Answer:
x = 3/4 x 21
Step-by-step explanation:
Answer:
I believe it is #2:
x = 3/4 × 21.
A pathologist knows that 14.9% of all deaths are attributable to myocardial infarctions (a type of heart disease). (Either you have myocardial infarction or you don’t)
a. Find the mean and standard deviation for the number of such deaths that will occur in typical region with 5000 deaths.
b. In one region, 5000 death certificates are examined, and it is found that 896 deaths were attributable to myocardial infarction. Is there cause for concern? Why or why not?
Answer:
a) The mean number is 745 and the standard deviation is 25.18.
b) 896 deaths is a significantly high number, which means that there is cause for concern.
Step-by-step explanation:
For each death, there are only two possible outcomes. Either it is attributable to myocardial infarctions, or it is not. The probability of a death being attributable to myocardial infarctions is independent of other deaths. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
A value X is significantly high is:
[tex]X > E(X) + 2\sqrt{V(X)}[/tex]
In this problem:
[tex]p = 0.149, n = 5000[/tex]
a. Find the mean and standard deviation for the number of such deaths that will occur in typical region with 5000 deaths.
[tex]E(X) = np = 5000*0.149 = 745[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5000*0.149*0.851} = 25.18[/tex]
The mean number is 745 and the standard deviation is 25.18.
b. In one region, 5000 death certificates are examined, and it is found that 896 deaths were attributable to myocardial infarction. Is there cause for concern? Why or why not?
Is 896 a significantly high number?
[tex]E(X) + 2\sqrt{V(X)} = 745 + 2*25.18 = 795.36[/tex]
895 > 795.36
896 deaths is a significantly high number, which means that there is cause for concern.
An isocost line Question 7 options: 1) represents the combinations of w and K that cost the firm the same amount of money. 2) represents the combinations of K and L that cost the firm the same amount of money. 3) has a convex shape. 4) represents the combinations of r and w that cost the firm the same amount of money.
Answer:
represents the combinations of K and L that cost the firm the same amount of money.
Step-by-step explanation:
Isocost is a graph representing factor inputs ( labour, capital ) ; which costs firm the same level of total production expenditure.
The curve is analogous to consumer's budget line - product combinations costing same to consumers. So, it is likely a straight line downward sloping curve also. Such because : factors are inversely related, given same total cost; and the slope is constant = price ratios of the two factor inputs.
An isocost line represents combinations of capital (K) and labor (L) that cost the same total amount for a firm. Option 2 correctly defines an isocost line. The line's slope is determined by the prices of labor and capital.
Explanation:An Isocost Line in Economics
An isocost line is a graphical representation in economics that shows all the combinations of inputs that cost a firm the same total amount. When referring to factors of production such as capital (K) and labor (L), the isocost line equation could be expressed as rK + wL = constant, where 'r' represents the cost of capital and 'w' represents the wage or cost of labor. If we are looking at the firm's input choices to minimize cost for a given level of output, the isocost line will have a negative slope that represents the trade-off between the quantities of capital and labor the firm can use subject to its budget constraint.
The correct option to describe an isocost line from the given choices would be 2) represents the combinations of K and L that cost the firm the same amount of money. This means that all input combinations lying on the same isocost line have the same total cost (TC). Also, the slope of the isocost line is determined by the ratio of the prices of the factors, i.e., -w/r.
In economic analysis, firms are often visualized as combining inputs of labor and capital in the most cost-efficient manner to produce a certain level of output, as shown by the isoquant curves. By finding the point where an isocost line is just tangent to an isoquant, a firm achieves the least-cost combination of labor and capital for producing the given quantity of output.
A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about 90m3 /hr at 6 am and increases steadily to about 280m3 / hr at 9 am. Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am.
Best estimate = __________________m3
Answer:
V = 3 * (70 + 230) / 2
V = 450 m^3
Step-by-step explanation:
Based on the two measured rates, and assuming that the rate of increase was uniform, the volume would be the average, hourly volumetric flow rate, multiplied by number of hours, or
Solve for a:
9+2a = -3-4a
Answer:
a=-2
Step-by-step explanation:
Let me know if you need the steps tho.
