A bicycle rider is going 4 m/s on her bike. If her kinetic energy is 550 J, what is her mass?
The mass of the bicycle rider is approximately 68.75 kg.
What is kinetic energy?Kinetic energy is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. The formula for kinetic energy is:
Kinetic Energy = 1/2 * mass * velocity²
where mass is the mass of the object and velocity is the speed at which it is moving. Kinetic energy is a scalar quantity and is measured in joules (J) in the SI system.
We can use the formula for kinetic energy to solve for the mass of the bicycle rider:
Kinetic Energy = 1/2 * mass * velocity²
Substituting the given values, we have:
550 J = 1/2 * mass * (4 m/s)²
Simplifying and solving for mass, we get:
mass = 550 J / (1/2 * (4 m/s)²
mass = 550 J / (8 kg m²/s²
mass = 68.75 kg
Therefore, the mass of the bicycle rider is approximately 68.75 kg.
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Hello and greetings lilliepruiett.
The mass of the cyclist who is going at 4 m/s, and who has a kinetic energy of 550 Joules, is 68.75 kilograms.
Step-by-step explanation:It is an exercise of kinetic energy, which is the energy that an object possesses due to its movement. It is defined as the energy required to accelerate an object of a given mass from rest to its current speed. Kinetic energy can be calculated using the following formula:
Ek = (m × v²)/2
where:
Ek is the kinetic energy in joules (J).m is the mass of the object in kilograms (kg).v is the speed of the object in meters per second (m/s).This formula indicates that the kinetic energy increases as the mass of the object increases and/or its speed increases. Kinetic energy is a direct measure of an object's ability to do work due to its motion.
We have that the cyclist is going at a speed of 4 m/s, when his kinetic energy is 550 Joules, we calculate the mass.
As we are asked to calculate the mass, we solve the formula:
Ek = (m × v²)/2m = (2 × Ek)/v²What we do now is; substitute the data into the cleared formula and solve for the mass of the cyclist.
m = (2 * Ek)/v²
m = (2 × 550 J)(4 m/s)²
m = (1100 J)/(16 m²/s²)
m = 68.75 kg
The mass of the cyclist who is going at 4 m/s, and who has a kinetic energy of 550 Joules, is 68.75 kilograms.
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3. Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over the course of 2 hours, 4 times Adrian’s favorite team was ahead by 3 points, and 4 times Adrian’s favorite team was behind by 4 points. All other times, the two teams were tied.
(a) What is the average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game? Show your work neatly.
(b) Explain what this value means about Adrian’s favorite team’s performance.
The average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game is -0.3333.
What is data set?
A data set is a group of related data. In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.
Here, we have
Given: Adrian kept an eye on the basketball game score by looking online every 10 minutes. Over 2 hours, 4 times Adrian’s favorite team was ahead by 3 points, and 4 times Adrian’s favorite team was behind by 4 points. All the other times, the two teams were tied.
The mean of a data set is given by the sum of all observations divided by the number of observations.
Adrian looked at the scores every 10 minutes in 2 hours, thus 12 times, as
= (2×60)/10 = 12
4 times ahead by 3 points, thus 4×3 = 12
4 times behind by 4 points, thus -4×4 = -16
At the other moments, the game was tied, thus the observation is 0.
Thus, the mean is of:
M = (12 - 16 = 0)/12 = -4/12 = -0.333
Hence, The average score of Adrian’s favorite team relative to its opponent using the observations Adrian made during the game is -0.3333.
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HELP Use the values of a, and S, to find the value of an.
a₁ = 8 and S40 = 6960; a40
a40
Answer:
a₄₀=340
Step-by-step explanation:
Sₙ=[(a₁+aₙ)/2]*n
a₁=8 n=40 S₄₀=6960
S₄₀=[(a₁+a₄₀)/2]*40
6960=[(8+a₄₀)/2]*40 /:40
174=(8+a₄₀)/2 /*2
348=8+a₄₀
a₄₀=340
27. The West Middle School Math Club has 15 sixth-grade members, 12 seventh-grade
members, and 13 eighth-grade members. What percent of the math club members are
either sixth- or seventh graders?
