Answer:
the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
Step-by-step explanation:
We can use the standard normal distribution to solve this problem. We first need to standardize the height requirements using the population mean and standard deviation.
a) To find the probability that a child can go on all rides, we need to find the probability of getting a height of at least 54 inches.
z-score = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of 0.25 or greater is 0.4013.
Therefore, the probability that a child can go on all rides is 0.4013 (rounded to three decimal places).
b) To find the probability that a child can participate in only mild and moderate rides, we need to find the probability of getting a height between 42 inches and 48 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 48 inches = (48 - 53) / 4 = -1.25
Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.75 and -1.25 is 0.2375.
Therefore, the probability that a child can participate in only mild and moderate rides is 0.2375 (rounded to three decimal places).
c) To find the probability that a child can only go on mild rides, we need to find the probability of getting a height of less than 42 inches.
z-score = (42 - 53) / 4 = -2.75
Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.75 or less is 0.0030.
Therefore, the probability that a child can only go on mild rides is 0.0030 (rounded to three decimal places).
d) To find the probability that a child is excluded from all rides, we need to find the probability of getting a height less than 42 inches or greater than 54 inches.
First, we find the z-scores for each height requirement:
z-score for 42 inches = (42 - 53) / 4 = -2.75
z-score for 54 inches = (54 - 53) / 4 = 0.25
Using a standard normal table or calculator, we find that the probability of getting a z-score of less than -2.75 or greater than 0.25 is 0.0987 + 0.4013 = 0.5000.
Therefore, the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).
Prove the first associative law from Table 1 by show-
ing that if A, B, and C are sets, then A ∪ (B ∪ C) =
(A ∪ B) ∪ C.
Answer:
Step-by-step explanation:
o prove the first associative law of set theory, we need to show that for any sets A, B, and C:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
To do this, we need to show that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa.
First, let's consider an arbitrary element x.
If x ∈ A ∪ (B ∪ C), then x must be in A, or in B, or in C (or in two or more of these sets).
If x ∈ A, then x ∈ A ∪ B, and so x ∈ (A ∪ B) ∪ C.
If x ∈ B, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
If x ∈ C, then x ∈ B ∪ C, and so x ∈ A ∪ (B ∪ C), which means that x ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if x ∈ A ∪ (B ∪ C), then x ∈ (A ∪ B) ∪ C.
Next, let's consider an arbitrary element y.
If y ∈ (A ∪ B) ∪ C, then y must be in A, or in B, or in C (or in two or more of these sets).
If y ∈ A, then y ∈ A ∪ (B ∪ C), and so y ∈ (A ∪ B) ∪ C.
If y ∈ B, then y ∈ A ∪ B, and so y ∈ A ∪ (B ∪ C), which means that y ∈ (A ∪ B) ∪ C.
If y ∈ C, then y ∈ (A ∪ B) ∪ C.
Therefore, we have shown that if y ∈ (A ∪ B) ∪ C, then y ∈ A ∪ (B ∪ C).
Since we have shown that any element that is in the left-hand side of the equation is also in the right-hand side, and vice versa, we can conclude that:
A ∪ (B ∪ C) = (A ∪ B) ∪ C
This proves the first associative law of set theory.
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The vertices of an isosceles trapezoid are located at (2,5), (6,5), (9,3) and:
A) (10, 5).
B) (-6, 5).
C) (-5, 3).
D) (-1, 3).
Answer:
D. (-1,3)
Step-by-step explanation:
You need to draw the figure on the graph. See attachment.
please help me out with this question! i appreciate it :))
Answer:
144,000
Step-by-step explanation:
you multiply 18,000 by 8 since its after one year and you get 144,000.
if 24 x 18 and x 1 are in proportion find the value of x
Answer:
x = 432.
Step-by-step explanation:
We know that 24 x 18 and x x 1 are in proportion, which can be written as:
(24 x 18) / (x x 1) = k, where k is a constant of proportionality.
