The equation to find x, the unknown dimension of the rectangle, can be written as x * 4 = 40. And, the dimensions of the rectangle are 10 units by 4 units.
Dividing 40 by 4, we find that x = 10. Therefore, the unknown dimension of the rectangle is 10 units.
The dimensions of the rectangle are now known. One side of the rectangle is x = 10 units, and the other side can be determined by dividing the area (40 square units) by the known side length. So, the second dimension is 40/10 = 4 units. Thus, the dimensions of the rectangle are 10 units by 4 units.
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Dawn is making an abstract painting with two triangles. The dimensions of the painting are shown below: Two triangles share the same height of 8 inches. One triangle has a base of 6 inches and the other is 10 inches. The total area of the two triangles is _____ square inches. Numerical Answers Expected! Answer for Blank 1:.
To find the total area of the two triangles, we need to calculate the area of each triangle and then add them together.
The formula for the area of a triangle is given by:
Area = (base * height) / 2
For the first triangle:
Base = 6 inches
Height = 8 inches
Area of the first triangle = (6 * 8) / 2 = 48 / 2 = 24 square inches
For the second triangle:
Base = 10 inches
Height = 8 inches
Area of the second triangle = (10 * 8) / 2 = 80 / 2 = 40 square inches
Now, we can find the total area of the two triangles by adding their individual areas together:
Total area = Area of the first triangle + Area of the second triangle
Total area = 24 square inches + 40 square inches = 64 square inches
Therefore, the total area of the two triangles is 64 square inches.
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Dean Ephraim has 8 gallons of water. Dean Barton has three times as much water as much water as Dean Ephraim. How many cups of water does dean Barton have?
Dean Barton has 384 cups of water. To determine the number of cups of water Dean Barton has, we need to calculate the amount of water he has based on given information about Dean Ephraim's water quantity.
Given information:
Dean Ephraim has 8 gallons of water.
Dean Barton has three times as much water as Dean Ephraim.
To find the amount of water Dean Barton has, we need to multiply Dean Ephraim's water quantity by three.
Dean Barton's water quantity = 8 gallons * 3 = 24 gallons.
Since we need to express the water quantity in cups, we need to convert gallons to cups.
Conversion factor: 1 gallon = 16 cups.
Dean Barton's water quantity in cups = 24 gallons * 16 cups/gallon = 384 cups.
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A recipe calls for 3/4 cup of oats to make 6 banana oat muffins. You only want to make 4 banana oat muffins. How many cups of oats do you need?
To make 4 banana oat muffins instead of the original recipe's 6, you would need 1/2 cup of oats.
The recipe states that to make 6 banana oat muffins, you need 3/4 cup of oats. Since you want to make 4 muffins instead, you can calculate the proportion of oats needed by setting up a ratio. By cross-multiplying, we find that (4/6) * (3/4) = (2/3) * (3/4) = 6/12 = 1/2. Therefore, you would need 1/2 cup of oats to make 4 banana oat muffins.
This calculation accounts for the adjustment in the recipe's quantities based on the desired serving size. Since you are making two-thirds of the original batch size, you proportionally reduce the amount of oats required by two-thirds, resulting in the need for 1/2 cup of oats.
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Diego collected x kg of recycling. Lin collected 2/5 more than that
Lin collected 1.4 times that of Diego's recycling collection.
Let x be the amount Diego collected in kg of recycling.
Then, Lin collected 2/5 more than that is
x + 2/5x = 7/5x kg of recycling
.Let x be the amount of recycling Diego collected in kg.
Then, Lin collected 2/5 more than that, so Lin's collection is
x + 2/5x,
which is equivalent to 7/5x kg of recycling.
This means that Lin's recycling collection is 1.4 times that of Diego's.'
For example, if Diego collected 10 kg of recycling, then Lin collected
2/5 * 10 = 4 kg
more than that, which is a total of 14 kg.
Therefore, Lin collected 1.4 times that of Diego's recycling collection.
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A flower pot is 85 cm tall . It is kept on the top of a shelf which is 260 cm tall . find the combined height of flower pot and the shelf
The combined height of the flower pot and the shelf is 345 cm
Given the height of the flower pot is 85 cm and the height of the shelf is 260 cm, we are to find the combined height of the flower pot and shelf.
