no.ofcustomers} [/tex]
[tex] ⟹ \frac{180}{25} = 7.2[/tex]
Therefore, on average, the satisfaction rating of the landscape company was 7.2
Point C has coordinates (24, 18).
Point D has coordinates (10, 28).
What are the coordinates of the midpoint of line CD?
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Hence , the coordinate of midpoint of line CD is (17 , 23) .
Midpoint refers to some extent that's within the middle of the road connexion 2 points. A centre could be a purpose lying between 2 points and is within the middle of the road connexion the 2 points. If a line is drawn connexion the 2 points, then the centre could be a purpose at the center of the road and is equal from the 2 points.The centre formula is outlined for the points within the coordinate axes. Let (x₁), (y₁) and (x₂), (y₂) be the endpoints of a line section is given by M = (x₁ + x₂ /2 , y₁ + y₂ /2 ).We have given two coordinate C (24, 18) and D(10, 28) .
Let M be the midpoint of line CD having coordinate (x,y) .
Using midpoint formula , we get
[tex](x,y) = ( \frac{24+10}{2} ,\frac{18+28}{2} )\\\\(x,y) =( \frac{34}{2} ,\frac{46}{2} )\\\\(x,y) =( 17 ,23 )[/tex]
On comparing , we get coordinate (17 , 23) .
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Write the expression of a polynomial given the roots:
x = √6
The expression is [tex](x - \sqrt{6} )^{n}[/tex] , n = 1, 2, 3....
Polynomial expression:
A polynomial expression is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
It is given that
x = √6
x - √6 = 0
[tex](x - \sqrt{6} )^{n}[/tex] where n = 1,2,3.....
Therefore the expression of the polynomial given roots is [tex](x - \sqrt{6} )^{n}[/tex] .
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A company is designing a new cylindrical water bottle. The volume of the bottle will be 179 cm to the power of 3. The height of the water bottle is 8.3 cm. What is the radius of the water bottle? Use 3.14 for [tex]\pi[/tex].
Answer: r=2.62 cm
Step-by-step explanation:
Cylinder Volume: V=πhr^2
179=π(8.3)r^2
179=8.3*3.14*r^2
179=26.062r^2
r^2=6.87
r=2.62 cm
9. A(n)
is the average of a set of values such that the values hold different levels of importance.
A mean is the average of set of values such that the values hold different levels of importance.
What is mean?
Mean can be defined as the mathematical average of a group or set of numbers.
It is also the most common value in a collection of numbers.
The formula for determining the mean of a group of data is;
Mean = sum of terms/number of terms
An important and distinct property of the mean is the inclusion of every value in a given set of data of the calculation.
Also, both discrete and continuous data are used in determining the mean.
Thus, a mean is the average of set of values such that the values hold different levels of importance.
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Solve.
-2x+3y-z = -2
3x+y=4
-2y + 2z = 4
Answer:
(x,y,z) = (1,1,4)
Step-by-step explanation:
[tex]A: -2x + 3y - z = -2\\B: 3x+y=4\\C: -2y+2z=4\\[/tex]
[tex]Solve\ B\ for\ y: y = 4-3x\\Solve\ C\ for\ z: 2z=4+2y\ \ z=2+y\\Substitute\ B_y\ into\ C_z: z = 2+4-3x\ \ z=6-3x\\Substitute\ B_{y\ in\ terms\ of\ x}\ and C_{z\ in\ terms\ of\ x} into A: \\-2x + 3(4-3x) - (6-3x) = -2\\Distribute: -2x + 12-9x-6+3x=-2\\Combine\ Like\ Terms\ on\ either\ side: -2x-9x+3x=-2-12+6\\Factor\ out\ x\ and\ perform\ arithmetic\ on\ right: x(-2-9+3) = -8\\Perform\ Arithmetic: x(-8)=-8\\Divide:x=1[/tex]
[tex]Plug\ x\ into\ B_y: y=4-3(1)\\Perform\ Arithmetic: y=1\\Plug\ y\ into\ C_z: z=2+2(1)\\Perform\ Arithmetic: z=4[/tex]
Write an equation of the line in point-slope form that passes through the
given points. (4, 2) and (1, 6)
The equation of line that passes through the given points in point-slope form is y - 2 = -4/3( x - 4 ).
