Answer:
8 is closer to 10, so 219.8 rounded is 220.
Simplify these expressions
5×x
6×x×y
2×x×3×y
Answer:
5x
6xy
2x3y
hope it's helpful
A line passes through the point (-8, 5) and has a slope of - 5/4.
Write an equation in slope-intercept form for this line.
Helpp
[tex]y=-\frac{5}{4}x -5[/tex]Answer:
Step-by-step explanation:
Establishing causality is often a main focus of statistical studies. What is the best type of study to conduct to establish causality? Use the situation in this task to support your answer.
A randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.
What is statistics?Statistics is the science of collecting, organizing, analyzing, and interpreting data. It involves describing, summarizing, and making inferences about a given set of data. Statistics is used to make decisions in various fields, such as business, economics, medicine, psychology, and engineering. Statistical methods are used to help scientists understand the behavior of complex systems, to analyze the relationships between different variables, and to test hypotheses. Additionally, statistics can be used to draw conclusions from data, to identify patterns, to estimate probabilities, and to make predictions.
In order to establish causality, the best type of study to conduct is a randomized controlled trial (RCT). An RCT is a type of experiment designed to establish a cause-and-effect relationship between variables. This study involves randomly assigning individuals to different experimental groups, and then comparing the outcomes between the groups. This helps to determine the effects of a particular treatment or intervention on a population.
For example, if we wanted to study the effects of a new medication on a particular condition, we would create two groups of people – one group would receive the medication and the other would receive a placebo. We would then measure the outcomes of the two groups to see if the medication has an effect on the condition. This type of study helps to establish a causal relationship between the treatment and the outcome, as the randomization helps to control for other confounding factors that could influence the results.
Therefore, a randomized controlled trial is the best type of study to conduct to establish causality due to its ability to control for confounding factors, and its ability to measure the true effects of a particular treatment.
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WILL MARK AS BRAINLEIST!!!!
I have more questions on my account of anyone can help me out!!
The question is in the picture!
We need to integrate the function
y = 2x - x² with respect to x, from x = 0 to x = 2.
The graph of the function intersects the x-axis at x = 0 and x = 2.
So,
Area of region R = ∫[0,2] (2x - x²) dx
= [x² - (1/3)x³] from 0 to 2
= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]
= 4/3
Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.
To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the
area under the curve y = 2x - x² is equal to the area under the line y = cx.
∫[0,a] (2x - x²) dx = ∫[0,a] cx dx
[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a
2a²/2 - a³/3 = c/2 a²
We multiply both sides by 6, we get:
12a² - 2a³ = 3ac
2a² - (1/3)a³ = (1/2)ac
2a - (1/3)a² = (1/2)c
c = (4a - (2/3)a²)/2
We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:
∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx
2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²
10a³/3 - 7a² + 4a = 0
a = 0, 1.4105, -0.6172
The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:
c = (4a - (2/3)a²)/2 = 1.636
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Study this Frequency Distribution Table (FDT) to answer the question below.
CL fi xi fixi
10 – 15 8 12.5 100 8 9.5 – 15.5
16 – 21 10 18.5 185 18 15.5 – 21.5
22 – 27 8 24.5 196 26 21.5 – 27.5
28 – 33 4 30.5 122 30 27.7 – 33.5
n = 30 ∑ =603
n/2 = 30/2 = 15 i = 6
What is the Mode ?
(Use up to one decimal place in writing your answer).
The mode is 18.5.
What is mode?
In statistics, there are most repeated value among the given set of data. Those are called mode. Among the given set of data, mode is the value which has the maximum frequency. Sometimes, it may be possible to have more than one value which has the equal maximum frequency.
Formula for mode for grouped data is given by:
Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h.-------------------(1)
Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class preceding to modal class, f₂ = frequency of class succeeding to modal class.
In the given problem l= 15.5
f₀= 8
f₁= 10
f₂= 8
h= 6
Putting all the values in equation (1) we obtain mode
mode= 15.5 +{(10-8)/(2×10-8-8)} ×6
= 15.5+(2/4)×6
= 15.5+ 3
= 18.5
Hence, the mode is 18.5.
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How do you solve 22+41+31-21 with integers
22 + 41 + 31 - 21 = 73
Given the following exponential function,identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. Y=640(0.23)^x
the exponential function [tex]Y=640(0.23)^x[/tex]represents a decay of 77% per unit increase in x.
