The data support the researcher's claim that the current ozone level is not at a normal level, at the 0.05 level of significance, concluded with the help of a one-sample t-test.
To test whether the current ozone level is significantly different from the normal level of 5.5 ppm, we can use a one-sample t-test.
The null hypothesis is that the mean ozone level is equal to 5.5 ppm:
H0: mu = 5.5
The alternative theory is that the average ozone level exceeds 5.5 ppm:
Ha: mu > 5.5
The significance threshold will be set at 0.05.
t = (x - mu) / (s / sqrt(n)) is the test statistic for a one-sample t-test.
where x is the sample mean, is the hypothesized population mean, s represents the sample standard deviation, and n represents the sample size.
When we substitute the provided values, we get:
t = (6.0 - 5.5) / (0.9 / sqrt(13)) = 1.936
Using a t-table with 12 degrees of freedom (n-1=13-1=12) and a significance level of 0.05, the critical value is 1.782. Since our calculated t-value (1.936) is greater than the critical value (1.782), we reject the null hypothesis.
Therefore, we can conclude that the data support the researcher's claim that the current ozone level is not at a normal level, at the 0.05 level of significance.
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luis has a pyramid shaped plant pot. it has a square base with a side length of 36 cm 36 cm36, start text, space, c, m, end text, and the height of the pot is 36 cm 36 cm36, start text, space, c, m, end text. s an upside down square-based pyramid with a base length of thirty-six centimeters and a height of thirty-six centimeters. an upside down square-based pyramid with a base length of thirty-six centimeters and a height of thirty-six centimeters. luis wants to fill the pot with soil so that the soil takes up 75 % 75u, percent of the pot's volume. how far up the pot will the soil reach? round to the nearest tenth.
The soil will reach about 27 cm up the pot when it fills 75% of the pot's volume.
To determine how far up the pot the soil will reach, we need to first find the volume of the pot, then find 75% of that volume, and finally calculate the height of soil in the pot.
Step 1: Calculate the volume of the pot
The volume of a pyramid can be calculated using the formula V = (1/3) * B * h,
where V is the volume, B is the area of the base, and h is the height.
Since the base is a square with a side length of 36 cm, the area of the base (B) is 36 cm * 36 cm = 1296 cm².
Now, plug the values into the formula:
V = (1/3) * 1296 cm² * 36 cm = 15552 cm³
Step 2: Calculate 75% of the pot's volume
75% of the pot's volume can be calculated as:
Soil volume = 15552 cm³ * 0.75 = 11664 cm³
Step 3: Calculate the height of the soil in the pot
To find the height of the soil, we can use the same formula for the volume of the pyramid, but we will solve for the height[tex](h_soil)[/tex] this time:
11664 cm³ = (1/3) * 1296 cm² * [tex]h_soil[/tex]
Solve for h_soil:
[tex]h_soil[/tex] = (11664 cm³ * 3) / 1296 cm² ≈ 27 cm.
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Carmen is trying to choose between two bike rental companies where h
is the number of hours rented and y
is the cost, in dollars. Company A charges a $30
fee and $2
for each hour rented, which can be represented by the equation y=2h + 30
. Company B charges a $10
fee and $4
for each hour rented, which can be represented by the equation y = 4h + 10
.
Select the coordinate below that represents the cost when renting from either company would be the same.
(10, 50)
(30, 50)
(50, 10)
(50, 30)
the coordinate that represents the cost when renting from either company would be the same is (10, 50). This means that if Carmen rents a bike for 10 hours, she would pay the same amount whether she rented from Company A or Company B.
How to determine the point?
To determine the point where the cost of renting a bike from Company A and Company B is the same, we need to find the values of h and y that satisfy the equations y = 2h + 30 and y = 4h + 10. We can solve for h by setting the two equations equal to each other:
2h + 30 = 4h + 10
Simplifying this equation, we get:
20 = 2h
h = 10
Now that we know h is 10, we can substitute that value into either equation to find y. Using the first equation:
y = 2h + 30 = 2(10) + 30 = 50
Therefore, the coordinate that represents the cost when renting from either company would be the same is (10, 50). This means that if Carmen rents a bike for 10 hours, she would pay the same amount whether she rented from Company A or Company B.
It's worth noting that as the number of hours rented increases, the difference in cost between the two companies becomes greater. For example, if Carmen rented a bike for 20 hours, the cost would be $70 from Company A and $90 from Company B. Therefore, it's important for Carmen to consider how long she plans to rent the bike for when deciding which company to rent from.