Debby, Ella and Unique invest $10,000 each into an oil company. Debby owns 2000 $1 common stocks, Ella owns 1000 of 5% $50 preferred stocks and Unique owns 2000 of 4% $20 preferred stocks. If the company pays $0.80 per share to common stockholders in the current year. Who will have the greatest return in the current year?
Answer:
Ella has the greatest return in the current year.
Step-by-step explanation:
Debby would receive $0.80 for each of her 2000 common stock in the oil company,hence Debby's return on investment in the current year is $1600($0.80*2000)
Besides,Ella's return on the stock investment in the current year is computed thus:
Ella's return= 5%*1000*$50=$2,500
In addition,Unique's dollar return on the investment is computed as follows:
Unique's return on investment=4%*2000*$20=$1,600
From the above computations,Ella seems to have the highest return in the current year of $2,500 whereas the two others managed to have $1600 return each
A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The expected value of LaTeX: \bar{x}x ¯ is
a.8
b.75
c.800
d.None of these alternatives is correct.
Answer:
b.75
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem:
Mean of the population is 75.
By the Central Limit Theorem,
The mean of the sample, [tex]\bar{x}[/tex], is expected to be also 75.
So the correct answer is:
b.75
This question is based on the concept of statistics.Therefore, the expected value of mean is 75. Hence, the correct option is (b) 75.
Given:
Mean = 75
Standard deviation = 8
Random sample size = 800
According to the question,
By using the central limit theorem states that,
This theorem states that, the distribution of sample means approximate normal distribution as the sample size gets larger.
Hence, for a skewed variable, the central limit theorem can also be applied, as long as n is at least 30.
By the above theorem, the mean of the sample, is expected to be also 75.
Therefore, the expected value of mean is 75. Hence, the correct option is (b) 75.
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Artemisia moves to a new house and she is "fifty-percent sure" that the phone number is 2537267. To verify this. she uses the house phone to dial 2537267. she obtains a busy signal. and concludes that this is indeed the correct number. Assuming that the probability of a typical seven-digit phone number being busy at any given time is 1%, what is the probability that Artemisia’s conclusion was correct?
Without additional information, it's not possible to calculate the exact probability that Artemisia's conclusion is correct using conditional probability and Bayes' theorem.
Explanation:Calculating the Probability of Artemisia's Conclusion Being CorrectTo calculate the probability that Artemisia's conclusion about her new phone number being correct, we need to use the concept of conditional probability. Since she is 50% sure that the number is correct, and given the probability of any seven-digit phone number being busy is 1%, we need to consider both pieces of information. We can use Bayes' theorem to update the probability of Artemisia's belief in light of the new evidence (getting a busy signal).
However, we need additional information to accurately calculate this. Specifically, we would need to know the probability that Artemisia would get a busy signal if the number was incorrect. Without this information, we cannot provide a definitive answer to the student's question.
Purchasing A regional survey found that 70% of all families who indicated an intention to buy a new car bought a new car within 3 months, that 10% of families who did not indicate an intention to buy a new car bought one within 3 months, and that 22% indicated an intention to buy a new car. If a family chosen at random bought a car, find the probability that the family had not previously indicated an intention to buy a car. Harshbarger, Ronald J.. Mathematical Applications for the Management, Life, and Social Sciences (p. 479). Cengage Learning. Kindle Edition.