Simplifying the left-hand side, we get:
24 x 18 = 432
x x 1 = x
Substituting these values, we get:
432 / x = k
To solve for x, we need to find the value of k. We can do this by using the fact that the two ratios are in proportion. That is:
24 x 18 : x x 1 = 432 : k
Simplifying the left-hand side, we get:
(24 x 18) / x = 432 / k
Multiplying both sides by x and k, we get:
24 x 18 k = 432 x
Dividing both sides by 24 x, we get:
18 k / 1 = 18
Solving for k, we get:
k = 1
Substituting k = 1 into the equation 432 / x = k, we get:
432 / x = 1
Multiplying both sides by x, we get:
432 = x
Therefore, x = 432.
(Stock Level). A.S. Ltd. produces a product 'RED' using two components X and Y. Each unit of 'RED' requires 0.4 kg. of X and 0.6 kg. of Y. Weekly production varies from 350 units to 450 units averaging 400 units. Delivery period for both the components is 1 to 3 weeks. The economic is 600 kgs. and for Y is 1,000 kgs. Calculate: (1) Re-order level of X; (ii) Maximum level of X; (iii) Maximum level of Y.
Answer:
Step-by-step explanation:
To calculate the reorder level of component X, we need to find out the average weekly consumption of X.
Average consumption of X per unit of 'RED' = 0.4 kg
Average weekly production of 'RED' = 400 units
Average weekly consumption of X for producing 400 units of 'RED' = 0.4 kg/unit x 400 units/week = 160 kg/week
Assuming lead time of 3 weeks for delivery of X, the reorder level of X would be:
Reorder level of X = Average weekly consumption of X x Lead time for delivery of X
Reorder level of X = 160 kg/week x 3 weeks = 480 kg
To calculate the maximum level of X, we need to take into account the economic order quantity and the maximum storage capacity.
Economic order quantity of X = Square root of [(2 x Annual consumption of X x Ordering cost per order) / Cost per unit of X]
Assuming 52 weeks in a year:
Annual consumption of X = Average weekly consumption of X x 52 weeks/year = 160 kg/week x 52 weeks/year = 8,320 kg/year
Ordering cost per order of X = 600
Cost per unit of X = 1
Economic order quantity of X = Square root of [(2 x 8,320 kg x 600) / 1] = 2,771.28 kg (approx.)
Maximum storage capacity of X = Economic order quantity of X + Safety stock - Average weekly consumption x Maximum lead time
Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:
Maximum storage capacity of X = 2,771.28 kg + (0.2 x 2,771.28 kg) - (160 kg/week x 3 weeks) = 2,815.82 kg (approx.)
To calculate the maximum level of Y, we follow the same approach as for X:
Annual consumption of Y = Average weekly consumption of Y x 52 weeks/year
Average consumption of Y per unit of 'RED' = 0.6 kg
Average weekly consumption of Y for producing 400 units of 'RED' = 0.6 kg/unit x 400 units/week = 240 kg/week
Annual consumption of Y = 240 kg/week x 52 weeks/year = 12,480 kg/year
Economic order quantity of Y = Square root of [(2 x Annual consumption of Y x Ordering cost per order) / Cost per unit of Y]
Ordering cost per order of Y = 1,000
Cost per unit of Y = 1.5
Economic order quantity of Y = Square root of [(2 x 12,480 kg x 1,000) / 1.5] = 915.65 kg (approx.)
Maximum storage capacity of Y = Economic order quantity of Y + Safety stock - Average weekly consumption x Maximum lead time
Assuming a safety stock of 20% of the economic order quantity and a maximum lead time of 3 weeks:
Maximum storage capacity of Y = 915.65 kg + (0.2 x 915.65 kg) - (240 kg/week x 3 weeks) = 732.52 kg (approx.)
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Sector 1 and sector 2 are sectors of different circles. They have the same arc length, x. Calculate the central angle of sector 2. Give your answer in degrees (°) to 1 d.p.
Therefore , the solution of the given problem of angle comes out to be Sector 2's centre angle is 57.3 degrees.
What does an angle mean?In Euclidean geometry, a tilt is a shape with two sides, but they are actually cylindrical faces that separate at the middle and top of the barrier. Two rays may merge to produce an angle at their intersection. Another result of two things interacting is an angle. They most closely rays resemble dihedral forms. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.
