The average rate of change of the function is 10
How to determine the average rate?The table of values is given as:
x= -1,0,1,2,3
y=1/10, 1/2, 5/2, 25/2, 125/2
The average rate of change is calculated using:
Rate = (y2 - y1)/(x2 - x1)
This gives
Rate = (25/2 - 5/2)/(2 - 1)
Evaluate the expression
Rate = 10
Hence, the average rate of change of the function is 10
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The average rate of change of the function is 10.
What is Average rate?
It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Here, given values are:
x= -1,0,1,2,3
y=1/10, 1/2, 5/2, 25/2, 125/2
The average rate of change is calculated using:
Rate = (y₂ - y₁)/(x₂ - x₁)
Rate = (25/2 - 5/2)/(2 - 1)
Rate = 10
Hence, the average rate of change of the function is 10
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Solve for x. Round your answer to the nearest tenth.
42
37
X=
units
Answer:
10
Step-by-step explanation:
That little square gives you a hint that it's an 90 degree angle/ acute angle First add 42 and 37 and you will get 79. Next subtract 79 from 90 and you will get 11. (5 or more, raise the score, for or less, let it rest.) 11 equals 10.
Numarical form:
47 + 37 = 79
90 - 79 = 11
11 = 10
Joe decided to track the temperature in his town for five consecutive days. On Monday, the temperature was 23°C. On Tuesday, it decreased by 9°C and then increased by 7°C on Wednesday. On Thursday, the temperature rose 4°C and then decreased by 5°C on Friday. What was the overall temperature change over those five days?
Using a subtraction operation, the overall temperature change over those five days that Joe tracked the temperature in his town was a decrease of 3°C.
How is the temperature change computed?The temperature change can be computed by determining the differences in temperature from one day to the next and summing the differences.
The temperature change can also be computed by finding the difference between the ending period's temperature and the beginning period's temperature.
Days Temperature Change
Monday 23°C 0
Tuesday 14°C (23 - 9) -9
Wednesday 21°C (14 + 7) +7
Thursday 25°C (21 + 4) +4
Friday 20°C (25 - 5) -5
Overall change = -3°C
= 20°C - 23°C = -3°C
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one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Select the closest answer. *
20 points
1. Find the surface area of a sphere with a radius of 4.2 centimeters.
A. 235.6 cm?
C. 121.4 cm
B. 310.3 cm
D. 221.7 cm
A
B
С
OD
Select the closest answer.
Answer:
D. 221.7 cm
Step-by-step explanation:
Surface area of a sphere is: \(SA=4\pi r^2\)
'r' - radius
We are given the radius of 4.2 centimetres.
\(SA=4\pi 4.2^2\\4 * \pi * 4.2^2\\\rightarrow 4.2^2 =17.64\\\text {Using 3.14 for pi: }\\4 * 3.14 *17.64\\12.56*17.64\\\boxed {221.5584}\)
221.5584 ≈ 221.6
The closest answer is Option D, therefore it should be the correct answer.
A truck is carrying
10
3
bushels of apples and
10
2
bushels of grapes. Each bushel of apples weighs 30 pounds and each bushel of grapes weighs 20 pounds. What is the total weight of the fruit?
A.
3,200 pounds
B.
32,000 pounds
C.
320,000 pounds
D.
32,000,000 pounds
Based on the given task content; the total weight of apples and grapes is 5,130 pounds
How to find total weight of fruitsTotal weight is the sum or addition of all the weight of all the fruits together.
Bushels of apples = 103Bushels of grapes = 102Weight of each bushel of apple = 30 poundsWeight of each bushel of grapes = 20 poundsTotal weight of the fruits = Bushels of apples(Weight of each bushel of apple) + Bushels of grapes(Weight of each bushel of grapes)
= 103(30) + 102(20)
= 3,090 + 2, 040
= 5,130 pounds
So therefore, the total weight of apples and grapes is 5,130 pounds.
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3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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if the area of a circle is 36.2 square inches, find the length of its radius. (use 3.14 for pi) round to the nearest tenth. group of answer choices
if the area of a circle is 36.2 square inches, the radius of the circle to the nearest tenth is 3.4 inches.
