The objective function that must be minimized is:
z = 40x + 50y
subject to the constraints:
0x + 4y ≥ 4 (protein constraint)
3x + 2y ≥ 11 (carbohydrate constraint)
2x + 4y ≤ 16 (fat constraint)
We want to find the number of ounces of fruit (x) and nuts (y) that will meet the requirement with the least number of calories.
Solving the system of inequalities, we get:
x = 2 ounces
y = 2 ounces
Therefore, the dietician should use 2 ounces of fruit and 2 ounces of nuts. These amounts will have a total of 180 calories (402 + 502).
Answer:
Step-by-step explanation:
Let's assume we need x ounces of fruit and y ounces of nuts to meet the requirements with the least number of calories. Then, the problem can be expressed as an optimization problem:
Minimize: 40x + 50y (since we want to minimize the number of calories) Subject to:
0x + 4y ≥ 4 (we need at least 4 units of protein)3x + 2y ≥ 11 (we need at least 11 units of carbohydrates)2x + 4y ≤ 16 (we cannot have more than 16 units of fat)
To solve this problem, we can use the simplex method. First, we convert the problem to standard form by introducing slack variables:
Minimize: 40x + 50y Subject to:
0x + 4y + s1 = 43x + 2y + s2 = 112x + 4y + s3 = 16
Now we can create the initial simplex tableau:
xys1s2s3RHSs1041004s23201011s32400116z-40-500000
We want to find the minimum value of z, so we need to choose the variable with the most negative coefficient in the bottom row as the entering variable. In this case, that is y. We then choose the variable with the smallest non-negative ratio between the right-hand side and the coefficient of the entering variable in its row as the leaving variable. In this case, that is s3, since 16/4 = 4 is the smallest non-negative ratio.
We then perform the pivot operation to eliminate the coefficient of y in the other rows:
x y s1s2s3RHSs1001-214y3/2101/2-1/24s2-1001-1/25z-100025-15200
We repeat this process until all the coefficients in the bottom row are non-negative. The final tableau is:
x
If p is a positive integer, then p(p + 1)(p − 1) is always divisible by
F. 7
G. 5
H. 4
J. 3
K. None of these
Answer:
K
Step-by-step explanation:
We can factor the given expression as:
p(p + 1)(p - 1) = p^3 - p
Notice that p^3 - p is the difference of two consecutive cubes. This can be factored further using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2):
p^3 - p = p(p^2 - 1) = p(p + 1)(p - 1)
So, we have shown that p(p + 1)(p - 1) is equal to p^3 - p, which is the product of three consecutive integers. By definition, this product is always divisible by 3.
However, we cannot conclude that p(p + 1)(p - 1) is divisible by 4, 5, or 7 for all positive integers p. Therefore, the answer is K) None of these.
The graph of y = 5x2 is
Answer:
................................
If a drug has a concentration of 5.315 mg per 3.743 mL, how many mL are needed to give 4.719 gram of the drug? Round to 1 decimal.
Answer:
888.4 mL.
Step-by-step explanation:
To solve this problem, we can use the following formula:
Amount of drug (in mg) = concentration (in mg/mL) × volume (in mL)
We are given the concentration of the drug as 5.315 mg per 3.743 mL. To find the volume of the drug needed to give 4.719 g, we need to rearrange the formula to solve for volume:
Volume (in mL) = amount of drug (in mg) ÷ concentration (in mg/mL)
First, we need to convert 4.719 g to mg by multiplying by 1000:
4.719 g × 1000 mg/g = 4719 mg
Now we can substitute the given concentration and the calculated amount of drug into the formula and solve for volume:
Volume (in mL) = 4719 mg ÷ 5.315 mg/mL
Volume (in mL) ≈ 888.5 mL
Therefore, approximately 888.5 mL of the drug are needed to give 4.719 g. Rounded to 1 decimal, the answer is 888.4 mL.
You are crossing two pea plants. One is heterozygous for yellow. The second pea plant is homozygous for green. Use "G/g" as the letter to represent the gene for this problem.
The result of the cross breeding between the heterozygous and homozygous pea plant is the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
What is the result of crossbreeding?In this problem, the heterozygous pea plant with yellow color is represented as "Gg" (where "G" is the dominant allele for yellow color and "g" is the recessive allele for green color). The homozygous pea plant with green color is represented as "gg" (where both alleles are recessive).
