The correct choice is To control voluntary response bias.
Random assignment helps to control voluntary response bias by icing that individualities are assigned to the treatment and control groups fully arbitrarily, without any input or influence from the individualities themselves.
Voluntary response bias occurs when individuals tone-elect into a particular group, frequently because they have a particular interest or opinion on the content being studied. This can lead to prejudiced results because the individuals who choose to share may not be representative of the larger population.
Random assignment helps to control for voluntary response bias by icing that individualities are assigned to the treatment and control groups fully at arbitrarily, without any input or influence from the individualities themselves. This helps to insure that the groups are representative of the larger population and that any observed differences between the groups are due to the treatment itself, rather than other factors that may be associated with certain individualities or groups.
thus, arbitrary assignment helps to minimize the implicit impact of voluntary response bias on the results of a trial.
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The correct question is given below-
What is the purpose of random assignment in an experiment? Check all that apply.
Group of answer choices
To select a sample that is representative of the population
To create similar treatment groups
To eliminate the effects of the explanatory variable
To control voluntary response bias
Control for confounding variables
The area of a rectangle is 8811m if the width of the garden is 89 m what’s the length
The length of the garden is 99 m.
What’s the length?The formula for the area of a rectangle is:
Area = Length x Width
We are given that the area of the rectangle is 8811 [tex]m^{2}[/tex] and the width is 89 m. Substituting these values into the formula, we get:
8811 [tex]m^{2}[/tex] = Length x 89 m
To solve for the length, we can divide both sides of the equation by 89 m:
Length = 8811 [tex]m^{2}[/tex] / 89 m
Simplifying, we get:
Length = 99 m
Therefore, the length of the garden is 99 m.
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Please help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equivalent exponential expression for this problem is given as follows:
A. 4^15 x 5^10.
How to simplify the exponential expression?The exponential expression in the context of this problem is defined as follows:
[tex]\left(\frac{4^3}{5^{-2}}\right)^5[/tex]
To simplify the expression, we must first apply the power of power rule, which means that when one exponential expression is elevated to an exponent, we keep the base and multiply the exponents, hence:
4^(15)/5^(-10)
The negative exponent at the denominator means that the expression can be moved to the numerator with a positive exponent, hence the simplified expression is given as follows:
4^15 x 5^10.
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HURRY 40 POINTS!!
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling in the boxes.
ft²
The surface area of the rectangular prism is 29 2/3 ft²
How to determine the surface areaThe formula for calculating the surface area of a rectangular prism is expressed as;
SA = 2(wl + hw + hl)
Where the parameters are;
SA is the surface areaw is the width of the prismh is the height of the prisml is the length of the prismFrom the information given, we have that;
Wl = 3 × 5/2
multiply the values
wl = 15/2
hw = 4/3 × 3
hw = 4
hl = 4/3 × 5/2 = 20/6 = 10/3
Substitute the values
Surface area = 2(4 + 10/3 + 15/2)
Surface area = 2(24 + 20 + 45/6)
Surface area = 2(89)/6
Surface area = 89/3 = 29 2/3 ft²
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At Robinson’s Steakhouse, you can choose from 2 steaks cooked to your liking and have the choice of 2 different sides. What is the probability that a customer will choose a Ribeye, well done or medium with corn?
A- 1/3
B- 1/12
C- 2/7
D- 1/6
the probability of a customer choosing a Ribeye, well done or medium with corn is [tex]1[/tex] out of [tex]12[/tex], which is answer B [tex]- 1/12[/tex] Thus, option B is correct.
What is the probability?There are two possible steaks that a customer can choose from, and for each steak, there are three possible ways to cook it: rare, medium, or well-done. Additionally, there are two possible sides to choose from: corn or some other option.
Thus, there are a total of [tex]2 \times 3 \times 2 = 12[/tex] possible meal combinations that a customer can choose from.
Out of these 12 possibilities, there is only one way to get a Ribeye cooked well-done or medium with corn, since there is only one Ribeye option on the menu.
