Answer:
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
Step-by-step explanation:
We can use the Poisson approximation to the binomial distribution when n (the number of trials) is large and p (the probability of success) is small. In this case, n = 100 and p = 0.05, so np = 5, which is not too small. However, we can still use the approximation as long as we adjust for continuity, by adding and subtracting 0.5 from the number of successes we're interested in.
Let X be the number of books with defective bindings out of 100. We want to find the probability that X = 2. Using the Poisson approximation, we have:
λ = np = 5
P(X = 2) ≈ P(1.5 < Y < 2.5), where Y is a Poisson random variable with parameter λ
To find this probability, we can use the cumulative distribution function (CDF) of Y:
P(X = 2) ≈ P(1.5 < Y < 2.5) = F(2.5) - F(1.5), where F(x) is the CDF of Y evaluated at x
The CDF of a Poisson distribution with parameter λ is given by:
F(x) = e^(-λ) * Σ(λ^k / k!, k = 0 to floor(x))
where floor (x) is the greatest integer less than or equal to x. Using this formula, we can calculate:
F(1.5) = e^(-5) * Σ(5^k / k!, k = 0 to 1) ≈ 0.0337
F(2.5) = e^(-5) * Σ(5^k / k!, k = 0 to 2) ≈ 0.1247
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
The probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution is 0.0842.
Since the number of books bound, n = 100, is large and the probability of defective bindings, p = 0.05, is small, we can use the Poisson approximation to the binomial distribution.
The mean, µ, of the Poisson distribution is µ = np = 100 x 0.05 = 5.
The probability of 2 defective bindings can be calculated using the Poisson probability formula:
P(X = 2) = (e^-µ) * (µ^x) / x!
= (e^-5) * (5^2) / 2!
= 0.0842 (rounded to four decimal places)
Using the Poisson approximation to the binomial distribution, the likelihood that 2 of the 100 volumes bound by this bindery will have faulty bindings is roughly 0.0842.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
The tiles to the correct boxes to complete the pairs-
A: [tex](-3^{-2} )^{0}[/tex] = 1; B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex] [tex]= 1/729[/tex] C: [tex]-3^{5} / -3^{8}[/tex] = -1/27 ; D: [tex]-3^{-3}. 3^{-3}[/tex] = - 1/729.
Explain about the indices:We can determine how many times a phrase has been multiplied by itself using an index, which is a tiny number.
Indexes is the plural of index.
Remember that a power is the result of a particular number of identical factors? For instance, the number [tex]3^{7}[/tex] is a power, where the base is the number 3, and the index or exponent is the number 7.
Given number with exponents :
A: [tex](-3^{-2} )^{0}[/tex]
[tex]= (-3^{0} )\\= 1[/tex]
B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex]
[tex]= 3^{3 + 1 + 2 -12}[/tex]
[tex]= 3^{-6}\\= 1/729[/tex]
C: [tex]-3^{5} / -3^{8}[/tex]
[tex]= -3^{5-8}\\= - 3^{-3}\\\= -1/27[/tex]
D: [tex]-3^{-3}. 3^{-3}[/tex]
[tex]= -3^{-3 - 3}\\= -3^{-6}\\\\= -1/729[/tex]
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An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 2662 feet and Plane B is taking off. Plane A is gaining altitude at 25.25 feet per second and Plane B is gaining altitude at 85.75 feet per second. How many seconds will pass before the plane are at the same altitude? What will their altitude be when they’re at the same altitude?
Write a counterexample to prove this is false:
Yes, The function with a frequency of 2 has a greater period than a function with a frequency of 1/2.
What does the word" function" signify in calculation?
As a set of inputs with one for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one affair. A sphere, codomain, or range exists for every function. generally, f( x), where x is the input, is used to represent a function.
frequency of f(x) = 1/period of f(X)
2 = 1/[tex]T_{f}[/tex]
[tex]T_{g}[/tex] = 1/2
frequency of g(X) = 1/period of g(X)
1/2 = 1/[tex]T_{g}[/tex]
[tex]T_{f}[/tex] = 2
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a ramp goes from a doorway of a building to the ground. the end of the ramp connected to the doorway is feet above the ground. the horizontal distance from the bottom of the ramp to the building is 15 feet. what is the angle of elevation of the ramp to the nearest degree?