What is the equation of line that passes through the given points?Given the data in the question;
Point A(4, 2)
x₁ = 4y₁ = 2Point B(1, 6)
x₂ = 1y₂ = 6First, we determine the slope of the line.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 6 - 2 )/( 1 - 4 )
Slope m = ( 4 )/( -3)
Slope m = -4/3
Next, plug the slope -4/3 and point (4,2) into the point slope formula y - y₁ = m( x - x₁ ) and simplify.
y - y₁ = m( x - x₁ )
y - 2 = -4/3( x - 4 )
Therefore, the equation of line that passes through the given points in point-slope form is y - 2 = -4/3( x - 4 ).
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James sold simi rare Pokemon cards for 11$ each after he paid 200 for a booster box. The equation y = 11x - 200 shows the profit James will make from selling Pokemon cards, where x is the number of Pokemon cards and y is the profit he makes. If James sales more than 17 cards but less than 26 cards, what would the range of the situation be
the range of possible profits, in dollars, is given by the inequality:
-13 < y < 86
what would the range of the situation be?We know that the linear equation:
y = 11*x - 200
Shows the profit for selling x pokemon cards.
We know that he sells more than 17 and less than 26, then:
17 < x < 26
Then the minimum profit is:
y = 11*17 - 200 = -13
The maximum profit is:
y = 11*26 - 200 = 86
We conclude that the range of possible profits, in dollars, is:
-13 < y < 86
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PLEASE ANSWER THIS FAST Lesson 16 Practice Problems
1. For each triangle, find the measure of the missing angle.
Figure 3
20°
Figure 1
28
729
128%
'В
K
D
Figure 4
Figure 2 122⁰ 389
7
2. Is there a triangle with two right angles? Explain your reasoning.
56°
89%
What is the factored form of this expression?
Answer:
The factored form of 27t^3 - 36t^2 - 12t + 16 is:
(3t - 4) (3t+2) (3t - 2)
9. What is the domain of this function: ((0, 1), (2, 3), (-1, 3), (4, 5)}?
a. (0, 2, -1, 4)
b.
(0, 2)
c. (3)
d.
(1,3,5)
e. None of the above
Check the picture below.
Answer:
g
Step-by-step explanation:
Ashley is participating in a 5-day cross-country biking challenge. She biked for 48, 58, 68, and 50 miles on the first four days. How many miles does she need to
bike on the last day so that her average (mean) is 54 miles per day?
Answer:
46 miles
Step-by-step explanation:
First, set up an equation:
(48 + 58 + 68 + 50 + x) ÷ 5 = 54
Add the miles in the parentheses:
(48 + 58 + 68 + 50 + x) ÷ 5 = 54
48 + 58 + 68 + 50 = 224
(224 + x) ÷ 5 = 54
Multiply by 5 on each side:
[(224 + x) ÷ 5] × 5 = (54) × 5
(224 + x) = 270
Subtract 224 on each side to isolate x:
(224 + x) - 224 = (270) - 224
x = 46 miles
Hope this helps! I'd appreciate brainliest but if not that's fine!
In the figure, =m∠16x° and =m∠2−x8°.
(a) The equation to find x is : (6x)° + (x-8)° = 90°
(b) The degree measure of the complementary angles, m∠1 = 84° and m∠2 = 6°
What are complementary angles?Complementary angles are two angles whose sum is 90 degree.