Therefore, the probability of a customer choosing a Ribeye, well done or medium with corn is 1 out of 12, which is answer B- 1/12
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Divide and write your answer in standard notation to the nearest whole number with commas.
Answer:
The answer is 1×10⁶ to the nearest whole number
Step-by-step explanation:
7.6×10⁰/5.4×10‐⁶
7.6×10^(0-(-6)/5.4
7.6×10^(0+6)/5.4
7.6×10⁶/5.4
=1×10⁶ to the nearest whole number
Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s correct. Provide an explanation
We can expect approximately 144 students in Chloe's school to own pets. The answer is 144.
What is mean by Proportion ?A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)
Based on the simulation results, we can count the number of times the number cube landed on digits 1, 2, 3, and 4, which represent the number of students who own pets. We add up these counts and divide by the total number of rolls (25) to get the proportion of rolls that resulted in a student owning a pet:
(5+1+4+4+3+3+2+2+2+1+5+2+1) / 25 = 0.6
So, approximately 60% of the rolls resulted in a student owning a pet. If we assume this proportion holds for the entire school, we can estimate the number of students who own pets out of the total number of students in the school:
Number of students who own pets = Proportion of students who own pets * Total number of students
Number of students who own pets = 0.6 * 240 = 144
Therefore, we can expect approximately 144 students in Chloe's school to own pets. The answer is 144.
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What is the equation of the line in slope-intercept form?
Answer:
y = 3/5x + 3
Step-by-step explanation:
points on the graph
(-5,0) and (0,3)
0- 3 = -3
-5 - 0 = -5
-3/-5= 3/5
y = 3/5x + B
use a point from the graph
3 = 3/5 x 0 + B
3 = 0 + B
3 -0 = 3
3 = B
check answer
(-5,0)
Y = 3/5 x -5 + 3
Y = -15/3 + 3
Y = -3 + 3
Y = 0
Making the equation true y = 3/5x + 3
what is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds ?
The maximum number of consecutive odd positive integers that can be added together before the sum exceeds 401 is 11.
Let's assume the first odd integer is x. Then, the sum of the next n consecutive odd integers would be given by:
x + (x+2) + (x+4) + ... + (x+2n-2) = nx + 2(1+2+...+n-1) = nx + n(n-1)
We want to find the largest n such that the sum is less than or equal to 401:
nx + n(n-1) ≤ 401
Since the integers are positive and odd, we can start with x=1 and then try increasing values of n until we find the largest value that satisfies the inequality:
n + n(n-1) ≤ 401
n² - n - 401 ≤ 0
Using the quadratic formula, we find that the solutions are:
n = (1 ± √(1+1604))/2
n ≈ -31.77 or n ≈ 32.77
We discard the negative solution and round down to the nearest integer, giving us n = 11. Therefore, the maximum number of consecutive odd positive integers that can be added together before the sum exceeds 401 is 11.
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Complete Question:
what is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds 401?
Aidan wants to find the mass of a
bowling ball.Which unit should he use
Answer:
Aiden should use the Standard unit of Mass
Kilogram.
Step-by-step explanation:
He can use other unit also like gram, pound, ounce, tone etc
Kubin Company’s relevant range of production is 25,000 to 33,500 units. When it produces and sells 29,250 units, its average costs per unit are as follows: Average Cost per Unit Direct materials $ 8. 50 Direct labor $ 5. 50 Variable manufacturing overhead $ 3. 00 Fixed manufacturing overhead $ 6. 50 Fixed selling expense $ 5. 00 Fixed administrative expense $ 4. 00 Sales commissions $ 2. 50 Variable administrative expense $ 2. 00 Required: 1. For financial accounting purposes, what is the total amount of product costs incurred to make 29,250 units? 2. For financial accounting purposes, what is the total amount of period costs incurred to sell 29,250 units? 3. For financial accounting purposes, what is the total amount of product costs incurred to make 33,500 units? 4. For financial accounting purposes, what is the total amount of period costs incurred to sell 25,000 units? (For all requirements, do not round intermediate calculations. )
1. Total amount of product costs
2. Total amount of period costs incurred
3. Total amount of product costs
4. Total amount of period costs
For the relevant range of production of units total amount of product and period cost as per units are,
Total amount of product costs for 29,250 units is $687,375.