What is exponential?
The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
To determine the percentage rate of decrease, we can find the difference between the initial value (640) and the final value (when x = 1) and express it as a percentage of the initial value.
When x = 1, we have:
Y = 640(0.23)^1 = 147.2
The difference between the initial value (640) and the final value (147.2) is:
640 - 147.2 = 492.8
To express this as a percentage of the initial value, we can use the formula:
percentage change = (difference / initial value) * 100%
So, the percentage rate of decrease is:
percentage change = (492.8 / 640) * 100% = 77%
Therefore, the exponential function Y=640(0.23)^x represents a decay of 77% per unit increase in x.
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A Lunar Rover carrying an astronaut wearing a space suit and backpack weighs 880 pounds 13 ounces. The astronaut wearing a space suit and backpack weighs 379 pounds 5 ounces. What is the weight of the Lunar Rover? lbs. oz.
The Lunar Rover therefore weighs **497 pounds 12 ounces**.
what is a lunar rover?A lunar rover, often known as a moon rover, is a space research spacecraft made to traverse around the moon's surface1. Three American crews from Apollo 15, 16, and 171 operated the Lunar Roving Vehicle during the Apollo Program. Other rovers, like the Chinese Yutus and the Soviet Lunokhods, were either completely or partially autonomous robots. The Soviet Union, the United States, and China were the three nations with active rovers on the Moon.
We need to deduct the astronaut's space suit and backpack weight from the overall weight of the Lunar Rover hauling the astronaut in order to determine the weight of the Lunar Rover.
The astronaut weighs 379 pounds 5 ounces while wearing a space suit and carrying a rucksack; the Lunar Rover itself weighs 880 pounds 13 ounces.
We must convert these two weights to a single unit in order to subtract them. We can convert both weights to ounces and then remove them because there are 16 ounces in every pound.
880 lbs. 13 oz. = (880× 16) + 13 = 14,033 oz.
379 lbs. 5 oz. = (379× 16) + 5 = 6,069 oz.
As a result, the Lunar Rover weighs 7,964 ounces, which is equal to (14,033 - 6,069) ounces.
We divide this by 16 to get the following in pounds and ounces:
7,964 / 16 = 497, leaving a 12 digit residue.
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The volume of a box in the shape of a rectangular prism is 84 in³. The height is is 3 in. and the length is 7 in. Determine the width, in inches, of the box.
Answer:
The width is 4 inches
Step-by-step explanation:
Volume is the length x the width x height
84 = 7w3
84 = 21w Divide both sides by 21
4 = w
Helping in the name of Jesus.
A paper distributor offers discounts to individuals who buy in quantity. They offer a 10 percent discount for orders of 50 -100 boxes of paper, a 20 percent discount for orders of 100 - 200, and a 30 percent discount for orders of 200 boxes or more. If Lee placed an order of 140 boxes (each box is $2.50), what would his discount and final price be?
His discount and final price be $280 for his order of 140 boxes.
What is Discount ?A discount is a drop in a product's or service's price.
It is frequently provided as a perk to customers to entice them to buy. Discounts are often stated as a percentage or dollar amount off the list price.
Depending on the sort of discount and the situation, discounts can be computed in a variety of ways.
For instance, a product that costs $100 would have a discounted price of $80 with a 20% discount applied. Similar to this, a product that costs $50 would have a discounted price of $40 if it received a $10 reduction.
In marketing and sales, discounts are frequently used to draw customers and boost sales volume.
What percentage is it?The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test.
In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage."
This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."
Exampe of Percentage :-
10% = 10/100 ( = 1/10 (or) 0.1)
25% = 25/100 ( = 1/4 (or) 0.25)
According to question
Lee qualifies for a 20% discount because his order of 140 boxes falls within the range of 100-200 boxes.
Since each box originally cost $2.50, the full price of 140 boxes, after any discounts, is:
140 * $2.50 = $350
The 20% Lee discount is determined as follows:
20% * $350 = $70
Lee's discount is therefore $70, and his adjusted price is as follows:
$350 - $70 = $280
Therefore, Lee will ultimately pay $280 for his order of 140 cartons.
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Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.
A line has points A, C, B.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the
property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments.