Given are two complementary angles ∠1 and ∠2 whose measures are given m∠1 = (6x)° and m∠2 =(x-8)°
From the given figure we can see that sum of ∠1 and ∠2 is 90°, which means they are complementary.
m∠1 + m∠2 = 90°
And (6x)° + (x-8)° = 90°
Or 6x +x-8 = 90
7x = 90+8
7x= 98
x= 98/7 =14
Then m∠1 = (6x)° = (6*14)° = 84° and m∠2 = (x-8)° = (14-8)° = 6°
Therefore, The equation to find x is (6x)° + (x-8)° = 90° and measure of the complementary angles, m∠1 = 84° and m∠2 = 6°
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reflection about common monomial factor plss pa hel po
Answer:
Step-by-step explanation:
A common monomial factor is a single-term polynomial that divides into each term of a given polynomial evenly.
point M(6.8) was rotated counterclockwise to M'(-8,6). Describe the degrees of the rotation and write an algebraic rule to represent the rotation
The point is rotated 90° counterclockwise. The algebraic rule for rotation of 90° counterclockwise is (x, y)→(-y, x) .
Rotation of a graph is a transformation where the graph is rotated about a fixed point.
Rotations can happen both clockwise and counterclockwise.To put the graph back in its original position, turn it 360 degrees.The rotated figure's side length is unchanged by rotation.When a polygon is rotated about a fixed point, the modified figure is equal to the original figure.The given point is M(6,8) . The figure is rotated counterclockwise to get the image M'(-8,6).
Now we have to calculate the degree of rotation of the point.
M(6,8) lies in the first quadrant and M'(-8,6) lies in the second quadrant.
Therefore the rotation is less than 180° .
Now from the figure attached below we can say that the figure was rotated 90°
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What is 4 60/72 written as a decimal?
OA) 0.483
OB) 0.83
OC) 4.83
OD) 0.483
Answer:
C. 4.83
Step-by-step explanation:
60/72 = 0.83333333
so the answer is 4.8333333
Can anyone help me for brainiest 50 points
Answer: Explanation
Step-by-step explanation:
For #1 first we have to convert all of the fractions to have the same denominator by finding the LCM(Least Common Multiple), which is 60. 1/4=15/60, 1/5=12/60, and 1/3=20/60. Then you add them up and get 47/60. You take that fraction and multiply it by 850 to get about 665.83, which is the estimate.
As for #2, I don't know sorry, I think you can just draw different lengthed lines to show the different distances traveled.
For #3 its 850/9 which is about 94.44
#4 I would recommend stopping through the night because they have about 184 miles to go and since they would only complete about 94 of those miles and would still have to drive tomorrow, they might as well do it all tomorrow.
A gopher has dug holes in opposite corners of a rectangular yard. one length of the yard is 7.3 meters and the distance between the gopher's holes is 9.8 meters. how wide is the yard?
The yard is 6 meters wide by use of Pythagoras crossing the diagonal to create a rectangular triangle.
What is Pythagoras?The formula for the Pythagoras theorem is written as c2 = a2 + b2, where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, to generate a Pythagoras triangle, the Pythagoras equation can be used to any triangle with one angle that is precisely 90 degrees.
d² = l² + w²
d = 10
l = 8
Solving for w, the width is
w² = d² - l²
So, we can replace the values with d = 10 and l = 8, to get
w² = 10² - 8²
w² = 100 - 64
w² = 36
w = 6
Hence the width of the yard is 6.
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You are solving a measurement problem where the numbers 4.5160 x 10−3, 2.09 x 107, and 5.8 x 103 are multiplied. how many significant digits should the product have?
The product should have a 1 significant digit.
Scientific notationsWhen multiplying Scientific notations, the significant figure of the final result must be approximated to the scientific notation that has the least decimal place.
From the question given, if we 4.5160 x 10^3, 2.09 x 107, and 5.8 x 10^3 are multiplied, the product should have 1 significant digits since the least decimal value that occur in question is 1dp
Hence the product should have a 1 significant digit.
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