Total amount of period costs incurred for 29,250 units is $58,511.50
Total amount of product costs for 33,500 units is equal to $787,250.
Total amount of period costs for 25,000 units is equal to $50,011.50.
Average Cost per Unit Direct materials = $ 8. 50
Direct labor = $ 5. 50
Variable manufacturing overhead = $ 3. 00
Fixed manufacturing overhead = $ 6. 50
Fixed selling expense = $ 5. 00
Fixed administrative expense = $ 4. 00
Sales commissions = $ 2. 50
Variable administrative expense = $ 2. 00
Total unit produced = 29,250 units,
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 29,250
= $23.50 x 29,250
= $687,375
The total amount of product costs incurred to make 29,250 units is $687,375.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 29,250)
= $5.00 + $4.00 + $2.50 + $58,500
= $58,511.50
The total amount of period costs incurred to sell 29,250 units is $58,511.50
For the number of units produced changed to 33,500.
Total product costs
= (Direct materials + Direct labor + Variable manufacturing overhead + Fixed manufacturing overhead) x Number of units produced
= ($8.50 + $5.50 + $3.00 + $6.50) x 33,500
= $23.50 x 33,500
= $787,250
The total amount of product costs incurred to make 33,500 units is $787,250.
The number of units sold changed to 25,000.
Total period costs
= Fixed selling expense + Fixed administrative expense + Sales commissions + (Variable administrative expense x Number of units sold)
= $5.00 + $4.00 + $2.50 + ($2.00 x 25,000)
= $5.00 + $4.00 + $2.50 + $50,000
= $50,011.50
The total amount of period costs incurred to sell 25,000 units is $50,011.50.
Therefore, the total amount of the product and period cost for different situations are,
Total amount of product costs is equal to $687,375.
Total amount of period costs incurred is equal to $58,511.50
Total amount of product costs is equal to $787,250.
Total amount of period costs is equal to $50,011.50.
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Simplify. 11 3/4-8 1/2
Therefore, 11 3/4 - 8 1/2 = 13/4, or 3 1/4 as a mixed number.
What is mixed number?A mixed number is a type of number that represents a whole number and a fraction together. It is written in the form of a whole number followed by a fraction, such as 3 1/2. The whole number represents the number of whole units, while the fraction represents the part of a unit.
For example, the mixed number 3 1/2 can be interpreted as three whole units and one half of a unit. Another example of a mixed number is 2 3/4, which represents two whole units and three-quarters of a unit. Mixed numbers are commonly used in everyday life, such as in cooking and measuring, and in mathematical calculations involving fractions.
To subtract mixed numbers like these, we need to convert them to improper fractions first:
[tex]11 3/4 = (4 * 11 + 3)/4 = 47/4[/tex]
[tex]8 1/2 = (2 * 8 + 1)/2 = 17/2[/tex]
Now, we can subtract the fractions:
[tex]47/4 - 17/2[/tex]
To subtract these fractions, we need to find a common denominator. The least common multiple of 4 and 2 is 4 × 2 = 8. We can convert both fractions to have a denominator of 8:
[tex]47/4 = (47/4) * (2/2) = 94/8[/tex]
[tex]17/2 = (17/2) * (4/4) = 68/8[/tex]
Now, we can subtract the numerators:
[tex]94/8 - 68/8 = 26/8[/tex]
Finally, we can simplify the result by dividing both numerator and denominator by their greatest common factor, which is 2:
[tex]26/8 = (2 * 13)/(2 * 4) = 13/4[/tex]
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1. In Design 2, what is the radius of the larger
grassy area?
Answer: 5 m
Step-by-step explanation:
A radius is half of the diameter which is the black line. Hope this helps!
