Using a normal approximation, the probability that at most 60 out of 200 randomly selected residents will choose the creamery's brand is approximately 0.0557 or 5.57%.
To calculate the probability that at most 60 out of 200 randomly selected residents will choose the creamery's brand, we can use a normal approximation.
Let's denote the number of residents who choose the creamery's brand as X. Since this is a binomial distribution problem, we can approximate it with a normal distribution using the mean (μ) and standard deviation (σ) of the binomial distribution.
The mean of a binomial distribution is given by μ = n * p, where n is the number of trials and p is the probability of success. In this case, n = 200 (number of residents surveyed) and p = 0.35 (market share of the creamery).
The standard deviation of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).
Therefore, μ = 200 * 0.35 = 70 and σ = sqrt(200 * 0.35 * (1 - 0.35)) ≈ 6.24499.
Now, we need to calculate the probability of X being at most 60. This can be expressed as P(X ≤ 60).
To use the normal distribution, we need to standardize the value of 60 using the z-score formula: z = (X - μ) / σ.
For P(X ≤ 60), we calculate the z-score as z = (60 - 70) / 6.24499 ≈ -1.5989.
Now, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of -1.5989. This represents the probability of observing a value less than or equal to 60.
Using the table or calculator, the probability comes out to be approximately 0.0557.
Therefore, the probability that at most 60 of the 200 residents will choose the creamery's brand, according to the normal approximation, is approximately 0.0557 or 5.57%.
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Find the value of x
Answer:
23 degrees
Step-by-step explanation:
5: 100 = 2x + 3 + 51
100 = 2x + 54
100 - 54 = 2x
46 = 2x
x = 23 degrees
Answer:
I hope you can understand this
SOMEBODY BRO PLEASE HELP ME OUT. Find the measure of the numbered angles in each isosceles trapezoid. DUED BY 11:59pmmmmm
Answer:
1) 136
2) 136
3) 44
Step-by-step explanation:
trapezoid = 360 degrees
44 = the 3rd angle because they are equal
add the two angles(44 and 44) 44 + 44 = 88
that makes up half the shape
next 360 - 88 to find the last two
272 is the remaining measurements, split in half to find 1 and 2
272/2 = 136
Which is equal to (3 + 4) - 50
Answer:
-43
hope this helps
have a good day :)
Step-by-step explanation:
3+4=7
7-50=-43
Answer:
Step-by-step explanation:
(3+4)-50
=7-50
=-43
find the area of the following figure. the triangular ends are congruent.
The area of the figure which consists of two congruent triangles and a rectangle is calculated as: 52 cm².
How to Find the Area of a Composite Figure?In the diagram given above, we see a composite figure consisting of two triangles that are congruent, and a rectangle, therefore:
Area of the figure = area of the two triangles + area of rectangle.
The Area of the two triangles:
base = 8 cm²
height = 4.5 cm²
Area of the two triangles = 2(1/2 * base * height) = base * height
Area = 8 * 4.5 = 36 cm²
Area of rectangle = length * width = 4 * 4
= 16 cm²
Total area = 36 + 16 = 52 cm²
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Jill borrows a pencil and returns it after the Warm Up. She then borrows a different pencil to show work on her CFA. The probability of selecting a mechanical pencil is 20%. The probability of selecting a wooden pencil is 40%. The probability of selecting a colored pencil is 30% What is the probability that Jill selects a wooden pencil and then a mechanical pencil?
Probabilities are used to determine the chances of events
The probability that Jill selects a wooden pencil and then a mechanical pencil is 8%
How to calculate the probabilityRepresent the events as follows:
A represents mechanical pencilB represents wooden pencilC represents colored pencilSo, we have
P(A) = 20%
P(B) = 40%
P(C) = 30%
The probability that Jill selects a wooden pencil and then a mechanical pencil is then calculated as:
P(B n A) = P(B) * P(A)
This gives
P(B n A) = 40% * 20%
Evaluate the product
P(B n A) = 8%
Hence, the probability that Jill selects a wooden pencil and then a mechanical pencil is 8%
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You are measuring temperature using a thermometer that gives degrees in Fahrenheit. You want to know what the temperature is in degrees Celsius. This formula converts temperatures from degrees Celsius to degrees Fahrenheit: F = 9/5C + 32. Rewrite this formula to convert Fahrenheit to Celsius. In your answer, use fractions instead of decimal numbers.
