The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
The samples, each comprised of 15 observations, were taken from the four populations.
How to find the degrees of freedom?The determine the degrees of freedom for the numerator and denominator for the critical value of F is given below:
k = 4
n = 15
Total degree of freedom;
= nk - 1
= 59
For numerator, it is
= k -1
= 4 - 1
= 3
For denominator it is
= T - (k -1 )
= 59 - 3
= 56
The degrees of freedom for the numerator and denominator for the critical value of F are _3 and 56, respectively_.
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The cost to produce a product is modeled by the function f(x) = 5x2 − 70x 258, where x is the number of products produced. complete the square to determine the minimum cost of producing this product. 5(x − 7)2 13; the minimum cost to produce the product is $13. 5(x − 7)2 13; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $258.
The minimum cost to produce the product is $7.
What are functions?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.To determine the minimum cost:
We have to determine the minimum cost of producing this product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].
Dividing the above equation by 5, we get
[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]
Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.
Since the coefficient of 'x' is 14, and half of 14 is '7'.
So, adding and subtracting from the above equation.
[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]
Now, we have to determine the minimum cost to produce the product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
[tex]f'(x) = 10x-70[/tex]
Now, let f'(x)=0
[tex]10x-70=0\\10x=70[/tex]
Therefore, x=7
Now, consider which is greater than 0.
Therefore, x= 7 is the minimum cost.
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Answer: The minimum cost to produce the product is $13.
I apologize for the late answer, hope this helps in the future!
Step-by-step explanation:
To complete the square, we need to rewrite the given function in the form:
f(x) = a(x - h)^2 + k
where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.
We start by factoring out the coefficient of x^2:
f(x) = 5(x^2 - 14x + 51.6)
To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:
f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)
= 5((x - 7)^2 + 13)
Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:
5(x − 7)2 + 13
Determine how much this home would cost to replace: 3,800 square feet at $102.00 per square foot
Answer: $
___
This is exactly what the questions look like, can’t find anything.
Find the probability of rolling a sum less than 5 or a sum greater than 7 when a pair of dice is rolled.
Answer:
Step-by-step explanation:
Solution
There are 36 possible ways to combine two dice. The ones you are interested in, are in the table below
Numbers less that 5 are with their probabilities
Number Probability How done.
2 1/36 1 + 1
3 2/36 2 + 1 1 + 2
4 3/36 2 + 2 1 +3 3 + 1
Total 6/36 1/6
Greater than 7
Number Probability How done
8 5/36 6+2 2+6 5 +3 3+5 4 + 4
9 4/36 6+3 3 + 6 5+4 4+ 5
10 3/36 6+4 4 +6 5 + 5
11 2/36 5+6 6 + 5
12 1 /36 6 + 6
Total 15/36
Answer
15/36 + 1/6 = 15/36 + 6/36 = 21/36
Final Answer: 7/12
how do i find x? pls tell me with working
Answer:
35
Step-by-step explanation:
Angle QRS is an inscribed angle, so measure of angle QRS is half the measure of the intercepted arc, arc SPQ. Therefore arc SPQ is 125*2 = 250 degrees, and arc QRS is 360 - 250 = 110 degrees.
Angle QPS is an inscribed angle, and arc QRS is its intercepted arc. Therefore angle QPS is 110/2 = 55 degrees. Since PS is the radius of the circle, angle PQS, the angle inscribed in the semicircle, is 90 degrees. Since interior angles of the triangle QPS add up to 180 degrees, angle QSP is 180 - 90 - 55 = 35 degrees.
Angles QSP and UST are vertical angles, and by the vertical angles theorem, they are congruent. Therefore x = 35.
For a fundraiser, 1000 raffle tickets are sold, and the winner is chosen at random. There is only one prize, $500 in cash. You buy one ticket. What is the probability you will win the prize of $500
Answer:
1/1000 = 0.001
Step-by-step explanation:
Out of the 1000 tickets only one will be chosen. And since you only bought one ticket you would get a 1/1000 chance to get chosen. If you turn 1/1000 into a decimal you get 0.001 or 0.1%. Say if you bought 2 tickets you would get a 2/1000 chance which would be a 0.2% chance and so on.