Answer:
The radius of the larger grass area is 5m
Step-by-step explanation:
d=2r
r=d/2
r=10/2
r=5m
I NEED HELP, LIKE NOW!\
What is -27 radical 72
Step-by-step explanation:
-27 [tex]\sqrt{72}[/tex] = -27 [tex]\sqrt{36*2}[/tex] = -27 (6) [tex]\sqrt{2}[/tex] = - 162 [tex]\sqrt{2}[/tex] = - 229.1
the rule T(-3,1) is applied to point 2,-7 in which part of the coordinate system is the translated point
the translated point is located in the third quadrant of the coordinate system, since both coordinates are negative.
What is Cartesian coordinate?
A coordinate system, also known as a Cartesian coordinate system, is a system used to describe the position of points in space. It is named after the French mathematician and philosopher René Descartes, who introduced the concept in the 17th century. In a coordinate system, each point is assigned a unique pair of numbers, called coordinates, that describe its position relative to two perpendicular lines, called axes. The horizontal axis is usually labeled x and the vertical axis is usually labeled y.
To apply the translation rule T(-3, 1) to the point (2, -7), we need to add the translation vector (-3, 1) to the coordinates of the point:
(2, -7) + (-3, 1) = (-1, -6)
The resulting point after the translation is (-1, -6).
Therefore, the translated point is located in the third quadrant of the coordinate system, since both coordinates are negative.
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a customer spends 21.50 on cupcakes and muffins. the numbet of muffins purchased is 1 few than number of cupcakes. each cupcake costs $2, and each muffin cost $1.25 create a system of equations
Answer: Let's use the following variables to represent the unknown quantities in the problem:
x: the number of cupcakes purchased
y: the number of muffins purchased
From the problem statement, we can write two equations:
The total amount spent on cupcakes and muffins is $21.50:
2x + 1.25y = 21.50
The number of muffins purchased is one fewer than the number of cupcakes:
y = x - 1
These two equations form a system of equations that can be solved simultaneously to find the values of x and y.
Substituting equation 2 into equation 1, we get:
2x + 1.25(x - 1) = 21.50
Simplifying and solving for x:
2x + 1.25x - 1.25 = 21.50
3.25x = 22.75
x = 7
Now that we know x, we can use equation 2 to find y:
y = x - 1 = 7 - 1 = 6
Therefore, the customer purchased 7 cupcakes and 6 muffins, spending a total of $21.50.
Step-by-step explanation:
pamela registered her new phone number on the do not call registry. how long will her number remain on the list?
If Pamela has registered for the first time, it will remain on the Do Not Call list permanently. If she has re-registered, it will remain on the list for an additional five years from the date of re-registration.
How long do phone numbers remain on the Do Not Call Registry?The length of time that Pamela's phone number will remain on the National Do Not Call Registry depends on whether she registered her number on the Do Not Call Registry for the first time or if she has re-registered her number after it has already been on the list for a while.
If Pamela registered her phone number for the first time, it will be added to the Do Not Call Registry within 31 days of her registration date. Her phone number will remain on the list permanently, unless she requests to remove it or the number is disconnected.
If Pamela has re-registered her phone number after it has already been on the list for a while, her number's registration will be extended for another five years from the date she re-registered it.
Therefore, if Pamela registered her phone number for the first time, it will remain on the list permanently. If she has re-registered her number, it will remain on the list for an additional five years from the date of re-registration.
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the dimensions of noah’s ark were reported as 3.0 × 102 cubits by 5.0 × 101 cubits. express this size in units of feet (1 cubit = 1.5 ft)
The dimensions of Noah's Ark in feet are 450 feet by 75 feet if the dimensions of Noah's Ark is 3.0 × 102 cubits by 5.0 × 101 cubits.
Noah's Ark is said to have dimensions of 3.0 × 10^2 cubits by 5.0 × 10^1 cubits. To convert these measurements to feet, we can use the conversion factor of 1 cubit = 1.5 feet.