The area of a circle is 36.2 square inches and we have to determine the radius of the circle to the nearest tenth.
The formula of the area of the circle is given as:
Area of circle = πR², where R is the radius of the circle.
We are given, Area of the circle = 36.2 square inches
So, πR² = 36.2 square inches
Now, π = 3.14
3.14R² = 36.2 square inches
R² = 36.2/3.14
R² = 11.53
Taking square root on both sides
R = √11.53
R = 3.39 inches
R ≈ 3.4 inch (Rounded to the nearest tenth)
Hence, the radius of the circle to the nearest tenth is 3.4 inches.
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The HCF of three numbers is 8 and the sum of these numbers is 80. List the possible set of such three numbers.
Let's denote the three numbers A, B, and C.
Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.
Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.
Let's list the possible combinations:
(8, 16, 56): In this case, A = 8, B = 16, and C = 56. All three numbers are divisible by 8, and their sum is 8 + 16 + 56 = 80.(16, 8, 56): Here, A = 16, B = 8, and C = 56. Again, all three numbers are divisible by 8, and their sum is 16 + 8 + 56 = 80.(24, 8, 48): In this combination, A = 24, B = 8, and C = 48. All three numbers are divisible by 8, and their sum is 24 + 8 + 48 = 80.(8, 24, 48): Similarly, A = 8, B = 24, and C = 48. All three numbers are divisible by 8, and their sum is 8 + 24 + 48 = 80.These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).
What is the radius of a sphere with a volume of 32398 cm 3 ,to the nearest tenth of a centimeter?
The radius of a sphere with a volume of \(32398 cm^ 3\) ,to the nearest tenth of a centimeter is \(r=21.1cm\)
How can the radius of a sphere be calculated?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. A sphere is formally defined as a collection of points in three-dimensional space that are all located at the same distance, or r, from a given point.
The formula for the volume of a sphere is \(V = 4/3 \pi r^3\)
V = volume
r = radius
Given \(32398 cm^ 3\)
\(V = 4/3 \pi r^3\)
\(32398 = 4/3 \pi r^3\)
\(r^3 = \frac{ 32398 }{\frac{4\pi }{3} }\)
\(r = \sqrt[3]{9393.931}\)
\(r=21.1cm\)
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What is the product of -2r^5y^2 and 4ry^3
Answer:
-8r^6y^5.
Step-by-step explanation:
In order to find the product, we multiply the coefficients and then add the powers of the same variable.
Coefficient of -2r^5y^2: -2
Coefficient of 4ry^3: 4
Power of r: 5 + 1 = 6
Power of y: 2 + 3 = 5
Product: -2 * 4 = -8
r^6 * y^5 = -8r^6y^5
Therefore, the product of -2r^5y^2 and 4ry^3 is -8r^6y^5.
MA.7.DP.1.4
A group of friends has been given $800 to host a party. They must decide how much money
will be spent on food, drinks, paper products, music and decorations.
Part A. As a group, develop two options for the friends to choose from regarding how to
spend their money. Decide how much to spend in each area and create a circle
graph for each option to represent your choices.
Part B. Mikel presented the circle graph below with his recommendations on how to
spend the money. How much did he choose to spend on food and drinks? How
much did he choose to spend on music?
Party Spending Proposal
Mail
17%
Paper Products
Answer: $130 money did Brenda and Hazel have all together before buying decorations and snacks.
Here, we have,
You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.
Setup
Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...
(x/2 -58) : (x/2 -37) = 1 : 4
Solution
Cross-multiplying gives ...
4(x/2 -58) = (x/2 -37)
2x -232 = x/2 -37 . . . . . . eliminate parentheses
3/2x = 195 . . . . . . . . . . . . add 232-x/2
x = (2/3)(195) = 130 . . . . . multiply by 2/3
Brenda and Hazel had $130 altogether before their purchases.
Alternate solution
The difference in their spending is $58 -37 = $21.