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The area of a rectangular room is 60m². If the length had been 25% less and breadth 4m more it would have been a square, find the length of the longest stick that can be put on the floor of the room.
Answer: Let's start by finding the dimensions of the original rectangular room.
We know that the area of the room is 60m², so we can write:
length x width = 60
We want to find the length and width of the original room, so let's call them "L" and "W", respectively. Then we can write:
L x W = 60
Now let's consider the modified room, where the length is 25% less and the width is 4m more. If the room is a square, that means the length and width are equal. Let's call this side length "S". Then we can write:
S x S = (L - 0.25L) x (W + 4)
Simplifying, we get:
S² = 0.75LW + 4(L - 0.25L)
Simplifying further, we get:
S² = 0.75LW + 3L
Now we can use the fact that LW = 60 to eliminate one variable. Substituting, we get:
S² = 45 + 3L
We want to find the length of the longest stick that can be put on the floor of the original room. This is the diagonal of the rectangle, which we can find using the Pythagorean theorem:
diagonal² = L² + W²
Substituting LW = 60, we get:
diagonal² = L² + (60/L)²
To maximize the diagonal, we can take the derivative of the right-hand side with respect to L and set it equal to zero:
d/dL (L² + (60/L)²) = 2L - 7200/L³ = 0
Solving for L, we get:
L³ = 3600
L = 15
Therefore, the length of the longest stick that can be put on the floor of the room is the diagonal, which is:
diagonal = sqrt(15² + (60/15)²) = sqrt(225 + 16) = sqrt(241) ≈ 15.52 meters
Step-by-step explanation:
Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you’ll find out. Consider ΔABC, whose vertices are A(2, 1), B(3, 3), and C(1, 6); let line segment AC represent the base of the triangle.
a. Find the equation of the line passing through B and perpendicular to AC
Type your response here:
b. Let the point of intersection of AC with the line you found in part a be point D. Find the coordinates of point D.
Type your response here:
c. Use the distance formula to find the length of the base and the height of ABC
Type your response here:
d. Find the area of ABC
Type your response here:
The line that is parallel to AC and passes through B has the equation y: 1/5x + 12/5.
What is the equation of the line?The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.
The benefit of expressing a linear equation in this way is that the values for m and b correspond to the slope and y-intercept, respectively.
This makes it easy to graph the line that the equation describes.
So, the slope of AC is:
6-1/1/2= 5/-1 = -5
The equation of line D, which passes through B and is perpendicular to AC, is given as y: mx + p.
Where p is the y value of the y-intercept point and m is the slope.
The fact that line D is perpendicular to line AC indicates that their slopes add up to one.
Therefore,
(−5) × m = −1
Now,
m = -1/-5 = 1/5
We discover that the D equation is:
Y: 1/5x + p
To complete the equation of D at this time, we still require the value of p.
B(3, 3)∈ D
3 = 1/5(3) + p
p = 3 - 3/5 = 12/5 = 2.4
Hence, equation D will be:
y: 1/5x + 12/5
Therefore, the line that is parallel to AC and passes through B has the equation y: 1/5x + 12/5.
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Correct question:
Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you’ll find out. Consider ΔABC, whose vertices are A(2, 1), B(3, 3), and C(1, 6); let line segment AC represent the base of the triangle.
Part A
Find the equation of the line passing through B and perpendicular to AC .
What is the surface area of a rectangular prism with a length of 5 cm, width of 6 cm, and a height of 7 cm?
The surface area of a rectangular prism can be found using the formula:
A = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
Substituting the given values, we get:
A = 2(5 cm)(6 cm) + 2(5 cm)(7 cm) + 2(6 cm)(7 cm)
A = 60 cm² + 70 cm² + 84 cm²
A = 214 cm²
Therefore, the surface area of the rectangular prism is 214 cm².
Write the word sentence as an equation.
Answer:
3 is greater than or equal to value a.
Step-by-step explanation:
HELP ME WITH THIS FIND ALL THESE ANSWERS HELP
The parts of the circle when named are listed below
Naming the parts of the circleAn inscribed angle is an angle between two chords
So, we have
inscribed angle = Angle GJI
A major arc is an arc with the greater central angle
So, we have
Major arc = AJG
Minor arc = GFH
Next, we have
GH = 55 degrees i.e angle at center = arc
GJI = 180 degrees i.e. semicircle
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Find the area of the figure below in square units.
