Consider the function as representing the value of an ounce of palladium in U.S. dollars as a function of the time t in days.†
R(t) = 240 + 30t^3; t = 1
Find the average rate of change of R(t) over the time intervals [t, t + h], where t is as indicated and h = 1, 0.1, and 0.01 days. (Use smaller values of h to check your estimates. Round your answers to one decimal place.)
The average rate of change of R(t) over the time intervals [t, t + h] , where t is as indicated and h = 1, 0.1, and 0.01 are 210,100 and 100.
What is Differentiation?
Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilising only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.
Given function : R(t) = 240 + 30t^3
R'(t) = 90 t²
So, the average rate of change of R(t) is 90 t² .
Now, over the time interval [t, t + h], it will be as follows:
we know that, f'(t) = {f(t+h) - f(t)} / h
So, when h = 1, f'(1) = {f(1+1) - f(1)} / 1
= f(2) - f(1)
= 480 - 270 = 210
when h = 0.1 , f'(1) = {f(1+0.1) - f(1)} / 0.1
= {f(1.1) - f(1)} / 0.1
= (280 - 270) / 0.1 = 100
when h = 0.01 , f'(1) = {f(1+0.01) - f(1)} / 0.01
= {f(1.01) - f(1)} /0.01
= (271 - 270) / 0.01 = 100
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question 6
help me asap
The approximate length of arc CB is given as follows:
14.17 cm.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:
C = 6.28r.
The radius for this problem is given as follows:
r = 7 cm.
The angle relative to arc CB is given as follows:
2 x 58º = 116º.
As an entire circumference has an angle of 360º, the approximate length of arc CB is obtained as follows:
116/360 x 6.28 x 7 = 14.17 cm.
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To estimate the percentage of a state's voters who support the current governor for reelection, three newspapers each survey a simple random sample of voters. Each paper calculates the percentage of voters in its sample who support the governor and uses that as an estimate for the population parameter. Here are the results:
Answer:
No OK so A. is the correct answer I think
Nayeli is going to an amusement park. The price of admission into the park is $40,
and once she is inside the park, she will have to pay $2 for every ride she rides on.
How much money would Nayeli have to pay in total if she goes on 9 rides? How much
would she have to pay if she goes on r rides?
Answer:
Step-by-step explanation:
The total cost for Nayeli to enter the amusement park is $40. If she goes on 9 rides, the cost for the rides would be 9 * $2 = $18. Therefore, the total cost for Nayeli to enter the park and go on 9 rides would be $40 + $18 = $58.
To find the total cost if she goes on r rides, we can use the formula:
Total cost = $40 + r * $2
So, if Nayeli goes on r rides, she would have to pay $40 + r * $2 in total.
To calculate the total cost, multiply the number of rides by the cost per ride and add it to the admission price.
To calculate the total amount Nayeli would have to pay if she goes on 9 rides, we need to first calculate the cost of admission. The admission price is $40. Then, we multiply the number of rides (9) by the cost per ride ($2) and add it to the admission price to get the total cost.
Total cost = Admission price + (Number of rides x Cost per ride) = $40 + (9 x $2) = $40 + $18 = $58.
If Nayeli goes on 'r' rides, we can use the same formula to calculate the total cost. The total cost would be the admission price ($40) plus the product of the number of rides ('r') and the cost per ride ($2). Total cost = $40 + (r x $2) = $40 + $2r.
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At the super market every can of tomatoes weighs at least 15ounces
The inequality representing the situation is w >= 15, where w represents the weight of a can of tomatoes and the inequality states that it must be greater than or equal to 15 ounces.
The inequality that represents the situation is w >= 15, where w represents the weight of a can of tomatoes. This inequality states that the weight of a can of tomatoes is greater than or equal to 15 ounces, meaning that every can of tomatoes weighs at least 15 ounces.
This inequality represents a constraint or a condition on the weight of a can of tomatoes. In mathematical terms, the inequality w >= 15 says that the value of w, which represents the weight of a can of tomatoes, must be greater than or equal to 15 ounces. Any value that satisfies this inequality is considered a valid solution for the weight of a can of tomatoes. For example, 15 ounces, 16 ounces, 17 ounces, and so on are all valid weights for a can of tomatoes that meet the requirement of weighing at least 15 ounces.
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The complete question is:
At a supermarket, Each tomato can in a store weighs at least 15 ounces.
Let w stand in for the can of tomatoes' weight.
Which inequality best captures the circumstances?
