If f ( x ) = f ( g ( x ) ) , where f ( 5 ) = 7 , f ' ( 5 ) = 5 , f ' ( 0 ) = 3 , g ( 0 ) = 5 , and g ' ( 0 ) = 3 ,f'(0) = 15
We start by using the chain rule to find the derivative of f(x) with respect to x:
f'(x) = f'(g(x)) * g'(x)
Next, we evaluate this equation at x = 0, and use the given values to solve for f'(0):
f'(0) = f'(g(0)) * g'(0)
f'(0) = f'(5) * 3 (since g(0) = 5 and g'(0) = 3)
Now, we need to find f'(5) using the given information. We can start by using the definition of the derivative:
f'(5) = lim h->0 [f(5+h) - f(5)] / h
We know that f(5) = 7, so we can simplify this expression:
f'(5) = lim h->0 [f(5+h) - 7] / h
Using the fact that f(x) = f(g(x)), we can substitute g(x) for x:
f'(5) = lim h->0 [f(g(5+h)) - 7] / h
Now, we can use the mean value theorem to approximate f(g(5+h)):
f'(5) = lim h->0 [f'(g(c)) * g'(5+h)] / 1
where 5 < c < 5 + h. Since f'(5) = 5 and g'(5) = 3, we can simplify this expression:
f'(5) = lim h->0 [5 * 3] / 1 = 15
Therefore, we have found that f'(0) = f'(5) * 3 = 5 * 3 = 15.
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2. Bucky walked 85 feet. His friend in Canada wanted to
know how many meters he walked.
Given that 1 foot = .3048 meter, how many meters
did Bucky walk?
The distance that Bucky walked is 25.908 meters
What is distance ?
Distance is a numerical measurement of how far apart two objects or points are in space. It is a scalar quantity, which means that it is defined only by its magnitude and not by its direction. Distance can be measured using various units, such as meters, feet, kilometers, miles, and so on, depending on the system of measurement being used.
Distance is an important concept in mathematics, physics, and other fields that deal with spatial relationships. It is often used to describe the length of a path traveled by an object or the separation between two objects in space.
According to the question:
To convert feet to meters, we can use the conversion factor 1 foot = 0.3048 meter.
The distance that Bucky walked is given as 85 feet. To find the distance in meters, we can multiply the number of feet by the conversion factor:
Distance in meters = 85 feet x 0.3048 meter/foot
Simplifying this expression, we get:
Distance in meters = 25.908 meters
Therefore, Bucky walked 25.908 meters.
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.
Answer:
She can create 9 outfits
Step-by-step explanation:
Imagine it's like a 3x3 grid of what she can and can't do. You can't wear two shirts and two pants at the same time, so for each input you have one equal output.
Therefore, for the first blouse, she can choose to wear either the jeans, khakis, or grey pants (3 options)
For the second blouse, she can wear either the jeans, khakis, or grey pants (3 options)
And again for the third blouse, she can wear either the jeans, khakis, or grey pants (3 options).
3 + 3 + 3 = 9, therefore 9 outfit choices :)
suppose the following table is gathered for a new study investigating childhood asthma.
Age at Interview Asthma? 0=No 1=Yes
18 0
16 0
16 1
17 1
14 1
13 1
15 0
16 1
19 1
12 0
16 0
13 1
13 1
18 1
13 0
what is the average age at interview?
The average age of the interviewees in the study investigating childhood asthma is 15.2 years.
To find the average age at the interview, you need to follow these steps. Here's how you can calculate it:
First, add up all the ages of the interviewees:18 + 16 + 16 + 17 + 14 + 13 + 15 + 16 + 19 + 12 + 16 + 13 + 13 + 18 + 13 = 228Next, count the total number of interviewees in the study:
15 interviewees
Finally, divide the sum of ages by the number of interviewees: 228 ÷ 15 = 15.2
Therefore, the average age calculated in the study while investigating childhood asthma is approximately 15.2 years.
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Question 3
Identify the equation of a line that passes through (1, 10) and (-4,-5).
O A)x1= 3(y - 10)
O B) y 1 = 3(x - 10)
OC) y-10=(x - 1)
O D) y 10 = 3(x - 1)
Answer:
y = 3x - 7
Step-by-step explanation:
We can use the two-point form formula to find the equation of a line that passes through two given points (x1, y1) and (x2, y2):
y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)
where (x1, y1) and (x2, y2) are the two points and (x, y) represents any point on the line.