Answer:
If a family chosen at random bought a car, we need to find the probability that the family had not previously indicated an intention to buy a car = P(I'|B) = 0.3362
Step-by-step explanation:
Let the event that a family that intends to buy a car be I
Let the event that a family does not intend to buy a car be I'
Let the event that a family buys a car in those 3 months be B
Let the event that a family does not buy a car in those 3 months be B'
Given,
P(B|I) = 0.70
P(B|I') = 0.10
P(I) = 0.22
P(I') = 1 - P(I) = 1 - 0.22 = 0.78
If a family chosen at random bought a car, we need to find the probability that the family had not previously indicated an intention to buy a car = P(I'|B)
The conditional probability P(A|B), is given as
P(A|B) = P(A n B) ÷ P(B)
So,
P(B|I) = P(B n I) ÷ P(I)
P(B n I) = P(B|I) × P(I) = 0.70 × 0.22 = 0.154
P(B|I') = P(B n I') ÷ P(I')
P(B n I') = P(B|I') × P(I') = 0.10 × 0.78 = 0.078
P(B) = P(B n I) + P(B n I') = 0.154 + 0.078 = 0.232
P(B') = 1 - 0.232 = 0.768
P(I'|B) = P(B n I') ÷ P(B)
= 0.078 ÷ 0.232 = 0.3362
Hope this Helps!!!
Using Bayes' theorem, the probability that a randomly chosen family bought a car without previously indicating the intention is 33.62%.
Calculating the Probability of a Randomly Selected Family Buying a Car Without Prior Intent
To find the probability that a family chosen at random bought a car without previously indicating an intention to buy a car, we need to use conditional probability and Bayes' theorem.
Given the survey results, 70% of families who intended to buy a new car did so within 3 months, and 10% of families without prior intent also bought a car.
Let I be the event that a family indicated an intention to buy a car, and N be the event that a family did not indicate an intention.
We're given that P(I) = 0.22 and P(N) = 0.78 (since there are only two options, either they intended or did not, which sums to 1).
Let C be the event that a family bought a car. We want to find P(N|C), which is the probability a family had not previously indicated the intention to buy a car given that they bought a car.
We use Bayes' theorem:
P(N|C) = [P(C|N) × P(N)] / [P(C|I) × P(I) + P(C|N) × P(N)]
Substitute the values we know:
P(N|C) = [(0.10) ×(0.78)] / [(0.70) × (0.22) + (0.10) × (0.78)]
Calculate the probability:
P(N|C) = (0.078) / (0.154 + 0.078)
P(N|C) = 0.078 / 0.232
P(N|C) = 0.3362 or 33.62%
Therefore, there's a 33.62% chance that a family chosen at random bought a car without having indicated an intention
Seating played eight basketball games this season. Her point total for each game were 8,14,4,7,6,14,4 and 7. What was the mean number of points she scored per game?
Answer:
The mean number of points she scored per game was 8.
Step-by-step explanation:
The mean number of points scored per game is the sum of total points scored divided by the number of games played:
Her point total for each game were 8,14,4,7,6,14,4 and 7.
This means that there were 8 total games.
She scored 8+14+4+7+6+14+4+7 = 64 total points
64/8 = 8
The mean number of points she scored per game was 8.
look at the picture down bellow.
Answer:
A
Step-by-step explanation:
3) 4 friends equally share 1/3 of a pan of brownies. How much of the whole pan of brownies does each friend get?
Answer:
The answer will be 1/12 of
Step-by-step explanation:
The basketball team scored a total of 79 points last game. They made 35 shots, including 2-point shots and 3-point shots. How many 2-point shots did they make? How many 3-point shots did they make?
The number of 2-point shots and the number of 3-point shots if, The basketball team scored a total of 79 points last game, They made 35 shots, including 2-point shots and 3-point shots, are 26 and 9 respectively.
What is the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
The basketball team scored a total of 79 points last game,
They made 35 shots, including 2-point shots and 3-point shots,
Write the equation as shown below,
x + y = 35
2x + 3y = 79
Here, x is the number of 2-point shots and y is the number of 3-point shots,
Solve the equation by elimination method,
y = 9, x = 35 - 9 = 26
Thus, the number of 2-point shots is 26 and the number of 3-point shots is 9.
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a force can never act by itself?