When these two plants are crossed, their offspring will inherit one allele from each parent, which will determine their phenotype (observable trait).
The possible combinations of alleles that the offspring can inherit from their parents are:
Gg x gg
Gametes from the Gg plant: G, gGametes from the gg plant: g, gPossible genotypes of offspring: Gg, gg (50% chance for each)Possible phenotypes of offspring: yellow (Gg) or green (gg) in a 1:1 ratioTherefore, in this cross, the offspring will have a 50% chance of inheriting the dominant "G" allele and displaying yellow color, and a 50% chance of inheriting the recessive "g" allele and displaying green color.
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Juan is constructing picture frames to create a collage on his bedroom wall. He constructs a square frame with side lengths of x inches. He constructs another frame with the same length, but a width that is 3.5 inches longer than the square frame. The area of the new, rectangular frame can be determined by the following expression.
please look at the picture attached then answer!
Select the best description of the term 3.5x.
A. the area of the original picture frame
B. the area of the new picture frame
C. the width of the new picture frame
D. the increase in area of the new frame
Answer:
The correct answer is D. the increase in area of the new frame.
Step-by-step explanation:
Hope this helps you!!
Find the standard normal area for each of the following Round your answers to the 4 decimal places
The standard normal areas are given as follows:
P(1.22 < Z < 2.15) = 0.0954. P(2 < Z < 3) = 0.0215.P(-2 < Z < 2) = 0.9544.P(Z > 0.5) = 0.3085.How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation 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 of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.Considering the second bullet point, the areas are given as follows:
P(1.22 < Z < 2.15) = p-value of Z = 2.15 - p-value of Z = 1.22 = 0.9842 - 0.8888 = 0.0954.P(2 < Z < 3) = 0.0215 = p-value of Z = 3 - p-value of Z = 1 = 0.9987 - 0.9772 = 0.0215.P(-2 < Z < 2) = p-value of Z = 2 - p-value of Z = -2 = 0.9772 - 0.0228 = 0.9544P(Z > 0.5) = 1 - p-value of Z = 0.5 = 1 - 0.6915 = 0.3085.More can be learned about the normal distribution at https://brainly.com/question/25800303
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A rain gutter is made of sheets of metal 9 inches wide. The gutters have a 3 inch base and two 3 inch sides, folded up at an angle of . What angle will maximize the cross sectional area of the rain gutter?
The value of angle that maximizes the cross sectional area is 60°
What is the cross sectional area of a solid?The cross sectional area of a solid is the two dimensional surface formed when the solid is sectioned by a plane.
The shape of the cross sectional area of the gutter is a trapezoid
Area of a trapezoid = ((Sum of the lengths of the parallel sides)/2) × Height
Let a and b represent the parallel sides of the trapezoid, and let a represent the base of the trapezoid we get;
A = ((a + b)/2) × h
a = 3 inches
b = The longer parallel side
h = The height of the trapezoid
The angle formed by the sides of a trapezium and the horizontal = θ
Therefore;
h = 3 × sin(θ)
b = 3 + 2 × 3·cos(θ)
A(θ) = ((3 + 3 + 2 × 3·cos(θ)) × 3 × sin(θ))/2 = 9·sin(θ)·cos(θ) + 9·sin(θ)
At the extremum value of θ, we get;
A'(θ) = 18·cos²(θ) + 9·cos(θ) - 9 = 0
Solving, we get;
cos(θ) = 0.5 or cos(θ) = -1
Therefore;
θ = arccos(0.5) = 60° and θ = arccos(0.5) = 180°
When θ = 60°, we get;
A(max) = 9·sin(60)·cos(60) + 9·sin(60) ≈ 11.69
The cross sectional area when θ is 60° is about 11.69 square inches which is larger than the 9 square inched when θ = 90°
The angle that maximizes the cross sectional area is θ = 60°
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Can some please help
Answer:
1.5
2.28
3.quadrilateral
4.heptagon
5.hexagon
6.15
7.54mm
8.25cm
9.im not sure
convert 69 3/4% to a fraction in the lowest terms
Answer:The fraction 69 3/4% is a mixed fraction
69 3/4% to a fraction in lowest term is 27603/400
How to simplify the fraction?
The fraction is given as:
69 3/4%
Rewrite the fraction as:
69 + 3/400
Add the fractions
(400 * 69 + 3)/400
Evaluate the sum
27603/400
The above fraction cannot be further reduced.