First, we need to convert the length of the ark from cubits to feet. To do this, we multiply the length of the ark in cubits (3.0 × 10^2) by the conversion factor of 1.5 feet/cubit. This gives us a length of
3.0 × 10^2 cubits x 1.5 feet/cubit = 450 feet
Similarly, we can convert the width of the ark from cubits to feet by multiplying the width in cubits (5.0 × 10^1) by the conversion factor of 1.5 feet/cubit. This gives us a width of:
5.0 × 10^1 cubits x 1.5 feet/cubit = 75 feet
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A large rectangular prism is 5 feet long, 3 feet wide, and 4 feet tall. A small rectangular prism is 2.5 feet long, 1.5 feet wide, and 2 feet tall.
How many small prisms would it take to fill the large prism?
Write your answer as a whole number or decimal. Do not round.
The answer of the given question based on the rectangular prism is , , it would take 8 small rectangular prisms to fill the large rectangular prism.
What is Rectangular prism?A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid object that has six rectangular faces, with opposite faces being congruent and parallel. It is a special case of a parallelepiped in which all angles are right angles and all six faces are rectangles.
To find how many small rectangular prisms will fit inside the large rectangular prism, we need to calculate the volume of each prism and then divide the volume of the large prism by the volume of the small prism.
The volume of the large prism is:
V_large = length × width × height = 5 ft × 3 ft × 4 ft = 60 feet³
The volume of the small prism is:
V_small = length × width × height = 2.5 ft × 1.5 ft × 2 ft = 7.5 feet³
Dividing the volume of the large prism by the volume of the small prism, we get:
number of small prisms = V_large / V_small = 60 ft³ / 7.5 ft³ = 8
Therefore, it would take 8 small rectangular prisms to fill the large rectangular prism.
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an agency has specialists who analyze the frequency of letters of the alphabet in an attempt to decipher intercepted messages. suppose a particular letter is used at a rate of 6.6%. what is the mean number of times this letter will be found on a typical page of 2650 characters? 174.9 what is the standard deviation for the number of times this letter will be found on a typical page of 2650 characters ? round your answer to 1 decimal place. in an intercepted message, a page of 2650 characters is found to have the letter occurring192 times. would you consider this unusual?
Standard deviation normal distribution table or calculator to determine the probability of observing a z-score of 1.3 or higher.
The probability is approximately 0.0968, or 9.68%.
To determine the mean number of times the letter appears on a page, we can multiply the probability of the letter appearing (0.066) by the total number of characters on the page (2650):
[tex]Mean = 0.066 \times 2650 = 174.9[/tex]
To calculate the standard deviation, we can use the formula:
Standard deviation = [tex]\sqrt(n \times p \times q)[/tex]
n is the sample size (2650), p is the probability of success (0.066), and q is the probability of failure [tex](1 - p = 0.934)[/tex].
Standard deviation = [tex]sqrt(2650 \times 0.066 \times 0.934) = 13.2[/tex] (rounded to 1 decimal place)
Determine whether 192 occurrences of the letter on a page is unusual, we can use the z-score formula:
z = (x - mean) / standard deviation
x is the observed number of occurrences (192), mean is the expected number of occurrences (174.9), and standard deviation is the standard deviation we just calculated (13.2).
[tex]z = (192 - 174.9) / 13.2 = 1.3[/tex]
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help please this is due tonight and im struggling
Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.
Explain about the cyclic quadrilateral:When you hear the word "cyclic," think of the two round wheels on you bicycle. A quadrilateral is a figure with four sides. The result is a cyclic quadrilateral, which is defined as any four-sided shape (quadrilateral) its four vertices (corners) are located on a circle.
A cyclic quadrilateral's opposite angles add up to 180 degrees, making them supplementary to one another.
Given data:
∠T = x + 60°∠R = x + 20°Using the property of cyclic quadrilateral: sum of opposite angle are 180 degrees.
∠T + ∠R = 180
x + 60 + x + 20 = 180
2x + 80 = 180
2x = 180 - 80
2x = 100
x = 50
Thus, the value of x for the given angle of cyclic quadrilateral is found as the x = 50.
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profitability empirical rule with this dataset? why or why not. no, the measures the proportion of a movies budget recovered. a profitability less than 1 the movie did not make enough money to cover the budget, while a profitability greater than means means it made a profit. a boxplot of the profitability ratings of 136 movies that came out in 2011 is shown below. (the largest outlier is the movie 1 insidi high gross revenue.)