A. 30%
B. 32.5%
C. 67.5%
D. 72%
There are 15 + 12 = <<15+12=27>>27 sixth and seventh-grade members.
The total number of members is 15 + 12 + 13 = <<15+12+13=40>>40.
The fraction of members that are either sixth- or seventh-grade members is 27/40.
To convert this to a percentage, we multiply by 100: 27/40 × 100% = 67.5%
Therefore, the answer is (C) 67.5%.
As of 2019, the Burj Khalifa, located in Dubai, was the tallest building in the world. Suppose a scale model of the Burj Khalifa (without antennae) is 30 inches tall.
1. To what scale is this model? You will need to use the internet or another resource to find the actual height of the building.
2. How tall would a model of the Eiffel tower be at this scale?
This scale is commonly referred to as 1/90.56.
A model of the Eiffel Tower at the same scale as the model of the Burj Khalifa would be 11.7 inches tall.
What is a model?A model is a simplified version of reality that can help explain the workings of a complex system.
The actual height of the Burj Khalifa is 2,717 feet (828 metres).
To determine the scale of the model, we must divide the actual height by the model height:
Scale = (Actual Height)/(Model Height)
= (2,717 feet)/(30 inches)
= 90.56 feet/inch
This scale is commonly referred to as 1/90.56.
To calculate the height of a model of the Eiffel Tower, we must multiply the actual height of the tower (1,063 feet) by the scale:
Model Height = (Actual Height) x (Scale)
= (1,063 feet) x (1/90.56)
= 11.7 inches
Therefore, a model of the Eiffel Tower at the same scale as the model of the Burj Khalifa would be 11.7 inches tall.
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how many ways are there to select 8 countries in the united nations to serve on a council if 3 is selected from a block of 52, 2 are selected from a block of 64 and 3 are selected from the remaining 73 countries?
Number of ways to select 8 countries from the United Nations is 48,054,722,400
To solve this problem, we need to use the combination method, which states that if there are m ways to perform one task and n ways to perform another task after the first task is completed, then there are m x n ways to perform both tasks in sequence.
Using this principle, we can break down the selection of 8 countries into three separate tasks
Selecting 3 countries from a block of 52: There are 52C3 ways to do this, where 52C3 is the binomial coefficient "52 choose 3," which can be calculated as follows
52C3 = (52 x 51 x 50) / (3 x 2 x 1) = 22,100
Selecting 2 countries from a block of 64: There are 64C2 ways to do this, where 64C2 is the binomial coefficient "64 choose 2," which can be calculated as follows
64C2 = (64 x 63) / (2 x 1) = 2,016
Selecting 3 countries from a block of 73: There are 73C3 ways to do this, where 73C3 is the binomial coefficient "73 choose 3," which can be calculated as follows
73C3 = (73 x 72 x 71) / (3 x 2 x 1) = 1,082,790
To find the total number of ways to select 8 countries, we simply multiply these three quantities together
22,100 x 2,016 x 1,082,790 = 48,054,722,400
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f the square below is enlarged by a scale factor of 2.2, what will be the perimeter of the new square?
A square is drawn with a length of 10 units and a width of 10 units
Answer: The perimeter of the original square is the sum of the lengths of all its sides, which are all equal to 10 units:
Perimeter of original square = 4 x 10 = 40 units
When the square is enlarged by a scale factor of 2.2, all of its sides will be multiplied by 2.2:
New side length = 2.2 x 10 = 22 units
The perimeter of the new square is the sum of the lengths of all its sides, which are all equal to 22 units:
Perimeter of new square = 4 x 22 = 88 units
Therefore, the perimeter of the new square is 88 units.
Step-by-step explanation:
The area of a square can be determined by the function A=s^2 , where A represents the area of the square and s represent the length of one side. Jada is buying square picture frames to hang her high school graduation pictures in her college dorm room
a.if the length of one side of the picture is s inches, what expression represents the area of the frame?
b.If Jada decides that she actually needs four picture frames, what expression represents the total area?
c.If Jada decided to buy one picture frame with a side 4 times longer than the first, what expression represents its area?
d.if the length of one side of the original frame was 8 inches, what was the area of
i. The original picture frame?
ii. Four of the original picture frames"
iii. One picture frame with a side 4 times as long?
please please help mee
The equation A=[tex]s^2[/tex] can be used to calculate the area of a square, where A stands for the square's surface area and s for one of its sides.
a. The area of the frame is equal to 4x * s + [tex]4x^2[/tex] if one side of the image is s inches long.
b. The overall area is 16x * s + [tex]16x^2[/tex] if Jada determines she actually wants four photo frames.
a. If the length of one side of the picture frame is s inches, then the length of one side of the frame is (s + x) inches, where x is the width of the frame (assuming the frame is a uniform width on all sides). The following expression is used to represent the frame's area:
Area of the frame = (s + 2x) * (s + 2x) - s * s
Area of the frame = 4x * s + [tex]4x^2[/tex]
b. In the event that Jada determines she actually requires four photo frames, the statement that denotes the entire space is:
Total area = 4 * (4x * s + [tex]4x^2[/tex])
Total area = 16x * s + [tex]16x^2[/tex]
c. If Jada decided to buy one picture frame with a side 4 times longer than the first, then the length of one side of the larger frame is 4s inches. The expression that represents the area of the larger frame is:
Area of the larger frame = (4s + 2x) * (4s + 2x) - (4s) * (4s)
Area of the larger frame = 16x * s + [tex]4x^2 + 16s^2[/tex]
d. If the length of one side of the original frame was 8 inches, then:
i. The original picture frame has an area of A = [tex]s^2[/tex]
The original picture frame has an area of A = [tex]8^2[/tex]
The original picture frame has an area of A = 64 square inches.
ii. Four of the original picture frames have a total area of:
Total area = 4 * A
Total area = 4 * 64
Total area = 256 square inches.
iii. One picture frame with a side 4 times as long has an area of:
Area of the larger frame = [tex](4s)^2[/tex]
Area of the larger frame = [tex]16s^2[/tex]
Area of the larger frame = [tex]16 * 8^2[/tex]
The area of the larger frame is 1024 square inches.
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Find the area of each figure.
Parallelogram ABDE is made up of square ACDF, triangle ABC, and
triangle FDE. Triangle ABC and triangle FDE are identical. The area of
square ACDF is 36 square meters. Find the area of triangle ABC.
Then find the area of parallelogram ABDE.
4 m
B
4 m
F
D
E
The area of Triangle ABC is 12² m while the area of parallelogram ABDE is 60² m.
What is parallelograms?
A parallelοgram is a simple quadrilateral with twο sets οf parallel sides in Euclidean geοmetry. A parallelοgram is a quadrilateral with twο sets οf οppοsite sides that are parallel and equal. There are fοur types οf parallelοgrams, three οf which are unique. Parallelοgrams, squares, rectangles, and rhοmbuses are the fοur different shapes.
When a quadrilateral has twο sets οf parallel sides, it is a parallelοgram. A parallelοgram's οppοsing sides and angles are bοth the same length. Internal angles οn the same side οf a Angles can alsο be hοrizοntal lines. There are 360 internal angles in tοtal.
Area of ACDF = 36² m (side × side)
Each side = √36
Each side = 6
AB = 6
Area of Triangle = 1/2(b)(h)
Area of Triangle ABC = 1/2(4)(6)
Area of Triangle ABC = (2)(6)
Area of Triangle ABC = 12² m
Area of parallelogram = (b)(h)
Area of parallelogram ABDE = (4 + 6)(6)
Area of parallelogram ABDE = (10)(6)
Area of parallelogram ABDE = 60² m
Thus, The area of Triangle ABC is 12² m while the area of parallelogram ABDE is 60² m.
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if the arrival rate is 15 cars per minute, what is the probability that something other than between 1 and 5 seconds will elapse between arrivals?
The probability that something other than between 1 and 5 seconds will elapse between arrivals is 0.917.
There are three parts to this question. First, you need to know the arrival rate which is 15 cars per minute. Second, you need to know the probability of a car arriving between 1 and 5 seconds which is 0.083.
Third, you need to know the probability that something other than between 1 and 5 seconds will elapse between arrivals which can be calculated as follows:
P (something other than 1 to 5 seconds elapse) = 1 - P (1 to 5 seconds elapse)
P (1 to 5 seconds elapse) = 0.083
P (something other than 1 to 5 seconds elapse) = 1 - 0.083 = 0.917
Therefore, the probability that something other than between 1 and 5 seconds will elapse between arrivals is 0.917 .
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What justifies the use of the normal distribution for the sampling distribution of proportion? The ability of the normal distribution to approximate the binomial distribution under appropriate conditions The Central Limit Theorem The large population size The Law of Large Numbers Question 3 0.25 pts The sampling distribution of the proportion follows the normal distribution when the values np and nq are greater than or equal to 0.05 50
The Central Limit Theorem justifies the use of the normal distribution for the sampling distribution of proportion.
The Central Limit Theorem states that under certain conditions, the sampling distribution of the mean of a random sample drawn from any population will be approximately normal, regardless of the shape of the population distribution. One of these conditions is that the sample size should be large enough, typically n >= 30. For the sampling distribution of proportion, the Central Limit Theorem applies because the proportion is essentially a mean of a sample of binary data of a normal distribution (e.g. success or failure). If the sample size is large enough, the sampling distribution of the proportion will be approximately normal, regardless of the shape of the population distribution. The condition np >= 5 and nq >= 5 is used to ensure that the sample size is large enough for the normal approximation to be valid. In essence, this condition ensures that there are enough successes and failures in the sample to satisfy the conditions of the Central Limit Theorem. If this condition is not met, then the normal approximation may not be valid and alternative methods, such as the binomial distribution, should be used instead.
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The ratio of apples to bananas in a bowl of fruit is 2 to
3. If there are 12 apples in the bowl, then how many
bananas are there?
We know that the ratio of apples to bananas is 2 to 3, which can also be written as 2/3.
Let's use a proportion to solve for the number of bananas:
2/3 = 12/x
Here, x represents the number of bananas in the bowl.
To solve for x, we can cross-multiply:
2x = 3 * 12
2x = 36
x = 18
Therefore, there are 18 bananas in the bowl.
Answer:
18 bananas
Step-by-step explanation:
for every 2 apples, there are 3 bananas.
So, if there are 12 apples then the original ratio of number of apples is being multiplied by 6
To prove this, 2 is the original ratio of apples and when 2 is multiplied by 6, you get 12 apples
To ensure the ratio of apples to bananas is the same, you multiply the original ratio of bananas by 3 as well. This leaves us with 18 bananas for every 12 apples (3*6 = 18)
To check if you are correct, you divide both the number of apples and the number of bananas by 6 and you get the original ratio, 2 to 3.
The ratio is essentially the same throughout except when you increase it by a constant ratio, it is no longer simplified but it is the same.
I tried explaining this the best I could and I really hope this made sense and helped!
A rectangular field is 150 metres long and 100 metres wide. How many
times would a runner have to go around the field to run 2 kilometres?
Answer:
about 1.5 times
Step-by-step explanation:
The time t in seconds for the pendulum of a large clock to make one swing is given by T=2√L/3.3 where L is the length of the pendulum in feet. if one swing takes 4 seconds, how long is the pendulum?
The length of the pendulum using equation is 43.56 feet.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here the given equation that represent the time of pendulum for one swing is
=> T = [tex]\frac{2\sqrt L}{3.3}[/tex]
Now T = 4 sec then ,
=> 4 = [tex]\frac{2\sqrt L}{3.3}[/tex]
=> 4*3.3 = 2[tex]\sqrt L[/tex]
=> [tex]\sqrt L = 2\times3.3 = 6.6[/tex]
=> L = 43.56 feet.
Hence the length of the pendulum using equation is 43.56 feet.
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The age of the mother will be five times the age of her daughter in five years time. If the sum of their ages now is 90 years, calculate the present age of the mother
The present age of the mother is 26.4 years.the age of the mother and the age of the daughter and then combined them to solve for the age of the mother. The answer is that the present age of the mother is 26.4 years.
Let x = present age of the mother ,Let y = present age of the daughter.According to the question, x + y = 90 and(x+5)=5(y+5).Substituting the value of x + y from the first equation in the second equation,(x+5)=5(y+5.Simplifying the equation, 2y + 5 = 5xRearranging the equation, 2y = 5x - 5,Dividing both sides by 2, y = (5x - 5) / 2 ,Substituting the value of y in the first equation, x + ((5x - 5) / 2) = 90 Simplifying, 2x + 5x - 5 = 180 .7x = 185 .Dividing both sides by 7, x = 185 / 7 ,x = 26.4 Therefore, the present age of the mother is 26.4 years.
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what is the best point estimate for the population's standard deviation if the sample standard deviation is 46.8 ?
The best point estimate for the population's standard deviation, given a sample standard deviation of 46.8, is 46.8 itself.
In mathematical terms, let's denote the population standard deviation as σ, and the sample standard deviation as s. The formula for calculating s is:
s = √(∑(x - [tex]\bar{x}[/tex])² / (n - 1))
where x is the value of each data point, [tex]\bar{x}[/tex] is the sample mean, n is the sample size, and ∑ means "sum of".
Now, if we assume that the sample is a representative sample of the population, we can use the sample standard deviation as an estimate for the population standard deviation. In other words:
σ ≈ s
This means that we can use 46.8 as an estimate for the population standard deviation.
However, it's important to keep in mind that this is just an estimate, and there is some level of uncertainty associated with it. The true population standard deviation may be slightly higher or lower than this estimate.
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In circle O, OP = 8 and the area of shaded sector = 8. Find the length of PRQ.
Express your answer as a fraction times .
The length of PRQ is 2, expressed as a fraction times .
What is circle?A circle is a two-dimensional shape defined by the set of points on a plane which are equidistant from a fixed point known as the center. Circles are one of the most basic shapes in geometry, and they are found in nature, architecture, and many other areas. They have many properties, including a circumference, a diameter, a radius, and an area. Circles are used in mathematics, science, engineering, and other fields.
Let θ denote the central angle of the shaded sector. Then, the area of the shaded sector is
Area of shaded sector = (1/2)r²θ = 8
where r is the radius of the circle.
Therefore, r²θ = 16
Since OP = 8, the radius of the circle is 8. Hence,
r²θ = 16
(8)²θ = 16
θ = 16/64
Now, PRQ is an arc of the circle. Let s denote the length of the arc PRQ. Then,
s = θr = (16/64)8 = 2
Hence, the length of PRQ is 2, expressed as a fraction times .
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how can i use models to add fractions
There are different models that can be used to add fractions, but one common model is the area model, which represents fractions as parts of a whole.
To use the area model to add fractions, you can follow these steps:
1. Draw a rectangle to represent the whole. The size of the rectangle can be arbitrary, but it should be divided into equal parts to match the denominators of the fractions you are adding.
2. Divide the rectangle into the appropriate number of equal parts to represent the denominators of the fractions. For example, if you are adding 1/3 and 1/4, divide the rectangle into 12 equal parts (3 x 4 = 12).
3. Shade the appropriate number of parts in each fraction. For example, shade 4 out of 12 parts for 1/3 and 3 out of 12 parts for 1/4.
4. Count the total number of shaded parts in the rectangle. This represents the numerator of the sum of the fractions.
5. Write the sum of the fractions as the total number of shaded parts over the total number of parts in the rectangle.
For example, to add 1/3 and 1/4 using the area model:
1. Draw a rectangle to represent the whole.
```
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
```
2. Divide the rectangle into 12 equal parts.
```
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
1 2 3 4
```
3. Shade 4 out of 12 parts for 1/3 and 3 out of 12 parts for 1/4.
```
+---+---+---+---+
|###|###|###| |
+---+---+---+---+
|###|###|###| |
+---+---+---+---+
|###|###| | |
+---+---+---+---+
The curve shifts to the right if the determinant causes demand to increase. This means more of the good or service are demanded even though there's no change in price. When the economy is booming, buyers' incomes will rise. They'll buy more of everything, even though the price hasn't changed.
The demand curve is a graphical representation of the relationship between the quantity of a good or service that buyers are willing and able to purchase at various prices. It is based on the law of demand, which states that as the price of a good or service increases, the quantity demanded decreases, and vice versa.
However, there are other factors that can affect demand besides price, such as changes in buyers' incomes, tastes and preferences, the prices of related goods or services, and expectations about future prices or economic conditions. When one or more of these factors changes, the entire demand curve can shift to the right or left, indicating a change in the quantity demanded at every price.
In the case of an increase in buyers' incomes, the demand curve for most goods or services will shift to the right. This means that at every price level, buyers will be willing and able to purchase more of the good or service than before. This can be explained by the fact that when buyers' incomes increase, they have more purchasing power and are able to buy more of everything, including the good or service in question.
For example, if the economy is booming and buyers' incomes are rising, they may be more willing to purchase luxury goods or services that they previously couldn't afford. This could lead to an increase in demand for high-end products such as luxury cars, designer clothing, and high-end restaurants, even though the prices of these goods or services have not changed.
In summary, changes in buyers' incomes are one of several factors that can cause the demand curve to shift to the right or left. When buyers' incomes increase, the demand for most goods or services will increase as well, indicating that buyers are willing and able to purchase more of the good or service at every price.
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The curve shifts to the right if the determinant causes demand to increase. This means more of the good or service are demanded even though there's no change in price. When the economy is booming, buyers' incomes will rise. They'll buy more of everything, even though the price hasn't changed. write a statement according to the context .
18. Subtract 5 5/21 from 13 1/7 (reducing to lowest terms if necessary).
O A. 71⁹/21
B. 1019/21
C. 71⁹/1
O D. 10¹⁹/7
Answer:
Your answer is: A) [tex]7\frac{19}{21}[/tex]
Step-by-step explanation:
An iPhone was reduced from $938.99 to $538.99. Find the percent of the reduction in the price. Round your answer to the nearest tenth.
Percent Decrease =
Please explain how you got ur answer or show your work.
Answer:
42.6%
Step-by-step explanation:
Initial price of the iPhone = $938.99
Final price of the iPhone = $538.99
Decrese in price = $(938.99 - 538.99 )
= $ 400 .
We can calculate decrease in percentage by ,
= Decrease / Initial price * 100
= $400/938.99 * 100
= 42.59%
= 42.6% ( nearest tenth)
Hence the required answer is 42.6% .
Determine the intercepts with the axes X³-12x²+36x
The intercepts of x- axis is (0, 0) (6,0) and y - axes is (0,0)
The x-intercept is the point on the x-axis that is the shortest distance from the origin to the point where the line cuts the x-axis, and the y-intercept is the point on the y-axis that is the shortest distance from the origin to the point where the line cuts the y-axis. Both of these are referred to as the origin.
The polynomial function is :
f(x) = [tex]x^3-12x^2+36x[/tex]
[tex]x^3-12x^{2} +36x=0[/tex] [x intercepts]
[tex]x(x^{2} -12x+36)=0[/tex]
[tex]x(x - 6)^2=0[/tex] [=> x = 0 x = 6]
x = 0 [y intercepts]
x = 0 [=> y = 0]
=> (0, 0) (6,0) [Interception point with x -axis]
=> (0, 0) [Interception point with y- axis]
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a man and woman both with normal vision had color-blind fathers. if this man and woman have a child, what is the probability that the child will be color blind?
The probability that the child will be color blind is 25%.
In this scenario, the father and mother are carriers of the color-blindness allele. They have one dominant normal vision allele and one recessive color-blindness allele, so they themselves do not have color blindness. Both of their fathers, however, had color blindness. This means that the fathers had two recessive color-blindness alleles, and so they had the condition.
The probability of the child being color-blind can be calculated by a Punnett square. Let's call the normal vision allele "N" and the color-blindness allele "n". The father's genotype is Nn, and the mother's genotype is also Nn. When these are crossed, there are four possible offspring genotypes:NN (normal vision)Nn (normal vision, but carrier of color-blindness allele)nn (color-blind)NN Nn Nn nnNN Nn Nn nnN N N N Nn Nn N n Nn Nn nn nnWhen we count up the possible offspring, we see that there is one chance of an nn genotype out of four possible genotypes, so the probability is 1/4 or 25%.
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HELP PLS!!!! if you could do it asap, that would be greatly appreciated
The angle between the intersecting tangents is 128° and the value of a is calculated to be 26° which makes the option A. 26° correct.