Answer:
F = 9/5C + 32
Step-by-step explanation:
F = 9/5C + 32
Since F means Fahrenheit and C means Celsius
Therefore the answer is already written
Answer: F = 9/5C + 32
Answer: C = 5/9 ( F - 32 )
Step-by-step explanation:
i dont know to do the 5 over 9 on the computer but thats the answer
Edmentum Answer
Which of the following is quadratic equations √ 3x² - 2x + 1/2 = 0?
The following equation √ 3x² - 2x + 1/2 = 0 is quadratic
What is quadratic?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.
Is a quadratic 2 or 4?Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."
As the expression √ 3x² - 2x + 1/2 = 0 has square root so it is a quadratic equation.
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V₁=
V₂=
V=
I have to use the cylinder to find the answer
The volume of the cylinder are:
V₁ = 4.8 unit³
V₂ = 5.6 unit³
V = 10.4 unit³
How to use the cylinder to find the volume?
To read the volume in a cylindrical tube, you need to locate the meniscus. The meniscus is the curve at the surface of the liquid in the tube. The bottom of the meniscus indicates the volume measurement.
In this case, the meniscus is at 4.8 and 5.6 for V₁ and V₂ respectively. Thus, the volume readings are:
V₁ = 4.8 unit³
V₂ = 5.6 unit³
V = V₁ + V₂
V = 4.8 + 5.6 = 10.4 unit³
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1. Suppose you are doing an F-test to test the following hypothesis: H
0
:β
1
=0&β
2
=0&β
s
=0&β
4
=0 How many of these restrictions would need to be violated in order to reject the null hypothesis?
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
In an F-test, the null hypothesis typically states that all specified coefficients are equal to zero. In this case, the null hypothesis is:
H0: β1 = 0, β2 = 0, βs = 0, and β4 = 0
To reject the null hypothesis, we need to find evidence that at least one of these restrictions is violated. This means that if we can show that any one of the coefficients (β1, β2, βs, or β4) is significantly different from zero, it would provide sufficient evidence to reject the null hypothesis.
Therefore, if any one of these restrictions is violated, meaning that its corresponding coefficient is not equal to zero, it would lead to rejecting the null hypothesis. In this case, only one violation among β1, β2, βs, or β4 is needed to reject the null hypothesis. Hence, the correct answer is:
(b) 1
It's important to note that the specific restriction that is violated can be different for each case, but as long as one restriction is violated, we have enough evidence to reject the null hypothesis in an F-test.
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Jeffery’s burgers cooks it’s burgers either well done or medium. Last night the restaurant served 8 burgers in all, 6 of which were well done. What percentage of the burgers were well done?
Answer:
75% were well done
Step-by-step explanation:
6*100=600
600/8 = 75
Which scenario could be modeled by the equation 2x+12=40
\(\huge\text{Hey there!}\)
\(\large\textsf{2x + 12 = 40}\)
\(\large\text{SUBTRACT 12 to BOTH SIDES}\)
\(\large\textsf{2x + 12 - 12 = 40 - 12}\)
\(\large\text{CANCEL out: \textsf{12 - 12} because that gives you \textsf{0}}\)
\(\large\text{KEEP: \textsf{40 - 12} because that helps solve for \textsf{x}}\)
\(\large\textsf{40 - 12 = \bf 28}\)
\(\large\text{New EQUATION: \textsf{2x = 28}}\)
\(\large\text{DIVIDE 2 to BOTH SIDES}\)
\(\mathsf{\dfrac{2x}{2}=\dfrac{28}{2}}\)
\(\large\text{CANCEL out: }\mathsf{\dfrac{2}{2}}\large\text{ because that gives you 1}\)
\(\large\text{KEEP: }\mathsf{\dfrac{28}{2}}\large\text{ because gives you the value of x}\)
\(\mathsf{x = \dfrac{28}{2}}\)
\(\boxed{\boxed{\large\textsf{Answer: \bf \huge x = 14}}}\huge\checkmark\)
\(\text{Good luck on your assignment and enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
If (a,b)=(4,6) then find the value of b.
