The eigenvalues of the matrix 0 3 3 -3 are 3 and -3 with each corresponding eigenspace having a dimension of 1.
An eigenvalue of a matrix is a scalar that satisfies the equation Av = λv, where A is the matrix, v is the eigenvector, and λ is the eigenvalue. The eigenvector v represents a direction in which the matrix transforms the space, and the eigenvalue λ represents the scale factor by which the eigenvector is stretched or shrunk.
In this case, the matrix 0 3 3 330 can be written as:
A = 0 3
3 -3
To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where I is the identity matrix. In this case, the characteristic equation is:
det(A - λI) = det
0 3 - λ 3 -3 - λ
3 3 -3 -3 - λ
= (0 - λ)(-3 - λ) - 9 = 0
= λ^2 + 3λ - 9 = 0
Solving for λ, we find that the eigenvalues are 3 and -3.
Next, we need to find the dimension of the corresponding eigenspaces, which are the subspaces spanned by the eigenvectors associated with each eigenvalue. In this case, the matrix is 2x2, so the maximum dimension of the eigenspaces is 2. However, since the matrix is symmetric, the eigenvectors are orthogonal, and therefore the sum of the dimensions of the eigenspaces is equal to the dimension of the matrix. So in this case, the dimension of each eigenspace must be 1, since the sum of the dimensions is 2.
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The graph shows the position (distant from home) of a bicycle rider on a 42-minute trip. Letters A through E are time intervals during the trip. The key defines the length of each interval.
Use the equation below to calculate the bicycle rider’s average speed in kilometers per minute for the first 30 minutes of the trip
Distance(km)/time(min) = average speed
The average speed on the first 30 minutes is 0.2 km per min.
How to get the average speed?Here we have the graph for the position of a bycicle rider on a 42-minute trip.
On the vertical axis we can see the position, and on the horizontal axis we can see the time.
Remember that:
speed = distance/time.
To find the average speed on the first 30 min, we need to take the quotient between the position after 30 minutes and 30 min.
At 30 min we can see that the position is at 6 km, then the speed will be:
S = 6km/30min = 0.2 km per min.
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Identify all English-language sentences below that are a strict translation of the formal statement that will follow. To be a strict translation, the English-language sentence must not drop any information that is explicit in the formal statement, nor can it add any information not explicit in the formal statement. [At least one of the statements will be a strict translation.] Formal Statement: Vn e Z+, Im E Z, m < n | m + n = 0 Note: Given an integer n, if there exists an integer m such that m + n = 0, then m is called the additive inverse of n. Every non-zero integer has a non-zero additive inverse. Every integer has an additive inverse. For every positive integer, there exists a unique lesser integer that when added to the positive integer results in an answer of zero. For every positive integer, there exists at least one lesser integer such that the lesser integer is the additive inverse of the positive integer.
The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.
The formal statement can be expressed mathematically as:
Vn e Z+, Im E Z, m < n | m + n = 0
This statement translates to: Given an integer n, if there exists an integer m such that m + n = 0, then m is the additive inverse of n.
To understand this statement more clearly, we can use an example. Let's say n = 5. This means that we are looking for an integer m such that m + 5 = 0. In this case, m = -5, which is the additive inverse of 5. We can also calculate this mathematically. We know that m + n = 0, so we can rearrange and solve for m: m = -n. Therefore, the additive inverse of n is -n.
In summary, given an integer n, the additive inverse of n is -n. This can be expressed mathematically using the statement Vn e Z+, Im E Z, m < n | m + n = 0.
The additive inverse of an integer n can be expressed mathematically as Vn e Z+, Im E Z, m < n | m + n = 0, which states that if an integer m exists such that m + n = 0, then m is the additive inverse of n.
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Do running times of American movies differ somehow from running times of French movies? The author investigated this question by randomly selecting 25 recent movies of each type, resulting in the following running times Am: 94 90 95 93 128 95 125 91 104 116 161 102 90 110 92 113 116 90 97 103 95 120 109 91 136 Fm: 123 116 90 158 122 119 125 90 96 94 137 102 105 106 95 125 122 103 96 111 81 113 128 93 92 Construct a comparative stem-and-leaf display by listing stems in the middle of your paper and then placing the Am leaves out to the left and the Fr leaves out to the right. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) American Stems French 10 12 13 14 15 16 Comment on interesting features of the display. (Select all that apply.) French movies are unimodal strongly positively skewed, while American movies appear to be bimodal American movies are unimodal strongly positively skewed, while French movies appear to be bimodal. O A typical French movie runs around 95 minutes, while American movies are typically either around 95 minutes or around 125 minutes
The results of this investigation provide valuable insights into the differences in the film-making practices of American and French film industries.