Robert bought a combination of 15 colored and normal pencils. Each pencil wad $0.60 and each colored pencil was $0.45. In total he paid $8.70. How many colored pencil and pencil did he buy?
Show equation
Answer:
Robert bought 13 colored pencils and 2 pencils
Step-by-step explanation:
13 x 0.60 = 7.8
2 x 0.45 = 0.9
7.8 + 0.9 = 8.70
13 colored pencils are $7.80
2 pencils are $0.9
15 total is $8.70
Nancy started the year with 400$ in the bank and is saving 10$ a week. Shane started with 700$ and is spending 20$ a week. When will they both have the same amount of money in the bank?
They will both have the same amount in the bank after 10 weeks
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, we have
Nancy
Initial = 400
Rate = 10
So, the equation is
y = 400 + 10x
700
Initial = 700
Spending = 20
So, the equation is
y = 700 - 20x
When they both have the same amount of money in the bank, we have
700 - 20x = 400 + 10x
Evaluate the like terms
30x = 300
Divide by 30
x = 10
Hence, they will both have the same amount in the bank after 10 weeks
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What is the equation of this graph?
The equation of the parabola given in the graph is:
(x - 5)² = -8(y + 4).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
a(y - k) = (x - h)²
In which a = 4p is the leading coefficient.
In this problem, the vertex is at point (5,-4), hence h = 5, k = -4, and the equation is:
a(y + 4) = (x - 5)²
The focus is at y = -6, which means that p = -6 - (-4) = -2, hence the leading coefficient is:
a = 4p = 4(-2) = -8
Hence the equation is:
(x - 5)² = -8(y + 4).
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find the zeros of the following
please solve step by step
1. x³+x²-4x-4=0
2. 2x³-11x²+17x-6=0
Question 1
[tex]x^3 + x^2 - 4x-4=0\\\\x^2 (x+1)-4(x+1)=0\\\\(x^2 -4)(x+1)=0\\\\(x-2)(x+2)(x+1)=0\\\\x=-2, -1, 2[/tex]
Question 2
By inspection, we know that [tex]x=2[/tex] is a root.
[tex]\frac{2x^3 - 11x^2 + 17x-6}{x-2}=2x^2 - 7x+3[/tex].
So, we can factor the equation as
[tex](x-2)(2x^2 - 7x+3)=0\\\\(x-2)(x-3)(2x-1)=0\\\\x=\frac{1}{2}, 2, 3[/tex]
Hazel is measuring two prisms whose bases are squares.
Given the volume V and the base's side length a of the first prism, Hazel uses the formula
h=V/a^2
to compute its height h to be 10 centimeters.
The base of the second prism has the same side length, but has 5 times the volume. What is its height?
The height of the second square base prism is 50 cm.
How to find volume of a square base prism?The volume of the first square base prism is represented as follows:
v = ha²
where
h = heighta = side length of the baseTherefore, the height of the prism is 10 cm.
v = 10a²
Hence, the volume of the initial prism is 5 times the volume. Therefore,
v = 5(10a²)
v = 50a²
Therefore,
50a² = ha²
divide both sides by a²
50a² / a² = ha² / a²
50 = h
h = 50 cm
Therefore, the height of the second square base prism is 50 cm.
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A girl get n cedis pocket money money each week. she saves her money for five weeks and buys a present for her mother which cost gh 7900 i. write an expression for the amount of the money left ii.what is the minimum amount she needs to save each week to be able to afford the gift
An expression for the amount of the money left = (5n-7900) cedis
The minimum amount she needs to save each week to be able to afford the gift: n = 7900/5.
What is a word problem?The term "word problem" refers to a type of math question where the answer is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real world."