To find the combined height, we need to add the height of the flower pot and the height of the shelf.
So, Combined height of flower pot and shelf = Height of the flower pot + Height of the shelf Combined height of flower pot and shelf = 85 cm + 260 cm
Combined height of flower pot and shelf = 345 cm
Therefore, the combined height of the flower pot and the shelf is 345 cm.
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Find the value of the power.5−5The value of the power is
The value of the given power, 5^(-5), can be found by calculating the reciprocal of 5 raised to the power of 5.
To find the value of 5^(-5), we need to calculate the reciprocal of 5 raised to the power of 5, which is equivalent to raising 5 to the power of -5.
Using the rule for negative exponents, we know that a negative exponent indicates the reciprocal of the base raised to the positive exponent. In this case, 5^(-5) is equal to 1/(5^5).
To simplify further, we can calculate 5^5, which is equal to 3125. Therefore, the reciprocal of 3125 is 1/3125.
Hence, the value of the power 5^(-5) is 1/3125.
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The letters in the given list are written on tiles, one letter per tile. A, B, C, F, G, I, K, L, O, P, Q, T, V, W, X, ZThe 16 tiles are placed in a bag and one is drawn randomly. Determine the probability of specific events using this situation. The probability of drawing any one of the letters is. The probability of drawing either an "F" or "P" tile is. The probability of drawing a vowel is. The probability of not drawing a "Q" tile is
The probability of drawing any one of the letters from the given list is 1/16. The probability of drawing either an "F" or "P" tile is 2/16 or 1/8. The probability of drawing a vowel is 4/16 or 1/4. The probability of not drawing a "Q" tile is 15/16.
In the given list, there are a total of 16 tiles with different letters. Since there is an equal chance of drawing any one of the tiles, the probability of drawing any specific letter is 1 out of 16, which can be written as 1/16.
To determine the probability of drawing either an "F" or "P" tile, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes. Since there are two tiles with either "F" or "P" out of the 16 total tiles, the probability is 2 out of 16, which simplifies to 1/8.
To calculate the probability of drawing a vowel, we need to count the number of vowel tiles and divide it by the total number of tiles. In this case, there are four vowel tiles (A, I, O, U) out of the 16 total tiles. Therefore, the probability of drawing a vowel is 4 out of 16, which can be simplified to 1/4.
Finally, to find the probability of not drawing a "Q" tile, we subtract the probability of drawing a "Q" from 1. Since there is only one "Q" tile out of the 16 total tiles, the probability of drawing it is 1 out of 16. Hence, the probability of not drawing a "Q" tile is 15 out of 16, which simplifies to 15/16.
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Write a function rule to represent the situation.
the total cost C for g grams of ham if each gram costs $5.77
Write a function rule using C and g as variables.
(Type an equation.)
The function rule representing the situation is C = 5.77g, where C is the total cost and g is the weight of ham in grams.
The function rule C = 5.77g represents the relationship between the total cost (C) and the weight of ham (g) in grams. In this situation, each gram of ham costs $5.77, so the total cost is obtained by multiplying the cost per gram ($5.77) by the weight of ham (g).
The equation C = 5.77g follows a linear relationship, where the cost (C) is directly proportional to the weight of ham (g). This means that as the weight of ham increases, the total cost also increases proportionally. For example, if we have 100 grams of ham, the total cost would be calculated as 5.77 * 100 = $577.
By using this function rule, we can easily determine the total cost of any given weight of ham. It provides a straightforward way to calculate the cost without needing to perform complex calculations or look up individual prices for different quantities. This equation can be useful in various situations, such as meal planning, budgeting, or determining the cost for commercial purposes.
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Hector helps out at an animal shelter. One of his jobs is to track the weights of the puppies. He recorded the number of ounces gained or lost by five puppies and tried to place them on a number line. . Which error did Hector make? A. He placed Puppy 3 at –3.4 instead of at –0.75. B. He placed Puppy 5 to the left of 0 instead of to the right. C. He placed Puppy 1 between 7 and 8 instead of between 15 and 16. D. He placed Puppy 2 between 3 and 3.5 instead of between 3.5 and 4.