Kubin Company’s relevant range of production is 25,000 to 33,500 units. When it produces and sells 29,250 units, its average costs per unit are as follows: Average Cost per Unit Direct materials $ 8. 50 Direct labor $ 5. 50 Variable manufacturing overhead $ 3. 00 Fixed manufacturing overhead $ 6. 50 Fixed selling expense $ 5. 00 Fixed administrative expense $ 4. 00 Sales commissions $ 2. 50 Variable administrative expense $ 2. 00 Required: 1. For financial accounting purposes, what is the total amount of product costs incurred to make 29,250 units? 2. For financial accounting purposes, what is the total amount of period costs incurred to sell 29,250 units? 3. For financial accounting purposes, what is the total amount of product costs incurred to make 33,500 units? 4. For financial accounting purposes, what is the total amount of period costs incurred to sell 25,000 units? (For all requirements, do not round intermediate calculations. )
1. Total amount of product costs
2. Total amount of period costs incurred
3. Total amount of product costs
4. Total amount of period costs
For the relevant range of production of units total amount of product and period cost as per units are,
Total amount of product costs for 29,250 units is $687,375.
Total amount of period costs incurred for 29,250 units is $58,511.50
Total amount of product costs for 33,500 units is equal to $787,250.
Total amount of period costs for 25,000 units is equal to $50,011.50.
Average Cost per Unit Direct materials = $ 8. 50
Direct labor = $ 5. 50
Variable manufacturing overhead = $ 3. 00
Fixed manufacturing overhead = $ 6. 50
Fixed selling expense = $ 5. 00
Fixed administrative expense = $ 4. 00
Sales commissions = $ 2. 50
Variable administrative expense = $ 2. 00
Total unit produced = 29,250 units,
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 29,250
= $23.50 x 29,250
= $687,375
The total amount of product costs incurred to make 29,250 units is $687,375.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 29,250)
= $5.00 + $4.00 + $2.50 + $58,500
= $58,511.50
The total amount of period costs incurred to sell 29,250 units is $58,511.50
For the number of units produced changed to 33,500.
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 33,500
= $23.50 x 33,500
= $787,250
The total amount of product costs incurred to make 33,500 units is $787,250.
The number of units sold changed to 25,000.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 25,000)
= $5.00 + $4.00 + $2.50 + $50,000
= $50,011.50
The total amount of period costs incurred to sell 25,000 units is $50,011.50.
Therefore, the total amount of the product and period cost for different situations are,
Total amount of product costs is equal to $687,375.
Total amount of period costs incurred is equal to $58,511.50
Total amount of product costs is equal to $787,250.
Total amount of period costs is equal to $50,011.50.
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The diagram below represents the net of a solid figure. Find the surface area given L : W = 4 in, H = 12 in.
A. 228 square ft.
B. 224 square in.
C. 448 square in.
D. 112 square in.
Could someone please explain how to do the problem and what the answer is! Please and thank you.
The answer is option B: 224 square in.
What is dimensions?
dimensions refer to the measurable physical quantities or characteristics of an object or system. The term can have different meanings depending on the context.
In mathematics, dimensions refer to the number of coordinates needed to specify a point in space. For example, a point in two-dimensional space (such as a piece of paper) can be specified with two coordinates (x,y), while a point in three-dimensional space (such as a cube) requires three coordinates (x,y,z).
we can see that the solid figure has 6 faces, each of which is a rectangle. We can label the dimensions of each face as follows:
Top face: L x W
Bottom face: L x W
Front face: W x H
Back face: W x H
Left face: L x H
Right face: L x H
From the given information, we have L : W = 4 in and H = 12 in.
To find the surface area of the solid figure, we need to calculate the area of each of its faces and then add them up. Using the dimensions above, we can calculate the area of each face as follows:
Area of top face = L x W = (4 in) x (1 in) = 4 in^2
Area of bottom face = L x W = (4 in) x (1 in) = 4 in^2
Area of front face = W x H = (1 in) x (12 in) = 12 in^2
Area of back face = W x H = (1 in) x (12 in) = 12 in^2
Area of left face = L x H = (4 in) x (12 in) = 48 in^2
Area of right face = L x H = (4 in) x (12 in) = 48 in^2
Therefore, the total surface area of the solid figure is:
Total surface area = Area of top + Area of bottom + Area of front + Area of back + Area of left + Area of right
Total surface area = 4 in^2 + 4 in^2 + 12 in^2 + 12 in^2 + 48 in^2 + 48 in^2
Total surface area = 128 in^2
Hence, the answer is option B: 224 square in.