This is the same as the difference in their final balances.
That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.
Their ending total is 1+4 = 5 ratio units, or $35.
The total they started with is $58 +37 +35 = $130.
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complete question:
Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?
Please help! Will give brainliest!
Step-by-step explanation:
\(\sqrt[3]{t^{2} } + 4\sqrt{t^{3} } \\=t^{\frac{2}{3} } + 4t^{\frac{3}{2} }\\\\then, \\u` = \frac{2}{3}t^{-\frac{1}{3}} + 6t^{\frac{1}{2} }\)
Refer to the illustration. Find b if a=8 and c= 10
Can you prove that the quadrilateral is a parallelogram based on the information given?
Answer:
No
Step-by-step explanation:
The photo provided doesn't necessarily prove that the diagonals bisect each other. It could be proven as a quadrilateral is the other line inside the shape had lines showing this as well.
Answer:the answer is no
Step-by-step explanation:
it dosent give enough info
Please help solve the problem in the picture
A bowl contains equal-sized gumdrops. If the bowl has 30 green gumdrops and 1 blue gumdrop, plot an X on the number line below which could represent the probability of randomly choosing a green gumdrop from the bowl.
Explain how you determined your answer.
Answer:
≈ 0.97
Step-by-step explanation:
Given that :
Number of green gum drops = 30
Number of Blue gum drops = 1
Total number of gum drops :
(Number of blue + number of green gum drops)
(30 + 1) = 31
Probability = Required outcome / Total possible outcomes
P(green gum drops) = number of green drops / total number of gum drops
P(green gum drops) = 30 / 31 = 0.967 ≈ 0.97
The point x will be drawn slightly to the right of the midpoint between the last two tick marks.
Two cylinders, a and b, each started with different amounts of water. The graph shows how the height of the water changed as the volume of water increased in each cylinder. Match the graphs of a and b to Cylinders P and Q. Explain your reasoning. height in centimeters b volume in milliliters P
To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.
Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.
The reasoning behind this is as follows:
Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.
Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.
In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.
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5.
8
10
р
9
2
1
65° 6
5 8 9
7
*
3
4
S
10/11
12/13
15
14/16
17/ 19
18
•
Answer:
What is this what grade are you in
Brand A has a box of 25 forks for 1.99 and Brand B has a box of 42 totals for 3.89. What is the unit price for each brand and what brand is a better buy based on unit price
Answer:
Brand A
Step-by-step explanation:
Brand A has a box of 25 forks for 1.99
Take the price per fork
1.99 /25 = .0796
.08 per fork
Brand B has a box of 42 totals for 3.89
3.89 / 42
.092319048
.09 per fork
7. Identify the axis of symmetry of the parabola.
y = -1
-8-6-4 P
-2/
X = 1
X = -1
y4
8
y = 1
6-
4-
2+
CO
+
4 68 X
Q
Answer:
The answer is y=-1 (answer is C).
A model train is in a 3 inches to 80 inches scale. If the model door is 4 inches how tall is the real train door?
Answer:
80
Step-by-step explanation:
I need help solving this thing.
Answer:
x=-3 y=-1
(-3,-1)
Step-by-step explanation:
-1(2x-7y=1)
-7x-7y=28
-2x+7y=-1
-9x=27
x=-3
-2*-3-7y=1
y=-1
helpppppppppppppppppppp...................................
Answer: Its quadrant 3
Step-by-step explanation:
Hope this helps!
Answer:
Quadrant 3
Step-by-step explanation:
Lets have an example
Lets say we are plotting the point (-4,-4)
so, we would go left on the x-axis, to -4. So we will be in either Quadrant 2 or Quadrant 3
Now we go down 4, so we end up in Quadrant 3
Hence, The answer is Quadrant 3
Hope this helps!^^
A survey of 800 randomly selected adults in a certain country found that 82% believed that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
a. Verify the Central Limit Theorem conditions.
b. Find a 95% confidence interval for the proportion of adults in the country who believe that
protecting the rights of those with unpopular views is a very important component of a strong
democracy.
c. Would a 90% confidence interval based on this sample be wider or narrower than the 95%
interval? Give a reason for your answer.
a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.
c) . A 90% confidence interval would be wider than the 95% interval
How to Verify the Central Limit Theorem conditions.To verify the Central Limit Theorem (CLT) conditions, we need to check the following:
1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.