Hence, 69 3/4% to a fraction in lowest term is 27603/400
Does the expression 56x+40y-48z=8(7x+5y-6z)
For all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
Explain expression using an example.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.
Indeed, for all values of x, y, and z, the expression 56x + 40y - 48z = 8(7x + 5y - 6z) holds true.
We can simplify both sides of the equation to understand why:
56x + 40y - 48z = 8(7x + 5y - 6z)
56x + 40y - 48z = 56x + 40y - 48z
As we can see, the equation is true for all values of x, y, and z because both sides are identical.
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The table shows some points on the graph of exponential function g(x)
0 1 2 3 4 g(x) 1 3 9 27 81 What is the range of g?
the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
How to solve and what is graph?
The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.
In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.
Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.
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Find an equation for a sinusoidal function that has period 47, amplitude 1, and contains the point
(-л, 2).
Write your answer in the form f(x) = Asin (Bx + C) + D, where A, B, C, and D are real numbers.
f(x) =
The sine function with the desired features is given as follows:
F(x) = sin(3.5π(x + π/2)) + 1.
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are listed as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function has an amplitude of 1, hence the parameter A is given as follows:
A = 1.
The period is of 4/7, hence the coefficient B is given as follows:
2π/B = 4/7
4B = 14π
B = 3.5π.
The function contains the point (-π, 2), hence the phase shift and the vertical shift are given as follows:
c = π/2, as the function has it's maximum value at x = π, while the standard function has at x = π/2.d = 1, as the function oscillates between 0 and 2.Hence the function is:
F(x) = sin(3.5π(x + π/2)) + 1.
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every nonzero real number has a reciprocal. zero does not have a reciprocal. therefore, zero is not a nonzero real number
The given argument is Valid because the conclusion follows the argument logically.
The argument is that "Every nonzero real number has a reciprocal. Zero(0) does not have a reciprocal. Therefore, zero is not a non-zero real number."
The argument can be expressed in logical form as:
⇒ Premise 1: For every nonzero real number x, there exists a reciprocal 1/x.
⇒ Premise 2: Zero does not have a reciprocal.
⇒ Conclusion: Therefore, zero is not a nonzero real number.
This argument is valid because the conclusion logically follows from the premises.
The premises establish that every nonzero real number has a reciprocal, and that zero does not have a reciprocal.
The conclusion then follows logically, as zero is explicitly excluded from the set of nonzero real numbers based on the definition of a reciprocal.
Therefore, the argument is valid.
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The given question is incomplete, the complete question is
Is The Following Argument Valid Or Invalid?
Every nonzero real number has a reciprocal. Zero does not have a reciprocal. Therefore, zero is not a nonzero real number.
3) ____ is the expression,
which tells the nature of the roots of a quadratic equation of the form
3) ____ is the expression,
which tells the nature of the roots of a quadratic equation of the form
If point c is between points A and B the. __+CB=AB
What is the difference between the longest and
shortest pieces of scrap wood?
The difference in length between the two pieces of scrap wood is 7/8 inches.
What is the difference between the longest and shortest pieces of scrap wood?
To get the difference we just need to take the difference between the two lenghs.
Remember that we only have pieces of scraph wood if we have an "x" over the correspondent value in the line diagram.
By looking at it we can see that the longest pice measures 5 inches, while the shortest one (there are two of these) measure (4 + 1/8) inches.
The difference is:
5 - (4 + 1/8) = 7/8
The longest piece is 7/8 inches longer.
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Determine the length of HK
Step-by-step explanation:
that height splits GK (32) into 2 parts :
8 and 32-8 = 24
then we use the geometric mean theorem for right-angled triangles
height = sqrt(p×q)
with p and q being the parts of the Hypotenuse.
so,
height = sqrt(8×24) = sqrt(192)
and now we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs,
to get HK.
HK² = height² + 24² = 192 + 576 = 768
HK = sqrt(768)
The area of a rectangular living room is 144 square feet. The length of the room is four times its width. Find the length and width of the living room.
quiz I need help D:
Answer:
Length equals 6
Width equals 24
Step-by-step explanation:
if you do 6 x 4 you get 24 and
24 x 6 equals 144.
Can Anyone Help?