The angle of elevation of the ramp to the nearest degree is 34°.
we can use trigonometry to determine the angle of elevation of the ramp.To begin, we need to draw a diagram to visualize the problem.
Let's assume that the height of the end of the ramp is h, and the horizontal distance from the bottom of the ramp to the building is d.
From the diagram, we can see that we have a right-angled triangle where the height of the triangle is h, the base of the triangle is d, and the hypotenuse of the triangle is the length of the ramp.
Using the tangent ratio, we can write:
tanθ = opposite/adjacent
where opposite is the height of the triangle, and adjacent is the base of the triangle. Substituting the values we have, we get:
tanθ = h/d
Rearranging this formula, we can write:
θ = tan⁻¹(h/d)
Substituting the values we have, we get:θ = tan⁻¹(10/15)θ = 33.69°
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I need help with the whole page please help!
The following points are 5 or more units apart: A and B, G and D, G and F, G and E, F and E, E and B, (4, 3 and (4, -2), (6, -2) and (0, -2), (3, -7) and (3, -1)
Identifying the points that are 5 or more units apartWhen two points on a graph are 5 or more units apart, it means that there is a significant difference in the values of the function at those points.
For example, if we have two vertical or horizontal points (x1, y1) and (x2, y2) on a graph such that |x1 - x2| ≥ 5, it means that the x-values of the two points are at least 5 units apart.
Similarly, if |y1 - y2| ≥ 5, it means that the y-values of the two points are at least 5 units apart.
Using the above as a guide, the following points are 5 or more units apart
A and B, G and D, G and F, G and E, F and E, E and B, (4, 3 and (4, -2), (6, -2) and (0, -2), (3, -7) and (3, -1)
The point that is 8 or more units apart from NWe have
N = (6, 8)
The point that is 8 or more units apart from N could be
Point = (6, 8 + at least 8)
So, we have
Point = (6, 8 + 9)
Point = (6, 17)
Hence, the point is (6, 17)
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perform a follow-up analysis of the test in exercise 38 by finding the individual compo- nents of the chi-square statistic. which cell(s) contrib- uted most to the final result and in what direction?
The cell that contributed most to the final result was Cell (1,2) with a contribution of 8.44.
How Cell (1,2) was contributed most to the final result?we need to calculate the expected frequencies for each cell in the contingency table. We can use the formula:
Expected frequency = (row total x column total) / grand total
The grand total for the table is 80, so we can calculate the expected frequencies for each cell as follows:
Expected frequency of Cell (1,1) = (44 x 42) / 80 = 23.1
Expected frequency of Cell (1,2) = (44 x 38) / 80 = 20.9
Expected frequency of Cell (2,1) = (36 x 42) / 80 = 18.9
Expected frequency of Cell (2,2) = (36 x 38) / 80 = 17.1
Next, we need to calculate the contribution of each cell to the chi-square statistic. We can do this by subtracting the expected frequency from the observed frequency, squaring the result, and then dividing by the expected frequency.
The contributions of each cell to the chi-square statistic are as follows:
Contribution of Cell (1,1) = (37 - 23.1)2 / 23.1 = 8.30
Contribution of Cell (1,2) = (7 - 20.9)2 / 20.9 = 8.44
Contribution of Cell (2,1) = (9 - 18.9)2 / 18.9 = 4.52
Contribution of Cell (2,2) = (27 - 17.1)2 / 17.1 = 6.04
Finally, we can sum up the contributions of all the cells to get the chi-square statistic:
Chi-square statistic = 8.30 + 8.44 + 4.52 + 6.04 = 27.30
The cell that contributed most to the final result was Cell (1,2) with a contribution of 8.44. This cell had an observed frequency of 7, which was much lower than the expected frequency of 20.9. This indicates that there is a significant association between the two variables in this cell, and it is driving the overall result of the test.
In conclusion, by breaking down the chi-square statistic into its individual components, we can identify the cells that contribute most to the result and gain a deeper understanding of the relationship between the variables.