Answer: 48.5 sq units
Step-by-step explanation:
7*8=56, 56-7.5= 48.5
suppose that a random sample of size 36 is to be selected from a population with mean 44 and standard deviation 8. what is the approximate probability that x will be more than .5 away from the population mean?
There is a 75.40% chance that the sample mean X will be more than 0.5 away from the population mean μ.
Let X be the random variable representing the sample mean of a random sample of size 36 selected from a population with mean μ=44 and standard deviation σ=8.
The Central Limit Theorem (CLT) states that, under certain conditions, the distribution of the sample mean X can be approximated by a normal distribution with mean μ and standard deviation σ/√(n), where n is the sample size. Since the sample size is 36, we can use this approximation.
The probability that X is more than 0.5 away from the population mean can be calculated as follows:
P(|X-μ| > 0.5) = P((X-μ)/ (σ/√(n)) > (0.5) / (σ/√(n))) + P((X-μ)/ (σ/√(n)) < (-0.5) / (σ/√(n)))
Using the standard normal distribution table, we can find the corresponding probabilities for each term on the right-hand side of the equation. We have:
P(Z > 0.3125) + P(Z < -0.3125)
where Z is a standard normal random variable with mean 0 and standard deviation 1.
Using the standard normal distribution table, we can find that P(Z > 0.3125) = 0.3770 and P(Z < -0.3125) = 0.3770.
Therefore, the approximate probability that X will be more than 0.5 away from the population mean is:
P(|X-μ| > 0.5) = 0.3770 + 0.3770 = 0.7540
In terms of percentage, we can rewrite it as,
P(|X-μ| > 0.5) = 0.7540*100 = 75.40%
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) let a1 be the event that the first marble is red and let a2 be the event that the second marble is red. are a1 and a2 independent? cs 70, spring 2023, hw 09 2 (b) what is the probability that rachel wins the game? (c) given that rachel wins the game, what is the probability that all of the marbles were red?
a) A and B are independent events.
b) The outcome of each game is independent of the other games so, Rachel's loss = p.
c) The probability of all marbles being red is 4
a) Given that a first marble is red and the second marble is also red, such that
P(1) = P(2) = 0.2, P(3) = P(5) = P(6) = 0.1 and P(4) = 0.3 and die is thrown two times. Also given that:
A1 = red
B1 = red.
So, P(A) = [P(1, 1) + P(2, 2) + P(3, 3) + P(4, 4) + P(5, 5) + P(6, 6)]
= P(1).P(1) + P(2).P(2) + P(3).P(3) + P(4).P(4) + P(5).P(5) + P(6).P(6)
= 0.2 x 0.2 + 0.2 x 0.2 + 0.1 x 0.1 + 0.3 x 0.3 + 0.1 x 0.1 + 0.1 x 0.1
= 0.04 + 0.04 + 0.01 + 0.09 + 0.01 + 0.01 = 0.20
Now, B = [(4, 6), (6, 4), (5, 5), (5, 6), (6, 5), (6, 6)]
P(B) = [P(4).P(6) + P(6).P(4) + P(5).P(5) + P(5).P(6) + P(6).P(5) + P(6).P(6)]
= 0.3 x 0.1 + 0.1 x 0.3 + 0.1 x 0.1 + 0.1 x 0.1 + 0.1 x 0.1 + 0.1 x 0.1
= 0.03 + 0.03 + 0.01 + 0.01 + 0.01 + 0.01 = 0.10
A and B both events will be independent if
P(A ⋂ B) = P(A).P(B) …. (i)
And, here (A ⋂ B) = {(5, 5), (6, 6)}
So, P(A ⋂ B) = P(5, 5) + P(6, 6) = P(5).P(5) + P(6).P(6)
= 0.1 x 0.1 + 0.1 x 0.1 = 0.02
From equation (i) we get,
0.02 = 0.20 x 0.10
0.02 = 0.02
Therefore, we can say that A and B are independent events.
b) We know that the outcome of each game is independent of the other games. Rachel's loss = p. As per the given information, the games in the series are unrelated, indicating the application of the probability multiplication principle.
c) The probability of all marbles being red is 4
Let a be the probability that the first player (ultimately) wins if the two players are tied in wins. Let b be the probability that she wins if she is 1 ahead. And let c be the probability she wins if she is 1 behind. We have the equations
a = rb + 1 - r x c
b = r + 1 - r x a
c = r x a
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there are 23 23 guests at your home for a dinner party. in how many ways could the guests arrange themselves on a four person couch?