Answer:
true
Step-by-step explanation:
An object can never act on itself. Forces related to Newton's third law apply to different bodies, therefore they cannot cancel each other out. For example, the reaction to Earth's gravitational pull on the Moon is the Moon's pull on Earth.
the price of a dvd is 24.00 plus 8% sales tax.what is the sales tax on this dvd in dollar and cents
Answer: 1.92
Step-by-step explanation:
24.00 x 0.08
1.92
$1.92
LAST ONE! -maybe hehe
A rectangular table is 5 1/4 feet by 3 3/4 feet. What is the area of the table?
I am wondering if I have the right answer (see my work below):
Equation = A = l x w
A = (3 x5) + (3 x 1/4) + (3/4 x 5) + (3/4 x 1/4)
15 + 3/4 + 15/4 + 3/16
Area = 19 11/16 feet2
Answer:
19 11/16 or 315/16
Steps:
Turn the fractions into an improper fraction and then multiply straight across
5 1/4 = 21/4
3 3/4 = 15/4
(21/4)*(15/4)= 315/16= 19 11/16
Yes you got it right :)
Answer:
Step-by-step explanation:
Area = Length times Width
5 1/4 times 3 3/4
5 x 4 + 1 = 21
21/4
3 x 4 +3 = 15
15/4
21/4 x 15/4 = 315 / 16 or 19 11/16 ft^2
Which product is shown on this number line
Answer:
Would ypu plz show us the number line so at least i could answer the question
Write an equation for the line parallel to the line −24x+8y=9 through the point (0,0).
Answer: y=3x
Step-by-step explanation:
Answer:
–3x + y = 0
Step-by-step explanation:
line through (0,0) always has zero constant, divide by 8 for simplicity we get –3x + y = 0
An algebra 2 test has 6 multiple choice questions with four
choices with one correct answer each. If we just randomly guess
on each of the 6 questions, what is the probability that you get
exactly 3 questions correct?
Answer:
1/64
Step-by-step explanation:
Each of the questions has 4 choices, making the chance to get the correct answer 1/4. So, to get 3 questions correct, you can use 1/4^3 to find the probability. So, the answer is 1/64.
The probability of exactly 3 questions are correct is, [tex]\frac{1}{64}[/tex]
Probability :In test every question has four choices with one correct answer.
So that, the probability of one question is correct [tex]=\frac{1}{4}[/tex]
the probability of exactly 3 questions are correct is,
[tex]P(E)=\frac{1}{4}*\frac{1}{4}*\frac{1}{4}\\ \\ P(E)=\frac{1}{64}[/tex]
The probability of exactly 3 questions are correct is, [tex]\frac{1}{64}[/tex]
Learn more about the probability here:
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Two 95 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and J. One confidence interval, I400, will be constructed using samples of size 400 from each of R and J, and the other confidence interval, I100, will be constructed using samples of size 100 from each of R and J.When all other things remain the same, which of the following describes the relationship between the two confidence intervals?a)The width of i400 will be 4 times the width of i100.b) The width of i400 will be 2 times the width of i100c)The width of i400 will be equal to the width of i100.d)The width of I400 will be 1/2 times the width of I100e)The width of I400 will be 1/4 times the width of I100.
Answer:
The correct option is (d).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two means with same sample size is:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm CV\times SD\times \sqrt{\frac{2}{n}}[/tex]
The width of the interval is:
[tex]\text{Width}=2\times CV\times SD\times \sqrt{\frac{2}{n}}[/tex]
From the formula of the width of the confidence interval it can be seen that the sample size is inversely related to the width.
That is, if the sample size is increased the width of the interval will be decreased and if the sample size is decreased the width of the interval will be increased.
It is provided that two confidence intervals are constructed for the difference between the means of two populations R and J.
One One confidence interval, will be constructed using samples of size 400 from each of R and J.
And the other confidence interval, will be constructed using samples of size 100 from each of R and J.