The comparative stem-and-leaf display is as follows:
90 | AM: 90 90 91 92 94 95 95 95 97 NONE
91 | AM: 104 110 113 113 116 116 116 120 125
92 | AM: 128 136
95 | FM: 90 95 96 97 102 103 105 106 111 113 113 125 125 128 158
96 | FM: 90 94 96
97 | NONE
102 | FM: 102
103 | AM: 103
104 | AM: 104
105 | FM: 105
106 | FM: 106
109 | AM: 109
110 | AM: 110
111 | FM: 111
113 | AM: 113
116 | FM: 116 122 123
120 | AM: 120
125 | FM: 125
128 | FM: 128
136 | AM: 136
158 | FM: 158
The display shows that American movies appear to be bimodal, with a typical running time of around 95 minutes and another peak around 125 minutes. On the other hand, French movies are unimodal and strongly positively skewed with a typical running time of around 95 minutes. This suggests that French movies tend to have a shorter running time compared to American movies, but with a larger range of running times compared to the peak of American movies around 95 minutes.
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a) is y=3/2x proportional and what is the constant of proportionality ?
b) is -x=y proportional and what is the constant of proportionality
Answer:
In y = 3/2x, x and y are inversely propotional
In -x = y, x and y are directly propotional
Step-by-step explanation:
In y = 3/2x, the constant of propotionality is 3/2.
In -x = y, the constant of propotionality is -1.
if a bullet is fired at 10 m/s at an angle of 60 degrees above the horizontal, what will be its horizontal velocity right before it hits the ground?
The horizontal velocity of a bullet right before it hits the ground is 10 m/s.
The horizontal velocity of a bullet remains constant throughout its flight, as it is only affected by gravity. This means that the horizontal velocity of the bullet right before it hits the ground will be the same as the initial horizontal velocity when it was fired.
In this case, the bullet was fired at an angle of 60 degrees above the horizontal, but the horizontal velocity remains constant, so it will still be 10 m/s right before it hits the ground. To determine the vertical velocity, we would need to know the time of flight and use the equations of motion to calculate the vertical acceleration due to gravity.
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from a set of 52 poker cards (without 2 jokers), we keep taking cards randomly one by one with replacement, until all the cards taken by us can cover all 4 shades. (1) compute the probability that we have picked exactly n cards. (2) verify that, after taking summation over n
1. To compute the probability that we have picked exactly n cards, we need to consider the number of ways to pick n cards out of 52 such that all 4 shades are represented, and divide that by the total number of possible n-card combinations from the deck of 52.
The number of ways to pick n cards such that all 4 shades are represented is given by the number of combinations of n items taken 4 at a time, with repetition allowed (denoted as C(n-1,3) or C(n+3-1,n)). This is because there are 4 shades, and we need to pick one card from each shade.
The total number of possible n-card combinations from the deck of 52 is given by C (52, n).
Therefore, the probability that we have picked exactly n cards is given by:
P(n) = C(n-1,3) / C(52, n)
2. To verify that the probability sums up to 1, we need to take the summation over all possible values of n, from n=4 to n=52:
P = sum(P(n)) from n=4 to n=52
If P is equal to 1, then the probability of picking exactly n cards over all possible values of n adds up to 1, which means that the event of picking all 4 shades is certain to occur at some point.
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In the function P(t) = 309.3 . 1.008', P represents the population in millions and represents the number of years since 2010. Find the population in 2019 and the rate at which the population is growing in 2019. Use h = 0.001 to estimate the derivative with the difference quotient. The population in 2019 is !! million. The rate at which the population is growing in 2019 is million people per year. (Round answers to three decimal places.) Hint: The population in 2019 is P(9). The rate of change in 2019 is P' (9).
The population in 2019 is 311.8 million and the rate of change of the population in 2019 is 0.083 million people per year.
To find the population in 2019 and the rate at which the population is growing in 2019, we can use the given function P(t) = 309.3 . 1.008. Here, P represents the population in millions and t represents the number of years since 2010. We can use the difference quotient to estimate the derivative. The difference quotient for this function is (P(t+h)-P(t))/h where h is the difference in the number of years. For this question, h = 0.001. The population in 2019 is P(9) = 309.3 . 1.008^9 = 311.8 million people. The rate of change in 2019 is P' (9), which is calculated using the difference quotient. This comes to (P(9+0.001)-P(9))/0.001 = (311.811 - 311.8)/0.001 = 0.083 million people per year.