There are 212520 ways by which guests arrange themselves on a four person coach.
What is Permutation?The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.
there are total 23 guests and they arranged themselves in 4 person coach,
so,
n = 23 and r = 4
npr = n!/(n-r)!
= 23!/(23-4)!
= 23!/19!
= 23x 22 x 21 x 20x 19!/19!
now cancel the factorial 19 from numerator as well as denominator
= 23x 22 x 21 x 20
= 212520
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(co 3) a process is normally distributed with a mean of 104 rotations per minute and a standard deviation of 8.2 rotations per minute. if a randomly selected minute has 118 rotations per minute, would the process be considered in control or out of control? g
Based on the calculated z-score of 17.07, and a corresponding p-value, the process would be considered out of control at the 0.05 significance level.
To determine whether the process is in control or out of control, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) is that the process is in control, and the alternative hypothesis (Ha) is that the process is out of control.
We can calculate the z-score as follows:
z = (x - μ) / (σ / sqrt(n))
where x is the observed value (118), μ is the mean (104), σ is the standard deviation (8.2), and n is the sample size (1).
Plugging in the values, we get:
z = (118 - 104) / (8.2 / sqrt(1)) = 17.07
The corresponding p-value for this z-score is virtually zero. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the process is out of control.
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Given sinx=725 and cosx=2425. What is ratio for tanx ?
The ratio for tanx is 7/24.
To find the ratio for tanx, we need to use the given values of sinx and cosx.
The formula for tanx is:
tanx = sinx / cosx
Given, sinx = 7/25 and cosx = 24/25.
Now, let's substitute these values in the formula:
tanx = (7/25) / (24/25)
To divide these fractions, multiply the first fraction by the reciprocal of the second fraction:
tanx = (7/25) * (25/24)
Now, simplify the fractions:
tanx = (7 * 25) / (25 * 24)
The 25 in the numerator and denominator will cancel out:
tanx = 7 / 24.
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Can anyone help me out on this please?
Simplifying rational expressions.
Answer:
A
Step-by-step explanation:
Cost for x shirts in a week (4x+150) divided by the shirts made in a week (x)
would be represented by A
Answer:
A is correct.
Step-by-step explanation:
The expression 4x + 150 represents the cost of manufacturing x shirts in a week. If x shirts are made in a week, the expression [tex]\frac{4x+150}{x}[/tex] (Answer A) represents the manufacturing cost per t-shirt (that's why we divide by x) where x shirts are made in a week (that's why we divide by just x, not 7x, because we're talking about 1 week, not 7 days)!
Alg 1 - 250 toothpick pyramid task
Write a function f(l) that determines the number of triangles in any given level of the pyramid.
f(l) =
pls help asapppp
Answer: The answer is 7
Step-by-step explanation:
an exam grade data for a statistics class has been observed to have a mean of 36.12 and standard deviation of 3.53. what is the probability that the exam scores are at least 37?
The probability that the exam scores are at least 37 is 0.4013 or 40.13%
The probability that the exam scores are at least 37 can be calculated using the normal distribution function. To calculate the probability, we first need to standardize the variable using the formula z = (x - μ) / σ, where x is the value of interest (in this case, x = 37), μ is the mean, and σ is the standard deviation.
z = (37 - 36.12) / 3.53 = 0.25
Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable is greater than or equal to 0.25, which is approximately 0.4013.
Therefore, the probability that the exam scores are at least 37 is 0.4013 or 40.13%
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Find the surface area of the figure. Round to the nearest hundredth when necessary (2 decimal places). SA = hp + 2B
The calculated surface area of the figure is 3100.8 square feet
Calculating the surface area of the figurefrom the question, we have the following parameters that can be used in our computation:
SA = hp + 2B
From the figure, we have
B = 1/2 * (10 + 34) * 24.7 = 543.4
p = 2 * (34 + 19) = 106
h = 19
So, we have
SA = 19 * 106 + 2 * 543.4
Evaluate
SA = 3100.8
Hence, the surface area is 3100.8 square feet
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On a map, the distance between Dallas Texas and Memphis Tennessee is 57.5 cm what is the actual distance if the map scale 1 cm:8mi
Answer:
57.5 cm × 8 mi./cm = 460 miles
Solvex - 6 = 8.