Answer:
Concepts: Mathematical Understanding
(a,b) is an ordered pair just like (x,y) Hence b= 6Evaluate the expression 9x for x = 2
The value of expression 9x for x= 2 is 18.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression = 9x
For x=2
Value of expression=9*2
=18
Hence,
After evaluating 9x for x=2 value will be 18.
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Suppose X is a random variable and a and b are real numbers. What does the variance V[aX+b] simplify to?
The variance V[aX+b] of a random variable X with real numbers a and b simplifies to a^2 * V[X].
Here's a step-by-step explanation:
1. Recall the definition of variance: V[Y] = E[(Y - E[Y])^2], where Y is a random variable and E[Y] represents its expected value.
2. Substitute Y with aX+b: V[aX+b] = E[((aX+b) - E[aX+b])^2].
3. Apply the linearity of expectation: E[aX+b] = aE[X] + b.
4. Substitute this back into the variance equation: V[aX+b] = E[((aX+b) - (aE[X] + b))^2].
5. Simplify the expression inside the expectation: (aX+b) - (aE[X] + b) = a(X-E[X]).
6. Square the simplified expression: (a(X-E[X]))^2 = a^2 * (X-E[X])^2.
7. Use the fact that E[aZ] = a * E[Z], where Z is a random variable: E[a^2 * (X-E[X])^2] = a^2 * E[(X-E[X])^2].
8. Recall that E[(X-E[X])^2] = V[X], so the final answer is: V[aX+b] = a^2 * V[X].
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find the vertex, focus, and directrix of the parabola. x2 = 2y vertex (x, y) = focus (x, y) = directrix
The vertex, focus, and directrix of the parabola. x2 = 2y vertex (x, y) = focus (x, y) = directrix, is calculated to be the vertex, focus, and directrix of the parabola. x2 = 2y vertex (x, y) = focus (x, y) = directrix.
Given: x² = 2y We know that the standard form of a parabolic equation is : (x - h)² = 4a (y - k) where (h, k) is the vertex
To write the given equation in this form, we need to complete the square
.x² = 2yy = (x²)/2
Putting this value of y in the above equationx² = 2(x²)/2x² = x²
To complete the square, we need to add (2/2)² = 1 to both sides.x² - x² + 1 = 2(x²)/2 + 1(x - 0)² = 4(1/2)(y - 0) vertex (h, k) = (0, 0) focal length, f = a = 1/2 focus (h, k + a) = (0, 1/2) directrix y - k - a = 0 ⟹ y - 0 - 1/2 = 0 ⟹ y = 1/2
Answer: Vertex = (0,0)Focus = (0,1/2)Directrix = y = 1/2
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Two candles start burning at the same time. One candle is 15 cm tall and burns at a rate of 5 cm every 6 hours. The other candle is 25 cm tall and burns at a rate of 2 1/2 cm every hour. How tall will the candles be when they first burn down to the same height?
Answer: 10 cm
Step-by-step explanation:
o=candle one. t=candle two. h=hours
5/6=5/6 cm per hour for o(candle one).
o=15-5h/6
t=25-5h/2
o=t
15-5h/6=25-5h/2
-5h/6=10-5h/2
(-5h/6=10-5h/2)*6
-5h=60-5h*6/2
-5h=60-30h/2
-5h=60-15h
10h=60
h=6
o=15-5h/6
o=15-5(6)/6
o=15-5
o=10 cm
Maggie and Jillian are both collecting postcards. Maggie has 4 times as many postcards as Jillian. Maggie has 40 postcards.