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The y-intercept of the estimated line of best fit is at (0,b). Enter the appropriate value of b.
Enter the appropriate slope of the estimated line of best fit.
please ♥️
Since the y-intercept of the estimated line of best fit is at (0, b), the appropriate value of b is 360.
The appropriate slope of the estimated line of best fit is -30
What is y-intercept?In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is at (0, 360).
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (12, 0).Points on y-axis = (0, 360).Substituting the given points into the slope formula, we have the following;
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (360 - 0)/(0 - 12)
Slope, m = -30.
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let the direction of a vector be the angle that the vector makes with the x -axis, measured counterclockwise from that axis. find the direction of the vector a1
The direction of vector a1 is found as: Ф = 75° with the x -axis, measured counterclockwise from that axis.
Explain about the vector?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, torque, electromagnetic fields, and weight are a few characteristics of vectors in nature.The stated vector is (-7.765,28.978)
Angle made is estimated by the formula:
Ф = tan ⁻¹ (y/x)
In which,
y = 28.978
x = -7.765
Put the given values;
Ф = tan ⁻¹ ( 28.978/-7.765)
Ф = - 74.99
Ф = 75°
So, the direction of the vector a1 is found as: Ф = 75° with the x -axis, measured counterclockwise from that x-axis.
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The complete question is-
let the direction of a vector be the angle that the vector makes with the x -axis, measured counterclockwise from that axis. find the direction of the vector a1 - (-7.765, 28.978)
You deposit $1000 into an account that pays interest compounded monthly. What interest rate do you need to double your money in 10 years? (as a percent, so change it back, write to two decimal places)
The interest rate required to double your money in 10 years with monthly compounding is approximately 133.27%.
How did we get the value?To calculate the interest rate required to double your money in 10 years with monthly compounding, you can use the formula:
rate = ( (2 * principal) / principal * (1 + n)^(t12) )^(1/t12) - 1
where
principal = $1000
t = 10 years
n = number of compounding periods per year (12 for monthly compounding)
Plugging in the values we get:
rate = ( (2 * 1000) / 1000 * (1 + 12)^(1012) )^(1/1012) - 1
rate = ( 2 * (1 + 12)^120 )^(1/120) - 1
rate = ( 2 * 169860981.54 )^(1/120) - 1
rate = 1.3327
So, the interest rate required to double your money in 10 years with monthly compounding is approximately 133.27%.
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Solve for x.
2x−45=x+4
Answer:
x=49
Step-by-step explanation: If we have the equation 2x-45=x+4 we would first subtract x from both sides of the equation giving us x-45=4. We then have to isolate x to do this we add 45 to both sides giving us the answer x=49.
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The minimum value on the interval [-11, 5] is -19, and the maximum value is 28.
What is linear function?In mathematics, a linear function is a function that expresses the relationship between two variables, x and y, in the form of y = mx + b, where m denotes the slope of the line and b the y-intercept. A linear function has a graph that is either a straight line passing through the origin if b = 0 or a point (0, b) if b 0.
A number of applications can benefit from linear functions because of their numerous beneficial characteristics. One of these characteristics is that they are always continuous, i.e., their graphs are seamless and devoid of gaps. They are the best candidates for simulating actual scenarios when two variables have a continuous relationship because of this characteristic.
According to question:
The function f(a) = Va + 3 is a linear function, and all linear functions have a minimum and maximum value that occur at either endpoint of the interval. In this case, the interval is [-11, 5].
To find the minimum value, we evaluate the function at -11:
f(-11) = V(-11) + 3 = -22 + 3 = -19
To find the maximum value, we evaluate the function at 5:
f(5) = V5 + 3 = 25 + 3 = 28
Therefore, the minimum value on the interval [-11, 5] is -19, and the maximum value is 28.
Minimum: -19
Maximum: 28
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draw segment XZ with Y in between X and Z. Label the following information. , , XY=7x,YZ=6x-11, and XZ=83 What is the value of x?
The value of x is 94/13 approximately equal to 7.23.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Line segment described in the question is given below.
Given that,
Length of XY = 7x
Length of YZ = 6x - 11
Length of XZ = 83
We have the equation,
XY + YZ = XZ
7x + 6x - 11 = 83
13x = 83 + 11
13x = 94
x = 94/13 ≈ 7.23
Hence the value of x is 94/13.