[tex]w < 15 w < 15 W > 15 w > 15[/tex]
URGENT URGENT
Pls this is needed urgently
1.) Common ailments of senior citizens are arthritis, arteriosclerosis and loss of hearing. A survey of 200 senior citizens found that 70 had arthritis, 60 had arteriosclerosis, 80 had loss of hearing, 35 had arthritis and arteriosclerosis, 33 had arthritis and loss of hearing, 31 had arteriosclerosis and loss of hearing and 15 had all three. How many of the senior citizens in the survey had; (1). none of these ailments, (f), arthritis but neither of the other two ailments, (iii), exactly one of these ailments, (iv). arteriosclerosis and loss of hearing but not arthritis, (v). arteriosclerosis or loss of hearing but not arthritis, (vi). exactly two of these ailments?
(i) none of these ailments, 26
(ii) arthritis but neither of the other two ailments, 17
(iii) exactly one of these ailments, 102
(iv) arteriosclerosis and loss of hearing but not arthritis, 16
We can use a Venn diagram to solve this problem.
Let A, B, and C represent the events of having arthritis, arteriosclerosis, and loss of hearing, respectively. Then, the given information can be represented as:
A = 70
B = 60
C = 80
A ∩ B = 35
A ∩ C = 33
B ∩ C = 31
A ∩ B ∩ C = 15
Using these values, we can find the answers to the questions:
(i) The number of senior citizens with none of these ailments is the complement of the union of A, B, and C. That is:
n(A ∪ B ∪ C)' = n(S) - n(A ∪ B ∪ C)
= 200 - (70 + 60 + 80 - 35 - 33 - 31 + 15)
= 26
Therefore, 26 senior citizens had none of these ailments.
(ii) The number of senior citizens with arthritis but neither of the other two ailments is:
n(A) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)' = 70 - 35 - 33 + 15
= 17
Therefore, 17 senior citizens had arthritis but neither of the other two ailments.
(iii) The number of senior citizens with exactly one of these ailments is the sum of the complements of the intersections of the events. That is:
n(A' ∩ B ∩ C') + n(A ∩ B' ∩ C') + n(A' ∩ B' ∩ C) = (200 - 60 - 31 - 15 - 33) + (200 - 70 - 31 - 15 - 33) + (200 - 70 - 60 - 15 - 35) = 102
Therefore, 102 senior citizens had exactly one of these ailments.
(iv) The number of senior citizens with arteriosclerosis and loss of hearing but not arthritis is:
n(B ∩ C) - n(A ∩ B ∩ C) = 31 - 15 = 16
Therefore, 16 senior citizens had arteriosclerosis and loss of hearing but not arthritis.
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FIRST 2 PEOPLE TO ANSWER GET POINTS AND BRAINLIEST!!!
Answer: $44.04
Step-by-step explanation: Add up all the prices 13.75+15.85+11.95 which is 41.55. Now times 41.55 by 6% which is 2.493. Now add the total and the tax. 41.55 + 2.493 = $44.04 as the final total.
Please help Find the sum of each infinite sum
18, 2, 2/9, ...
the sum of each infinite geometric series sum is 36
Why is this process known as geometric progression?If the ratio between any two consecutive terms in a series of numbers is always the same, the progression is said to be geometric. The ratio of any two successive terms in the sequence (common difference) must be the same for the sequence 2, 4, 8, or 16 to be a general prime.
How can you calculate the infinite sum?S = a/1-r is a general formula for calculating the sum of an infinite geometric series, where s stands for the sum, a1 is the series first term, and r is the common ratio.
a = first term = 18
r = common ratio = 1/2
sum of Geometric progression
r< 1
S∞ = a/(1-r)
S∞ = 18/(1-1/2) =36
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a scratch off lottery ticket can be purchased for $2. there are multiple prize options, shown along with the probability, in the table below. what is the expected win (or loss) for this lottery ticket? round your answer to the nearest cent. do not round until your final answer.
a result of -$2.00, indicating that, on average, you will lose $2.00 when buying this lottery ticket.
Lose (-$2.00)
The expected win (or loss) for this lottery ticket is -$2.00.
The expected win (or loss) for this lottery ticket is calculated by multiplying the prize amount by the probability of winning and then subtracting the cost of the ticket.
($50 x 0.1%) - $2 = -$2.00
The expected win (or loss) for this lottery ticket is calculated by multiplying the prize amount of $50 by the probability of 0.1% (or 0.001) of winning and then subtracting the cost of the ticket, which is $2. This gives us a result of -$2.00, indicating that, on average, you will lose $2.00 when buying this lottery ticket.
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before using census data, researchers need to consider the timeliness of the data. group startstrue or falsetrue, unselectedfalse, unselected
The statement "Before using census data, researchers need to consider the timeliness of the data." is true because census data is only accurate and useful when it is up to date.