A poster is to have a total area of 245cm2. There is a margin round the edges of 6cm at the top and 4cm at the sides and bottom where nothing is printed.What width should the poster be in order to have the largest printed area?
The poster should have width ____ cm
Answer: The poster should have width 17.50 CM
Step-by-step explanation:
Given that boasted I have a total area 245 cm square area of a poster is 200 and 45 20 m square. And it is in the rectangle format. So we know that the poster is always in the rectangle format and the area of rectangular area is equal to L N T W. So 245 will be equal to Ln tW. From this. We need to find L. So L is equal to 245 divided by W. Now consider the diplomatic representation of the poster. So it has mentioned that there is a margin around the edges of six cm at the top. This is 6cm and four cm at the sites. All the four sides 3 sides are four cm. So from this we need to find land and the doctor posted area that is printed area. The first wine printed with www. Z. Quilter. Now let this be total birth will be W. And this will be four and this will be four. Therefore posted with will be we need to find this part alone. So W -4 -4 will give the this part with. So W -4 -4. So post printed with PW will be equal to W -8. Similarly printed lunch will be equal to The total length is already we have found 245 by W. And we need to find this part length. So we have to subtract six and four from the total length so that that will give them this part length, So -6 -4. So printed length will be equal there 245 Divided by W -10. And we know that formula for area of a rectangle. Urz D is equal to L W. Now substitute the printed with and printed length in the area formula. We have to find the printed area. So Printed area Zeke Walter W -8 into 245 Divided by W -10. To simplify this, we get 325 minus 10. W -100 and 30,960 W. to the power of -1. Now fine D A by D. T. Not D D. This is D. W. So this is equal to differentiation of constant alma zero, this is minus 10 plus 900 and 60 W. to the power of -2 and equate this to be equal to zero. We out to find the maximum width so D A by D W is equal to zero, therefore minus 10 1960 W. To the power of -2 will be equal to zero. To simplify this, we get them maximum with value the W is equal term I wrote off 196. Therefore the value of W. Z quilter plus or minus 14. We will neglect the negative values since we cannot be negative. So one we assume the positive values. So what will be equal to 14 and length will be equal to 245 divided by 14, So which will be equal to 17.50 centimeters. And they have concluded that At W is equal to 14 cm and lunch will be equal to 17.50 cm needed to print the largest area. I hope you found the answer to school. Thank you.
Find the slope of the line that passes through the pair of points.
(5, 4), (8, –1)
Answer:
m = -5/3
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (5, 4) (8, –1)
We see the y decrease by 5 and the x increase by 3, so the slope is
m = -5/3
What is the value of 2/2 exponent -3
Answer:1
Step-by-step explanation:
2/2=1
1^-3=1
1/1times1times1
Answer:
1
Step-by-step explanation:
[tex]\frac{2}{2}[/tex] = 1
[tex]1^{-3}[/tex] To make a negative exponent positive, put it under one.
[tex]\frac{1}{1^{3} }[/tex] = [tex]\frac{1}{1}[/tex] = 1
Helping in the name of Jesus.
Standard Error of the Mean =
Confidence Interval Estimate for the Mean
Margin of Error E= Z
= Z. V
±Z
You want to rent a one-bedroom apartment near BCIT for next term. The mean monthly rent for a random sample of 36 apartments advertised for rent on Craigslist is $1,235. Assume that the population standard deviation is $150.
(a) Give the point estimate of the true mean monthly rent for one-bedroom
apartments available for rent near BCIT.
Answer=$
(b) At the 95% confidence level, what is the margin of error on your estimate of the true mean monthly rent for one-bedroom apartments available for rent near
BCIT.
Answer=$
(c) Construct a 95% confidence interval for the true mean monthly rent for one-bedroom apartments.
Lower value=$
Upper value=$
Choose the correct statement to interpret the confidence interval.
• I am totally confident that the population mean belongs to this confidence interval.
• I am 95% confident that the true population mean belongs to this confidence interval.
(d) A friend claims the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300. Based on your confidence interval do you agree?
• Yes
• No
(e) What is the z-score used to construct a 92% confidence interval?
Answer= (Enter a positive value in 2 decimal places)
"I am 95% convinced that the true population mean corresponds to this confidence interval," is the appropriate sentence to use when interpreting the confidence interval.