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1 Write down: 1.1.1 The factors of 18
Answer:
1 2 3 6 9 and 18
Step-by-step explanation:
the 111 factors of 18 is 1 2 3 6 9 ang 18
the physician order vancomycin 400 mg oral every 6 hours for a child that weighs 99 lbs. the vancomycin is available in 250mg/ml concentration. the recommended dose is 40mg/kg/24 h divided in four doses. how many milligrams per kilogram per 24 hours is the patient receiving?
The patient is recieving nearly 35.5 miligrams of the drugs for per kilogram per 24 hours.
First, we need to convert the child's weight from pounds to kilograms:
99 lbs / 2.205 = 44.9 kg
Next, we calculate the recommended dose for this weight:
40 mg/kg/24h x 44.9 kg = 1796 mg/24h
Since the recommended dose is divided into four equal doses, each dose should be:
1796 mg/24h ÷ 4 doses = 449 mg/dose
However, the physician ordered 400 mg every 6 hours, which is not the same as 449 mg every 6 hours. To calculate the actual dose per kilogram per 24 hours, we need to convert the ordered dose to the recommended dose:
400 mg/dose x 4 doses = 1600 mg/24h
Then, we divide the actual dose by the child's weight in kilograms:
1600 mg/24h ÷ 44.9 kg = 35.6 mg/kg/24h
Therefore, the patient is receiving 35.6 mg/kg/24h, which is slightly lower than the recommended dose of 40 mg/kg/24h.
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PLEASE HELP! 10 POINTS! URGENT!
Answer: 32
Step-by-step explanation:
Multiply by reciprocal. -> y >or= 32
32=32
24<32
16<32
8<32
What is the volume?
5 1/3in
3 3/4 in
4 in
whoever tells me the correct answer wins
The commute times are shorter for City A but more predictable for City B. Thus, option c is correct.
What is interval?In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded.
The interval [1, 5] represents a set of real numbers that includes all the numbers between 1 and 5, including 1 and 5 themselves. The square brackets indicate that the endpoints of the interval are included in the set. The left bracket "[" indicates that the interval includes the number 1, and the right bracket "]" indicates that the interval includes the number 5.
In interval notation, we can write this interval as:
[1, 5] = {x | 1 ≤ x ≤ 5}
This means that the set of all real numbers x, such that x is greater than or equal to 1 and less than or equal to 5, is equal to the interval [1, 5].
Graphically, we can represent this interval on a number line as follows:
|-----|-----|-----|-----|-----|
0 1 2 3 4 5
The interval [1, 5] is the closed interval between 1 and 5, including both endpoints, so we use closed circles to indicate that the endpoints are included in the interval:
|-----|-----|-----|-----|-----|
0 1 2 3 4 5
[ ○-----○ ]
1 5
The interval includes all the numbers on the number line between 1 and 5, including 1 and 5 themselves, but no other numbers outside of that range.
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The areas of two circles are 92 2 and 62 2
respectively. Find the radius of the circle
having its area equal to the sum of the areas of the two circles.
Answer:
formula for area of a circle = πr²
πr² = 92cm² first circle
πr² = 62cm² second circle
now to find the radius of a circle having the sum of the other circle.
πr² = 92 + 62
3.142 × r² = 154
r² = 154/3.142
r² = 49.013
take square root of both sides
r = √49.013
r = 7.000cm ≈ 7cm
What if FC
F-2,0,0,8,2,1
C12,0,3/2,1,-6,7
The vector FC is (14, 0, 3/2, -7, -8, 6).
If you are given two vectors FC and F and C, with F represented as F(-2, 0, 0, 8, 2, 1) and C represented as C(12, 0, 3/2,
1, -6, 7), you can find the vector FC by subtracting the F vector from the C vector component-wise.
Step 1: Write down the F and C vectors.
F = (-2, 0, 0, 8, 2, 1)
C = (12, 0, 3/2, 1, -6, 7)
Step 2: Subtract the F vector from the C vector component-wise.
FC = C - F
FC = (12 - (-2), 0 - 0, 3/2 - 0, 1 - 8, -6 - 2, 7 - 1)
Step 3: Simplify the subtraction.