Here,
The following algorithm determines the central angle of a sector of a circle:
=>θ = (arc length / radius) * (180/π)
Since Sectors 1 and 2 have the same arc length, the following can be written:
θ1 = (x / r1) * (180/π)
θ2 = (x / r2) * (180/π)
where r1 and r2 are the radii of the circles, and 1 and 2 are Sector 1 and Sector 2's corresponding central angles.
Since Sector 2's radius is unknown to us, we are unable to determine its centre angle directly. However, since both sections have the same arc length, we can write as follows:
=> x / r1 = x / r2
When we multiply both parts by r2, we obtain:
=> r2 * x / r1 = x
=> r2 = r1 * x / x
=> r2 = r1
Since the two circles' radii are identical as a result, the formula for Sector 2's central angle can be made simpler:
=> 2 Equals (x/r1) * (180/), (x/r2) * (180/), and (x/r1) * (180/)
=> θ2 = (180/π) 57.3 degrees in radians (rounded to 1 decimal place)
As a result, Sector 2's centre angle is 57.3 degrees.
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find thenonpermissible replacment for x in this expression 1/-8x
If any number is divided by zero. the result is indeterminate.
Therefore, zero is the non-permissible replacement for x.
The weights of ice cream cartons are normally distributed with a mean weight of 7 ounces and a standard deviation of 0.6 ounces. A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 7.19 ounces?
The probability that the mean weight of the sample of 25 cartons is greater than 7.19 ounces is given as follows:
0.0571 = 5.71%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 7, \sigma = 0.6, n = 25, s = \frac{0.6}{\sqrt{25}} = 0.12[/tex]
The probability that the mean weight is greater than 7.19 ounces is one subtracted by the p-value of Z when X = 7.19, considering the standard error s, hence:
Z = (7.19 - 7)/0.12
Z = 1.58
Z = 1.58 has a p-value of 0.9429.
Hence:
1 - 0.9429 = 0.0571 = 5.71%.
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mathhhhhhhhhhh i need help
Answer:
what in the world
Step-by-step explanation:
number 1. is c
number 2. is d
number 3. is a
number 4. is c
number 5. is b
hope this helps
b) If 2x+y=5 and y-3, what is the value of x?
Answer:
x=4
Step-by-step explanation:
2x+(-3) =5
2x-3+3=5+3
2x/2=8/2
x=4
please help me with question one it should not be to long as you see the space provided thanks
Answer:
1. Draw a coordinate plane with a circle on it somewhere
2. B. and C.
Step-by-step explanation:
1. What is a function?A function is a set of points that has a specific input (x-value) and a specific output (y-value). Let's take the example of y = 2x. Let's start by plugging in 1 for x. 1 will be our input value, and 2• 1 = 2 will be our y-value because the x-value was changed to get to our output, the y-value.
In a function, it is possible to have the same y-value for different x-values; take the example of y = x^2. X can have 2 values, but because it is squared, it will give the same y-value. However, a function that has the same x-values for one y-value is not a function. For example, take a circle, with the equation x^2 + y^2 = 0. This is not a function, because, for 2 y-values, it will equal the same x-value. For your answer, you can draw a coordinate plane with a circle on it. IMPORTANT: 2 x-values cannot equal one y-values in a function.
2. What is a linear function?
A linear function is a function that has an x and y-value, as well as sometimes a coefficient to either variable and a constant. For example, the equation y = 5x +4 is a linear function because there is one y and one x-value, a coefficient (even though it is not necessary), and a constant (even though it is not necessary). It doesn't matter where the coefficients are, but there has to be one y-value and one x-value. Since there can be only one x and y, equations like y = x^2 does not work, because there are 2 x's (in the x^2). Using this information, we can figure out the correct solutions:
A. doesn't work, because there are 3 y-values.
B. works because there is one x and y, and a coefficient (although it isn't necessary)
C. works because like b, it has only one x and y, a coefficient (although it isn't necessary)
D. doesn't work because there is only one y-value and no x-value.
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A chemist has two alloys, one of which is 10% gold and 20% lead in the other which is 40% gold and 30% lead. How many grams of each of the two alloys should be used to make an alloy that contains 57 g of gold and 94 g of lead 
Answer:
The chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.
Step-by-step explanation:
Let's call the amount of the first alloy used "x" and the amount of the second alloy used "y". We can set up a system of two equations based on the amount of gold and lead needed in the final alloy:
Equation 1: 0.10x + 0.40y = 57 (the amount of gold in the first alloy is 10%, and in the second alloy is 40%)
Equation 2: 0.20x + 0.30y = 94 (the amount of lead in the first alloy is 20%, and in the second alloy is 30%)
We can then solve for x and y using any method of solving systems of equations. One way is to use substitution:
Solve equation 1 for x: x = (57 - 0.40y)/0.10 = 570 - 4ySubstitute this expression for x in equation 2: 0.20(570 - 4y) + 0.30y = 94Simplify and solve for y: 114 - 0.8y + 0.3y = 94 → -0.5y = -20 → y = 40Substitute this value of y into the expression for x: x = 570 - 4y = 410Therefore, the chemist should use 410 grams of the first alloy (which is 10% gold and 20% lead) and 40 grams of the second alloy (which is 40% gold and 30% lead) to make an alloy that contains 57 grams of gold and 94 grams of lead.
This shows a function. F(x)=4x^3+8 which statement describes f(X)? A. The function does not have an inverse function because F(x) fails the vertical line test. B. The function does not have an inverse function because f(x) fails the horizontal line test. C. The function has an inverse function because f(x) passes the vertical line test. D. The function has an inverse function because f(x) passes the horizontal line test
Answer:
Step-by-step explanation:
The statement that describes the function f(x) = 4x^3 + 8 is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
To see why this is the correct answer, let's first define what the vertical line test and the horizontal line test are.
Vertical line test: A function passes the vertical line test if any vertical line intersects the graph of the function at most once. This means that no two points on the graph have the same x-coordinate.
Horizontal line test: A function passes the horizontal line test if any horizontal line intersects the graph of the function at most once. This means that no two points on the graph have the same y-coordinate.
Now, let's look at the function f(x) = 4x^3 + 8. We can graph this function by plotting points or by using a graphing calculator. The graph of the function looks like a curve that goes up and to the right.
If we draw a vertical line anywhere on the graph, we can see that it intersects the graph at most once, which means that f(x) passes the vertical line test. However, if we draw a horizontal line on the graph, we can see that it intersects the graph at more than one point. This means that f(x) fails the horizontal line test.
The fact that f(x) fails the horizontal line test tells us that there are some values of y that correspond to more than one value of x. This means that f(x) is not a one-to-one function, and therefore it does not have an inverse function.
Therefore, the correct statement that describes the function f(x) is:
A. The function does not have an inverse function because f(x) fails the vertical line test.
Weight on Earth (pounds) a. If a person weighs 12 pounds on the Moon, how much does the person weigh on Earth? Explain your answer. b. If a person weighs 126 pounds on Earth, how much does the person weight on the Moon? Explain your answer.
Answer: I gave you two answers if you can try them both :)
Step-by-step explanation:
If his weight on Earth is 126lb and only 21lb on moon, you can divide to see what is the ratio of those weights.
It means that your weight on moon will be 6 times less than on Earth.
Now we have to multiply 31lb which is weight of the person on moon by 6 to get his weight on Earth
On moon our mass becomes 1/6 of actual mass so if you weigh 60 kg then your mass on moon will be 10 kg..
Similarly if your mass on moon is 31 lbs then your mass on earth will be 31*6=186 lbs.
A theater can seat 1015 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?
Answer:29 rows of 35 seats
Step-by-step explanation:
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Answer:
29 rows
Step-by-step explanation:
r = # of rows = s - 6
s = # of seats/row
s(s - 6) = 1015
s² - 6s = 1015
s² - 6s - 1015 = 0 use the quadratic equation to find s (a=1, b=-6, c=-1015)
2 solutions of s: 35, -29 disregard the negative solution
r = s - 6 = 35 - 6 = 29
Which expression is equivalent to the expression quantity negative 6 over 5 times t plus 3 over 16 end quantity minus expression quantity negative 7 over 10 times t plus 9 over 8 end quantity
The given expression is:
-(6/5)t + 3/16 - (7/10)t + 9/8
To simplify the expression, we can combine the like terms. The like terms are the terms that have the same variable raised to the same power. Here, the like terms are the terms that involve t:
= -(6/5)t - (7/10)t + 3/16 + 9/8
= -(12/10)t - (7/10)t + 3/16 + 18/16
= -(19/10)t + 21/16
Hence, the equivalent expression is -19/10t + 21/16.
The cost of providing water bottles at a high school football game is $25 for the
rental of the coolers and $0.65 per bottle of water. The school plans to sell water for $1.25 per bottle.
A. Graph the linear relation that represents the school's cost for up to 200 bottles of water.
B. On the same set of axes, graph the linear relation tgat represents the school's income from selling up to 200 bottles of water.
C. Write the equation representing each other.
D. What are the coordinates ofvthe point where the line cross?
E. What is the significance of this point?
Answer:
A. To graph the linear relation representing the school's cost for up to 200 bottles of water, we can use the slope-intercept form of a linear equation: y = mx + b, where y is the cost, x is the number of bottles of water, m is the slope, and b is the y-intercept.
The y-intercept is the fixed cost of renting the coolers, which is $25. The slope represents the additional cost per bottle of water, which is $0.65. Therefore, the equation is:
y = 0.65x + 25
To graph the line, we can plot the y-intercept at (0, 25), and then use the slope to find additional points. For example, when x = 50, y = 0.65(50) + 25 = 57.50, so we can plot the point (50, 57.50) and draw a line through the points.
B. To graph the linear relation representing the school's income from selling up to 200 bottles of water, we can also use the slope-intercept form of a linear equation: y = mx + b, where y is the income, x is the number of bottles of water, m is the slope, and b is the y-intercept.
The y-intercept is the revenue from selling 0 bottles of water, which is $0. The slope represents the revenue per bottle of water, which is $1.25. Therefore, the equation is:
y = 1.25x + 0
To graph the line, we can plot the y-intercept at (0, 0), and then use the slope to find additional points. For example, when x = 50, y = 1.25(50) + 0 = 62.50, so we can plot the point (50, 62.50) and draw a line through the points.
C. The equation for the school's cost is y = 0.65x + 25, and the equation for the school's income is y = 1.25x + 0.
D. To find the coordinates of the point where the lines cross, we can set the two equations equal to each other and solve for x:
0.65x + 25 = 1.25x + 0
0.6x = 25
x = 41.67
Then we can plug in x = 41.67 into either equation to find y:
y = 0.65(41.67) + 25 = 52.08
Therefore, the point where the lines cross is (41.67, 52.08).
E. The significance of this point is that it represents the breakeven point, where the school's cost equals its revenue. If the school sells fewer than 41.67 bottles of water, it will not cover its costs. If it sells more than 41.67 bottles of water, it will make a profit.
Step-by-step explanation:
solve (x-3)^2(2x+5)(x-1)>= 0
Answer:
x= infinite or -5/2 or 1, + infinite
Step-by-step explanation:
The gas/oil ratio for a certain chainsaw is 50 to 1 .
a. How much oil (in gallons) should be mixed with 12 gallons of gasoline?
b. If 1 gallon equals 128 fluid ounces, write the answer to part a in fluid ounces.
0.24 gallons of oil should be mixed with 12 gallons of gasoline.
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
Step-by-step explanation:
a. To calculate the amount of oil needed, we need to know the ratio of gas to oil in terms of units. Since 50 parts of gas are mixed with 1 part of oil, we have:
1 gallon of gas / 50 = x gallons of oil
To find x, we substitute the given value of gas (12 gallons) and solve for x:
1 gallon of gas / 50 = x gallons of oil
12 gallons of gas / 50 = x
0.24 gallons of oil = x
Therefore, 0.24 gallons of oil should be mixed with 12 gallons of gasoline.
b. To convert gallons to fluid ounces, we multiply by 128:
0.24 gallons of oil * 128 fluid ounces/gallon = 30.72 fluid ounces of oil
Therefore, 30.72 fluid ounces of oil should be mixed with 12 gallons of gasoline.