What does the statistical term "population" mean?Each whole group that shares at least one trait is referred to be a population. People do not make up all populations. Individuals, animals, groups, organisations, edifices, edifices, buildings, houses, farms, items, or events can all be considered populations.
As a rough estimate, the true mean monthly rent is $1,235.
At a 95% confidence level, the critical value (Z) for a two-tailed test is 1.96. The margin of error can be calculated as follows:
The 95% confidence interval can be obtained as follows:
CI = 1235 1.96*(150/36) CI = X Z*(n/n)
Lower value: 1.96 * (150/36) * 1235 = $1,175.20
Higher value: $1,294.80 = 1235 + 1.96 * (150/36).
Higher value: $1,294.80; Lower value: $1,175.20
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The base of a triangle is 3 inches shorter than its height. Its area is 275 square inches. Set up a quadratic equation and solve to find its base and height.
Answer: hope its help
Let's start by assigning variables to the unknown quantities in the problem. Let h be the height of the triangle in inches, and let b be the base of the triangle in inches.
According to the problem, the base of the triangle is 3 inches shorter than its height. This can be expressed as:
b = h - 3
The formula for the area of a triangle is:
A = (1/2)bh
We are given that the area of the triangle is 275 square inches, so we can substitute these values into the formula to get:
275 = (1/2)(h)(h-3)
Simplifying the right-hand side, we get:
275 = (1/2)(h^2 - 3h)
Multiplying both sides by 2 to eliminate the fraction, we get:
550 = h^2 - 3h
Rearranging this equation to standard quadratic form, we get:
h^2 - 3h - 550 = 0
Now we can solve for h using the quadratic formula:
h = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -3, and c = -550, so we can substitute these values into the formula to get:
h = (-(-3) ± sqrt((-3)^2 - 4(1)(-550))) / (2(1))
Simplifying the expression inside the square root, we get:
h = (3 ± sqrt(2209)) / 2
We can ignore the negative solution since height must be positive, so we get:
h = (3 + sqrt(2209)) / 2 ≈ 29.04
Now that we know the height of the triangle is approximately 29.04 inches, we can use the equation b = h - 3 to find the length of the base:
b = 29.04 - 3 = 26.04
Therefore, the base of the triangle is approximately 26.04 inches, and the height is approximately 29.04 inches.
Step-by-step explanation:
4u^2(a-3)+q(a-3)=
please answer
The simplified expression is (4u^2 + q)(a-3).
To simplify the expression 4u^2(a-3) + q(a-3), we can factor out the common factor (a-3) from both terms:
4u^2(a-3) + q(a-3) = (4u^2 + q)(a-3)
This is the factored form of the expression.
The value of the expression depends on the values of u, a, and q. When (a-3) is factored out, it remains as a common factor, while the terms 4u^2 and q are combined into a single term (4u^2 + q).
The abbreviated expression is therefore (4u2 + q)(a-3).
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You earned $1600 in a summer job and you were paid with a check. You are going to open a checking account at Hometown Bank and put $800 into the account. What amount would you fill in for each letter? Please include the letter and then the amount. If there isn't an amount you can write, for example, A) 0 or A) none
The amount in each letter for checking account is Bills - A = 0, Coin B = 0, Checks C = $800, Total D = $1600, Less cash E = $800, and Net deposit F = $800.
What is checking account?A checking account is a type of bank account that enables regular deposits and withdrawals of money by account holders. Checking accounts frequently come with amenities like check writing, debit cards, and internet banking, making them practical for daily usage. Checking accounts typically do not pay interest on the account balance, in contrast to savings accounts. Yet, many checking accounts don't have to maintain a minimum balance and permit unrestricted withdrawals, which makes them perfect for daily transactions.
Given that, you earn $1600, and put $800 in a checking's account thus,
Bills - A = 0
Coin B = 0
Checks C = $800
Total D = $1600
Less cash E = $800
Net deposit F = D - $800 = $1600 - $800 = $800.
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There are two coins. One of them is a biased coin such that P (head): P (tail) is 1 : 3 and the other coin is a fair coin. A coin is selected at random and tossed once. If the coin showed head, then find the probability that it is a biased coin.
Answer:
Step-by-step explanation:
Let B be the event that the selected coin is biased, and F be the event that the selected coin is fair. Let H be the event that the coin toss shows a head.