Determine the formula of width for both sample sizes as follows:
[tex]\text{Width}_{1}=2\times CV\times SD\times \sqrt{\frac{2}{400}}\\[/tex]
[tex]=2\times CV\times SD\times \frac{\sqrt{2}}{20}[/tex]
[tex]\text{Width}_{2}=2\times CV\times SD\times \sqrt{\frac{2}{100}}\\[/tex]
[tex]=2\times CV\times SD\times \frac{\sqrt{2}}{10}[/tex]
So, the width of I₄₀₀ is half times the width of I₁₀₀.
The correct option is (d).
Answer:
D
Step-by-step explanation:
I got 18/18
If x=1/3 and y=2/5, evaluate xy+×
Answer:
7/15
Step-by-step explanation:
We assume you want xy+x. Put the numbers where the variables are and do the arithmetic.
(1/3)(2/5) +(1/3) = 2/15 + 5/15 = 7/15
. A hawk drops its prey from a certain height above the ground.The height, h metres, of the prey can be modelled by h = 4 + 11 t – 3t2, where t is the time in seconds after it is dropped by the hawk. At what height above the ground does the hawk drop its prey? At what time will the pray fall onto the ground?
Answer:
The hawk drops the prey from a height of 4 meters.
The prey reaches the ground 4 seconds after.
Step-by-step explanation:
Notice that the equation gives you information about the height of the prey at any time counting from the moment the hawk drops it. Therefore, if we want to find the height at which the hawk drops the prey, we just need to evaluate the expression for time = zero (the starting time). SUch gives as the answer to the first question:
[tex]h=4+11t-3t^2\\h=4+11\,(0)-3\,(0)^2\\h=4\, \,meters[/tex]
Now, in order to find the time at which the prey reaches the ground, we want "h" to be zero (height zero), and solve for "t".
Notice that this gives a quadratic equation that can be solved using the quadratic formula:
[tex]h=4+11t-3t^2\\0=4+11t-3t^2\\-3t^2+11t+4=0\\t=\frac{-11+-\sqrt{11^2-4\,(-3)(4)} }{2\,(-3)} \\t=\frac{-11+-\sqrt{121+48} }{-6} \\t=\frac{-11+-13 }{-6} \\t= 4\,\,and \,\, t=-\frac{1}{3}[/tex]
Since negative times will not make sense, we select the positive 4 (4 seconds)
List all the permutations of three objects m comma l comma and n taken two at a time without repetition. What is 3 Upper P 2? List all the permutations of three objects m comma l comma and n taken two at a time without repetition. Choose the correct answer below.
The number of permutations of 3 objects taken 2 at a time without repetition is 3. The permutations are ml, mn, lm, ln, nm, nl.
Explanation:The number of permutations of three objects taken two at a time without repetition is given by the formula 3P2 = 3!/(3-2)! = 3!/1! = 3.
The permutations of three objects (m, l, and n) taken two at a time without repetition are:
mlmnlmlnnmnl
In the lab tab in the data file, there is data on the IQs for first graders at a university lab school. a. Calcualte a point estimate of the mean value of IQ for the population of first graders at this school. What estimator did you use? b. Calculate a point estimate of the IW value that separates the lowert 50% of all such students from the highest 50% of students. c. Calculate a 99% confidence interval for the population mean. What sampling distribution did you use? Why? d. Test the hypothesis that this population of first graders is not smarter nor less smart than the wider population (which has average IQ equal to 100).
Answer:
a. 113.72
b. 115
c. 107, 120
d. 100
Step-by-step explanation:
Hypothesis is seen as an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true. In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review.
Sampling distribition can be seen as the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
Please go to attachment for the detailed analysis.