FC = (14, 0, 3/2, -7, -8, 6)
So, the vector FC is (14, 0, 3/2, -7, -8, 6).
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what is the product of these binomials [tex](x-9)(x+2)=
The product of the binomials (x-9) and (x+2) is x² - 7x - 18.
How to calculate the product of these binomials?To find the product of the binomials (x-9) and (x+2), we can use the FOIL method, which stands for First, Outer, Inner, Last.
First: Multiply the first terms of each binomial: xx = x²
Outer: Multiply the outer terms of each binomial: x × 2 = 2x
Inner: Multiply the inner terms of each binomial: -9 × x = -9x
Last: Multiply the last terms of each binomial: -9 × 2 = -18
Now we can add up these four products to get the final answer:
x² + 2x - 9x - 18
Simplifying this expression, we get:
x² - 7x - 18
Therefore, the product of the binomials (x-9) and (x+2) is x² - 7x - 18.
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C is between A and D , and B is the midpoint of AC . If BC=2 and BD=7 , find AD
Answer:
AD = 9
Step-by-step explanation:
B is the midpoint of AC and BC = 2 so AC = 4.
BD is given as 7 so all we need to do is add up the given values:
AC + BD - BC = AD
4 + 7 - 2 = 9
a bug ran along a number line at a speed at 11 units per minutes. It never changes direction. If the bug is at 100 units at 7:15,where could it be at 7:20
Answer:
Step-by-step explanation:
Answer:
155 Units
Step-by-step explanation:
Rate of Bug (given) = 11 units PER MINUTE
It never changed direction, so it was going in positive direction (assume).
In 7:15 pm (evening), it was at Point 100,
We want the point at which it was at 7:20 pm.
7:20pm - 7:15pm = 5 minutes
So, time passed 5 minutes. It's rate is 11 units PER MINUTE, so in 5 mins:
11 * 5 = 55 units
Assuming he is going in positive direction, the bug will be at:
100 + 55 = 155 Units
Find the perimeter of AIJK. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale. F 35 349 499 978 H GJ K 49° 44 34
Using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.
What are triangles?A triangle is a polygon with three edges and three vertices.
It belongs to the basic geometric shapes.
A triangle having vertices A, B, and C is known as triangle ABC.
Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.
The closed, two-dimensional shape known as a triangle has three sides, three angles, and three vertices.
A triangle is part of a polygon.
So, we know that:
We must ascertain the value of x in order to determine the triangle's perimeter, IJK.
Using the ratio of comparable triangles and the triangles above, we have:
HF/KI = FG/IJ
Where,
HF = 35, KI = 77, FG = 27 and IJ = x
By changing the values, we obtain:
35/77 = 27/x
Take the cross product of the aforementioned equation, and we have:
35x = 27*77
x = 27*77/35 = 27 * 11/5 = 59.4
The triangle's perimeter is thus equal to the sum of its sides:
△IJK = 44 + 77 + 59.4 = 180.4
Therefore, using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.
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Correct question:
Watch the help video on the perimeter of AIJK. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Shama draws a model of her garden on the coordinate grid. Each unit on the
grid represents 1 foot. Shama buys 1 plant for every 4 square feet of the garden.
How many plants does Shama buy?
y
87
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
X
14 plants
10 plants
7 plants
18 plants
Done->
Shama needs to buy 10 plants for her garden.
Calculating the number of plants she buysFrom the graph, we have
Area = 8 * 5 = 40
To determine how many plants Shama needs to buy, we need to use the given rule that she buys 1 plant for every 4 square feet of the garden.
Therefore, we can divide the total area of the garden by 4 to find how many plants she needs to buy:
Number of plants = Area of garden ÷ 4
Substituting the given values, we get:
Number of plants = 40 ÷ 4
Number of plants = 10
Therefore, Shama needs to buy 10 plants for her garden.
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In an orchard, there are 12 apple trees, 24 orange trees, and a cherry tree. What is the ratio of orange trees to cherry trees?
Answer: 24:1
Step-by-step explanation:
In the first step, you have to acknowledge how many of each tree there are in the question asked.
There is one cherry tree and 24 orange trees.
So the ratio of orange trees to cherry trees would be 24:1
0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5
how many numbers are there
Answer:
There are 46 numbers in this sequence.
A large to-go order at a local coffee shop consists of 20 cups of coffee. Five of the cups of coffee have sugar, 12 of the cups of coffee have artificial sweetener, and the others are black, containing no sugar or sweetener. Suppose an experiment involves a person taking a cup of coffee from this order. The person does not put that coffee back with the others, and then takes another coffee from the order. What is the probability that the person selects 2 coffees with artificial sweetener? Express your answer as a simplified fraction.
The probability that the person selects 2 coffees with artificial sweetener is 33/95.
How to find the Probability?Let A be the event that the first cup of coffee has artificial sweetener, and B be the event that the second cup of coffee also has artificial sweetener.
We want to find the probability of the intersection of A and B, i.e., the probability that both cups have artificial sweetener. We can use the formula for conditional probability:
According to given data:P(A and B) = P(B|A) * P(A)
where P(B|A) is the probability of B given that A has occurred, and P(A) is the probability of A.
The probability of selecting a cup of coffee with artificial sweetener on the first draw is:
P(A) = 12/20
After the first cup has been drawn, there are now 11 cups with artificial sweetener left in the order, out of a total of 19 cups (since one cup has already been drawn). Therefore, the probability of selecting another cup with artificial sweetener on the second draw, given that the first cup had artificial sweetener, is:
P(B|A) = 11/19
So the probability of selecting two cups with artificial sweetener is:
P(A and B) = P(B|A) * P(A) = (11/19) * (12/20) = 33/95
Therefore, the probability that the person selects 2 coffees with artificial sweetener is 33/95.
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What is the circumference of the circle pictured below? (Use π = 3.14
For the given circle the circumference is 34.54.
What is circumference?
Circumference is the distance around the edge of a circle or any curved, circular object. It can be thought of as the perimeter of a circle.
The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle.
Substituting the given value of the diameter, we get:
C = π(11)
Using π = 3.14, we can evaluate the expression:
C = 3.14(11)
C = 34.54
Therefore, the circumference of the circle is 34.54 (rounded to two decimal places).
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Write an exponential function
y = abx
for a graph that passes through
(2, 1)
and
(3, 4).
An exponential function y = abx for a graph that passes through (2, 1) and (3, 4) is [tex]y = (1/16)(4)^x[/tex].
To write an exponential function in the form[tex]y = ab^x[/tex] that passes through the points (2, 1) and (3, 4), follow these steps:
Step 1: Write the general form of the exponential function:
[tex]y = ab^x[/tex]
Step 2: Plug in the coordinates of the first point (2, 1):
[tex]1 = ab^2[/tex]
Step 3: Plug in the coordinates of the second point (3, 4):
[tex]4 = ab^3[/tex]
Step 4: Solve for "a" and "b" using the equations from Steps 2 and 3.
We have two equations:
1)[tex]1 = ab^2[/tex]
2) [tex]4 = ab^3[/tex]
Divide equation 2 by equation 1 to eliminate "a":
[tex](4/1) = (ab^3)/(ab^2)[/tex]
4 = b.
Now that we have found "b," we can find "a" by plugging "b" back into either equation 1 or 2.
We'll use equation 1:
[tex]1 = a(4)^21 = a(16)[/tex]
a = 1/16
Step 5: Write the final exponential function using the values of "a" and "b":
[tex]y = (1/16)(4)^x[/tex].
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4 Assignment
K
Question 4, 2.4.20
Part 3 of 8
Fill in the Venn diagram with the appropriate numbers based on the following information.
n(A)=33
n(B)=36
n(B n C) = 14
n(An C) = 9
n(AnBn C) = 5
n(U)= 70
n(C) = 24
n(An B) = 17
A Venn diagram is a graphical representation of sets. Remember that n(A) is the number of
elements in set A.
Region I contains 12 elements.
Region Il contains 12 elements.
Region III contains elements.
I
=
II
HW Score: 73.15%, 6.58 of S
Points: 0 of 1
VII
VI
V
с
VIII
III
IV
B
U
Note that the sum of all the regions equals the size of the universal set U, as it should be:
5 + 12 + 4 + 24 + 19 + 9 + 5 + 6 = 70.
To fill in the Venn diagram, we start with the given information:
n(A) = 33
n(B) = 36
n (B ∩ C) = 14
n (A ∩ C) = 9
n (A ∩ B ∩ C) = 5
n(U) = 70
n(C) = 24
n (A ∩ B) = 17
We can use the formula for the size of a set union to find n (B ∪ C):
n (B ∪ C) = n(B) + n(C) - n (B ∩ C)
n (B ∪ C) = 36 + 24 - 14
n (B ∪ C) = 46
We can also use the formula for the size of a set intersection to find n(A ∩ B):
n (A ∩ B) = n(A) + n(B) - n (A ∪ B)
n (A ∪ B) = n(A) + n(B) - n (A ∩ B)
n (A ∪ B) = 33 + 36 - 17
n (A ∪ B) = 52
n (A ∩ B) = 33 + 36 - 52
n (A ∩ B) = 17
Now we can start filling in the Venn diagram:
I = A ∩ B ∩ C = 5
II = A ∩ B - C = 12 (since n(A ∩ B) = 17 and n(A ∩ B ∩ C) = 5)
III = A ∩ C - B = 4 (since n(A ∩ C) = 9 and n(A ∩ B ∩ C) = 5)
IV = A - B - C = 24 (since n(A) = 33 and n(A ∩ B) = 17 and n(A ∩ C) = 9 and n (A ∩ B ∩ C) = 5)
V = B - A - C = 19 (since n(B) = 36 and n(A ∩ B) = 17 and n(B ∩ C) = 14 and n (A ∩ B ∩ C) = 5)
VI = B ∩ C - A = 9 (since n(B ∩ C) = 14 and n(A ∩ B ∩ C) = 5)
VII = C - A - B = 5 (since n(C) = 24 and n(A ∩ C) = 9 and n(B ∩ C) = 14 and n (A ∩ B ∩ C) = 5)
VIII = U - (A ∪ B ∪ C) = 6 (since n(U) = 70 and n(A) = 33 and n(B) = 36 and n(C) = 24)
Therefore, the completed Venn diagram would have:
I = 5
II = 12
III = 4
IV = 24
V = 19
VI = 9
VII = 5
VIII = 6
Note that the sum of all the regions equals the size of the universal set U, as it should be:
5 + 12 + 4 + 24 + 19 + 9 + 5 + 6 = 70
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l(x-1)(x-3)l=mx If m has four different possibilities, what is the range of m
Answer:
0 < m < 4-√12 ≈ 0.535898
Step-by-step explanation:
You want to know the range of values of m that will give |(x-1)(x-3)| = mx four distinct solutions.
Absolute valueThe quadratic function f(x) = (x -1)(x -3) will be negative for values of x between the zeros: 1 < x < 3. Hence the absolute value function will invert the graph in that interval, as shown by the red curve in the attachment.
The line y = mx can only intersect that graph in 4 places in the first quadrant. The value of m must be greater than 0 and less than 1.
Upper limitThe upper limit of the slope will be defined by the value of m that makes the line intersect the inverted quadratic exactly once. That is, the discriminant of mx -(-f(x)) = 0 will be zero.
mx +(x -1)(x -3) = x² +(m -4)x +3 = 0
D = (m -4)² -4(1)(3) = (m -4)² -12 = 0
Solving for m gives ...
(m -4)² = 12
m -4 = ±√12
m = 4 ±√12 ≈ 0.54 or 7.46
We can see from the attached graph that m ≈ 7.46 is an extraneous solution. This means the range of m will be ...
0 < m < 4-√12
5c + 4c + 2 and 5c + 2[2c] + 1]
The final expression is 9c + 2.
What is an equation?
In mathematics, an equation asserts the equality of two expressions, usually separated by an equal sign (=). An equation is formed when two expressions are set equal to each other. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
To simplify the expressions:
5c + 4c + 2 = 9c + 2
In this expression, we can add the coefficients of the like terms 5c and 4c to get 9c. Then we simply combine the constant term 2.
5c + 2[2c + 1] = 5c + 4c + 2
In this expression, we can distribute the 2 outside the brackets to get:
5c + 2(2c) + 2(1) = 5c + 4c + 2
Then, as in the previous expression, we can combine the like terms 5c and 4c to get 9c and simplify to get:
9c + 2
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Scott has been working out to get in shape. Each night, he does 3 bent-leg sit-ups for every 2 straight-leg sit-ups. If Scott does 10 straight-leg sit-ups every night, how many sit-ups does he do altogether?
Scott does 35 sit-ups altogether every night.
What is ratio?A ratio is a comparison of two quantities, expressed as the quotient of one quantity divided by the other. Ratios can be written in different forms, such as using a colon (:) or a fraction (/).
According to question:For every 2 straight-leg sit-ups, Scott does 3 bent-leg sit-ups. Therefore, the ratio of straight-leg sit-ups to bent-leg sit-ups is 2:3.
If Scott does 10 straight-leg sit-ups every night, we can use this ratio to find out how many bent-leg sit-ups he does.
First, we can write the ratio as a fraction:
2/5 = 10/x
where x is the number of bent-leg sit-ups Scott does.
To solve for x, we can cross-multiply:
2x = 50
x = 25
Therefore, Scott does 25 bent-leg sit-ups every night.
To find the total number of sit-ups Scott does every night, we can add the number of straight-leg sit-ups to the number of bent-leg sit-ups:
10 + 25 = 35
Therefore, Scott does 35 sit-ups altogether every night.
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the grand canyon is 1600 meters deep at its deepest point. a rock is dropped from the rim above this point. express the height of the rock as a function of the time t in seconds. how long will it take the rock to hit the canyon floor? a(t)
The grand canyon is 1600 meters deep at its deepest point. a rock is dropped from the rim above this point. express the height of the rock as a function of the time t in seconds. It will take approximately 18.05 seconds for the rock to hit the canyon floor.
The height of a rock dropped from the rim of the Grand Canyon can be expressed as a function of time, t, in seconds. To do this, we will use the free-fall equation, which states that the height of an object in free fall is given by:
a(t) = -1/2 * g * t^2 + h
where:
- a(t) is the height of the rock at time t,
- g is the acceleration due to gravity (approximately 9.81 meters per second squared),
- t is the time in seconds, and
- h is the initial height of the rock (1600 meters, in this case).
For the rock dropped from the rim of the Grand Canyon, the function becomes:
a(t) = -1/2 * 9.81 * t^2 + 1600
To find how long it will take the rock to hit the canyon floor, we need to find the value of t when the height, a(t), is equal to 0 (i.e., the rock reaches the floor).
0 = -1/2 * 9.81 * t^2 + 1600
Now, we'll solve for t:
1/2 * 9.81 * t^2 = 1600
t^2 = (1600 * 2) / 9.81
t^2 ≈ 325.99
t ≈ √325.99
t ≈ 18.05 seconds
Therefore, it will take approximately 18.05 seconds for the rock to hit the canyon floor.
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The diameter of the circle above is 6cm what is the circumference of the circle?
Answer:
A
Step-by-step explanation:
r=d/2
=6/2 =3
2πr
2×3.14×3
=18.84
A fourth grade class surveys students as to their shoe size.
Which type of graph would best display the results of this survey?
A. Circle graph
B. Histogram
C. Line plot
D. Blox plot
The best type of graph to display the results of this survey would be a histogram. A histogram is a graph that uses bars to represent the frequency distribution of a set of data. In this case, the shoe sizes would be grouped into intervals (e.g., 1-3, 4-6, 7-9, etc.) and the height of each bar would represent the number of students who have shoe sizes within that interval. A histogram is an effective way to show the overall pattern of the distribution of shoe sizes in the class.
A circle graph, also known as a pie chart, is useful for showing parts of a whole. It may not be the best choice for this survey since it does not show the distribution of shoe sizes as effectively as a histogram would.
A line plot, also known as a dot plot, is useful for showing the frequency of individual values in a small data set. It may not be the best choice for this survey since it may not be practical to list every individual shoe size.
A box plot, also known as a box-and-whisker plot, is useful for showing the distribution of a large data set. It may not be the best choice for this survey since the data set is likely to be small, and a histogram would be more appropriate for displaying the results.