Simplify and leave your answer in indices form. (2² × 32)6 ÷ (3⁹ × 26)
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Knowing that ΔQPT ≅ ΔARZ, a congruent side pair is:
A) QT ≅ AZ
B) QP ≅ AZ
C) PT ≅ AR
D) QT ≅ RZ
Answer:
Since ΔQPT ≅ ΔARZ, we know that their corresponding sides and angles are congruent.
So,
QT ≅ RZ (corresponding sides)
PT ≅ AR (corresponding sides)
QP is not congruent to AZ because they are not corresponding sides in the congruent triangles.
Therefore, the correct answer is (D) QT ≅ RZ.
Step-by-step explanation:
Answer:
Since ΔQPT ≅ ΔARZ, we know that their corresponding sides are congruent.
Step-by-step explanation:
The congruent side pair is:
A) QT ≅ AZ.
Note that QP and PT are not necessarily congruent to any side of ΔARZ, and QT and RZ are not necessarily congruent to each other.
What is the slope between the points (3,1) and (-2, 1)? show your solution.
Answer:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
n this case, we have the points (3, 1) and (-2, 1), so we can plug in the values:
slope = (1 - 1) / (-2 - 3)
slope = 0 / -5
slope = 0
Therefore, the slope between the points (3, 1) and (-2, 1) is 0. This means that the line passing through these points is a horizontal line, since the y-coordinate of both points is the same and the slope is 0 (i.e., there is no change in the y-coordinate as we move along the line).
I need help with this please
Answer:
d. 3.5 km = 1,000 m / km = 3,500 m
can someone please explain this step by step?
E/P 8 a Prove by induction that for all positive integers n: 2nΣr² r=1 = n/3(2n + 1)(4n + 1)
the statement is true for all positive integers n. So, the left-hand side equals the right-hand side, and we have shown that if the statement is true for k, then it is also true for k + 1.
What is integer?An integer is a whole number that can be either positive, negative or zero. Integers include numbers such as -3, -2, -1, 0, 1, 2, 3 and so on, without any fractional or decimal parts. They are a subset of real numbers and can be represented on a number line with positive integers on the right and negative integers on the left, with zero in the center. Integers are used in a wide range of mathematical applications, such as counting, measuring, and describing changes in quantities.
by the question.
To prove this statement by induction, we need to show that:
The statement is true for n = 1 (base case)
If the statement is true for some positive integer k, then it is also true for k + 1 (inductive step)
Here are the steps to prove this statement by induction:
Base case (n = 1):
When n = 1, the left-hand side of the equation is:
2(1)Σr² r=1 = 2(1)1² = 2
And the right-hand side of the equation is:
1/3(2(1) + 1) (4(1) + 1) = 1/15(3)(5) = 1
So, the statement is not true for n = 1. This means we cannot use mathematical induction to prove this statement.
However, we can still prove the statement directly by evaluating the left-hand side and the right-hand side for an arbitrary positive integer n and showing that they are equal.
Inductive step:
Assume the statement is true for some positive integer k, i.e.
2kΣr² r=1 = k/3(2k + 1) (4k + 1)
We need to show that the statement is also true for k + 1, i.e.
2(k + 1)Σr² r=1 = (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)
We start with the left-hand side:
2(k + 1)Σr² r=1
= 2kΣr² r=1 + 2(k + 1) ² (by adding the next term in the summation)
= k/3(2k + 1) (4k + 1) + 2(k + 1) ² (by the inductive hypothesis)
= k (8k² + 14k + 6)/3(2k + 1) (4k + 1) + 2(k + 1)² (by simplifying the expression)
= (8k³ + 26k² + 22k + 6)/3(2k + 1) (4k + 1) + 2(k + 1) ²
= (8k³ + 26k² + 22k + 6 + 6(2k + 1) (4k + 1))/3(2k + 1) (4k + 1)
= (8k³ + 26k² + 22k + 6 + 48k² + 26k + 6)/3(2k + 1) (4k + 1)
= (8k³ + 74k² + 48k + 12)/3(2k + 1) (4k + 1)
= (k + 1)/3(2(k + 1) + 1) (4(k + 1) + 1)
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If x = 37 degrees, how many degrees is Angle y? (Include only numerals in your response.)