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Cigarette Taxes The increases (in cents) in cigarette taxes for 17 states in a 6-month period are 60, 20, 40, 40, 45, 12, 34, 51, 30, 70, 42, 31, 69, 32, 8, 18.50 )g Find the range, variance, and standard deviation for the data. Use the range rule of thumb to estimate the stand- ard deviation. Compare the estimate to the actual stand- ard deviation.
Solve: -3(x + 7) = 0 0 and -7 -7 -3 and -7 None of these choices are correct.
The solution of the equation -3(x+7)=7 is x=-7.
How to solve an algebric expression:
An algebraic expression is a mathematical phrase that contains numbers and/or variables. Though it cannot be solved because it does not contain an equals sign (=), it can be simplified. You can, however, solve algebraic equations, which contain algebraic expressions separated by an equals sign.
To solve the given equation:-3(x+7)=0
Now I need to find the value of x by sorting the variables. This expression has an x variable, so find the value of the variable.
The formula is:
-3(x+7) =0
give:
-3(x+7) =0
(divide both sides of the equation by the coefficient of the variable)
x+7=0
(reorder variables on the left side of the expression)
x=-7
The answer is x= -7.
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Miguel Rodriguez borrowed $300 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months
with simple annual interest at 6.6%. What is the simple interest?
The simple interest is given as SI = $ 9.90
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as S
Now , the equation will be
The principal amount be P = $ 300
The rate of interest R = 6.6 %
The number of months T = 6 months = 1/2 year
So , the simple interest S = PRT / 100
Substituting the values in the equation , we get
S = ( 300 x 6.6 x 0.5 ) / 100
On simplifying the equation , we get
S = 3 x 6.6 x 0.5
S = $ 9.90
Hence , the simple interest is $ 9.90
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As you were orginizing your closet you counted 20 shirts and 12 pairs of pants what was the pants to shirts ratio
The ratio of the given distribution of pants to shirts is; 5:3
How to solve ratio problems?The ratio of shirts to pants can be expressed by putting the number of shirts and pants in the following way;
Number of shirts : Number of pants
20 : 12
Then we will have to reduce this ratio to the lowest term by dividing by the highest common factor of both numbers.
The highest common factor of 12 and 20 is 4 and as such when divided by 4 we get:
20/4 : 12/4
= 5 : 3
This represents the ratio.
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What is the value of x in the triangle 5 squared2 ,x ,5 squared 2
The value of x must be less than 50.
What is triangle?Triangle is a three sided polygon which has three vertices. The three sides are connected with each other end to end at a point which forms the angles of the triangle.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Given that the two sides have lengths 5^2 and 5^2, we can write the inequality:
x < 5^2 + 5^2
Now, we can evaluate the expressions 5^2 and 5^2:
5^2 = 25
So, x < 25 + 25 = 50.
Therefore, the value of x must be less than 50.
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If a model of the hexagon is made by using a scale factor of 6, which applies to the model? Select two options..
The effect of scaling on a hexagon by the scale factor of 6 is discussed above.
What is a hexagon?In geometry -
a hexagon is a six-sided polygon creating the outline of a cube. the total of the internal angles of any simple hexagon is 720°.Given is a model of the hexagon that is made by using a scale factor of 6.
If the initial length is equivalent to {a}. Then, after the scaling by the scale factor of {K}, the length becomes {Ka}. So, we can write the perimeter of the hexagon, before and after the scaling as -
P{i} = P{before scaling} = 6 x side = 6a
P{i} = 6a ... Eq { 1 }
P{f} = P{after scaling} = 6 x 6a = 36a
P{f} = 36a ... Eq { 2 }
The total of the internal angles of the hexagon will remain 720° only.
Therefore, the effect of scaling on a hexagon by the scale factor of 6 is discussed above.
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What is the value of x?
Enter your answer in the box.
x =
Answer:
x=98
Step-by-step explanation:
a 7 sided shape has 900 degrees in it so
146+142+142+140+122+110=802
so
900-802=98
x=98
each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100.
a) The mean of the sample of size 5 is equals to 103.
b) The mean of the sample of size 12 is equals to 103.3.
c) Median of sample of size 5 is 104.
d) Median sample of size 30 is 105.5.
Mean: Sum of observations is divided by number of observations in the sample is named as mean, which is denoted by X- bar. Moreover, the sample mean signifies the measure of centre of the data.