O A. x 14 and x = -14
OB. x = 14 and x = -2
C. x = -14 and x = 2
D. x = -14 and x = -2
Answer: the corect answer is B
Step-by-step explanation: Please give me brainly
A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are: 10 are red, 8 are blue, 5 are green, and 2 are white
Based on the random sample results, how many of the 200 gumballs are red?
In the given Sample Space, there are 80 red gumballs in the entire population of 200 gumballs.
What exactly is a sample space?
In probability theory, a sample space is the set of all possible outcomes or results of an experiment or random process. It is denoted by the symbol "S". The sample space depends on the nature of the experiment or process and consists of all the possible values or events that could occur.
Now,
If the random sample of 25 gumballs contains 10 red gumballs, we can estimate the proportion of red gumballs in the entire population of 200 gumballs by using the formula:
proportion of red gumballs = number of red gumballs in sample / sample size
Substituting the given values, we get:
proportion of red gumballs = 10 / 25
= 0.4
This means that the proportion of red gumballs in the entire population of 200 gumballs is estimated to be 0.4. To find the estimated number of red gumballs in the entire population, we can use the formula:
number of red gumballs in population = proportion of red gumballs x population size
Substituting the given values, we get:
number of red gumballs in population = 0.4 x 200
= 80
Therefore, based on the random sample results, it is estimated that there are 80 red gumballs in the entire population of 200 gumballs.
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what determines the decision of whether to use a one-tailed test or a two-tailed test when testing hypotheses to make inferences about a population mean?
The decision to use a one-tailed or two-tailed test depends on the specific research question and the directionality of the hypothesis.
When testing a hypothesis about a population mean, researchers may use a one-tailed or two-tailed test. A one-tailed test is used when the research question only focuses on one direction of an effect, for example, if the researcher is interested in whether the population mean is greater than a specific value. In contrast, a two-tailed test is used when the research question is interested in any significant difference between the sample mean and the hypothesized population mean, regardless of the direction of the difference.
The decision to use a one-tailed or two-tailed test should be based on the specific research question, and it is essential to clearly define the directionality of the hypothesis before selecting the appropriate test.
Therefore, the choice of a one-tailed or two-tailed test should be based on the research question and the specific direction of the hypothesis.
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fifa has made a football of leather od diameter 21 cm .if 10 % is wasted and cost of leather including labor is rs 25 find total no of leather bounght to mak a football
FIFA created a football with a 21 cm circumference out of leather. If 10% of the leather is wasted, the cost of leather with labour is Rs. 25 per square centimetre. All total, Rs. 31,173.90 worth of leather was purchased to produce one football.
The diameter of the leather used to make the football is 21 cm, so its radius is 10.5 cm (half of the diameter).
The formula for calculating a sphere's surface area can be used to determine how much leather is required to produce a football:
Surface area = [tex]4\pi r^2[/tex]
Surface area = 4π[tex](10.5)^2[/tex]
Surface area = 1385.44 sq. cm
If 10% of the leather is wasted, then the actual amount of leather used is 90% of the total leather bought. So, we need to calculate the cost of 90% of the leather:
Cost of leather = 90% of the total leather cost
Cost of leather = 0.9 x 1385.44 sq.cm x Rs. 25/sq.cm
Cost of leather = Rs. 31,173.90
Therefore, the total cost of the leather bought to make the football, including the labour cost, is Rs. 31,173.90.
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Divide a line segment of 140cm into the proportion 2:3; 5 How long is the shortest piece!
Answer:
28cm
Step-by-step explanation:
see image for explanation.
What is the value of 1/6+3/6+1/12
A. 5/12
B. 7/12
C. 9/12
D. 8/12
Answer: First, we can simplify 1/6 and 3/6 by finding a common denominator of 12:
1/6 = 2/12
3/6 = 6/12
Now we have:
2/12 + 6/12 + 1/12
Combining the numerators, we get:
9/12
Simplifying this fraction by dividing the numerator and denominator by their greatest common factor of 3, we get:
3/4
Therefore, the answer is C. 9/12.
Please provide a through explanation its much appreciated :)))
Part A: The side length of triangle EF = 10.35.
Part B: ∠E = 78
Define about the sine rule:The law of sines, often known as the sine rule or sine formula, is a formula that links a triangle's sides to the sine of its diagonally opposed angles.Both the sides and the angles of a triangle can be determined using the law of sine.You must apply the form of the sine rule at which lengths are now the numerators in order to determine the length of a side: a/Sine (A) = b/Sine (B) = c/Sine (C)Sine rule :
e/sinE = f/sinF = d/sinD
Where D, E, and F are the angles and d,e and f are the angles' opposing sides.