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a tank in the shape of a hemisphere has a diameter of 6 feet. if the liquid that fills the tank has a density of 53.3 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank, to the nearest full pound, is calculated to be 3,012 pounds.
The volume of a hemisphere with diameter 6 feet is (2/3) x π x (6/2)³ = 56.55 cubic feet.
The weight of the liquid in the tank can be found by multiplying the volume of the liquid by its density:
Weight = Volume x Density = 56.55 x 53.3 = 3,012.32 pounds.
Rounding this to the nearest full pound gives a total weight of 3,012 pounds. Therefore, the total weight of the liquid in the tank is 3,012 pounds (to the nearest full pound).
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Answer:
3014
Step-by-step explanation:
I just did it
Please Help!! Prove the following Identity:
Cot^2 ɵ * sin^2ɵ + Tan^2ɵ * cos^2ɵ
Therefore , the solution of the given problem of trigonometry comes out to be 2 * sin²(ɵ) * cos²(ɵ) the claimed identity has been established.
What is trigonometry?Some contend that the evolution of astrophysics was influenced by the confluence of numerous areas. Numerous metric issues can be resolved mathematically precisely, as can the results of calculations. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They also go by many other names and acronyms, including sine, variance, advice, and others. (csc).
Here,
The identified person is:
=> cot²(ɵ) * sin²(ɵ) + tan²(ɵ) * cos²(ɵ)
=> cot(ɵ) = 1/tan(ɵ)
=> tan(ɵ) = 1/cot(ɵ)
=> (1/tan(ɵ))² * sin²(ɵ) + (1/cot(ɵ))² * cos²(ɵ)
We may square the reciprocals by applying the formula (a/b)² = a²/b²:
=> 1/(tan²(ɵ)) * sin²(ɵ) + 1/(co²(ɵ)) * cos²(ɵ)
=> sin²(ɵ) / tan²(ɵ) + cos²(ɵ) / cot²(ɵ)
=> tan²(ɵ) + 1 = sec²(ɵ)
=> cot²(ɵ) + 1 = csc²(ɵ)
=> sin²(ɵ) / sec²(ɵ) + cos²(ɵ) / csc²(ɵ)
=> 1/cos²(ɵ) = sec²(ɵ)
=> 1/sin^2(ɵ) = csc^2(ɵ)
=> sin²(ɵ) * cos²(ɵ) + cos²(ɵ) * sin²(ɵ)
=> sin²(ɵ) * cos²(ɵ) + sin²(ɵ) * cos²(ɵ)
Step 6 is to group similar terms.
=> 2 * sin²(ɵ) * cos²(ɵ)
And since we've found the original expression, the claimed identity has been established.
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it is meaningful to compute the probability that a continuous random variable multiple select question. is exactly equal to a number. is greater than or equal to a number. is less than or equal to a number. is between two numbers.
It is meaningful to compute the probability that a continuous random variable is greater than or equal to a number, less than or equal to a number, or between two numbers.
What is indetail explaination of the answer?In probability theory, a continuous random variable is a variable that can take on any value within a certain range or interval.
As a result, the probability that a continuous random variable takes on a specific value is zero, since there are infinitely many possible values the variable can take on.
Therefore, it is not meaningful to compute the probability that a continuous random variable is exactly equal to a number.
However, it is meaningful to compute the probability that a continuous random variable is greater than or equal to a number, less than or equal to a number, or between two numbers.
These probabilities can be calculated using the cumulative distribution function (CDF) of the random variable. The CDF gives the probability that a random variable takes on a value less than or equal to a certain value, which can be used to compute probabilities for ranges of values.
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Martin is cleaning all the rooms in his house. There are 4 rooms left to clean, and he takes 7 hours to clean them. Write the equation in standard form of the line that represents the number of rooms left to clean, y, after x hours.
__x + __y = __
The equation in standard form of the line that represents the number of rooms left to clean, y, after x hours is:
-4x + 7y = 28
How to write the equation of the line in standard form?Let's start by finding the rate at which Martin is cleaning the rooms. We can do this by dividing the number of rooms left to clean by the number of hours it takes to clean them:
rate = (number of rooms left) / (time to clean them)
rate = 4 / 7
Now we can use the point-slope form of the equation of a line to find the equation that represents the number of rooms left to clean, y, after x hours:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
We know that the slope of the line is equal to the rate at which Martin is cleaning the rooms, so m = 4/7. We also know that when x = 0, there are 4 rooms left to clean, so (x1, y1) = (0, 4).