[tex]7 {}^{ - 1 } \div 7 {}^{2} [/tex]
Answer:
1/343
Step-by-step explanation:
[tex]\dfrac{7^{-1}}{7^2}=7^{-1-2}=7^{-3}=\dfrac{1}{7^3}=\boxed{\dfrac{1}{343}}[/tex]
__
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
point
1. Challa drank 6,500 mL of water before her soccer game. She drank the
water out of 1 liter bottles. How many bottles of water did she drink? Hint: 1
liter= 1000 ml
Answer:
6.5 bottles
Step-by-step explanation:
convert liters to ml 1 bottle= 1000ml
divide how much she drank by 1000ml
6500÷1000=6.5
If the warehouse is 10 feet tall what could the side lengths of the floor be
Answer:
exactly I need help with this one to
A right triangle has legs measuring 18 in. and 26 in. What is the length of the hypotenuse? Round to the nearest tenth. A) 18.8 in. B) 31.6 in. C) 44.0 in. D) 100.0 in.
Answer:
a
Step-by-step explanation:
The dingram shows a spinner innde up of a picce of card in the shape of a regular pentagon, with a toothpick pushed through its ceuter. The five triangles are mambered from I to 5. Each time. the spner is spin atil it lands on one of the five edges of the pentagon. The spinener is spun five tinmes. Use the binomial probability formula to enleulate the probability of at most three 4'sThe ratio of boys to girts at birth in Singapore is quite high at 1.09:1 What proportion of Singapore families with exactly 6 children will have at least 3 boys? (ignore the probability of multiple births) what is the answer?
Answer:
a) [tex]P(X \leq 3) = 0.99328[/tex]
b) 0.6957
Step-by-step explanation:
Let X represent the number of 4's when n = 5 independent spins
each has a probability of 0.2 (i.e p = 0.2)
This notation is represented as:
X [tex]\approx[/tex] Binomial (n = 5, p = 0.2)
Probability of [tex]x[/tex] number of 4's is:
[tex]P(X=x)= (\left \ n \atop x \right) p^x (1-p)^{(n-x)}[/tex]
here; [tex](\left \ n \atop x \right)[/tex] is the combinatorial expression
[tex](\left \ n \atop x \right)[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]
[tex]P(X \leq3), n =5 , p = 0.2[/tex]
[tex]P(X \leq3) = 1-P(X > 3)[/tex]
So; let's first find:
[tex]P(X > 3)[/tex]
[tex]= P(3 <X \leq 5) \\ \\ = P(4 <X \leq 5) \\ \\ = P (X = 4, 5) \\ \\ = P (X=4)+P(X = 5 ) \ \ \ (disjoint \ events)[/tex]
[tex]P(X = 4) =( \left \ {{5} \atop {4}} \right. ) (0.2)^4 (1-0.2)^1 \\ \\ P(X = 4) = 5(0.2)^4(0.8)^1 \\ \\ P(X = 4) = 0.0064[/tex]
[tex]P(X = 5) =( \left \ {{5} \atop {5}} \right. ) (0.2)^5 (1-0.2)^0 \\ \\ P(X = 5) = 5(0.2)^5(0.8)^0 \\ \\ P(X = 5) = 0.00032[/tex]
[tex]P (X=4)+P(X = 5 ) \\ \\ = 0.0064 + 0.00032 = 0.006720 \\ \\ \approx 0.007[/tex]
[tex]P(X > 3 ) = 0.00672 \\ \\ P(X \leq 3) = 1- P(X > = 3 ) \\ \\ =1 - 0.00672 \\ \\ = 0.99328[/tex]
[tex]P(X \leq 3) = 0.99328[/tex]
b)
Given that:
The ratio of boys to girls at birth in Singapore is quite high at 1.09:1
What proportion of Singapore families with exactly 6 children will have at least 3 boys?
Probability of having a boy = [tex]\frac{1.09}{1+1.09}[/tex] = 0.5215
Binomial Problem with n = 6
P(3<= x <=6) = 1 - P(0<= x <=2)
= 1 - binomial (6,0.5215,2)
= 0.6957
What is the area of this triangle? *
2 points
Captionless Image
13 square meters
45 square meters
40 square meters
20 square meters
Answer:
20m squared
Step-by-step explanation:
The formula for working the area os a triangle is
base x height/2
5x8=40
40/2= 20
hope it helps