Using the given points, we have:
x1 = 1, y1 = 10
x2 = -4, y2 = -5
Substituting these values into the formula, we get:
y - 10 = (-5 - 10) / (-4 - 1) * (x - 1)
Simplifying the equation, we have:
y - 10 = 3(x - 1)
Expanding and rearranging, we get:
y = 3x - 7
Therefore, the equation of the line that passes through (1, 10) and (-4, -5) is y = 3x - 7
chatgpt
1 1/2 x 2 2/3
im not quite sure how to solve this can someone help?
Firstly, you turn 2 2/3 into an improper fraction, which will become
=4/3
Lastly, you multiply them, which would be 11/2 x 4/3=22/3=7 1/3
Step-by-step explanation:
the answer will be
11 x 22 / 2x3
that will give us
242/6
reducing it to the lowest term by dividing it by two that will give us 121 / 3
121 / 3 will give us 40.33
There are 8 students on the curling team and 11 students on the badminton team. What is the total number of students on the two teams if 4 students are members on both teams
Well the first 4 you can see there is for the players who are only in curling team, the second 4 is for players on both teams, the 7 is for players in only badminton team
So the answer is 4 + 7 + 7 = 15
Area = ______ in^2
Help please!
Answer:
Area = 50 in^2
Step-by-step explanation:
Area = B x H
The dotted line is saying that the left and right sides of the triangle are 5 inches
So just multiply 10 x 5 and get 50in^2
The diagram shows a solid cuboid with base 10 cm by 6 cm.
The height of the cuboid is x centimetres.
x
10
6
(a) Find an expression, in terms of x, for the total surface area of the cuboid.
(b) The total surface area of the cuboid is 376 cm².
Form an equation in x and solve it to find the height of the cuboid.
Answer (a)
(b)
cm² [1]
cm [2]
The answers to both the subparts of the given cuboid:
(A) The expression: (SA)=120+32x
(B) The height x=4.875
What is a cuboid?A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces.
Cuboid is short for "like a cube."
A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.
So, we have the values:
x, 10 and 6
Total surface area formula:
(SA)=2lw+2lh+2hw
Now, insert values to form the expression:
(SA)=2lw+2lh+2hw
(SA)=2(10*6)+2(10*x)+2(x*6)
(SA)=120+20x+12x
(A) The expression: (SA)=120+32x
Now, the height would be:
376=120+32x
32x = 376-120
32x=156
x=156/32
(B) x=4.875
Therefore, the answers to both the subparts of the given cuboid:
(A) The expression: (SA)=120+32x
(B) The height x=4.875
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if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie in
If 1,000 points are selected randomly inside the square with all points equally likely to be selected, points to lie inside the circle is 785.4 points.
We can find the answer by finding the ratio of the areas of the regions and then multiplying by the total number of points.
The square has an area of 1 (since it has sides of length 1).
The circle has a radius of 1/2 and an area of pi/4.
So the ratio of the areas is:
(π/4) / 1 = π/4
Therefore, we would expect:
(π/4) * 1000 = ( 3.14 / 4 ) 1000
(π/4) * 1000 = 1000 × ( 0.785 ) = 785 points
points to lie inside the circle. This is approximately 785 points.
Your question is incomplete but mos probably your full question was
If 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?
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Juan Carlos claims that he cannot graph a point at (- 3.25, 6.5) because his coordinate plane only has whole numbers on the axis.
The intersection of two numerical axes creates a two-dimensional plane known as a coordinate plane. The x-axis, which is a horizontal number axis, and the y-axis, which is a vertical number axis, are two different types of number axes.
The French mathematician René Descartes enhanced the coordinate plane that had been created centuries earlier. The system is occasionally referred to as the Cartesian coordinate system in his honor. You can doodle points and lines on coordinate planes. With the aid of this method, we may generate and communicate algebraic concepts as well as visually express algebraic relations.
The coordinate plane has a horizontal axis, a vertical axis, and a right angle where numerous straight lines intersect. In a coordinate plane, the horizontal axis is represented by the x axis. The vertical axis is referred to as the y-axis. The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0.
As ordered pairs, positions on the coordinate plane are described.
By connecting the position of the point along the x-axis (the first value in the ordered pair) and the y-axis (the second value in the ordered pair), an ordered pair reveals the location of the point.