What is the first step in solving word problem?Read the problem in its full to get a clear understanding of what you need to do in order to solve it before you start. Following reading it, you may choose which components of the issue need to be resolved the most and which ones are not.
According to the given data:She gets n cedis a week.
she will get n x 5 cedis for 5 wks =5n cedis.
She buys a present worth 7900.
An expression for the amount of the money left = (5n-7900) cedis.
The minimum amount she needs to save each week to be able to afford the gift.
5n-7900 = 0
n = 7900/5.
7900/5 = ____ per week
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Membership to two different clubs are represented by the equations below. The x-value represents the number of months dues are paid. The y-value represents the total cost of dues over time. How many months will it take for the membership of both clubs to be the same?
y = 3x − 5
4x − 3y = 5
2 months
5 months
3 months
4 months
It would take 2 months for the membership of both clubs to be the same
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the total cost of dues over x months, hence given that:
y = 3x - 5 (1)
Also:
4x - 3y = 5
y = (4x - 5)/3 (2)
For the membership of both clubs to be the same:
3x - 5 = (4x - 5)/3
9x - 15 = 4x - 5
x = 2
It would take 2 months for the membership of both clubs to be the same
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A sample statistic becomes more accurate as the sample size increases due to ______.
A. The Law of Large Samples
B. The Central Limit Theorem
C. The Law of Large Numbers
D. The Law of Reduced Variability
A sample statistic becomes more accurate as the sample size increases due to the law of large numbers.(option C)
What is the law of large numbers?The law of large numbers is a theorem in statistics that states that as the number of experiments increases, the sample mean becomes closer to the theoretical mean. The law of large numbers was first proved by Jacob Bernoulli.
For example, if you carry out an experiment to determine how many students in the US attend high school and the only person you ask tells you he does not attend high school. If you conclude the experiment based on the response of that one person, it is likely that you would conclude that on average, people in the US do not attend high school. If you ask more people, it is likely that your opinion would change and you could come to the conclusion that majority of US citizens attend high school.
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I don't understand the question
Answer: 7 pigeons sitting on the branches, 5 pigeons under the tree
=12 in total
Step-by-step explanation:
Upper branch has x pigeons, lower has y.
Top branch said: "If one of you flies up to us our number will be double yours":
Well, if one of the bottom branch flies up, the top branch will have x+1 birds and the bottom will have (y−1). The top will have double the bottom, so:
x+1=2(y−1)
Top branch said: "If one of us flies down to you, our numbers will be equal":
Now, the top branch will have x−1 and the bottom y+1. The numbers should be equal:
x−1=y+1
In a survey conducted among the people,200 like fruit and100 like both of them . using veen diagram, find the number of people who like at least. one of them
your question is not clear
The Williard family was saving up for their summer vacation. Mrs. Williard had $475.88 in their savings account for the trip. Mr. Williard received a bonus at work for $609.00 that he is saving for the trip. If the trip will cost the Warren's a total of $1675.98, how much more money do they need for their vacation
Answer:
$591.10
Step-by-step explanation:
First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.
Q. An ornithologist wants to estimate the number of parrots in a large field. She uses a net to catch some, and catches 32 parrots, which she rings and sets free. The following week she manages to net 40 parrots, of which 8 are ringed.
(1) What fraction of her second catch is ringed?
(2) Find an estimate of the total number of parrots in the field.
Need help! Urgent!
Total parrot=40
Caught=8
Fraction
8/401/5#2
Out of 40 parrots 8 are ringed
Parrots per one ringed=40/8=5
Total ringed before=32
Total no of parrots
32(5)160There are 160 parrots
Answer:
[tex]\sf 1) \quad \dfrac{1}{5}[/tex]
[tex]\sf 2) \quad 160\:parrots[/tex]
Step-by-step explanation:
Question 1Given information:
Second catch = 40 parrotsRinged = 8 parrotsTherefore, the fraction of ringed parrots from the second catch is:
[tex]\implies \sf \dfrac{ringed\:parrots}{total\:caught\:parrots}= \dfrac{8}{40}=\dfrac{1 \times 8}{5 \times 8}=\dfrac{1}{5}[/tex]
Question 2If she caught and ringed 32 parrots in her first catch, but only 1/5 of the parrots caught in the second catch were ringed, then 32 parrots represents 1/5 of the total number of parrots. To find the total number of parrots, simply multiply the total number of ringed parrots by 5:
[tex]\implies \sf \textsf{Total number of parrots}=32 \times 5 = 160[/tex]
help me plss its ttm
For the first representation, the equation is : y = 3x-5.