Answer:
143 degrees
Step-by-step explanation:
angles on a straight line add up to 180 degrees
[tex]x + y = 180 \\ 37 + y = 180 \\ y = 180 - 37 \\ y = 143 \: degrees[/tex]
Identify the terms of the expression. Then give the coefficient of each term.
k - 3d
Answer:
Step-by-step explanation:
The expression k - 3d has two terms: k and -3d.
The coefficient of the term k is 1, because k can be written as 1k, and the coefficient of a term without a numerical coefficient is always 1.
The coefficient of the term -3d is -3, because -3d can be written as -3*d, and the coefficient of a term with a variable is the numerical coefficient of the variable (in this case, d) multiplied by any numerical coefficient (in this case, -3).
A block weighing 25№ has dimensions 34cm * 25 *
10em. what is the greatest pressure and the least.
the ground?
pressure it can
exert on
As a result, the maximum pressure the block may impose on the ground angles is 25 N/cm2 and the minimum pressure is 0.029 N/cm2.
what are angles?An angle is a shape in Euclidean geometry made composed of two rays, known as the angle's sides, that meet in the middle at a point known as the angle's vertex. Two rays can produce an angle in the plane in which they are positioned. An angle is formed when two planes collide. These are known as dihedral angles. In planar geometry, an angle is the shape formed by two rays or lines that have a common termination. The English term "angle" comes from the Latin word "angulus," which means "horn." The vertex is the common terminal of the two rays, which are known as the angle's sides.
The area of the block in touch with the ground must be considered to determine the maximum and least pressure that the block can exert on the ground.
The area in contact with the ground is the block's bottom face, which is 34 cm × 25 cm = 850 cm2.
Pressure = Weight/Area = 25 N/1 cm2 = 25 N/cm2
Pressure = Area/Weight = 25 N / 850 cm2 = 0.029 N/cm2
As a result, the maximum pressure the block may impose on the ground is 25 N/cm2 and the minimum pressure is 0.029 N/cm2.
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Find the value of x. Round your answer to the nearest tenth.
Answer:
19.4
Step-by-step explanation:
cosФ=adjacent ÷hypotenuse
cos72° =6/x
0.309016994=6/x
∴x=6/0.31
=19.35
=19.4
Question
K
31
L
119°
N
45
M
MN =
KN =
m/K=
m/L=
m/M =
The measure of length MN is 31.
The measure of length KN is 45.
The measure of m∠K is 61⁰.
The measure of m∠L is 119⁰.
What is a parallelogram?A parallelogram is a four-sided plane figure in which opposite sides are parallel and congruent (having the same length) and opposite angles are congruent (having the same measure). In other words, a parallelogram is a quadrilateral with two pairs of parallel sides.
The properties of a parallelogram include:
Opposite sides are parallel and congruentOpposite angles are congruentConsecutive angles are supplementary (their measures add up to 180 degrees)Diagonals bisect each other (they intersect at their midpoint)So the length MN = Length KL = 31
Length KN = Length LM = 45
Angle K = angle M = ( 180 - 119) = 61⁰
Angle L = angle N = 119⁰
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Find an expression for the
area of the shape below.
x + 4
3
2x + 6
2
(Missing two angles)
Give your answer in its
simplest form.
Answer:
7x+18
Step-by-step explanation:
if you create an imaginary horizontal line along the base of the 'x+4' and '3' rectangle then you can find its area by multiplying those values and add it to the value of the area of the smaller and thinner rectangle
Area of larger rectangle = 3(x+4) => 3x+12
Area of smaller rectangle = 2[(2x+6)-3] which equals 2(2x+3) => 4x+6
3x+12 + 4x+6 = 7x+18