The error Hector made is that he placed Puppy 3 at -3.4 instead of at -0.75, which aligns with option A.
From the given options, it appears that the error Hector made is represented by option A: He placed Puppy 3 at -3.4 instead of at -0.75.
To determine this, let's examine the given information about the placements of the puppies on the number line:
Puppy 1: Between 15 and 16
Puppy 2: Between 3 and 3.5
Puppy 3: At -3.4
Puppy 4: Between -6 and -5.5
Puppy 5: To the left of 0
Looking at these placements, we can see that options B, C, and D do not correspond to the given information. Hector correctly placed Puppy 5 to the left of 0, and Puppy 1 between 15 and 16.
However, option A states that Hector placed Puppy 3 at -3.4 instead of at -0.75. This suggests an error in Hector's placement because -0.75 is the correct placement for Puppy 3, not -3.4.
Therefore, the error Hector made is that he placed Puppy 3 at -3.4 instead of at -0.75, which aligns with option A.
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Which statement correctly compares the values in the statement?
StartAbsoluteValue negative 0.45 EndAbsoluteValue blank box StartAbsoluteValue negative 0.0045 EndAbsoluteValue
The correct statement that compares the values is "The absolute value of -0.45 is greater than the absolute value of -0.0045."
Absolute value is a mathematical operation that yields the distance between a number and zero on the number line, regardless of its sign. In the given statement, we are comparing the absolute values of two negative numbers: -0.45 and -0.0045.
The absolute value of a negative number is always positive. In this case, the absolute value of -0.45 is greater than the absolute value of -0.0045. This is because -0.45 is closer to zero than -0.0045 on the number line, thus resulting in a larger absolute value. The absolute value of -0.45 is 0.45, while the absolute value of -0.0045 is 0.0045. Therefore, the statement correctly states that the absolute value of -0.45 is greater than the absolute value of -0.0045.
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Find the lateral surface area of the cylinder. Use 3. 14 for at and round to the nearest
whole number.
The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius of the circular base and h is the height of the cylinder. Using the given value of π as 3.14 and rounding to the nearest whole number, the formula becomes: Lateral surface area = 2 × 3.14 × 8 × 18Lateral surface area = 904.32The lateral surface area of the cylinder is 904.32 square units.
The lateral surface area of a cylinder is the area of the curved surface that connects the two circular bases of the cylinder. It can be calculated using the formula 2πrh, where r is the radius of the circular base and h is the height of the cylinder. To find the lateral surface area of the given cylinder, we need to first identify the values of r and h. From the problem statement, we know that the value of π is 3.14.
We are also told to round our answer to the nearest whole number. Using the given formula, we have: Lateral surface area = 2πrh where r is the radius of the circular base and h is the height of the cylinder. From the problem statement, we are not given the radius of the cylinder directly. However, we are given the diameter of the cylinder, which is 16. The radius is half of the diameter, so the radius can be calculated as: r = d/2 = 16/2 = 8 units We are also given the height of the cylinder as 18 units. Substituting these values in the formula, we get: Lateral surface area = 2 × 3.14 × 8 × 18Lateral surface area = 904.32 square units Rounding to the nearest whole number, the lateral surface area of the cylinder is 904 square units.
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Elsa pumpkin weighs 2/4 pound . her pumpkin is 1/4 pound heavier than Carson's pumpkin . Elsa thinks that Carson's pumpkin must weight 3/4 pound. how can else correct her mistat
Elsa can correct her mistake by informing that Carson's pumpkin weighs 1/2 pounds instead of 3/4 pounds.
Weight is a measure of the force exerted on an object due to gravity. It is the gravitational force acting on an object's mass. The weight of an object depends on its mass and the strength of the gravitational field it is in.
Weight plays a significant role in various fields such as physics, engineering, sports, and everyday life. It determines the force exerted by objects on surfaces, affects the performance of structures and vehicles, and is relevant in areas like weightlifting, aviation, and space exploration.
Given that Elsa pumpkin weighs 2/4 pounds and is 1/4 pound heavier than Carson's pumpkin.
Elsa thinks that Carson's pumpkin must weight 3/4 pound.