For the second representation, the equation is : y = -12x+2.
For the third representation, the equation is : y = 5/4x-5.
For the fourth representation, the equation is: y = -6x+3.
Analyze the representations given in the question, in order to find its corresponding equation.
According to the question,
For the first representation, y=1 when x=2, y=-2 when x=1 and y=4 when x=3. On substituting these values of x and y in the given equations, we get that y = 3x-5.
Similarly, for the second representation, we get, y = -12x+2.
For the third representation, we get, y = 5/4x-5.
For the fourth representation, we get, y = -6x+3.
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A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 3y 4z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ 4 (3y 4z = 1) ⋅ 4 (y z = 6) ⋅ −3 (3y 4z = 1) ⋅ 3
Option C is correct (y + z = 6) ⋅ −3
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.As per the statement -
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6 ....[1]
Equation Q: 3y + 4z = 1 ....[2]
Multiply the equation [1] by -3 to both sides we have;
-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)
Add equation [2] and [3] to eliminate the y-term;
z = -17
Therefore, the possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3
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The complete question is -
A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ 4
(3y + 4z = 1) ⋅ 4
(y + z = 6) ⋅ −3
(3y + 4z = 1) ⋅ 3
The black graph is the graph of y =f(x). Choose the equation for the red graph. A. y - 1 = f() B. y + 1 = f() C. = f(x - 1) D. f(x)
Answer: C
Step-by-step explanation:
The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.
what is the digit of 7 in 906point7
On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r?
The coordinates of point r(-8,0).
What is midpoint formula in coordinate geometry?The coordinates of the point r(x,y) which divides the line segment joining the points p([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and q([tex]x_{2}[/tex],[tex]y_{2}[/tex]) internally in the ratio :[tex]m_{1}[/tex][tex]m_{2}[/tex] are
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
Given that,
Two end points on the line q(-14,0) and s(2,0). point r(x,y) is the partition of the line segment from q to s in a ratio 3:5
[tex]m_{1}[/tex] = 3 and [tex]m_{2}[/tex] = 5
By using the midpoint formula
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
[tex]\left(\frac{3(2)+ 5(-14) }{3+5 } ,\frac{3(0)+ 5(0) }{3+5 }\Rifgt)[/tex]
[tex]\left(\frac{-64}{8 } ,\frac{0 }{8 }\Rifgt)[/tex]
[tex]\left(-8 ,0\Rifgt)[/tex]
Hence, The coordinates of point r(-8,0).
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What is the center of the ellipse x2+5y2–45=0?
Write your answer in simplified, rationalized form.
(___,___)
Answer:
Center is at (0,0)
Step-by-step explanation:
An equation of ellipse in standard form is:
[tex]\displaystyle{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2} = 1[/tex]
Where center is at point (h,k)
From the equation of [tex]\displaystyle{x^2+5y^2-45=0}[/tex]. First, we add 45 both sides:
[tex]\displaystyle{x^2+5y^2-45+45=0+45}\\\\\displaystyle{x^2+5y^2=45}[/tex]
Convert into the standard form with RHS (Right-Hand Side) equal to 1 by dividing both sides by 45:
[tex]\displaystyle{\dfrac{x^2}{45}+\dfrac{5y^2}{45}=\dfrac{45}{45}}\\\\\displaystyle{\dfrac{x^2}{45}+\dfrac{y^2}{9}=1}[/tex]
Therefore, the center of ellipse is at (0,0) since there are no values of h and k.
can someone help? will award brainliest
Answer:
B
Step-by-step explanation:
The beginning temperature is -12 and then it rises 5 degrees each hour at the end of the game it is 32 degrees.