The first value in an ordered pair, like (x, y), is referred to as the x coordinate, and the second value is referred to as the y coordinate. The x coordinates are presented before the y coordinates; take note of this. The ordered pair of the origin is represented as (0, 0), since it has an ordinate and abscissa of 0.
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Complete Question:
Juan Carlos asserts that he is unable to graph a point at coordinates (-3.25,6.5) because his coordinate plane's axis only contains whole numbers. Correcting Juan Carlos's reasoning and elaborating on how to graph this point will help. Juan Carlos claims that he cannot graph a point at (-3.25,6.5) because his coordinate plane only has whole numbers on the axis. Help Juan Carlos by correcting his thinking and explaining how to graph this point.
Simplify (5/2x -16/5)-(-35/3x1/7x21)
Answer:
Before we can simplify this expression, we need to first find a common denominator for all the fractions. The prime factorization of the denominators is:
2 × 5
3 × 7 × x
Therefore, a common denominator is:
2 × 5 × 3 × 7 × x = 210x
Using this common denominator, we can rewrite the expression as:
[(5 × 21) / (2 × 5 × x) - (16 × 42) / (5 × 2 × 21 × x)] - [(-35) / (3 × x × 7 × 21)]
Simplifying each fraction, we get:
[105 / (10x) - 672 / (210x)] - [-5 / (3 × 7 × x × 21)]
Combining the two fractions and simplifying, we get:
[105 - 672] / (10x) + [5 / (3 × 7 × x × 21)]
= -567 / (10x) + 1 / (3 × 7 × x)
= (-567 × 21 + 10) / (210x)
= -11897 / (210x)
Therefore, the simplified expression is:
-11897 / (210x)
Carmen is trying to choose between two bike rental companies where h
is the number of hours rented and y
is the cost, in dollars. Company A charges a $30
fee and $2
for each hour rented, which can be represented by the equation y=2h + 30
. Company B charges a $10
fee and $4
for each hour rented, which can be represented by the equation y = 4h + 10
.
Carmen is comparing two bike rental companies, A and B. Company A charges a flat rate fee of $30 and $2 per hour, while company B charges a flat rate fee of $10 and $4 per hour.
Carmen can use mathematical equations to compare the costs of the two companies and make an informed decision.
The equation for the cost of renting from Company A is y=2h+30, where y represents the total cost in dollars and h represents the number of hours rented. The equation for the cost of renting from Company B is y=4h+10, where y represents the total cost in dollars and h represents the number of hours rented.
To compare the cost of renting from Company A and Company B for a specific number of hours, Carmen can substitute the value of h into each equation and solve for y. For example, if Carmen plans to rent a bike for 5 hours, the cost of renting from Company A would be y=2(5)+30=$40, and the cost of renting from Company B would be y=4(5)+10=$30. In this case, renting from Company B would be the more cost-effective option.
Carmen can also use algebraic methods to determine the break-even point, or the point at which the cost of renting from Company A is the same as the cost of renting from Company B. To find the break-even point, Carmen can set the two equations equal to each other and solve for h:
2h+30=4h+10
2h=20
h=10
This means that if Carmen plans to rent a bike for 10 hours or less, it would be more cost-effective to rent from Company B. If she plans to rent a bike for more than 10 hours, it would be more cost-effective to rent from Company A.
Another method of comparing the two companies is to graph the two equations on the same coordinate plane. The x-axis can represent the number of hours rented (h), and the y-axis can represent the total cost in dollars (y). Carmen can plot the two equations and visually compare the graphs to determine which company is more cost-effective for a specific number of hours rented.
In summary, Carmen can use mathematical equations, algebraic methods, and graphing to compare the costs of renting from Company A and Company B based on the number of hours rented. By comparing the costs, she can make an informed decision about which company to rent from based on her budget and the duration of the rental period.
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This thinking of a number, which he calls n. He finds of the number and then subtracts 5.
Write an expression to represent TJ's number.
000000
K
40
C
The expression to represent TJ's number is 1/3n - 3 and this can be determined by using the arithmetic operations and the given data.
What does a math equation mean?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
For instance, the equation 3x + 5 = 14 contains two expressions, 3x + 5 and 14, which are separated by the 'equal' sign. When two expressions are joined by an equal sign, a mathematical statement is called an equation.