X-bar = (x₁ + x₂ + --- + xₙ)/n
Median: Median divides the observations into two equal parts. It represents the middle value for a set of observations when they are arranged in order of magnitude. There are two cases arises.
Case (1): Sample size (n) is odd: First, arrange the data in ascending order. Then, the median is the middle value and lies at the position.
Case (2): Sample size (n) is even: First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on either side of the position. Median = ( n/2)ᵗʰ term , n is odd
=[(( n/2)ᵗʰ term + (n/2 + 1)ᵗʰ term]/2, n is even
Now, a) Mean of first sample with sample size, n = 5.
Sum of values = 105 + 111 + 97 + 94 + 108 = 515
So, mean = 515/5 = 103
b) Sample 2, sample size , n = 12
Sum of values = 105 + 111 + 97 + 94 + 108 + 101 + 112 + 114 + 103+ 102+ 91 + 101
= 515 + 724 = 1239
Mean = 1239/12 = 103.25
c) Now, we have to determine median for sample size 5. Here, sample values are odd in number, i.e., 5. So, middle term is median after arranging in order. Ascending order is 94,97, 104, 108, 111 and middle term is 104, so median is 104.
d) Now, we have a sample of size 30, which is an even number. First arrange the numbers in ascending order as 91,92,92,94,95,97,100,101,101,101,101,102,103,105,105,105,106,107,107,108,110,111, 111, 112,113,114,115,115,116,116. So,
Median is [((n/2)th + (n/2 + 1)th ]/2 i.e, [ 30/2)th + 30/2 + 1)th ]/2
=( 15th + 16th)/2 ( observations)
= (105 + 106 )/2 = 211/2 = 105.5
Hence, the median of sample size 30 is 105.5.
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Complete question:
See the above figure, each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100.
a) What is the mean of the sample of size 5? Full data set Sample of Size 108 114 (Type an integer or decimal rounded to one decimal place as needed._ Sample of Size 12
b) What is the mean of the sample of size 12? 114 105 115 (Type an integer or decimal rounded to one decimal place as needed:)
c) What is the median of the sample of size 5? (Type an integer or decimal rounded to one decimal place as needed:)
d) What is the median of the sample of size 30? (Type an integer or decimal rounded to one decimal place as needed:)
describe the x-values at which the function is differentiable. (enter your answer using interval notation.) y
The function is differentiable at these two x-values, the x-values at which the function is differentiable is (-1, 1/3).
The x-values at which the function is differentiable can be found by taking of the function and setting it equal to 0. The derivative of the function y = x3 + 2x2 - 5x + 8 is 3x2 + 4x - 5. Setting this equal to 0 and solving for x yields x = -1 and x = 1/3. So, the x-values at which the function is differentiable is (-1, 1/3).
In order to find the derivative of the function, the power rule was used. The power rule states that the derivative of a function f(x) = xn is f'(x) = nxn-1. Applying this to the function y = x3 + 2x2 - 5x + 8, the derivative is 3x2 + 4x - 5. Next, setting this equal to 0 and solving for x yields two solutions: x = -1 and x = 1/3. Since the function is differentiable at these two x-values, the x-values at which the function is differentiable is (-1, 1/3).
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One number is 4 more than another. If 3 times the smaller number is equal to twice the larger increased by 5. Find the numbers
The smaller number is x and the larger number is 17
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: One number is 4 more than another. And 3 times the smaller number is equal to twice the larger increased by 5.
Let the smaller number be x then we have
3x=2(x+4)+5
3x-2x=8+5
x=13
Thus the smaller number is x and the larger number is 17
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Find the volume of the cylinder
Answer:
Volume
[tex]\pi r ^{2} h[/tex]
[tex]\pi = \frac{22}{7} [/tex]
[tex]r = 8[/tex]
[tex]h = 15[/tex]
[tex] \frac{22}{7} \times 8 {}^{2} \times 15 = 3015.93[/tex]
What is the equation of this line in slope-intercept form?
y=-2/3x+1
y=2/3x+1
y=3/2x+1
I don’t know
The equation of the line is y = -2/3x + 1
How to detemrine the equation of the lineFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following highlights
The graph intersect the y-axis at y = 1
This means that the intercept c is 1
Also, as x changes by 1, the y values changes by -2/3
This mean sthat the slope is -2/3
So, we have
y = mx + c
This gives
y = -2/3x + 1
Hence, the equation is y = -2/3x + 1
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A farmer in the south exports 1220kg of mangoes in one week one week has 7 days, how many kilogram of mangoes does the farmer export in two days?