Put the values:
DF/sinE = 11.7/sin55 = EF/sin47
Part A: EF = ?
11.7/sin55 = EF/sin47
EF = 11.7 * sin47 / sin55
EF = 10.35
Part B: ∠E = ?
Using angle sum property of triangles.
∠E + ∠D + ∠F = 180
∠E + 47 + 55 = 180
∠E = 78
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Question
The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
With the given values, the surface area of the rectangular prism is 544 square units.
What is prism?A prism is a three-dimensional geometric shape that consists of two identical parallel polygonal bases and a set of parallelograms connecting the corresponding sides of the two bases.
In general, the area of any prism can be found by adding together the areas of its bases and lateral faces.
To find the surface area of the rectangular prism represented by the given net, we need to calculate the area of each face and add them together. The rectangular prism has six faces, so we need to find the area of each face.
The top and bottom faces are rectangles with dimensions 8 x 6, so each has an area of 8 x 6 = 48 square units. There are two of these faces, so their combined area is 2 x 48 = 96 square units.
The front and back faces are rectangles with dimensions 8 x 16, so each has an area of 8 x 16 = 128 square units. There are two of these faces, so their combined area is 2 x 128 = 256 square units.
The left and right faces are rectangles with dimensions 16 x 6, so each has an area of 16 x 6 = 96 square units. There are two of these faces, so their combined area is 2 x 96 = 192 square units.
Therefore, the total surface area of the rectangular prism represented by the given net is:
96 (top and bottom) + 256 (front and back) + 192 (left and right) = 544 square units.
So, the surface area of the rectangular prism is 544 square units.
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Someone help wit this please
In a rectangle, the length is 5m less than twice the width and the area is 97m^2 . Approximate the dimensions to the nearest tenth of a meter. Do not round any intermediate steps. Find the length and width.
Therefore, the approximate dimensions of the rectangle to the nearest tenth of a meter are width = 7.9 m and length = 10.8 m.
What is area?Area is a measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).
Here,
Let's denote the width of the rectangle as "w" in meters. Then, according to the problem statement, the length of the rectangle can be expressed in terms of the width as:
length = 2w - 5
The area of the rectangle is given as 97 square meters, so we can write:
area = length × width
Substituting the expression for length in terms of the width, we get:
area = (2w - 5) × w
Expanding this expression, we get a quadratic equation in standard form:
2w² - 5w - 97 = 0
We can solve this equation using the quadratic formula:
w = (-(-5) ± √((-5)² - 4×2×(-97))) / (2×2)
Simplifying this expression, we get:
w ≈ 7.9 or w ≈ -6.2
Since the width of a rectangle cannot be negative, we discard the negative solution and approximate the width to the nearest tenth of a meter:
w ≈ 7.9 m
Using the expression for the length in terms of the width, we can find the length:
length = 2w - 5
≈ 10.8 m
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Help, please I need it now
Step-by-step explanation:
Find the frontal area = triangle PLUS square...then multiply by depth ,a.
1/2 * a * b + a * a all of this times the depth 'a'
[ 1/2 ( 7 *5) + 7*7 ] * 7 = 465.5 units^3
acellus find the surface area of the composite figure its the yellew and green one the green is the triangle and the yellow is the rectangle
The surface area of the composite figure is 446 cm².
What is surface area?Surface area is the sum of the areas of all faces (or surfaces) on a 3D object. It is a two-dimensional measure of the space occupied by the object, and is measured in units of square units, such as square inches, square feet, and square meters. Surface area is often used to determine the amount of material needed for a solid object or the amount of paint needed to cover it.
The surface area of the composite figure can be calculated using the formula SA = 2(L x W) + (2 x H x L) + (2 x H x W). In this case, L = 9 cm, W = 10 cm, and H = 7 cm.
Therefore, the surface area of the composite figure is SA = 2(9 cm x 10 cm) + (2 x 7 cm x 9 cm) + (2 x 7 cm x 10 cm) = 180 cm²+ 126 cm²+ 140 [tex]cm^2[/tex] = 446 cm².
Therefore, the surface area of the composite figure is 446 [tex]cm^{2}[/tex].
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Complete questions as follows-
Surface Area of Composite Figures Acellus Find the surface area of the composite figure. 1 9 cm 10 cm cm 7 cm 8 cm 2 cm SA [? ] cm? Enter Copyright 02003 2021 Acellus Corporation. All Rights Reserved:'