The following steps can be used in order to determine the expression to represent TJ's number:
According to the given data, the number TJ's thinking about is 'n'.
Now, TJ's find 1/3 of the number 'n'. That is
= 1/3n
Now, he subtracts that number obtained in the above step by 3.
= 1/3n - 3
So, the expression to represent TJ's number is 1/3 n - 3.
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The complete question is -
TJ is thinking of a number which he calls n. he finds 1/3 of the number and then subtracts 5. write an expression to represent tj's number.
Jospeh has no more than $60 to spend on clothes. He wants to buy a pair of jeans for $32 and spend the rest of his money on t-shirts. Each t-shirt costs $7. What is the maximum number of t-shirts that he can buy? Question 2 options:
The inequality to find the maximum number of t-shirts is:
32 + 7x <= 60
A type of inequality expression known as a compound inequality is made up of two or more simple inequalities.
Inequality with a "and" indicates that both disparities are real.
If there is a "Or" inequality, any of the statements is true.
Considering inequality,
Jospeh has at most $60 to spend
Then it will be <=60
Now she has to spend 32 dollars on jeans so 32 will be add to the initial amount for sure.
And
Let x be the number of t-shirts
Then the cost of x t-shirts will be 7x
Putting this in to inequality will be:
32 + 7x <= 60
The inequality to find the maximum number of t-shirts is:
32 + 7x <= 60
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A yard cleanup service charges a $365 fee plus $14.75 per hour. Another cleanup service charges a $250 fee plus $20.50 per hour. How long is a job for which the two companies' costs are the same?
Answer:
20 hours
Step-by-step explanation:
[tex]\text{x} = \text{number of hours}[/tex]
A yard cleanup service charges a $365 fee plus $14.75 per hour.
[tex]365 + 14.75x[/tex]
Another cleanup service charges a $250 fee plus $20.50 per hour.
[tex]250 + 20.50x[/tex]
How long is a job for which the two companies' costs are the same?
[tex]365 + 14.75x = 250 + 20.50x[/tex]
[tex]365 - 250 = 20.50x - 14.75x[/tex]
[tex]115 = 5.75x[/tex]
x = 20
Does the table below represent a linear relationship? If so, write an equation for that relationship. If not, explain
TABLE BELOW
Answer:
Yes
Step-by-step explanation:
Imagine that time is x and distance is y. 0x+11=11 for the first equation.
3x+11=17 for the second. So x is 2, plug it in for the 3rd, then you see that it is linear. The equation is 2x+11=y
i’m very confused need help Asap
The opposite angles formed when two lines intersect are vertically opposite angles.
It should be noted that the value of x based on the information given about the perpendicular lines will be A. 28°.
How to calculate the value of angle xBased on the information given, it should be noted that the total value of the angle on a straight line is 180°.
Therefore, the value of x will be calculated thus:
55 + 2x - 49 + 90 + x = 180
3x + 96 = 180
Collect the like terms
3x = 180 - 96
3x = 84
Divide through by 3
3x / 3 = 84 / 3
x = 28
The value of the angle is 28°.
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the sum of the exterior angles of any given polygon is always equal to ?
Answer:360 degrees
Step-by-step explanation:
Solving in equality
Answer:
x < or = to -20.
Step-by-step explanation:
first mutliply both sides by three.
next, add 5 to both siddes.
finally, negate both sides ( remeber to flip the sign)!
hope this helped!
~Cain
which number has which number has the lowest value? 1/6 1/3 - 1/9 1/3 - 1/6 1/4 - 1/6the lowest value?
the fraction with the lowest value is 1/12.
Company revenue quadratic function.
Angel
The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:
r(x) = a(x - h)^2 + k
where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
We can use the given revenue values to set up a system of three equations:
2.7 = a(0 - h)^2 + k
3.4 = a(1 - h)^2 + k
2.7 = a(6 - h)^2 + k
Subtracting the first equation from the second, and the first equation from the third, we get:
0.7 = a(1 - h)^2
0 = a(6 - h)^2
Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:
6 - h = 10
which gives us h = -4.
Substituting h = -4 into the first equation, we get:
2.7 = a(0 - (-4))^2 + k
2.7 = 16a + k
Substituting the revenue value for 2005, we get:
3.9 = a(3 - (-4))^2 + k
3.9 = 49a + k
Solving for a and k, we get:
a = -0.1
k = 4.3
Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:
r(x) = -0.1(x + 4)^2 + 4.3
The vertex of this function is at (-4, 4.3).