The empirical rule does not apply to this dataset because the empirical rule is used to describe data that is normally distributed.
The empirical rule is a statistical rule that states that for a normal distribution.
Approximately 68% of the data will fall within one standard deviation of the mean, 95% of the data will fall within two standard deviations of the mean, and 99.7% of the data will fall within three standard deviations of the mean.
The dataset is normally distributedThe dataset is normally distributed, determine if the empirical rule appliesThe empirical rule does not apply, identify an alternative method to describe the datasetThe empirical rule does not apply to this dataset because the empirical rule is used to describe data that is normally distributed.
This dataset does not appear to be normally distributed, as evidenced by the large outlier (1 Insidi High Gross Revenue).
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what is the degree of the polynomial 8 x to the power of 5 plus 4 x cubed minus 5 x squared minus 9 ?
Out of these powers, the highest is 5.
Therefore, the degree of the polynomial is 5.
The degree of a polynomial is the highest power of the variable in the polynomial. In the given polynomial, the highest power of x is 5,
so the degree of the polynomial is 5.
The degree of a polynomial is the highest power of the variable (x) in the expression.
In the polynomial you provided:
[tex]8x^5 + 4x^3 - 5x^2 - 9[/tex]
Let's identify the terms and their respective powers of x:
[tex]8x^5[/tex]has a power of 5.
[tex]4x^3[/tex]has a power of 3.
[tex]-5x^2[/tex] has a power of 2.
-9 is a constant term, so there is no power of x.
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please help someone..50 points
Answer:
We can find the sum of the interior angles of any polygon using the formula
[tex]S_{n}=180(n-2)[/tex], where n is the number of sides.
Because each of these polygons have four sides, we can use one formula where our n is 4 to find the sum of the interior angles:
[tex]S_{4}=180(4-2)\\ S_{4}=180*2\\ S_{4}=360[/tex]
Thus, for all four problems, we can set the four angles equal in the four polygons equal to 360 and solve for the variables
(15) *Note the right angle symbol in this problem which always equals 90°
[tex]84+90+(2x+118)+(2x+68)=360\\174+2x+118+2x+68=360\\360+4x=360\\4x=0\\x=0[/tex]
Now, to find the measure of <Y, we simply plug in 0 for x in its equation
m<Y = 2(0) + 118 = 118°
(16):
[tex]82+105+(8x+11)+10x=360\\187+8x+11+10x=360\\198+18x=360\\18x=162\\x=9[/tex]
To find the measure of <F, we plug in 9 for x in its equation
m<F = 10(9) = 90°
(17):
[tex]95+95+(10x-5)+(8x+13)=360\\190+10x-5+8x+13=360\\198+18x=360\\18x=162\\x=9[/tex]
To find the measure of <M, we plug in 9 for x in its equation
m<M = 10(9) - 5 = 85°
(18):
[tex](14x-7)+(11x-2)+93+76=360\\14x-7+11x-2+169=360\\25x+160=360\\25x=200\\x=8[/tex]
To find the measure of <M, we plug in 8 for x in its equation
m<M = 11(8) - 2 = 86°
Answer every question. Pick one option for each question. Show your work.
1. Over one week, a snack booth at a fair sold 362 cans of soft drinks for $1.75 each and
221 hot dogs for $2.35 each. Which calculation will give the total sales of soft drinks and
hot dogs?
A. 362(2.35) + 221(1.75)
B. 221(2.35) + 362(2.35)
C. 221(1.75) + 362(1.75)
D. 362(1.75) + 221(2.35)
assume that arrivals occur according to a poisson process with an average of seven per hour. what is the probability that exactly two customers arrive in the two-hour period of time between a 2:00 p.m. and 4:00 p.m. (one continuous two-hour period)? b 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m. (two separate one-hour periods that total two hours)?
a) The probability that exactly two customers arrive between 2:00 p.m. and 4:00 p.m. is 0.0915 (or approximately 9.15%).
b) The probability of at least one customer arriving between 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m. is approximately 0.99999917.