To find out how Elsa can correct her mistake, let's assume the weight of Carson's pumpkin to be x pounds.
It is given that Elsa's pumpkin weighs 1/4 pound heavier than Carson's pumpkin.
Therefore, Elsa's pumpkin weighs (x + 1/4) pounds. As per the question, Elsa thinks that Carson's pumpkin weighs 3/4 pounds.
But according to the information provided in the question, Elsa's pumpkin weighs (x + 1/4) pounds.
So, it can be inferred that: (x + 1/4) = 3/4⇒ x + 1/4 - 1/4 = 3/4 - 1/4⇒ x = 1/2
Therefore, Carson's pumpkin weighs 1/2 pounds which is different from what Elsa thought.
Therefore, Elsa can correct her mistake by informing that Carson's pumpkin weighs 1/2 pounds instead of 3/4 pounds.
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Abdicate has two electric train sets:A and B each trani
When the two sets are coupled together, the speed of the train is 96 km/h, and it takes 5 minutes to travel around the track. Abdicate has two electric train sets, A and B. Each train can be operated independently, or the two trains can be coupled together for double-head operation.
Abdicate has two electric train sets, A and B. Each train can be operated independently, or the two trains can be coupled together for double-head operation. Each set has a power car and two passenger cars, which can carry a total of 50 passengers. Set A has a top speed of 80 km/h, while set B has a top speed of 120 km/h. The sets operate on a circular track that is 4 km long.
If set A is operated independently, it takes 3 minutes to travel around the track. If set B is operated independently, it takes 2 minutes to travel around the track. If the two sets are coupled together for double-head operation, what is the speed of the train and how long will it take to travel around the track?
To determine the speed of the train when coupled together, we need to calculate the total distance travelled around the track and the total time taken.
When the two sets are coupled together, they operate as one train with a total of four cars, including two power cars and two passenger cars. Therefore, the total number of passengers that can be carried is 100.
Since the length of the track is 4 km, the distance travelled by the train will be twice that, or 8 km.
To determine the time taken for the train to travel around the track, we can use the formula:
time = distance/speed
When set A is operated independently, it takes 3 minutes to travel around the track, so the speed is:
speed = distance/time = 8 km / 3 min = 160/60 km/min = 2.67 km/min
When set B is operated independently, it takes 2 minutes to travel around the track, so the speed is:
speed = distance/time = 8 km / 2 min = 240/60 km/min = 4 km/min
To determine the speed of the train when coupled together, we can use the formula:
speed = distance/time = 8 km / t min
where t is the time taken for the train to travel around the track when coupled together.
We know that the total time taken for the train to travel around the track when coupled together is the sum of the times taken for set A and set B to travel around the track independently:
t = 3 min + 2 min = 5 min
Therefore, the speed of the train when coupled together is:
speed = distance/time = 8 km / 5 min = 96 km/h
So, when the two sets are coupled together, the speed of the train is 96 km/h, and it takes 5 minutes to travel around the track.
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Janice works at a cell phone company. She wants to make a presentation to her team about the features of a new phone. She makes a scale drawing of the phone using a scale of 1 inch to 0. 5 centimeter. The length of the scaled drawing is 28 inches, and its width is 15 inches. What are the actual dimensions of the phone? A. The length is 14 inches, and the width is 7. 5 inches. B. The length is 56 inches, and the width is 30 inches. C. The length is 56 centimeters, and the width is 30 centimeters. D. The length is 14 centimeters, and the width is 7. 5 centimeters. E. The length is 12 centimeters, and the width is 5. 5 centimeters.
The actual dimensions of the phone are 14 inches in length and 7.5 inches in width, confirming option A as the correct answer.
Janice created a scale drawing of the phone using a scale of 1 inch to 0.5 centimeters. The length of the scaled drawing is given as 28 inches, and its width is 15 inches. To find the actual dimensions of the phone, we need to convert the scaled dimensions back to their actual values.
Since the scale is 1 inch to 0.5 centimeters, we can use this ratio to convert the scaled dimensions to actual dimensions. For the length, we have 28 inches in the scaled drawing, so the actual length would be 28 inches * 0.5 centimeters/inch = 14 centimeters. Similarly, for the width, we have 15 inches in the scaled drawing, so the actual width would be 15 inches * 0.5 centimeters/inch = 7.5 centimeters.