What is an angle between intersecting tangentsThe angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.
The 2 right angles formed are congruent which implies that the sum of half the angle between the intersecting tangents and (a + 90) will be 180°.
angle between the intersecting tangents = 180 - 52
angle between the intersecting tangents = 128
half angle between the intersecting tangents = 128/2
half angle between the intersecting tangents = 64
a + 90 + 64 = 180° {sum of interior angles of a triangle}
a = 180 - 154
a = 26.
Therefore, the angle between the intersecting tangents is 128 which makes the value of a equal to 26.
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Select all that apply. Which of the following are linear factors of p(x) = x3 - 2x2 - 5x + 6 ?
Numbers 2, 3, and 4 are the following are linear factors of p(x).
What does a linear equation mean in mathematics?
A linear equation is one that only has a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
Occasionally, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The term "linear equation" refers to equations with power 1 variables. Where ax+b = 0 is one example with only one variable, where a and b are real numbers and x is the variable.
We can know the answer to this by letting p(x) be equal to zero and by substituting the values of x to the function.
p(x) = x3 - 2x2 - 5x + 6
To know what to substitute, we equate all factors to zero since even if only one of these factors is zero, the product of all factors would immediately be zero.
1 . x + 1 = 0 ; x = -1
2. x + 2 = 0 ; x = -2
3. x - 1 = 0 ; x = 1
4. x - 3 = 0 ; x = 3
We then try to substitute each value of x to the original polynomial and see if it will equal to zero.
1. (-1)³ - 2(-1)² - 5(-1) + 6 = 8 ≠ 0
2. (-2)³ - 2(-2)² - 5(-2) + 6 = 0
3. (1)³ - 2(1)² - 5(1) + 6 = 0
4. (3)³ - 2(3)² - 5(3) + 6 = 0
As we can see, all but number 1 equated to zero therefore numbers 2, 3, and 4 are all linear factors of p(x).
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Molly is filling bags of marbles. She makes each bag so that 3 out of every 8 marbles are blue. Which equation correctly compares the number of marbles she uses, x, to the number of blue marbles, y?
The equation y = 3/8x can be used to compare the number of marbles Molly uses, x, to the number of blue marbles, y, in each bag.
To calculate the number of blue marbles Molly uses, we can use the equation y = 3/8x.
To start, we need to identify the variables in the equation. In this case, x represents the number of marbles Molly uses and y represents the number of blue marbles.
Next, we can substitute in the given information. In this case, we know that 3 out of every 8 marbles are blue, so we can set y equal to 3 and x equal to 8.
This gives us the equation 3 = 3/8x. We can then solve for x by dividing both sides by 3/8 to get x = 8.
This tells us that for every 8 marbles Molly uses, 3 of them are blue.
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- Ansel is a maid at the hotel. He receives tips from the guests at the
ends of their stay. One week he earned $452.67 in tips and $5.23
per hour for 40 hours. What did he earn?
To calculate Ansel's earnings, we need to add up his tips and his hourly wages for the week.
First, let's calculate his earnings from his hourly wage:
$5.23 per hour x 40 hours = $209.20
Now, let's add that to his earnings from tips:
$209.20 + $452.67 = $661.87
Therefore, Ansel earned $661.87 for that week.
A juice factory labels bottles with customary and metric units. Do you think a bottle labeled 32fl oz and 960 mL is correctly labeled? Explain.
Quantity US Customary FL oz. UK (Imperial) US Nutrition labeling
960 ml 32,46 FL oz. 33,79 FL oz. 32,00 FL oz.
Which means 960 milli liter is equal to 32,46 FL oz.
This one is relatively simple. Once you know how much liquid a liter contains, you just need to divide it by a conversion factor equal to 1000. The result is 1 ml. That's what "mili" means - 1/1000th. If you have 1000 ml, it's actually 1 liter.
For this page, we are talking about fluid ounces (FL oz.). We're not talking about ounces, which are used to measure solids like metals. The fluid phone (fl Oz) is only for measuring the volume of liquids.
The problem is that you first need to know what fluid you are using. If you're a US citizen, you probably use US customary fluid ounces (US fl oz.).