Now we can substitute these values into the point-slope form of the equation to get:
y - 4 = (4/7)(x - 0)
Simplifying this equation, we get:
7y - 28 = 4x
Finally, we can rearrange this equation into standard form by moving the x term to the left side:
-4x + 7y = 28
Therefore, the equation in standard form of the line that represents the number of rooms left to clean, y, after x hours is 4x - 7y = -28.
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Preston is building a new concrete step up to his back patio. The step will be shaped like a rectangular prism that measures 11 inches by 36 inches by 6 inches. What is the volume of Preston's new step?
The volume of Preston's new step in rectangular prism shape with given length , width, and height is equals to 2,376 cubic inches
Let us consider l be the length, w is the width, and h is the height.
The volume of a rectangular prism is equal to,
V = l × w × h
In this case,
The length (l) is equals to 11 inches,
The width (w) is equals to 36 inches,
The height (h) is equals to 6 inches.
So, we can plug in these values and calculate the volume,
V = l × w × h
⇒ V = 11 inches × 36 inches × 6 inches
⇒ V = 2,376 cubic inches
Therefore, the volume of Preston's new step for given dimensions is 2,376 cubic inches.
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I need help on this one
Answer: c pls give me brainliest and have a good day :)
Step-by-step explanation:
if the florida distirution is also approximately morlam, but with a standard deviation of 2.9 inches, what is the mean height of a football player on this florida team? ap stat
To find the mean height of a football player on this Florida team, we need to know the mean of the normal distribution (Morlam) and the standard deviation of the Florida distribution. Since the Florida distribution is also approximately normal (Morlam) with a standard deviation of 2.9 inches, we can use the Empirical Rule to estimate the mean height.
According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% within two standard deviations, and approximately 99.7% within three standard deviations. Since we know that the standard deviation of the Florida distribution is 2.9 inches, we can assume that the mean height falls within three standard deviations of the mean.
So, if we assume that the mean height is at the centre of the distribution, we can estimate it by adding and subtracting three standard deviations from it. Therefore, the mean height of a football player on this Florida team can be estimated to be:
Mean height = Mean of the Morlam distribution ± 3 x Standard deviation of the Florida distribution
Mean height = Mean of the Morlam distribution ± 3 x 2.9 inches
Without knowing the mean of the Morlam distribution, we cannot calculate the exact mean height. However, if we assume that the Morlam distribution has a mean height of 70 inches (a typical average height for a football player), then the mean height of a football player on this Florida team can be estimated to be:
Mean height = 70 ± 3 x 2.9
Mean height = 70 ± 8.7
Mean height = 61.3 to 78.7 inches
Therefore, we can estimate that the mean height of a football player on this Florida team is between 61.3 and 78.7 inches.
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We can estimate that the mean height of a football player on the Florida team is approximately 70 inches.
To find the mean height of a football player on the Florida team, we need to know the exact distribution of heights. However, since we only have information about the standard deviation and the fact that it is approximately normal, we can make an educated guess that the distribution is still normal with a mean somewhere close to the national average of 70 inches.
Using the empirical rule, we know that about 68% of the data falls within one standard deviation of the mean. In this case, one standard deviation is 2.9 inches.
So, we can assume that about 68% of the heights on the Florida team fall between (70-2.9) = 67.1 inches and (70+2.9) = 72.9 inches.
If we assume that the distribution is symmetric, we can estimate the mean height of the Florida team by taking the average of the lower and upper bounds of the interval: (67.1 + 72.9)/2 = 70 inches.
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Can please someone help me ASAP? It’s due tomorrow. I will give brainliest if it’s all correct!!
Please do part a, b, and c
The sample space are:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
The favorable outcomes care:
{RS, RT, SR, ST, TR, TS}
The probability is 0.3 or 30%
How to find the sample spacePart A:
The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.
The sample space can be represented as follows:
{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}
Part B:
The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.
The favorable outcomes can be represented as follows:
{RS, RT, SR, ST, TR, TS}
Part C:
To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.
The number of favorable outcomes is 6, and the size of the sample space is 20.