Therefore, the actual dimensions of the phone are 14 inches in length and 7.5 inches in width. Option A correctly represents these dimensions.
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Miguel's coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $ 5. 95 per pound, and Type B coffee costs $ 4. 65 per pound. This month's blend used three times as many pounds of Type B coffee as Type A, for a total cost of $ 796. 0. How many pounds of Type A coffee were used?.
The cost Type A coffee were used in the blend 40 pounds .
assume the number of pounds of Type A coffee used is 'x'.
Given:
Cost of Type A coffee = $5.95 per pound
Cost of Type B coffee = $4.65 per pound
Total cost of the blend = $796.0
The blend used three times as many pounds of Type B coffee as Type A.
set up the equation to represent the total cost:
Total cost = Cost of Type A coffee + Cost of Type B coffee
$796.0 = $5.95 × x + $4.65 × (3x)
Simplifying the equation:
$796.0 = $5.95x + $13.95x
Combining like terms:
$796.0 = $19.9x
Dividing both sides by $19.9:
x = $796.0 / $19.9
x ≈ 40
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"The area of a solar cover to a rectangular pool is 12w-w^2, where w res presents the width. Write an expression for the length of the cover
The expression for the length of the cover is 12 - w, where w represents the width of the pool.
The expression for the area of a solar cover to a rectangular pool is given as 12w - w^2, where w represents the width of the pool. To write an expression for the length of the cover, we need to consider that the area of a rectangle is given by the product of its length and width.
Let L represent the length of the cover. We know that the area of the cover is equal to 12w - w^2. Therefore, we can write the equation:
L * w = 12w - w^2
To solve for L, we divide both sides of the equation by w:
L = (12w - w^2) / w
Simplifying the expression, we get:
L = 12 - w
Therefore, the expression for the length of the cover is 12 - w, where w represents the width of the pool.
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What is the vertex of the absolute value function defined by f(x)=|x+9|+1?
The vertex of the absolute value function defined by f (x) = |x + 9 | + 1 = (-9, 1).
The modulus function is also called the absolute value of a function gives the magnitude or absolute value of a number irrespective of the number being positive or negative.
It always gives a non-negative value of any number or variable. (-9, 1).
The function given is
ƒ(x) = |x + 9| + 1
The vertex is denoted as (h, k)
h: |x + 9| = 0
x + 9 = 0
x = - 9
k can be found by substituting the x value in the given function.
ƒ(-9) = |-9 + 9| + 1
f(-9) = 0 + 1
f(-9) = 1
Therefore, the vertex of the absolute value given function (-9, 1).
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David hosts a podcast and he is curious how much his listeners like his show. He decides to poll the next 100100100 listeners who send him fan emails.
They don't all respond, but 949494 of the 979797 listeners who responded said they "loved" his show.
Which direction of bias is more likely in this scenario?
Choose 1 answer:
Choose 1 answer:
A
The results are probably an underestimate of the percentage of all listeners that love the show.
B
The results are probably an overestimate of the percentage of all listeners that love the show.
C
The results are probably an unbiased estimate.
David hosts a podcast and he is curious how much his listeners like his show. He decides to poll the next 100 listeners who send him fan emails. They don't all respond, but 94 of the 97 listeners who responded said they "loved" his show. It is requested to determine which direction of bias is more likely in this scenario.
Bias is a tendency or inclination towards one side of an argument or viewpoint. In the given scenario, David decides to poll the next 100 listeners who send him fan emails, however, only 97 listeners responded. This could cause a bias towards those who love the show and have sent fan emails, and the opinion of those listeners who have not sent fan emails may not be taken into consideration.
The response rate is 97/100=0.97=97%.Therefore, the direction of bias in this scenario is "B. The results are probably an overestimate of the percentage of all listeners that love the show."This is because the response rate is only 97% which means that the opinions of 3% of the listeners who did not respond are not considered.
Additionally, there is a bias towards those who love the show and have sent fan emails, which does not represent the opinions of all the listeners.
Therefore, David should consider polling more listeners or find another way to gather feedback from his audience to get a more accurate representation of how much his listeners enjoy his show.
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If aplusb/a-b equals 3/5 what are the following ratios
If aplusb/a-b equals 3/5, then the ratios are as follows:apb / a-b = 3/5apb / 3 = a - bapb / 3 = a - b
Let's begin by assuming that aplusb/a-b equals 3/5:apb / a-b = 3/5
The cross-multiplication rule allows us to simplify the equation as follows:5apb = 3a - 3b
Rearrange the above equation and factor out a common factor of a - b to get: apb / 3 = a - b
Thus, the following ratios are obtained:
apb / 3 = a - b
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Consider a Hot Jupiter with a temperature of 3118 K orbiting the star Vega. At what wavelength (in nanometers) would the Hot Jupiter would be brightest?
The wavelength at which the Hot Jupiter would be brightest can be estimated using Wien's displacement law, which states that the peak wavelength of radiation emitted by a black body is inversely proportional to its temperature.
According to Wien's displacement law, the wavelength (λ) is given by the formula λ = b/T, where b is the Wien's displacement constant and T is the temperature in Kelvin.
Using the given temperature of the Hot Jupiter (3118 K) and the Wien's displacement constant, which is approximately equal to 2.898 × 10^6 nm·K, we can calculate the peak wavelength as follows:
λ = (2.898 × 10^6 nm·K) / (3118 K) ≈ 928.51 nm
Therefore, the Hot Jupiter would be brightest at a wavelength of approximately 928.51 nanometers.
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a triangle has 3 angles the first angle is 40 degrees less then the second sngle and the the first angle is 50 less than then the third angle
Therefore, the three angles of the triangle are:
First angle: 50 degrees
Second angle: 90 degrees
Third angle: 70 degrees
Let's denote the three angles of the triangle as follows:
First angle: x
Second angle: y
Third angle: z
According to the given information, we can write the following equations:
The first angle is 40 degrees less than the second angle:
x = y - 40
The first angle is 50 degrees less than the third angle:
x = z - 50
Since a triangle has a total of 180 degrees, we can express the relationship between the three angles as:
x + y + z = 180
Now, let's solve the system of equations:
Substituting the value of x from equation (1) into equation (3):
(y - 40) + y + z = 180
2y + z = 220
Substituting the value of x from equation (2) into equation (3):
(z - 50) + y + z = 180
2z + y = 230
We now have a system of two equations with two variables (2y + z = 220 and 2z + y = 230).
Solving this system of equations, we find:
y = 90 degrees
z = 70 degrees
Substituting these values back into equation (1):
x = y - 40
x = 90 - 40
x = 50 degrees
Therefore, the three angles of the triangle are:
First angle: 50 degrees
Second angle: 90 degrees
Third angle: 70 degrees
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A spinner is divided into six equal-sized sectors labeled 1 through 6. Dwayne spins this spinner 12 times. Let X represent the number of 1s that are spun. What are the mean and standard deviation of X? Mu Subscript x Baseline = 1, Sigma Subscript x Baseline = 1. 29 Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1. 29 Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1. 67 Mu Subscript x Baseline = 10, Sigma Subscript x Baseline = 2. 78.
Given that a spinner is divided into six equal-sized sectors labeled 1 through 6 and Dwayne spins this spinner 12 times. Let X represent the number of 1s that are spun.
We need to find the mean and standard deviation of X.Mean of X:Mean of a binomial distribution is given by the formula:μx = n * Pwhere n is the number of trials and P is the probability of success.Here, n = 12 and P = Probability of getting 1 on a single spin = 1/6.∴ μx = 12 × (1/6) = 2Standard Deviation of X:Standard deviation of a binomial distribution is given by the formula.
σx = √(n × P × Q)Where Q is the probability of failure and is given by:Q = 1 - PHere, n = 12, P = Probability of getting 1 on a single spin = 1/6 and Q = 1 - P = 5/6.∴ σx = √(12 × (1/6) × (5/6))= √1 = 1Hence, the mean and standard deviation of X are:Mean = 2Standard deviation = 1Therefore, the option that represents the correct values of mean and standard deviation of X is:Mu Subscript x Baseline = 2, Sigma Subscript x Baseline = 1.
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The ages of armadillos are normally distributed, with a mean of 14 years and a standard deviation of 1. 2. Approximately what percentage of the armadillos are between 13 and 17 years old? 20. 33% 49. 38% 47. 62% 79. 5%.
Approximately 79.5% of the armadillos are between 13 and 17 years old.
To determine the percentage of armadillos between 13 and 17 years old, we need to calculate the cumulative probability within that range using the normal distribution.
Given that the ages of armadillos are normally distributed with a mean (μ) of 14 years and a standard deviation (σ) of 1.2 years, we can use the properties of the normal distribution to find the desired percentage.
To calculate the percentage, we need to find the z-scores corresponding to the values of 13 and 17, and then find the cumulative probability associated with those z-scores.
First, let's calculate the z-score for 13:
z = (x - μ) / σ
= (13 - 14) / 1.2
≈ -0.833
Next, let's calculate the z-score for 17:
z = (x - μ) / σ
= (17 - 14) / 1.2
≈ 2.5
Using a standard normal distribution table or a statistical software, we can find the cumulative probabilities associated with these z-scores.
The cumulative probability for a z-score of -0.833 is approximately 0.2023 (or 20.23%).
The cumulative probability for a z-score of 2.5 is approximately 0.9938 (or 99.38%).
To find the percentage of armadillos between 13 and 17 years old, we subtract the cumulative probability of 13 from the cumulative probability of 17:
Percentage = (0.9938 - 0.2023) * 100
≈ 79.5%
Therefore, approximately 79.5% of the armadillos are between 13 and 17 years old.
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Approximately what percentage of the armadillos are between 13 and 17 years old?
∠1 and ∠2 are supplementary. ∠1=124°∠2=(2x+4)°What is the value of x?Select from the drop down menu to correctly answer the question. X =Choose. A. 13B. 26C. 40D. 36E. 41
Since it is given that ∠1 and ∠2 are supplementary angles, the value of x=26.
Given that ∠1 and ∠2 are supplementary.
∠1=124°
∠2=(2x+4)°
We know that the sum of supplementary angles is 180°.
For, example if ∠A, ∠B ,∠C and ∠D are four angles of a quadrilateral, and ∠A and ∠D are supplementary. Then,
∠A + ∠D= 180°
Therefore,
∠1 + ∠2 = 180°
Substituting the values given, we have:
124° + (2x + 4)° = 180°
Simplifying, we have:
2x + 128° = 180°
2x = 180° - 128°
2x = 52°
x = 52°/2
x = 26
Hence, the value of x is 26. Therefore, the correct answer is option B.
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(m + 2)4 = (1)(m4)(20) + (4)(m3)(21) + (6)(m2)(22) + (4)(m1)(23) + (1)(m0)(24)
Simplify each term to complete the expansion.
(m + 2)4 = m4 +
m3 +
m2 +
m +
The expanded form of (m + 2)4 is m4 + m3 + m2 + m + 16. To simplify each term, we can apply the binomial expansion formula.
The formula states that for any binomial expression (a + b)n, the expanded form can be written as the sum of the terms obtained by raising each term to the power of n and multiplying it by the corresponding coefficients. In this case, our binomial expression is (m + 2)4.
Expanding the binomial using the formula, we get:
(m + 2)4 = (1)(m4)(20) + (4)(m3)(21) + (6)(m2)(22) + (4)(m1)(23) + (1)(m0)(24)
Simplifying each term, we have:
(m4)(20) = m4
(4)(m3)(21) = 4m3
(6)(m2)(22) = 12m2
(4)(m1)(23) = 8m
(1)(m0)(24) = 16
Combining all the simplified terms, we get:
m4 + 4m3 + 12m2 + 8m + 16
Therefore, the expansion of (m + 2)4 is m4 + m3 + m2 + m + 16.
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Petro made a tally chart shown below. Hours Spent Watching TVA 2-column table with 4 rows titled Hours Spent Watching TV. Column 1 is labeled Hours with entries 4, 5, 6, 7. Column 2 is labeled Tally with entries 4, 4, 3, 4. Which would be a good statistical question based on the tally chart?Did you watch four hours of TV today?Did you watch TV today?Did you watch five or six hours of TV today?How many hours did you spend watching TV today?