Angel
What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?
We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:
3 - 4 + 5 - 6 + ... + 101
We can group the terms into pairs:
(3 - 4) + (5 - 6) + ... + (99 - 100) + 101
Each pair of terms adds up to -1, so we can simplify the expression to:
-1 -1 -1 ... -1 + 101
where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:
-50 + 101 = 51
Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.
Angel
What is 12 7/8 - 56/17?
To subtract mixed numbers like 12 7/8, we first need to convert it to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction, and adding the result to the numerator. This gives us:
12 7/8 = (12 × 8 + 7)/8 = 103/8
Now we can subtract 56/17 from 103/8. To do this, we need to find a common denominator for the two fractions. The least common multiple of 8 and 17 is 136, so we can rewrite the fractions with this denominator:
103/8 = (103/8) × (17/17) = 1751/136
56/17 = (56/17) × (8/8) = 448/136
Now we can subtract the two fractions:
1751/136 - 448/136 = (1751 - 448)/136 = 1303/136
We can simplify this fraction by finding a common factor to divide both the numerator and denominator. Since both 1303 and 136 are relatively prime, we cannot simplify it any further. Therefore, the final answer is:
12 7/8 - 56/17 = 1303/136
Angel
A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14). An equation of this circle is (x-2)^2+(y-9)^2=r^2 ,where r is a positive constant. What is the value of r?
The center of the circle is the midpoint of the diameter, which is at (2, (4+14)/2) = (2, 9). We can substitute this center point into the equation of the circle to get:
(x - 2)^2 + (y - 9)^2 = r^2
(2 - 2)^2 + (9 - 9)^2 = r^2
0 + 0 = r^2
So we see that r = 0. Therefore, the equation of the circle is just:
(x - 2)^2 + (y - 9)^2 = 0
This describes a single point in the xy-plane, which is the center of the circle. Note that this point is already on the given diameter, so it makes sense that the radius is zero.
Angel
which number has which number has the lowest value? 1/6 1/3 - 1/9 1/3 - 1/6 1/4 - 1/6the lowest value?
To compare these fractions, we can first find a common denominator for all of them. The least common multiple of 2, 3, and 4 is 12, so we can rewrite the fractions with this denominator:
1/6 = 2/12
1/3 - 1/9 = (3/12) - (1/12) = 2/12
1/3 - 1/6 = (2/6) - (1/6) = 1/6
1/4 - 1/6 = (3/12) - (2/12) = 1/12
So the fractions can be ordered as follows, from least to greatest:
1/12 < 1/6 < 2/12 = 1/3 - 1/9 < 1/3 - 1/6
Therefore, the fraction with the lowest value is 1/12.
Peter’s gym membership costs $23 per month. Which table shows the sum of the amounts that Peter will pay for his gym membership over the next 4 months?
How will changes in the base pairs affect the structure of DNA?
changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.
The structure of DNA is determined by the sequence of its base pairs. There are four types of base pairs in DNA: adenine (A), thymine (T), guanine (G), and cytosine (C). The base pairs form the rungs of the DNA ladder, with the backbone consisting of sugar and phosphate groups.
The sequence of base pairs determines the overall shape of the DNA molecule. The base pairs are held together by hydrogen bonds, which are relatively weak but collectively provide enough stability to maintain the double helix structure of DNA. The sequence of base pairs also determines the specific interactions between different regions of the DNA molecule, such as the interaction between the two complementary strands.
Changes in the base pairs can have a significant impact on the structure of DNA. For example, a substitution of one base pair for another can result in a different hydrogen bonding pattern, which can affect the stability of the double helix. This can result in a change in the shape of the DNA molecule, and can also affect the specific interactions between different regions of the DNA.
Insertions or deletions of base pairs can also have a significant impact on the structure of DNA. These types of mutations can disrupt the regular spacing of base pairs along the DNA molecule, which can cause kinks or bends in the DNA. This can also affect the specific interactions between different regions of the DNA, and can potentially interfere with the normal functioning of the DNA molecule.
In general, changes in the base pairs can alter the overall shape of the DNA molecule, disrupt specific interactions between different regions of the DNA, and potentially affect the normal functioning of the DNA.
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a box contains 4 white, 5 red and 2 blue marbles. a sample of six marbles is drawn with replacement. find the probability that one is blue, two are white and three are red.