Answer:
348.6 kg
Step-by-step explanation:
(1220 kg / 7 days) x 2 days = 348.6 kg
-There are some small cubes and some large cubes in a bag.
-The cubes are red or the cubes are yellow
-The ratio of the number of small cubes to the number of large cubes is 4:9
-The ratio of the number of red cubes to the number of yellow cubes is 3:5
a) What is the least possible number of cubes in the bag?
-All the small cubes are yellow.
b) Work out the least number of large yellow cubes in the bag.
The answers include the following:
The least possible number of cubes in the bag is 104.The least number of large yellow cubes in the bag is 45.What is Probability?This is referred to as the branch of mathematics concerning numerical descriptions of how likely an event is to occur,
The Red to Yellow ratio is given as 3:5.
Red = 3 to 8 and yellow = 5 to 8.
Small to Large ball ratio = 4:9
Small = 4/13 and large = 9/13
5/8 × 9 / 13 × 104
= 5 * 9
= 45
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A bag of garden soil weighs 40 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the volu
of 15 bags in cubic yards.
The weight of 15 bags in kilograms and the volume of 15 bags in cubic yards are 272. 15 kilograms and 1. 1 cubic yards
How to determine the valuesIt is important to note the conversion rate of the pounds to kilograms and also cubic feet to cubic yards
1 pound = 0. 453592 kilogram
If a bag of soil weighs 40 pounds which is equivalent to 0. 453592 kilogram
1 bag = 40(0.453592)
15 bags = x
x = 272. 15 kilograms
Then, we have that;
1 bag = 2 cubic feet
15 bags = 30 cubic feet
But, 1 cubic feet = 0. 037037 cubic yards
30 cubic feet = x
x = 1. 1 cubic yards
Hence, the values are 272. 15 kilograms and 1. 1 cubic yards
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Charlotte is making 6 pounds of trail mix using raisins and 3 different types of nuts.
The table shows the amounts of different types of nuts that she has.
To find the exact amount of raisins Charlotte will
D. Add 7/8 pound, 1 1/2 pounds, and 2 3/8 pounds. Then subtract that total from 6 pounds.How to find the exact amount of raisinsFrom the problem, it can be deduced that Charlotte uses all of the almonds, cashews, and peanuts. hence we add the amounts of the nuts
= almonds + cashews + peanuts
= 7/8 + 1 1/2 + 2 3/8
= 19/4
= 4 3/4
hence Charlotte will need 4 3/4 pounds of nuts
The amount remaining for raisings
= 6 pounds of trail mix - total amount of nuts
= 6 pounds - 4 3/4 pounds
= 5/4
= 1 1/4
hence Charlotte will need 1 1/4 pounds of raisins
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complete question
Charlotte is making 6 pounds of trail mix using raisins and 3 different types of nuts. The table shows the amounts of different types of nuts that she has.
Type of Nut Amount (in pounds)
Almonds 7/8
Cashews 1 1/2
Peanuts 2 3/8
Pecans 1 1/4
Walnuts 1 3/4
Charlotte uses all of the almonds, cashews, and peanuts that she has Which of the following explains how she can find the exact amount of raisins she needs?
A Round 7/8 pound to 1 pound, 1 1/2 pounds to 2 pounds, and 2 3/8 pounds to 2 pounds. Then add the rounded almonds and subtract that total from 6 pounds.
B. Add 7/8 pound, 1 1/2 pounds, 2 3/8 pounds, 1 1/4 pounds, and 1 3/4 pounds. Then subtract 6 pounds from that total.
C. Subtract 7/8 pound from 6 pounds, subtract 1 1/2 pounds from 6 pounds, and subtract 2 3/8 pounds from 6 pounds. Then add all three differences.
D. Add 7/8 pound, 1 1/2 pounds, and 2 3/8 pounds. Then subtract that total from 6 pounds.
if none of these structures will allow the flying crow to break the walnut without it being stolen, the crow must fly away to another location. given that the average crow can take off from a standing position at a speed of 19 feet per second, what should the flying crow do? explain your answer.
Answer: Based on the information given, it seems like the crow is unable to break open the walnut in its current location without it being stolen. To overcome this problem, the best solution would be for the crow to fly away to another location where it can safely break open the walnut. With a take-off speed of 19 feet per second, the crow should be able to quickly reach a new location where it can safely open the walnut.
Step-by-step explanation: