Answer:
The formula for slope is sometimes referred to as "rise over run", because the fraction onsists of the "rise" (being the change in y, going up or down) divided by the "run" (being the change in x, going from left to the right).
Step-by-step explanation:
verbal expression to algebraic expression
Answer:
35. 3y³ - 6
37. 2(x-9)
Those are the answers. Follow mee please
13 A group of three friends
order a combo meal which
includes two slices of pizza
and a drink. Each drink is
priced at $2.50. If the
combined total is $31.50, how
much is the cost of a slice o
pizza?
Step-by-step explanation:
if I understand correctly, then the 3 friends ordered a combo meal each.
so, 3 drinks and 3×2 = 6 slices of pizza are ordered.
and that costs in total $31.50.
each drink costs $2.50.
so, the calculation is (with x being the price of a pizza slice) :
3×2.5 + 6x = 31.5
7.5 + 6x = 31.5
6x = 24
x = 4
so, each slice of pizza costs $4.
complete the function table for the given domain and plot the points on the graph f(x)=(x-5)^2+1
Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
f(x) = (x-5)²+1
put x = 2
f(2) = (2-5)²+1 = (-3)²+1 = 9+1 = 10
put x = 3
f(3) = (3-5)²+1 = (-2)²+1 = 4+1 = 5
put x = 4
f(4) = (4-5)²+1 = (-1)²+1 = 1+1 = 2
put x = 5
f(5) = (5-5)²+1 = (0)²+1 = 0 + 1 = 1
put x = 6
f(5) = (6-5)²+1 = (1)²+1 = 1 + 1 = 2
Thus, the table wil be completed as:
x 2 3 4 5 6
f(x) 10 5 2 1 2
Please check the attached figure for the plotting graph.
Answer:
He is correct^^^^^^
Step-by-step explanation:
just took the test
The cost to make each T-shirt is $10. You estimate that you will
sell 50 shirts. If you want to make a profit of at least $250, what
price will you charge for these T-shirts? Show your solution in two
different ways.
The price per T-shirt should be at least $15 to achieve a profit of $250.
To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.
Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.
Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.
Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.
Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.
By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.
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The method of sampling where the person most knowledgeable of the subject of study selects the elements of the population that he or she feels are the most representative of the population is?
The method of sampling where the person most knowledgeable of the subject of study selects the elements of the population that he or she feels are the most representative of the population is judgement sampling
The judgement sampling is a non probability that the researcher selects units to be sampled based on his own knowledge and professional judgement. Here the probability is not a factor.
The given question is the person most knowledgeable of the subject of study selects the elements of the population that he or she feels are the most representative of the population.
Here the given sampling is matches the judgement sampling, because the selecting the units to be samples based on her or his knowledge and judgement
Therefore, the sampling method is judgement sampling
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can someone pls help? i've been waiting over an hour
Answer:
22
Step-by-step explanation:
5(7)=35
3(8)=24
35-24+11=22
Answer:
22
Step-by-step explanation:
\(5c - 3d + 11\\\rule{150}{0.5}\\5(7)-3(8)+11\\\\35 - 24 + 11\\\\11 + 11\\\\\boxed{22}\)
Hope this helps!
If f(x)=16x-30 and g(x)=14x-6, for which value of x does (f-g)(x)=0?
12
13
14
The value of x for which (f - g)(x) = 0 is x = 12.
To find the value of x for which (f - g)(x) = 0, we need to subtract g(x) from f(x) and set the resulting expression equal to zero. Let's perform the subtraction:
(f - g)(x) = f(x) - g(x)
= (16x - 30) - (14x - 6)
= 16x - 30 - 14x + 6
= 2x - 24
Now, we can set the expression equal to zero and solve for x:
2x - 24 = 0
Adding 24 to both sides:
2x = 24
Dividing both sides by 2:
x = 12
Therefore, the value of x for which (f - g)(x) = 0 is x = 12.
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If the lateral surface area of a cylinder with height 4cm is 24pi cm squared then what is its volume?
We are given –
Height of cylinder is = 4cmLateral surface area of cylinder is = 24πcm²We are asked to find volume of the given cylinder.
Let the radius be "r".Then according to the question,it’s given –
\(\qquad\) \(\pink{\twoheadrightarrow\bf Curved\: surface\: area _{(Cylinder)}= 2\pi r h }\)
\(\qquad\) \(\twoheadrightarrow\sf 2\pi r h = 24 \pi\)
\(\qquad\) \(\twoheadrightarrow\sf 2\cancel{\pi} rh = 24 \cancel{\pi}\)
\(\qquad\) \(\twoheadrightarrow\sf r =\dfrac{24}{2h}\)
\(\qquad\) \(\twoheadrightarrow\sf r = \dfrac{24}{2\times 4}\)
\(\qquad\) \(\twoheadrightarrow\sf r = \dfrac{24}{8}\)
\(\qquad\) \(\twoheadrightarrow\sf r = \cancel{\dfrac{24}{8}}\)
\(\qquad\) \(\pink{\twoheadrightarrow\bf r = 3 \: cm}\)
Now, Let's find volume of cylinder
\(\qquad\) \(\purple{\twoheadrightarrow\bf V_{(Cylinder)} = \pi {r}^{2}h}\)
\(\qquad\) \(\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 3^2\times 4 \)
\(\qquad\) \(\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 9 \times 4\)
\(\qquad\) \(\twoheadrightarrow\sf V_{(Cylinder)} = \pi \times 36\)
\(\qquad\) \(\purple{\twoheadrightarrow\bf V_{(Cylinder)} = 36 \pi \: cm^3}\)
Henceforth, volume of cylinder is 36π cm³.Step-by-step explanation:
Given :-
Height is = 4cmLateral surface area of cylinder is = 24πcm²to find :-
volume of the given cylinder.Solution :-
Lateral surface area of cylinder = 2πrh
24π cm = 2πrh
Cancelling π on both the sides ,
24/2h = r
putting the value of h i.e, 4 cm
24/2×4 cm = r
3 cm = radius
Now volume of Cylinder = πr²h
putting all the values ,
Volume = 3.14 × 3² × 4 cm³
Volume = 113.04 cm³
Summarize, represent, and interpret data on a single count or measurement variable.
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Summarizing, representing, and interpreting data on a single count or measurement variable involves using statistical techniques like calculating mean and standard deviation, fitting to a normal distribution, and using specialized tools to estimate areas under the normal curve. However, not all data sets follow a normal distribution, and alternative techniques may be more suitable.
To summarize, represent, and interpret data on a single count or measurement variable, you can use various statistical techniques. One common approach is to calculate the mean and standard deviation of a data set. The mean represents the average value of the data, while the standard deviation measures the variability or spread around the mean.
To fit the data set to a normal distribution, you can use the mean and standard deviation to determine the parameters of the distribution. The normal distribution, also known as the bell curve, is characterized by its symmetric shape and specific mean and standard deviation values. By fitting the data to a normal distribution, you can make inferences and estimate population percentages.
However, it's important to recognize that not all data sets are appropriate for this procedure. Some data sets may not follow a normal distribution, which could lead to inaccurate results. In such cases, alternative statistical techniques may be more suitable.
To estimate areas under the normal curve, you can use calculators, spreadsheets, and tables specifically designed for this purpose. These tools allow you to input the mean, standard deviation, and desired range of values to calculate the area under the curve. This can be useful for estimating probabilities or making predictions based on the normal distribution.
Overall, summarizing, representing, and interpreting data on a single count or measurement variable involves understanding the mean and standard deviation, fitting the data to a normal distribution when appropriate, and using specialized tools to estimate areas under the normal curve.
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a 2 foot vertical post casts a 14 inch shadow at the same time a nearby cell phone tower casts a 119 foot shadow. how tall is the cell phone tower?
So, the cell phone tower is 17 feet tall.
To find the height of the cell phone tower, we can use the concept of similar triangles. Since the post and the tower are both vertical, and their shadows are cast on the ground, the angles are the same for both.
First, let's convert the measurements to the same unit. We will use inches:
1 foot = 12 inches, so 2 feet = 24 inches.
Now, we can set up a proportion with the post and its shadow as one pair of corresponding sides and the tower and its shadow as the other pair:
(height of post)/(length of post's shadow) = (height of tower)/(length of tower's shadow)
24 inches / 14 inches = (height of tower) / 119 feet
To solve for the height of the tower, we can cross-multiply:
24 * 119 = 14 * (height of tower)
2856 inches = 14 * (height of tower)
Now, divide both sides by 14:
height of tower = 2856 inches / 14 = 204 inches
Finally, convert the height back to feet:
204 inches ÷ 12 inches/foot = 17 feet
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which choice is equivalent to the quotient shown here when x>=0 square root of 35x^5 divided by the square root of 7x^3
A. 5x
B. 5x^2
C. x^2 square root 5
D. x square root 5
Answer:
x√5 = x square root 5
Step-by-step explanation:
√35x^5 ÷ √7x^3 = √(35x^5 / 7x^3)
√(35x^5 / 7x^3) = √(5x^5 / x^3)
√(5x^5 / x^3) = √5x^(5-3) = √5x²
√5x² = x√5
Convert the integral ∫∫ r √4 −x2−y2da where r = {(x, y) : x2 y2≤ 4, x ≥ 0} to polar coordinates, and then evaluate.
The integral ∫∫ r √4 −x2−y2da where r = {(x, y) : x2 y2≤ 4, x ≥ 0} conversion to polar coordinates the value of the integral is (4/3)π.
To convert the integral to polar coordinates, we need to express the limits of integration in terms of the polar coordinates.
Recall that in polar coordinates, x = r cosθ and y = r sinθ, where r is the radial distance from the origin and θ is the angle measured counterclockwise from the positive x-axis to the line connecting the origin to the point (x, y).
In this case, the region r is defined by \(x^2 + y^2\) ≤ 4 and x ≥ 0. In polar coordinates, this corresponds to the region 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/2. To see why, note that x ≥ 0 implies 0 ≤ θ ≤ π/2, and \(x^2 + y^2 = r^2\), so r ≤ √4 = 2.
So we have:
∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) ∫(r=0 to 2) r√(4-\(r^2\)) dr dθ
To evaluate this integral, we can use the substitution u = 4 - \(r^2\), du = -2r dr, which gives:
∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) ∫(u=4 to 0) -1/2 √u du dθ
Now we can evaluate the inner integral:
∫(u=4 to 0) -1/2 √u du = [-1/3 u^(3/2)](u=4 to 0) = (1/3)(8 - 0) = 8/3
Substituting this back into the original integral, we have:
∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) (8/3) dθ = (8/3) (π/2 - 0) = (4/3)π
Therefore, the value of the integral is (4/3)π.
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Terry sees this offer:
Refurbished Phone = 35% off
Now only £78
How much was the phone before the discount?
Line p passes through points (-2, 5) and (3, 8). Line q passes through the points (-1, 4) and (4, 7). Which statements are true?
The equation of line p is y = (3/4)x + 13/2.
The equation of line q is y = (3/5)x + 23/5.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Line p passes through points (-2, 5) and (3, 8).
This means,
Slope = (8 - 5) / (3 + 2) = 3/4
m = 3/4
And,
Consider (-2, 5) = (x, y)
5 = (3/4) x -2 + c
5 = -3/2 + c
c = 5 + 3/2
c = 13/2
So,
y = (3/4)x + 13/2
Line q passes through the points (-1, 4) and (4, 7).
Slope = (7 - 4) / (4 + 1) = 3/5
m = 3/5
And,
Consider (-1, 4) = (x, y)
4 = (3/5) x (-1) + c
4 = -3/5 + c
c = 4 + 3/5
c = 23/5
So,
y = (3/5)x + 23/5
Thus,
The equation of line p is y = (3/4)x + 13/2.
The equation of line q is y = (3/5)x + 23/5.
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The complete question:
Find the equation of the Line p passes that passes through points (-2, 5) and (3, 8) and Line q that passes through points (-1, 4) and (4, 7).
What is (f*g)(x) f(x) = - x ^ 2 g(x) = x + 1
Answer:
Purplemath
First you learned (back in grammar school) that you can add, subtract, multiply, and divide numbers. Then you learned that you can add, subtract, multiply, and divide polynomials. Now you will learn that you can also add, subtract, multiply, and divide functions. Performing these operations on functions is no more complicated than the notation itself. For instance, when they give you the formulas for two functions and tell you to find the sum, all they're telling you to do is add the two formulas. There's nothing more to this topic than that, other than perhaps some simplification of the expressions involved.
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Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.
(f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
(f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
(f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15x2 – 10x
= –15x2 + 2x + 8
\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(
g
f
)(x)=
g(x)
f(x)
= \small{\dfrac{3x+2}{4-5x}}=
4−5x
3x+2
Step-by-step explanation:
Purplemath
First you learned (back in grammar school) that you can add, subtract, multiply, and divide numbers. Then you learned that you can add, subtract, multiply, and divide polynomials. Now you will learn that you can also add, subtract, multiply, and divide functions. Performing these operations on functions is no more complicated than the notation itself. For instance, when they give you the formulas for two functions and tell you to find the sum, all they're telling you to do is add the two formulas. There's nothing more to this topic than that, other than perhaps some simplification of the expressions involved.
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Given f (x) = 3x + 2 and g(x) = 4 – 5x, find (f + g)(x), (f – g)(x), (f × g)(x), and (f / g)(x).
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.
(f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
(f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
(f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15x2 – 10x
= –15x2 + 2x + 8
\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(
g
f
)(x)=
g(x)
f(x)
= \small{\dfrac{3x+2}{4-5x}}=
4−5x
3x+2
1/3 Person who anwsner get brainlist
Answer:
1/3 is the same as 0.33...(The decimal continues on from here.)
Graph the inequality x<3.
To graph an inequality, select the correct type of ray and then select the correct endpoint on the number line.
Answer:
You would start at 3 and then go backwords till the end.
So you'd choose the 3 option. <-o
Only use the filled in o if the equation is <_ with the line underneath, if its like < then its o
Hope this helps! <3
What is the equation of the axis of symmetry for this function? H(x) = -X2 + 10x - 11 x = -5 0 x= -10 x = 5 x = 10
Given:
The equation of a quadratic function is:
\(H(x)=-x^2+10x-11\)
To find:
The equation of the axis of symmetry for the given function.
Solution:
If a quadratic function is \(f(x)=ax^2+bx+c\), then the equation of the axis of symmetry is:
\(x=-\dfrac{b}{2a}\) ...(i)
We have,
\(H(x)=-x^2+10x-11\)
Here, \(a=-1,b=10,c=-11\). So, the equation of axis of symmetry by using (i), is
\(x=-\dfrac{10}{2(-1)}\)
\(x=-\dfrac{10}{-2}\)
\(x=5\)
Therefore, the correct option is C.
The function & models the height h(t), in meters, of a football t seconds after it is kicked. What is the interpretation of h(2)=0.40 in this context? A) The football has a maximum height of 0.40 meter.
The interpretation of h(2) = 0.40 in the context of the given function is that, two seconds after the football is kicked, its height is 0.40 meters.
The interpretation of the equation h(2) = 0.40 in the given context is that the football reaches a height of 0.40 meters, approximately 2 seconds after it is kicked. This equation represents the relationship between time and height, with h(t) denoting the height of the football at time t.
Since the input value is 2, it implies that 2 seconds have passed since the football was kicked. The output value, 0.40, represents the height of the football at that specific time. This interpretation assumes that the height is measured from the ground or the initial position of the football.
It is important to note that the equation does not provide information about the maximum height the football reaches. To determine the maximum height, you would need additional information, such as the form of the function or other data points. The given equation simply gives the height of the football at a specific time, in this case, 2 seconds after it was kicked.
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The function h(t) models the height of a football 't' seconds after it is kicked. The interpretation of h(2)=0.40 is that the height of the football is 0.40 meters at exactly 2 seconds after it is kicked.
Explanation:In the given function, h(t) represents the height of the football at any time 't' after it is kicked. The given value h(2)=0.40 depicts that the height of the football is 0.40 meters at 2 seconds after the kick. So, at exactly two seconds into its trajectory, the football reaches a height of 0.40 meters.
This does not imply that the ball has reached its maximum height. The maximum height of the ball can be different and would be dependent on various factors such as the initial velocity of the kick, the angle of projection, and the force of gravity.
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The weights of 11 1111 different babies are recorded on the line plot below. Each weight was rounded to the nearest 1 8 8 1 start fraction, 1, divided by, 8, end fraction pound. 6 6 6 4 8 6 8 4 7 7 7 4 8 7 8 4 8 8 8 4 8 8 8 4 9 9 9 4 8 9 8 4 10 10 A line plot labeled 6 to 10 with tick marks every one-eighth unit. Above the tick mark at six and six-eighths is one dot. Above the tick mark at seven and one-eighth is a column of three dots. Above the tick mark at seven and two-eighths is a column of two dots. Above the tick mark at eight and three-eighths there is a column of three dots. Above the tick mark at eight and four-eighths there is one dot. Above the tick mark at nine and two-eighths is one dot. What is the difference, in weight, between the two heaviest babies? pounds pounds start text, space, p, o, u, n, d, s, end text
Answer:
6/8
Step-by-step explanation:
Answer: The answer is 6/8 ☻
Step-by-step explanation: I took the quiz and got it corrected. ヾ(^▽^*)))
Need help will give five starst and a thanks and MAYBE just MAYBE a brainleist.
Explain how to use the GCF and the distributive property to rewrite and solve subtraction problems.
Answer:
here u go
Step-by-step explanation:
How to solve systems by elimination?
Answer:
Step-by-step explanation:
Method to solve system by elimination :
Let me give an example :
a(x) + b(y) = c
d(x) + e(y) = f
multiply equation 1 by d and 2 by a
ad(x) + bd(y) = cd
ad(x) + ae(y) = a(f)
Now subtract or add as given in the situation .
y(bd - ae) = cd - a(f)
y = (cd - a(f))/(bd - ae)
Now put the value of y in 1 or 2 and get the value of x
three mutually tangent spheres of radius 1 rest on a horizontal plane. a sphere of radius 2 rests on them. what is the distance from the plane to the top of the larger sphere?
According to the statement the distance from the plane to the top of the larger sphere is 3 + 2 = 5 units.
The distance from the plane to the top of the larger sphere can be found by considering the arrangement of the spheres.
We have three smaller spheres of radius 1 that are mutually tangent to each other and the plane.
On top of them, there is a larger sphere of radius 2.
Let's denote the distance from the plane to the center of the larger sphere as h.
Since the spheres are tangent to each other, the distance from the plane to the top of the larger sphere will be equal to the sum of the radii of the smaller spheres (3 x 1 = 3) plus the radius of the larger sphere (2).
Therefore, the distance from the plane to the top of the larger sphere is 3 + 2 = 5 units.
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A rectangular garden 30 m by 40 m has two paths of equal width crossing through it as shown. Find the width of each path if the total area covered by the paths is 325 m^2
The width of the two paths is 5 m.
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.
Let the width of the two paths be x.
Thus, the total area covered by the paths is = (30×x) + (40×x) - x²
The total area covered by the paths is 325 m².
Equate both of them.
⇒ (30×x) + (40×x) - x² = 325
⇒ 30x + 40x - x² = 325
⇒ x² -70x + 325 = 0
Solving the above equation, we get
x = 65 or x = 5
The valid solution is x = 5.
Thus, the width of the two paths is 5 m.
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de un numero se sabe que si a su cuadrado le restamos su mitad, se obtiene el mismo numero, Cuál es?
Answer:
2
Step-by-step explanation:
el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2
Answer: 2
Step-by-step explanation : el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2 Espero que ayude Ten un día maravilloso :)
2
y
b
P
0
The equation of the line / in the diagram is y = 5-x.
The line cuts the y-axis at P.
a
Write down the co-ordinates of P.
Write down the gradient of the line 1.
NOT TO
SCALE
Given that the equation of the line in the diagram is `y = 5 - x`. The line cuts the y-axis at P. So, the coordinates of point P are (0,5) and the gradient of the line is `-1`.
The equation of the line can be written as `y = -1x + 5`.Therefore, the y-intercept of the line is 5. Therefore, the coordinates of point P are (0,5).
To find the gradient of the line, we have to write the equation of the line in the form of `y = mx + c`.
We can rewrite `y = -1x + 5` as `y = (-1)x + 5`.From the above form of the equation, we can see that the gradient `m` is `-1`.Therefore, the gradient of line 1 is `-1`.Hence, the required answer is: Coordinates of point P is `(0,5)`.The gradient of the line is `-1`.
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The quality of computer disks Is measured by sending the disks through a certifier that counts the number of missing pulses. A certain brand of computer disk has averaged 0. 1 missing pulse per disk. Find the probability that two next inspected disk will have no missing pulse, Find the probability that the next inspected disk wkl have more than one missing pulse, Find the probabihty that neither of the next two inspected disks will contain any missing pulse
Using Poisson distribution ,
a) The probability that two next inspected disk will have no missing pulse is 0.905...
b) The probability that the next inspected disk will have more than one missing pulse is 0.005..
c) The probabihty that neither of the next two inspected disks will contain any missing pulse is 0.819..
Poisson distribution:
It can be defined as a probability distribution resulting from a Poisson experiment. A Poisson experiment is a statistical experiment that divides the experiment into two categories Success or Failure. The Poisson distribution is a restricted process of the binomial distribution.
A Poisson random variable “x” defines the number of successes in the experiment.
Poisson Probability function is represent as given below i.e Mathematically,
P(x, lamda ) = (e ⁻λ (λ ))/x!
where, λ --> an average rate of value
x --> Poission random variable
e ----> base for the logarithm
we have given that,
The quality of computer disk is measured .
averaged missing pluse per disk in a computer disk brand (λ) = 0.1
let x be Poisson random variable which represents the number of missing pulse.
a) we want to find the probability that two next inspected disk will have no missing pulse
P(x= 0 ) = (e⁰·¹ )(0.1)^0/0! = 1/e⁰·¹ ×1/1
=> P(x=0) = 0.905
b) The probability that the next inspected disk will have more than one missing pulse, P(x>1)
P(x>1) = 1 - P(x=0) - P(x=1) = 1 - 0.905 - e⁰·¹(0.1)/1!
= 1 - 0.905 - 0.0905 = 0.0045 ~ 0.005
c) We can assume the disks are independent. the probabihty that neither of the next two inspected disks will contain any missing pulse
P(X = 0 on first disk and x = 0 on second disk) = P(X = 0).P(X = 0) =(0.905)².
= 0.819
Hence, we got all the required probabilities for different cases that is for a) 0.905 b) 0.005 c) 0.81
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For which equation is g = 5 not the solution?
8g = 40
4, g, = 20
g - 2 = 3
2, g, = 25
Therefore, the equation for which g = 5 is not the solution is 4g = 20.
What is equation?An equation is a mathematical statement that shows the equality between two expressions or values. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations can be used to solve problems or to describe relationships between quantities. They are commonly written in the form of "expression 1 = expression 2" or "expression 1 - expression 2 = 0", where the goal is to find the value(s) of the variable(s) that make the equation true.
To check for which equation g = 5 is not the solution, we can substitute g = 5 into each equation and see which ones result in a false statement.
\(8g = 40\)
Substituting g = 5 gives: 8(5) = 40, which is true. Therefore, g = 5 is a solution to this equation.
4g = 20
Substituting g = 5 gives: 4(5) = 20, which is false. Therefore, g = 5 is not a solution to this equation.
g - 2 = 3
Substituting g = 5 gives: 5 - 2 = 3, which is true. Therefore, g = 5 is not a solution to this equation.
2g = 25
Substituting g = 5 gives: 2(5) = 25, which is false. Therefore, g = 5 is not a solution to this equation.
Therefore, the equation for which g = 5 is not the solution is 4g = 20.
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let an n>0 be a sequence defined by an = n^2 -3n +2 for n>=0. a) find the first three elements of the sequence. b) show that the sequence satisfies the recurrence relation an =2an-2 -an-2 +2 for ever n >=2
a) To find the first three elements of the sequence defined by an = n^2 - 3n + 2, we simply substitute n = 0, 1, 2 into the expression for an and simplify: a0 = 2, a1 = 0, a2 = 0.
b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we can use mathematical induction. Assume the relation holds for some arbitrary k >= 2. Then we can show that it also holds for k+1 by substituting k+1 into the expression and using the fact that an = (k+1)^2 - 3(k+1) + 2 = k^2 - k + 2 + 2k. After simplification, we arrive at the expression for ak+1 in terms of ak and ak-2, showing that the relation holds for k+1.
a) To find the first three elements of the sequence, we simply substitute n = 0, 1, 2 into the expression for an and simplify:
a0 = (0)^2 - 3(0) + 2 = 2
a1 = (1)^2 - 3(1) + 2 = 0
a2 = (2)^2 - 3(2) + 2 = 0
Therefore, the first three elements of the sequence are 2, 0, 0.
b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we need to show that the expression for an can be written in terms of the previous two terms of the sequence, a(n-2) and a(n-1), using the given recurrence relation.
We can write:
an = n^2 - 3n + 2
= (n-2)^2 - 3(n-2) + 2 + 2(n-2)
= (n-2)^2 - 3(n-2) + 2n
Next, we can substitute n-2 for n in the expression for a(n-2) to get:
a(n-2) = (n-2)^2 - 3(n-2) + 2
Finally, we can substitute n-1 for n in the expression for a(n-1) to get:
a(n-1) = (n-1)^2 - 3(n-1) + 2
Now, we can use these expressions to write an in terms of a(n-2) and a(n-1) as follows:
an = (n-2)^2 - 3(n-2) + 2n
= a(n-2) + 2(n-1) - (n-1)^2 + 3(n-1)
= 2a(n-2) - a(n-1) + 2
Therefore, we have shown that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2.
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Aiden found 6 pieces of milk chocolate in two boxes of assorted
chocolate. How many pieces of milk chocolate would he probably find
in 12 boxes of assorted chocolate?
Answer:
36
Step-by-step explanation:
6 divided by 2 = 3
12 times 3 = 36