The United States Census Bureau updates the data every ten years, so the most recent data will be from 2010. Additionally, researchers should be aware of any changes to the census information over time and make sure they are using the most up-to-date version. Furthermore, researchers need to understand the scope of the census data and what it is designed to measure.
The United States Census covers the entire population of the United States, but it is important to know the specific topics covered by each census and what population groups are included. Finally, researchers should be aware of how the census data is collected and the potential for error or bias in the data.
If the data is outdated, it could lead to inaccurate results or conclusions. Therefore, researchers must consider the timeliness of the data before using it in any research project.
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The complete question is:
True or False: Before using census data, researchers need to consider the timeliness of the data.
Question 6: What are the vertex and range of y = |x - 2 + 1? *
Answer:
Step-by-step explanation:
The vertex of the equation y = |x - 2 + 1| is (2, 1). The range of the equation depends on the value of x. When x < 2, the equation becomes y = -x + 1, which gives us a line with a slope of -1 that intersects the y-axis at (0,1) and has a minimum value of 1. When x >= 2, the equation becomes y = x - 1, which gives us a line with a slope of 1 that intersects the y-axis at (0,-1) and has no minimum value. Therefore, the range of the equation y = |x - 2 + 1| is [1, infinity).
Find the diameter with of
Circumference 31.4ft
The diameter of a circle is 10 feet.
What is circumference of a circle?The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.
Given that, the circumference of a circle is 31.4 ft.
We know that, circumference of a circle is 2πr
Now, 2πr=31.4
2×3.14×r=31.4
6.28r=31.4
r=31.4/6.28
r=5 feet
Then, diameter=2×radius =10 feet
Therefore, the diameter is 10 feet.
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Use the following data set to answer the question.
(54, 45, 48, 51, 53, 44, 52}
Which statements about the data set are true? Select all that apply.
Based on the given data set, the following statements are true:
The standard deviation is approximately 3.7. The interquartile range is 8.Why are the other statements false?The other statements are false because:
There is one outlier, which is 54. This is determined using the rule that any data point that falls more than 1.5 times the interquartile range (IQR) below the first quartile (Q1) or above the third quartile (Q3) is considered an outlier. In this case, Q1 is 46 and Q3 is 52, so any value less than 39.0 or greater than 59.0 would be considered an outlier. Since 54 falls within this range, it is not an outlier. The standard deviation is not approximately 49.6. This value is too high for the given data set, which has a range of only 10 values.Lastly, The interquartile range is not 10. As calculated above, Q1 is 46 and Q3 is 52, so the IQR is 52-46=6.
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See transcribed text below
Use the following data set to answer the question.
(54, 45, 48, 51, 53, 44, 52}
Which statements about the data set are true? Select all that apply.
The standard deviation is approximately 3.7.
The interquartile range is 10.
There are no outliers.
The outlier is 54.
The standard deviation is approximately 49.6.
The interquartile range is 8.
The advertised price of a plasma tv is n99990 including vat at 5%. If the government raises vat to 8%, calculate the new price of the tv. (to the nearest 10 naira)
The price of new Tv is 107,990 including VAT .The percentage increase in price of tv is 8% in rate.
The current price of the plasma TV including VAT at 5% is 99,990 naira.
If the government raises VAT to 8%, the new price of the TV including VAT can be calculated as follows:
New price = current price * (1 + new VAT rate)
New price = 99,990 * (1 + 0.08)
New price = 107,992.2
Rounding the new price to the nearest 10 naira gives: 107,990 naira.
The increase in price of the TV can be calculated as follows:
Price increase = new price - current price
Price increase = 107,990 - 99,990
Price increase = 8,000
The percentage increase in price of the TV can be calculated as follows:
Percentage increase = (price increase / current price) * 100%
Percentage increase = (8,000 / 99,990) * 100%
Percentage increase = 8.0%
Therefore, the new price of the TV including VAT at 8% is 107,990 naira, and there is a 8.0% increase in price.
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____The given question is incomplete, the complete question is given below:
The advertised price of a plasma tv is 99,990 naira including vat at 5%. If the government raises vat to 8%,calculate the new price of the tv ,(to the nearest 10 naira) what is the percentage increase in price of the tv?
the median should often be used to describe: select one: a. normal distributions. b. skewed distributions. c. large distributions. d. percentages.
The median should be used to describe a normal or skewed distribution, as it is a better measure of the central tendency than the mean for these types of distributions.