How many postcards does Jillian have?
A 10
B. 14
C. 36
D. 44
E. 160
Answer:
10
Step-by-step explanation:
40/4=10
A test statistic is a one-sample t test test is described as t(15). from this, we know that the:
a.mean of the t distribution is 15
b. sample size used is15
c.sample size used is 16
d.sample size used are 14
In the context of a one-sample t-test described as t(15), the information provided refers to the degrees of freedom for the t-distribution, not the mean or sample size.
The answer is option d: the sample size used is 14. In a one-sample t-test, the notation t(df) represents the t-distribution with degrees of freedom (df). The degrees of freedom depend on the sample size and are calculated as df = n - 1, where n is the sample size. In this case, t(15) indicates that the test statistic follows a t-distribution with 15 degrees of freedom. To calculate the degrees of freedom, we subtract 1 from the sample size. Therefore, the sample size used in this one-sample t-test is 14.
The degrees of freedom are important because they determine the shape of the t-distribution and the critical values used in hypothesis testing. As the sample size increases, the t-distribution approaches a standard normal distribution. However, with smaller sample sizes, the t-distribution has thicker tails, allowing for greater variability and accounting for the additional uncertainty in estimating the population parameters.
Hence, it is crucial to correctly interpret the notation in a one-sample t-test, understanding that the number following "t" represents the degrees of freedom, not the mean or the sample size.
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Five students write measurements for the three side lengths of various triangles.
Student
Side Lengths
1 3, 4, and 5
2 4, 7, and 10
3 5, 12, and 16
4 6, 8, and 10
5 7, 11, and 13
Which students' measurements form a right triangle? Select ALL that apply.
A Student 1
B
Student 2
С
Student 3
D
Student 4
I
E
Student 5
Answer:
student 3 i think yea
Step-by-step explanation:
Which action completes this
diagram?
Answer: Establish a national bank
Step-by-step explanation:
Match the correlation to the statement:
I cannot be confident at all.
I can be a little confident; my prediction could be close or way off.
I can be somewhat confident; my predicted value could be close but not exact.
I can be certain that my predicted value will be exact.
-1 -0.645 0 0.347
Also If someone doesnt mind can you please explain this??? I dont understand at all lol.
The correct matching relating the correlation coefficients are given as follows:
0: I cannot be confident at all.0.347: I can be a little confident; my prediction could be close or way off.0.645: I can be somewhat confident; my predicted value could be close but not exact.-1: I can be certain that my predicted value will be exact.What is a correlation coefficient?A correlation coefficient is an index that measures the association between multiple variables.
The closer the absolute value of the correlation coefficient is of 1, the stronger is the association, meaning that the statement has more certainity.
Closer to zero, the correlation coefficient gives no confidence of the assessment, and values above 0.6 are considered as indicating strong correlation.
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what value of x will make the sides equal
7(x-19) = 7*3
Can anyone please help
After 3.94 hours, the price of stock A and stock B will become same.
What do you mean by price?
Price can be defined as the amount of money that get paid for something.
Lets assume that after x hours the price of stock A is equal to price of stock B.
Since the price of stock A is increasing at rate of 0.11 per hour, so after x hours it will become:
$12.15 + 0.11x
Since the price of stock B is decreasing at rate of 0.08 per hour, so after x hours it will become:
$12.90 - 0.08x
Equating both price to get the value of x:
12.15 + 0.11x = 12.90 - 0.08x
(0.11+0.08)x = 12.90 - 12.15
x = 0.75/0.19
x = 3.94
Hence, after 3.94 hours the price will be same.
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Jeffery surveyed 50 randomly selected workers at a factory. He collected data about the individual output of a worker on an average day. The results are shown using the box-and-whisker plot. What percent of workers have output more than 70 units?