We want to find P(B|H), the probability that the selected coin is biased given that the coin toss shows a head. By Bayes' theorem, we have:
P(B|H) = P(H|B) * P(B) / P(H)
We know that P(H|B) = 1/4 (since the biased coin has a probability of 1/4 of showing a head), and that P(B) = 1/2 (since there are two coins, one of which is biased).
To find P(H), we can use the law of total probability:
P(H) = P(H|B) * P(B) + P(H|F) * P(F)
P(H) = (1/4) * (1/2) + (1/2) * (1/2)
P(H) = 3/8
Putting it all together:
P(B|H) = P(H|B) * P(B) / P(H)
P(B|H) = (1/4) * (1/2) / (3/8)
P(B|H) = 1/3
Therefore, the probability that the selected coin is biased given that the coin toss shows a head is 1/3.
Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0≤t≤38
Step 1 of 2:
What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.
Step 2 of 2:
What is the average waiting time?
The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.
Step 1:
The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:
P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38
= (38/38) - (26/38) = 12/38 = 0.316
So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.
Step 2:
The average waiting time can be calculated by finding the expected value of the probability density function:
E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt
= [(t²)/(238)] from 0 to 38
= (38²)/(238) = 19
Therefore, the average waiting time is 19 minutes.
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Jamal has 19 seeds. Kiara has 4 more seeds than Jamal.
Answer: Kiara has 23 seeds.
Step-by-step explanation:
Let k = the amount of seeds Kiara has.
If Kiara has 4 more seeds than Jamal, then you use the equation 19 + 4 = k.
19 + 4 = k
23 = k
Kiara has 23 seeds.
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in nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
The correct option is (C). In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: ΔY = f(x₁ + ΔX₁, X₂ + ΔX₂, ..., Xk + ΔXk) - f(x₁, X₂, ..., Xk)
where ΔX₁, ΔX₂, ..., ΔXk are the changes in the respective explanatory variables. This equation represents the change in Y due to a simultaneous change in all the explanatory variables by ΔX₁, ΔX₂, ..., ΔXk. Option (C) represents the same equation in a slightly different notation. Option (A) only considers one explanatory variable, and option (B) does not include the baseline value of the function. Therefore, option (C) is the correct answer.
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Complete question:
In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by
A. ΔY= f(x₁ +Xq, X2, Xx) = f(Xq, X2....XK). 1 1'
B. ΔY = F(X,+ ΔX₁₁ X2, Xx) - F(X₁₁ X2, Xk). ---
C. ΔY = f(x,+ ΔX₁₁ X₂ + ΔX2, Xx+ ΔX x) - F(X₁₁ X2, Xx). 1°
D. ΔY = f(x₁ +Xq, X2, Xk).
help quick pls im stuck
If necessary Therefore, the value of x is √2, in radical form.
What is radical ?Radical is a term used to describe ideas, actions, and attitudes that are extreme or break with tradition. It is often used to refer to a political or social movement that advocates for drastic change in society. Radicals challenge the status quo, often by challenging the existing power structures and existing norms. They are often willing to take extreme measures in order to create change.
Given: ^2−2=0
Solution: To find the value of x, we need to solve the given equation.
We can solve the equation by taking the square root of both sides.
√(^2−2)=0
Since the square root of a number squared is equal to the number itself, we can rewrite this equation as:
=√2
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For the given figure of right angled triangle, the value of x in radical form is √168.
Give a brief account on Pythagorean theorem.The Pythagorean theorem, the well-known geometric theorem that the sum of the squares crossing the sides of a right triangle equals the square crossing the hypotenuse (opposite the right angle) – or in common algebraic notation, a² + b² = c².
Name the given triangle as mentioned below:
Now, in triangle ABC:
AB² + AC² = BC² [Using Pythagoras theorem]
AB² + AC² = 24²
AB² = 24² - AC² [eq. 1]
In triangle AOB:
AO² + OB² = AB² [Using Pythagoras theorem]
x² + 17² = AB² [eq. 2]
In triangle AOC:
AO² + OC² = AC² [Using Pythagoras theorem]
x² + 7² = AC² [eq. 3]
Using eq. 1 and 2
24² - AC² = x² + 17²
Since, AC² = x² + 7²
24² - (x² + 7²) = x² + 17²
576 - x² + 49 = x² + 289
625 - x² = x² + 289
625 - 289 = 2x²
336 = 2x²
168 = x²
x = √168
x = 12.96
x ≈ 13
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