The median is a better measure of the central tendency than the mean when describing a normal or skewed distribution. A normal distribution is a symmetrical distribution of data in which values are evenly spread around the mean. A skewed distribution is when one side of the distribution is longer than the other, with the mean being pulled away from the center. The median is the most appropriate measure of central tendency for both normal and skewed distributions because the mean can be distorted by outliers and extremes in the data. The median is the midpoint in the data and provides a better representation of the middle of the distribution, which can be useful in interpreting the data. Using the median to describe a large distribution or percentage is not as common as it is better to use the mean or mode for these types of distributions.
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On the first night of Rosh Hashanah, David cuts 5 apples into slices and gives 3/8 of an apple to each of his guests. He has 2 apples left over. How many guests does david have? Let g equal the number of guests David has. Write an equation that represents the situation.
Based on the information provided, the number of guests was 8 guests and the equation to represent this situation is 3/8 x + 2 = 5.
How to calculate the number of guests?The first step to get to know the number of guests is to write an equation, this will help us discover the number of x or guests. To write the equation, let's include the variable and values given:
3/8 x + 2 = 5
Now, let's solve this equation:
0.375x + 2 = 5
x = 5 -2/ 0.375
x = 3 / 0.375
x = 8 guests
Based on the above, it can be concluded that the number of guests, in this case, was 8.
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Which quantity is unknown?
the number of guest
_____________________________________
Write an equation that represents the situation.
3/8g + 2 = 5
_____________________________________
How many guests does David have?
g = 8
observations are drawn from a bell-shaped distribution with a mean of 110 and a standard deviation of 4. a. approximately what percentage of the observations fall between 98 and 122?
The empirical rule tells us that for a normal distribution with mean μ and standard deviation σ, approximately 99.7% of the observations fall between 98 and 122.
Since the distribution is bell-shaped, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of observations that fall within certain ranges.
According to the empirical rule, for a normal distribution with mean μ and standard deviation σ:
About 68% of the observations fall within one standard deviation of the mean, i.e., between μ - σ and μ + σ.
About 95% of the observations fall within two standard deviations of the mean, i.e., between μ - 2σ and μ + 2σ.
About 99.7% of the observations fall within three standard deviations of the mean, i.e., between μ - 3σ and μ + 3σ.
In this case, the mean is 110 and the standard deviation is 4. Therefore:
About 68% of the observations fall between 110 - 4 = 106 and 110 + 4 = 114.
About 95% of the observations fall between 110 - 2(4) = 102 and 110 + 2(4) = 118.
About 99.7% of the observations fall between 110 - 3(4) = 98 and 110 + 3(4) = 122.
So approximately 99.7% of the observations fall between 98 and 122.
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if you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?
If you were to graph a sine function from the data listed in the table the days since Jan 8 is an independent variable and amount of moon visible is dependent variable
Given that, we have to graph a sine function from the data listed in the table
From the table we can see that there a two types of variables, The days since the Jan 8 and the amount of moon visible
The independent variable is defined as the variables that does not depends on any other variables
The dependent variable is defined as the variables that depends on other variables
Here the days since the Jan 8 does not depends on any other variables, so it is an independent variable. similarly the amount of moon visible depends on the days since Jan 8 value, so it is a dependent variable
Therefore, the days since Jan 8 is an independent variable and amount of moon light visible is dependent variable
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The given question is incomplete, the complete question is :
if you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?
factorize this: 12x²y_6x²
The factored form of 12x²y - 6x² is 6x²(2y - 1).
How to factorise?The expression to be factorise is as follows: 12x²y - 6x².
Factorisation is the is defined as the breaking down of an entity . Factorisation simply implies we decompose the expression.
Therefore,
12x²y - 6x²
let's find the factors of 12x²y and 6x².
Hence, the factors are 6x²
12x²y - 6x² = 6x²(2y - 1)
Therefore, the factored form is 6x²(2y - 1)
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a bag contains red and white balls. the ratio of red to white balls is 3:4. if the bad contains 36 white balls then find the number of red balls?
Answer:
P (of red ball) = 1 - ( 310 + 25 ) = 1 - (3 + 410 ) = 1 - 710 = 10 - 710 P (of red ball) = 310 No. of black balls = 20total no. of balls 25 = 20total balls
Step-by-step explanation:therya goo
Answer:
48
Step-by-step explanation:
If the ratio is 3:4, we can just divide 35 by 3.
Then we get 12, and to get the red balls we can multiply by 4 because that is the ratio
4*12= 48
there are 48 red balls
Two different investment companies offer college savings plans, one at 8. 4% compounded continuously and the other at 8. 6% compounded quarterly. Which is the better investment?
The 8.4% compounded quarterly is the better investment because it gives a good return.