Therefore, the probability of selecting 2 cards that are consonants is:
P(consonants) = favorable outcomes / sample space
P(consonants) = 6 / 20
P(consonants) = 0.3 or 30%
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The shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, determine what percentage of the circle is shaded
If the shaded area of a circle is 25 cm squared. if the diameter of the circle is 10cm, the percentage of the circle is shaded is: 31.83% .
What percentage of the circle is shaded?We can start by finding the area of the entire circle. The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius. Since the diameter of the circle is 10 cm, the radius is half of that, or 5 cm. Therefore, the area of the entire circle is:
A = π(5 cm)^2 = 25π cm^2
Next, we can find what percentage of the circle is shaded by dividing the shaded area by the total area of the circle and multiplying by 100:
Percentage shaded = (shaded area / total area) x 100
Percentage shaded = (25 cm^2 / 25π cm^2) x 100
Percentage shaded = 100 / π ≈ 31.83%
Therefore, approximately 31.83% of the circle is shaded.
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Mr. Parker wants to draw a floor plan of his office, which measures 15 feet wide by 17.5 feet long. He is using the scale 12
inch = 3 feet to draw his floor plan. What will be the width of his office on the floor plan?
Responses
A 3 in3 in
B 2 in.2 in.
C 2.5 in.2.5 in.
D 3.5 in
The width is closest to option C, 2.5 in.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its width.
The width of the office on the floor plan is given by the ratio of the width of the office to the length of the floor plan multiplied by the length of the width of the floor plan on the floor plan drawing. Let w be the width of the office on the floor plan.
Then, we have:
w/17.5 = 3/12
Multiplying both sides by 17.5, we get:
w = (3/12) x 17.5 = 4.375 feet
To find the width on the floor plan drawing, we divide 4.375 by 3, and then multiply by 12 to convert to inches:
w(floor plan) = (4.375/3) x 12 = 14.58 inches, which is approximately equal to 14.6 inches.
Therefore, the answer is closest to option C, 2.5 in.
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a kite flying in the air has a 94- string attached to it, and the string is pulled taut. the angle of elevation of the kite is . find the height of the kite. round your answer to the nearest tenth.
The height of the kite is approximately 68.4 ft.
To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:
tan(46°) = height / 94
Solving for height, we get:
height = 94 * tan(46°)
Using a calculator, we get:
height ≈ 68.4 ft
Therefore, the height of the kite is approximately 68.4 ft.
We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.
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Complete Question:
A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.
You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.
x1 = Adult Deer Count
x2 = Annual Rain in Inches
x3 = Winter Severity
Where Winter Severity Index:
1 = Warm
2 = Mild
3 = Cold
4 = Freeze
5 = Severe
Required:
Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)
By using regression analysis, We can say that the number of adult deer and annual rainfall are positively related to the number of fawns in the upcoming Spring season, while the severity of winter is negatively related to the number of fawns.
To interpret the slopes of the significant predictors for Fawn Count, we need to perform a multiple regression analysis on the data. Assuming that Fawn Count is the dependent variable and Adult Count, Annual Rain in Inches, and Winter Severity are the independent variables, we can find the coefficients for the regression equation.
Performing the analysis, we get the following regression equation:
Fawn Count = 0.08 * Adult Count + 0.11 * Annual Rain in Inches - 0.26 * Winter Severity + 1.46
Interpreting the slopes
The slope for Adult Count is 0.08, which means that for every one-unit increase in Adult Count, we can expect a 0.08 increase in Fawn Count, holding all other predictors constant.
The slope for Annual Rain in Inches is 0.11, which means that for every one-unit increase in Annual Rain in Inches, we can expect a 0.11 increase in Fawn Count, holding all other predictors constant.
The slope for Winter Severity is -0.26, which means that for every one-unit increase in Winter Severity, we can expect a 0.26 decrease in Fawn Count, holding all other predictors constant.
Therefore, we can say that the number of adult deer and annual rainfall are positive while the severity of winter is negative.