2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.
3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.
Therefore, the Central Limit Theorem conditions are met.
b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:
CI = p ± z * √(p(1-p)/n)
where:
- p is the sample proportion (82% or 0.82 in decimal form).
- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.
- n is the sample size (800).
Calculating the confidence interval:
CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)
CI = 0.82 ± 1.96 * √(0.82*0.18/800)
CI = 0.82 ± 1.96 * √(0.1476/800)
CI = 0.82 ± 1.96 * √0.0001845
CI ≈ 0.82 ± 1.96 * 0.01358
CI ≈ 0.82 ± 0.0266
The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.
c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.
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What is the slope of a line graphed below?
Answer:
Undefined
Step-by-step explanation:
The slope of a horizontal line is zero. The slope of a vertical line is undefined.
Simplify 4(4a+5b-3)
On Monday, Eric planted a 3-centimeter-high tomato plant and a 5-centimeter-high tomato plant in his garden. The graph models the growth of
each plant since the day they were planted.
12
11
10
9
8
Height 74
of Plant 6-
(cm) 5
4
3
1
1
3
Days After Being Planted
How many days after being planted were the two plants the same height?
OA 2
B. 3
OC. 5
The option A that is 2 days after being planted, the two plants will of the same height( Where the two lines intersect in a graph).
How to know if the lines intersect in the graph of a function?
All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
And after solving both equations if the values of x and y satisfies both equations then they intersect at that values of x and y.
Now,
On Monday, Eric planted a 3-centimeter-high tomato plant and a 5-centimeter-high tomato plant in his garden.
The graph models the growth of each plant since the day they were planted.
The intersection of the two lines represents the days after being planted were the two plants the same height.
The answer is that 2 days after being planted, the two plants are the same height.
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The answer is that 2 days after being planted, the two plants are the same height.
How to know if a point lies in the graph of a function?
All the points (and only those points) which lie on the graph of the function satisfy its equation.Thus, if a point lies on the graph of a function, then it must also satisfy the function.On Monday, Eric planted a 3-centimeter-high tomato plant and a 5-centimeter-high tomato plant in his garden.The graph models the growth of each plant since the day they were planted.We need to find How many days after being planted were the two plants the same height.The intersection of the two lines represents the days after being planted were the two plants the same height.The answer is that 2 days after being planted, the two plants are the same height.
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(3, 5) is an example of a(n) ___. Three is the horizontal value and five is the vertical value.
Answer:
its ordered pair
Step-by-step explanation:
just got it right on flocab so hope this helped.
(3, 5) is an example of a(n) ordered pair. Three is the horizontal value and five is the vertical value. Option B is correct.
Given that,
(3, 5) is an example of a(n) ___. Three is the horizontal value and five is the vertical value. To determine the best fir for the blank given.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
here,
(3, 5). is an example of the ordered pair, which represents 3 as abscissa and 5 represents as ordinate, on the x and y axis respectively.
Thus, (3, 5) is an example of a(n) ordered pair. Three is the horizontal value and five is the vertical value. Option B is correct.
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A recent survey showed that exactly 38%
of people in a town buy the local
newspaper. There are 2450 people in the
town.
a) How many people in the town buy the
local newspaper?
b) How many people in the town do not
buy the local newspaper?
Answer:
a) .38 × 2,450 = 931 people buy the local newspaper.
b) 2,450 - 931 = 1,519 people do not buy the local newspaper.
What is the value of x?
Step-by-step explanation:
Given in the picture that,
2x + 2x + 2x + 2x + 2x = 11
So, by the problem,
=> 2x + 2x + 2x + 2x + 2x = 11
=> 10x = 11
\( => x = \frac{11}{10} or \: 1.1(ans)\)
Hence required value of x is 1.1 (Ans)