Compound interest is “interest-on-interest”, or the ability of a financial instrument to generate earnings on its earnings. Compound interest, can be calculated using the formula :
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
where A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
(i)S = P
S = P(1.0854) (1.0854)
AP(1) = 1.0846 - 1
AP(1)= 0.08546 or 8.546%
(ii)r = 0.084/4
AP(2) = (1 + 0.084/4)⁴ -1
AP(2) = 1.08688 - 1
AP(2) = 8.668%
The 8.4% compounded quarterly investment is therefore preferable.
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Nicole james and jenny shared one - third of pizza. What fraction of the the whole pizza did each of them receive
The fraction of pizza that each of them gets out of the whole pizza is 1/9.
What is meant by a fraction?
The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A piece or sector of any quantity is another name for the fraction. Some of the different types of fractions are:
proper fractions, improper fractions, mixed fractions and so on.
Given 1/3rd portion of the pizza is shared by Nicole, James and Jenny.
Let us are assuming they shared the 1/3rd portion equally among themselves.
Then,
1/3 pizza = 3 people
1 person = 1/(3*3) = 1/9
Therefore the fraction of pizza that each person gets out of the whole pizza is 1/9.
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what the hell is a plane
At a railway station, trains are either eastbound or westbound.
An eastbound train leaves the station every 25 minutes.
A westbound train leaves the station every 45 minutes.
An eastbound train and a westbound train both leave the station at 8 ar
When is the next time that two trains leave the station together?
If both bound trains leave together at 8, they will also start together at 11:45 the next time.
What is the LCM (least common multiple) of two numbers?The LCM of two numbers is the smallest possible number that is divisible by both of those two numbers. The prime factorization and the division methods are generally used to find the LCM.
An eastbound train leaves the station every 25 minutes whereas a westbound train leaves the station every 45 minutes.
These two types of trains will leave the station together if the time is divisible by both 25 and 45, that is, the LCM of them.
Find the LCM of 25 and 45 using the prime factorization method.
25=5×5
45=3×3×5
LCM(25,45)=3×3×5×5
=225
As 1 hour equals 60 minutes, it follows that 225 minutes equals 3 hours and 45 minutes.
If 3 hours 45 minutes is added to 8 hours, it will be 11 hours 45 minutes.
Therefore, the two trains leave the station together at 11 hours 45 minutes.
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simplify each expression. 3x + 7 + 4x - 2
Answer: 3x+7+4x-2
Step-by-step explanation: 3x+4=7x
7-2=5
so the answer should be 7x+5
Thiago used the 20% off coupon and paid $100. Yasmine used the $20 off coupon. How much did she pay and how do you know?
Answer:
I suppose she also paid $100 because a 20% off from Thiago could mean that the original price was 120.
Step-by-step explanation:
Anna runs 3/4 miles in 6 minutes, or 1/10 hour. Assuming she runs at a constant rate, what is her speed, in miles per hour?
Speed of Ana = 7.5miles/hour
Step-by-step explanation:
Given,
Ana runs 3/4 mile in 6 minutes.
To find,
The speed of Ana in miles per hour
Recall the formula,
Speed = distance travelled/time taken
60 minutes = 1 hour
Solution:
Distance traveled = 3/4 mile
Time taken = 6 minutes
Since 60 minutes = 1 hour, we have
1 minute =1/60 hour
6 minutes = 6/60 hour
=1/10 hour
Hence speed = distance travelled/time taken
= 3/4 / 1/10 miles/hour
= 15/2 miles/hour
= 7.5miles/hour
∴ Speed of Ana = 7.5miles/hour
- a gambler offers you to pay even odds if you get 9, 10 or 11 heads in 20 tosses. should you take the bet?
5. What is the experimental probability of selecting the name Alex? * O Option 1 O Option 3 406 = 27/35 10 טחת O Option 2 Option 4 23 25 10 points
The experimental probability of selecting the name Alex would be 40 % or 2 / 5
How to find experimental probability ?The experimental probability of selecting the name Alex can be found by the formula :
= Number of times Alex is drawn / Number of total draws x 100 %
Number of times Alex is drawn = 4 times
Number of total draws = 10 draws
The experimental probability of selecting Alex would therefore be :
= 4 / 10 x 100 %
= 0. 4 x 100 %
= 40 % or 2 / 5
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1. Find the area of the trapezoid. 14 mm 15 mm 36 mm A-270 mm² B- 375 mm² C- 750 mm² D- 3780 mm²
Answer:The answer is B
Step-by-step explanation:
The formal is A = a+b/2 time h
You just substitute the variables and get the answer