A good statistical question based on the tally chart would be: "How many hours did you spend watching TV today?"
The tally chart provides information about the hours spent watching TV, with corresponding tallies for each hour category. A good statistical question seeks to gather information and analyze the data.
While the other options are yes-or-no questions or limited to specific hour values, the question "How many hours did you spend watching TV today?" allows for a broader range of responses. It encourages individuals to provide quantitative data regarding their TV-watching habits.
By collecting this data, researchers can calculate measures such as mean, median, or mode to understand the average time spent watching TV and analyze patterns or trends. It provides a basis for further statistical analysis and exploration of TV viewing habits.
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Martina asked her boss for a salary of $500 per week. She was offerd a salary of $19,500 per year. How much less was that then what she requested.
The amount that Martina's offered salary is less than what she requested is $6,500.
To determine how much less Martina's offered salary is compared to her requested salary, we need to calculate the difference between the two amounts.
Martina requested a salary of $500 per week. To calculate her annual requested salary, we can multiply $500 by the number of weeks in a year (52 weeks):
Requested salary = $500/week * 52 weeks/year = $26,000/year
Martina was offered a salary of $19,500 per year. To find the difference between the offered salary and the requested salary, we subtract the offered salary from the requested salary:
Difference = Requested salary - Offered salary
= $26,000 - $19,500
= $6,500
Therefore, the amount that Martina's offered salary is less than what she requested is $6,500.
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Sam’s brother is 4 years older than him. Their mother is 3 times older than Sam. Their ages together total 74 years. How old are the family members?
Let's assign variables to represent the ages of Sam, his brother, and their mother.
Let:
Sam's age = S
Brother's age = B
Mother's age = M
According to the given information, we can form the following equations:
1. Brother's age is 4 years older than Sam's age: B = S + 4
2. Mother's age is 3 times older than Sam's age: M = 3S
3. The sum of their ages is 74: S + B + M = 74
We can substitute the values from equations 1 and 2 into equation 3 to solve for the ages:
S + (S + 4) + 3S = 74
5S + 4 = 74
5S = 70
S = 14
Substituting the value of S back into equations 1 and 2:
B = S + 4 = 14 + 4 = 18
M = 3S = 3(14) = 42
Therefore, Sam is 14 years old, his brother is 18 years old, and their mother is 42 years old.
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What property allows one to set aside the order of operations how
The property that allows one to set aside the order of operations is called the Commutative Property. The order of operations is also known as the PEMDAS rule.
The order of operations, also known as the PEMDAS rule (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), is a fundamental principle in mathematics that dictates the sequence in which operations should be performed in an arithmetic expression. However, there are instances where the order of operations can be set aside or rearranged without affecting the final result. This is possible due to the Commutative Property, which applies to addition and multiplication.
The Commutative Property states that the order in which numbers are added or multiplied does not change the result. For addition, it means that the sum of two numbers remains the same regardless of the order in which they are added.
By applying the Commutative Property, one can rearrange the order of addition or multiplication operations, allowing for more flexibility in evaluating expressions. This property is particularly useful when simplifying or solving mathematical equations, as it enables us to change the order of terms without altering the final outcome. However, it's important to note that the Commutative Property does not apply to subtraction or division operations, and the order of operations should be followed strictly in such cases.
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The question is incomplete, so this is a general answer.
A bottle holds 1/5 L of water Sarah uses 10 bottles of water to make juice. How many liters of water does Sarah used to make juice?
Sarah uses 10 bottles of water to make juice, and each bottle holds 1/5 L of water. To find the total amount of water Sarah used, we multiply the number of bottles by the amount of water in each bottle. Therefore, Sarah used a total of 2 liters of water to make juice.
Given that each bottle holds 1/5 L of water, we can calculate the total amount of water used by multiplying the amount of water per bottle by the number of bottles.
Amount of water per bottle = 1/5 L
Number of bottles = 10
To find the total amount of water, we multiply:
Total water = (Amount of water per bottle) x (Number of bottles)
= (1/5 L) x (10 bottles)
= 2 L
Therefore, Sarah used a total of 2 liters of water to make juice.
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