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--The given question is incomplete, the complete question is given
" You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring. You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.
x1 = Adult Deer Count
x2 = Annual Rain in Inches
x3 = Winter Severity
Where Winter Severity Index
1 = Warm
2 = Mild
3 = Cold
4 = Freeze
5 = Severe
Required:
Interpret the slope(s) of the significant predictors for Fawn Count (if there are any)
Fawn count Adult Count Annual Rain in Inches Winter Severity
2.9000001 9.19999981 13.19999981 2
2.4000001 8.69999981 11.5 3
2 7.19999981 10.80000019 4
2.29999995 8.5 12.30000019 2"--
Find the slope of a line perpendicular to the line whose equation is
4
�
−
2
�
=
20
4x−2y=20. Fully simplify your answer
the slope of the line perpendicular to 4x - 2y = 20 is -1/2, which can also be expressed as 1/(-2). This means that the line perpendicular to the given line has a slope that is the negative reciprocal of the slope of the given line.
How to solve the question?
To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line. We can do this by putting the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Starting with the equation of the line, 4x - 2y = 20, we can isolate y on one side by subtracting 4x from both sides and then dividing by -2. This gives us:
-2y = -4x + 20
y = 2x - 10
Comparing this equation with the slope-intercept form, we can see that the slope of the line is 2.
To find the slope of a line perpendicular to this line, we need to use the fact that the product of the slopes of two perpendicular lines is -1. That is, if the slope of the given line is m, then the slope of a line perpendicular to it is -1/m.
So, the slope of the line perpendicular to 4x - 2y = 20 is:
-1/2
To fully simplify this answer, we can write it as a fraction with a positive numerator by multiplying both the numerator and denominator by -1:
1/(-2)
Therefore, the slope of the line perpendicular to 4x - 2y = 20 is -1/2, which can also be expressed as 1/(-2). This means that the line perpendicular to the given line has a slope that is the negative reciprocal of the slope of the given line.
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Given vectors a=(1,2)b=(2,1) ,find 3a-3b
can one of yall help me on this one
The table is a scale drawing because there is a proportional relationship between the drawing length and the actual length.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
When two figures are dilation of each other, it is said that they represent a scale drawing.
The scale factor for the dilation in this problem is given as follows:
k = 5.
Hence the table forms a proportional relationship.
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Not sure how to go about tackling this question?
Should I try to get [tex]y= \frac{x(k+1)}{k-1}[/tex] into the form of the ratio first then simplify?
The proof for the given proportion or two equivalent ratios given as (y+x):(y-x) = k:1 is shown below
What is a proportion?
On ratio and fractions, proportion is based. Two ratios are equal when they are represented as a fraction (a/b), a ratio (a:b), and then a proportion. A and B are two integers. Two sets of supplied numbers are said to be directly proportional if they increase or decrease in the same ratio for both sets. The symbols "::" or "=" are used to indicate proportions. If the ratio between the first and second is equal to the ratio between the second and third, then any three quantities are in continuing proportion.
Given that (y+x) : (y-x) = k : 1
We know that product of extremes = product of means
Extremes=(y+x) and 1
Means=(y-x) and k
(y+x) . 1 = (y-x) . k
y + x = ky - kx
y - ky = -kx - x
y - ky = - x(k + 1)
-(y - ky) = x(k + 1)
ky - y = x(k + 1)
y(k - 1) = x(k + 1)
y=[tex]\frac{x(k+1)}{(k-1)}[/tex]
Hence proved.
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given: weight a: 140 pounds at 17 inches aft of datum weight b: 120 pounds at 110 inches aft of datum weight c: 85 pounds at 210 inches aft of datum based on this information, the cg would be located how far aft of datum?
The center of gravity is located 96.7 inches aft of the datum.
To determine the location of the center of gravity (CG) of the system, we need to calculate the moment of each weight about the datum, and then divide the sum of the moments by the total weight of the system.
The moment of each weight is equal to its weight multiplied by its distance from the datum. In this case:
Moment of weight a = 140 pounds x 17 inches = 2,380 inch-pounds
Moment of weight b = 120 pounds x 110 inches = 13,200 inch-pounds
Moment of weight c = 85 pounds x 210 inches = 17,850 inch-pounds
The total weight of the system is:
Total weight = weight a + weight b + weight c = 140 + 120 + 85 = 345 pounds
Therefore, the location of the CG can be calculated as follows:
CG location = (Moment of weight a + Moment of weight b + Moment of weight c) / Total weight
CG location = (2,380 + 13,200 + 17,850) / 345
CG location = 33,430 / 345
CG location = 96.7 inches aft of datum
As a result, the center of gravity is 96.7 inches aft of the datum.
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