Answer:
the answer is 30% of the workers have output more than 70 units.
Step-by-step explanation:
Answer: I believe the answer is 25%.
Which math statement compares the decimal numbers 0.34 and 0.8 correctly?
Answer:
0.34 < 0.8
Step-by-step explanation:
On compares the decimal numbers 0.34 and 0.8 the correct math statement is 0.34 < 0.8.
To compare the decimal numbers 0.34 and 0.8 correctly, we need to determine which one is greater or if they are equal. One way to do this is by aligning the decimals and comparing the digits from left to right.
0.34 and 0.8 have a different number of decimal places. To make the comparison easier, we can add a trailing zero to 0.34:
0.34 ( or 0.340 ) and 0.8
Now, we can compare them:
0.340 < 0.8
So, the correct math statement is: 0.34 < 0.8.
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2+5x=7x-18+2x
——— ————-
3x 3x
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
Perhaps you want to solve for x the rational equation ...
(2+5x)/(3x) = (7x -18 +2x)/(3x)
Multiplying by 3x and collecting terms, we have ...
2 +5x = 9x -18
20 = 4x . . . . . . add 18-5x to both sides
5 = x . . . . . . . . divide both sides by 4
The solution is x=5.
Determine whether the ordered pair (1,2) solves the following system of equations. 3x-5y=-7 x-3y = -7 1. Does the ordered pair solve equation 1?. 2. Does the ordered pair solve equation 2? 3. Does the ordered pair solve the system?
The ordered pair (1,2) solves equation 1 but does not solve equation 2. Therefore, the ordered pair (1,2) does not solve the system of equations formed by Equation 1 and Equation 2.
To determine if the ordered pair (1,2) solves equation 1, we substitute x=1 and y=2 into the equation:
3(1) - 5(2) = -7
3 - 10 = -7
-7 = -7
Since both sides of the equation are equal, the ordered pair (1,2) satisfies equation 1.
Next, to check if the ordered pair (1,2) solves equation 2, we substitute x=1 and y=2 into the equation:
1 - 3(2) = -7
1 - 6 = -7
-5 = -7
Since the equation is not true, the ordered pair (1,2) does not satisfy equation 2.
Since the ordered pair (1,2) does not satisfy both equations simultaneously, it does not solve the system of equations formed by equation 1 and equation 2.
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food safety guidlines recommend that a beef rib roast should cook for 23 minutes per pound based on 325f oven setting. how many hours should it take to cook a 5.17 pound roast?
It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.
Cooking time in minutes = 5.17 pounds * 23 minutes/pound
Cooking time in minutes = 118.91 minutes
To convert minutes to hours, we divide the total minutes by 60:
Cooking time in hours = 118.91 minutes / 60
Cooking time in hours ≈ 1.98 hours
Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
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9w + 13u - 4v + 5u - 7w?
Answer:
2w + 18u - 4v
Step-by-step explanation:
1) The area of the shaded sector is 51.3 square feet. What is an estimate for the radius of the
circle? Round the answer to the nearest foot.
B
60°
D
120°
C
3.31 is an estimate for the radius of the circle.
What precisely is a circle?The circle fοrm is a clοsed twο-dimensiοnal shape because every pοint in the plane that makes up a circle is evenly separated frοm the "centre" οf the fοrm.
Each line tracing the circle cοntributes tο the fοrmatiοn οf the line οf reflectiοn symmetry. In additiοn, it rοtates arοund the center in a symmetrical manner frοm every perspective.
he radius of the circle, we need to use the formula for the area of a sector, which is:
Area of sector = (θ/360) x π x r
the radius of the circle "x" for now, and set up an equation using the given information
51.3 = (120/360) x π x
Simplifying this equation, we get:
= (51.3 x 360)/(120 x π)
x² ≈ 10.95
x ≈ √10.95
x ≈ 3.31
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