As you can see, the numbers you need to divide 960 can be very impractical and unwieldy. Typing those long strings of numbers can be tedious. But you can also round them off to get a result that isn't too far off from a more accurate calculation.
For US v oz, divide volume in ml by 29.58 to get v oz.
So, 960ml equals 32.46oz when rounded up.
For amounts in milliliters on US food labels, divide the amount in milliliters by 30 to get the US fluid ounce equivalent. Similarly, you divide 960 by 30 to get 32.00 fluid ounces (fl oz).
For UK (Imperial) fluid ounces, divide 960 ml by 28.41 to get 33.79 UK fluid ounces.
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HELP ASAP!
Jason decides to see a movie. When he arrives at the snack counter to buy his popcorn, he has two choices in the shape of the popcorn container.
Using what you know about unit rate, determine which container is a better buy per $1.
One popcorn container is a cone and costs $6.75 the other is a cylinder and costs $6.25 .
Find the volume of BOTH popcorn containers. Determine which popcorn container will hold THE MOST popcorn.
Answer:
The cylinder is better to buy because it can hold more.
Step-by-step explanation:
If the heights of a cone and a cylinder are equal, then the volume of the cylinder is three times as much as the volume of a cone. Cylinder has a greater volume.
Example:
let's say you have a container. one shaped as a cylinder and one as a cone. both of them have a height of 1. Which one do you think will hold more?
the cylinder will hold more because of its shape and volume.
I hope this helps
hang in there ;)
Circle Q is centered at Q(-2, 1) with a diameter
Does P(0.5, 7) lie on circle Q?
yes or no
Answer:
Yes, point P(0.5, 7) lies on circle Q.
Step-by-step explanation:
To determine if point P lies on circle Q, first create an equation for circle Q using the equation of a circle formula.
[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
The diameter of a circle is twice its radius.
Therefore, the radius of circle Q is:
[tex]\implies r=\dfrac{d}{2}=\dfrac{13}{2}=6.5[/tex]
Given the center is (-2, 1) and the radius is 6.5, substitute these values into the equation of a circle formula to create an equation for circle Q:
[tex]\implies (x-(-2))^2+(y-1)^2=6.5^2[/tex]
[tex]\implies (x+2)^2+(y-1)^2=42.25[/tex]
To determine if point P(0.5, 7) lies on circle Q, substitute x = 0.5 and y = 7 into the equation of circle Q. If it equals 42.25, the point lies on the circle.
[tex]\begin{aligned}\implies (0.5+2)^2+(7-1)^2&=(2.5)^2+(6)^2\\&=6.25+36\\&=42.25\end{aligned}[/tex]
Therefore, point P(0.5, 7) does lie on circle Q.
Answer:
Yes , the point lies on the circle.Step-by-step explanation:
To find:-
If point (0.5 , 7) lies on the circle Q .Answer:-
We are here given that the diameter of the circle is 13 and its centre is (-2,1) . As we know that radius is half of diameter , hence the radius of the circle would be,
[tex]\longrightarrow r =\dfrac{d}{2}=\dfrac{13}{2}=\boxed{6.5} \\[/tex] .
Now if the given point (0.5,7) lies on the circle, then it's distance from the centre would be equal to the radius of the circle . We can calculate the distance between two points using the distance formula . The distance formula is,
Distance formula:-
[tex]\longrightarrow\boxed{\boldsymbol{ d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}} \\[/tex]
Here we need to find out the distance between (-2,1) which is the centre and (0.5,7) . So on substituting the respective values, we have;
[tex]\longrightarrow d =\sqrt{ ( -2-0.5)^2+(7-1)^2}\\[/tex]
[tex]\longrightarrow d = \sqrt{ (-2.5)^2 + (6)^2}\\[/tex]
[tex]\longrightarrow d =\sqrt{6.25 + 36 } \\[/tex]
[tex]\longrightarrow d = \sqrt{ 42.25}=\sqrt{(6.5)^2} \\[/tex]
[tex]\longrightarrow d = 6.5 \\[/tex]
Hence here we conclude that ,
[tex]\longrightarrow \boxed{\boldsymbol{ d = r }}\\[/tex]
Hence the point (0.5,7) lies on the circle .