If a sample of 6-marbles is drawn with replacement, then probability that 1 is blue, 2 are white and 3 are red is 0.2597.
The different number and color of marbles that the box contains 4 white, 5 red and 2 blue marbles.
The total number of marbles are = 4+5+2 = 11 marbles,
We can choose 6 marbles in ¹¹C₆ ways,
The one blue marble can be chosen in ²C₁ ways, the two white marbles can be selected in ⁴C₂ ways and the three red marbles in ⁵C₃ ways.
⇒ The number of ways in which we can choose the marbles with the given color combinations is = ²C₁ × ⁴C₂ × ⁵C₃ ways.
So, Probability that one is blue, two are white and three are red
⇒ (²C₁ × ⁴C₂ × ⁵C₃)/¹¹C₆,
⇒ (2 × 6 × 10)/462,
⇒ 0.2597.
Therefore, the required probability is 0.2597.
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Angle A is circumscribed about circle O. What is the measure of angle ∠O?
A. 70
B. 65
C. 130
D. 50
Answer:
angle o = 2×angle D (central angle twice inscribed angle)
angle a= angle d = 65
Find the value of :
[tex]5 { }^{2} +2 {}^{5} [/tex]
What is the image of (−12,−12) after a dilation by a scale factor of 1 4 centered at the origin?
the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin is (-3, -3).
How to find?
To find the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin, we can use the following formula:
(x', y') = (kx, ky)
where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, and k is the scale factor.
In this case, the scale factor is 1/4 and the center of dilation is the origin (0, 0). Therefore, we have:
x' = (1/4) × (-12) = -3
y' = (1/4) × (-12) = -3
So the image of point (-12, -12) after a dilation by a scale factor of 1/4 centered at the origin is (-3, -3).
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A tabletop in the shape of a trapezoid has an area of 7,722 square centimeters. Its longer base measures 131 centimeters, and the shorter base is 85 centimeters. What is the height?
By answering the presented question, we may conclude that Therefore, trapezium the height of the trapezoid is 71.5 centimeters.
What is trapezium?A trapezium is a two-dimensional geometric figure with four sides, one pair parallel to the other. It is also called as a trapezium in certain locations. The parallel sides are known as bases, whereas the non-parallel sides are known as legs. The distance between the two bases is the trapezoid's height or altitude. The area of a trapezium is given by A = 0.5 * (b1 + b2) * h, where b1 and b2 are the lengths of the two bases and h is the height.
To find the height of the trapezoid,
Area = (b1 + b2) × h / 2
h = 2 × Area / (b1 + b2)
h = 2 × 7722 / (131 + 85)
h = 2 × 7722 / 216
h = 71.5
Therefore, the height of the trapezoid is 71.5 centimeters.
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The population of a town is decreasing at a rate of 2% per year. In 2000 there were 1100 people. Question 1 Part A Find an exponential decay function to model this situation
Answer:
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Step-by-step explanation:
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The volume of the figure is given as 144 ft²
What is a pyramid?You should recall that a pyramid (from Greek: πυραμίς pyramís) is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense
The volume of a pyramidal pyramid can be calculated using the formula volume = (1/3) × basearea × height, which works for any type of base polygon and oblique and right pyramids
Area of base is a square = 4*4 = 16 ft²
volume = 16*9 ft
Therefore the Volume of the figure is = 144 ft²
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circular cloud of poison gas from a factory explosion is expanding so that hours after the explosion the radius of the cloud is meters. how fast is the area of the cloud increasing hours after the explosion?
The rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the square of the radius of the cloud.
Therefore, the rate at which the area of the cloud is increasing is equal to the product of the rate of expansion and the radius of the cloud. The rate of expansion can be calculated using the equation . Therefore, the rate at which the area of the cloud is increasing can be calculated as .
The area of a circle is determined by the square of its radius. Thus, when the radius of the cloud is expanding at a rate, the area of the cloud is increasing at a rate that is proportional to the square of its radius.
Therefore, in order to calculate the rate at which the area of the cloud is increasing, we must calculate the rate of expansion of the radius of the cloud and then multiply it by the square of the radius of the cloud. To calculate the rate of expansion of the radius of the cloud, we can use the equation .
After we have calculated the rate of expansion, we can then multiply it by the square of the radius of the cloud to calculate the rate at which the area of the cloud is increasing.
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