A right rectangular prism has these dimensions:
Length: Fraction 1 and 1 over 3 units
Width: Fraction 5 over 6 unit
Height: Fraction 2 over 3 unit
How many cubes of side length 1 over 6 unit are required to completely pack the prism without any gap or overlap?
160 cubes required to completely pack the prism without any gap or overlap
How to determine the number of cubes?The dimensions of the rectangular prism are given as:
Length = 1 1/3
Width = 5/6
Height = 2/3
The volume is
Volume = Length * Width * Height
This gives
Volume = 1 1/3 * 5/6 * 2/3
Evaluate the product
Volume = 20/27
The side length of the cube is
L = 1/6
The volume of the cube is
V = (1/6)^3
Evaluate
V = 1/216
The number of cubes required to completely pack the prism without any gap or overlap is
n = (20/27) / (1/216)
Evaluate
n = 160
Hence, 160 cubes required to completely pack the prism without any gap or overlap
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HELP If there are 79 people in a hip-hip dance group and 14 are girls,
what is the probability that a person chosen at random will be a boy?
State your answer as a fraction.
Answer:
you better give me brainliest
65/79
Step-by-step explanation:
number if boys =79-14 = 65
p of selecting a boy >> 65/79
can't cancel out so leave your answer like that
pls help with Trigonometric
The value of the given trigonometry function is 2√15/15
Half anglesHalf angles are trigonometric identities used to express sine, cosine and tangent of half angles.
For instance the value of cos theta is expressed as shown below;
cosФ = cos(Ф/2+Ф/2)
cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ = 1 - 2cos²Ф/2
Given the following parameters
cosФ = -7/15
Substitute
cosФ = 1 - 2cos²Ф/2
-7/15 = 1 - 2cos²Ф/2
-2cos²Ф/2 = -7/15 - 1
-2cos²Ф/2 = -8/15
cos²Ф/2 = 4/15
cosФ/2 = 2/√15
Rationalize
2/√15 * √15/√15
2√15/15
Hence the value of the given trigonometry function is 2√15/15
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please answer this fast
The numeric values from the function are given by:
f(a) = 4 - 2a + 6a²f(a + h) = 6a² + 12ah + 6h² - 2a - 2h + 4.[f(a + h) - f(a)]/h = 12a + 6h - 2.What is the function for this problem?The function is:
f(x) = 4 - 2x + 6x².
When x = a:
f(a) = 4 - 2a + 6a².
When x = a + h:
f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.
For the last question
[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h
Hence:
[f(a + h) - f(a)]/h = 12a + 6h - 2.
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Powers of 10 and Exponents (number 4 is a 10 incase u can’t see of the ripped page.)
Answer:
below
Step-by-step explanation:
2) 10², the second power of ten
3) 10⁴, the fourth power of ten
4) 1000
5) 400
6) 90,000
7) 10
8) 100,000
9) 50
10) 7000
11) 8
12) 24 x 10⁴
13) 93,000,000
Answer + Step-by-step explanation:
help help help help help help pleaseeeeee
The maximum height is; 180 ft and the Total time in the air is 12 seconds
How to solve projectiles?We are given the equation that represents the height of the rocket as;
d = 60t - 5t²
Taking the derivative of the formula gives us;
d' = 60 - 10t.
-10t represents the acceleration. The 60 represents the initial velocity.
Set 60 - 10t = 0 and solve for t to get;
t = 60/10 = 6seconds.
That's when the maximum height occurs. Plug that value of t into the original quadratic equation to get the maximum height.
d(6) = 60t - 5t²
d(6) = 60(6) - 5(6²)
d(6) = 180
So, maximum height is about 180 ft.
Thus, total time in air = 2 * 6 = 12 seconds
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