For a Poisson process, the number of arrivals in a fixed time interval follows a Poisson distribution.
Let's denote the number of arrivals in a two-hour period as X.
Since the average number of arrivals per hour is 7, the average number of arrivals in a two-hour period is 14.
Therefore, we have λ = 14.
a) Probability of exactly 2 customers arriving between 2:00 p.m. and 4:00 p.m.:
Using the Poisson distribution formula, the probability of X arrivals in a two-hour period is:
[tex]P(X = x) = (e^{-\lambda} * \lambda^x) / x![/tex]
So, for X = 2, we have:
[tex]P(X = 2) = (e^{-14} * 14^2) / 2! = 0.0915[/tex] (rounded to four decimal places)
Therefore, the probability that exactly two customers arrive between 2:00 p.m. and 4:00 p.m. is 0.0915 (or approximately 9.15%).
b) Probability of at least one customer arriving between 1:00 p.m. and 2:00 p.m. or between 3:00 p.m. and 4:00 p.m.:
We can approach this problem by using the complementary probability. The complementary probability of at least one customer arriving in a two-hour period is the probability of no customers arriving in that period. Since the arrival rate is the same for each hour, we can divide the two-hour period into two one-hour periods and use the Poisson distribution formula for each period separately.
The probability of no customers arriving in a one-hour period with λ = 7 is:
[tex]P(X = 0) = (e^{-7}* 7^0) / 0! = 0.000911[/tex]
The probability of no customers arriving in a two-hour period is the product of the probabilities for each one-hour period:
P(no customers in two-hour period) = P(X = 0) * P(X = 0) = 0.000911 * 0.000911 = 8.30e-7
The complementary probability of at least one customer arriving in a two-hour period is:
P(at least one customer in two-hour period) = 1 - P(no customers in two-hour period) = 1 - 8.30e-7 = 0.99999917 (rounded to eight decimal places).
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Which of the following best describes the expression 9(x + 7)? (20 brainly points)
A: The sum of constant factors 9 and x + 7
B: The product of constant factors 9 and x + 7
C: The product of a constant factor 9 and a 2-term factor x + 7
D: The sum of a constant factor 9 and a 2-term factor x + 7
The statement that express 9(x + 7) is product of constant factors 9 and x + 7. The Option B.
What does the expression 9(x + 7) represent?The expression 9(x + 7) represents the product of constant factors 9 and x + 7. To evaluate the expression, you would distribute the 9 to both terms inside the parentheses, resulting in 9x + 63.
This expression can also be written as a 2-term factor of 9 and x + 7. It is important to understand the different terms and factors in an expression to simplify and solve equations.
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answer these questions
Answer:
a) model a: 50/hr
model b: 40/hr
b) model a
Step-by-step explanation:
b) since the money raised started at 0, the rate of change can be found by calculating 400/8
Footy. You play in an inter- school footy competition. Curiously, in one of the rounds the total number of points scored by each team is the same, so that all games are not only drawn, but also have the same final score. In that same round your team scored 1/13th of all goals and 1/15th of all behinds. How many teams play in the competition?
There are 195 games played in the competition.
Let the total number of points scored in each game be represented by the variable "x". Since a goal is worth 6 points and a behind is worth 1 point, we can write an equation in terms of "x":
6a/13 + b/15 = x
where "a" is the total number of goals scored and "b" is the total number of behinds scored by your team in the round.
Since all games have the same final score, we know that the total number of points scored in the round is equal to the number of games played times the final score:
x * number of games = total points scored
We also know that the total number of points scored in the round is equal to the total number of goals scored (by all teams) times 6 plus the total number of behinds scored (by all teams):
x * number of games = 6 * total number of goals + total number of behinds
Substituting the first equation into the second equation, we get:
(6a/13 + b/15) * number of games = 6 * total number of goals + total number of behinds
Simplifying this equation and solving for "number of games", we get:
number of games = 1170/(2a/13 + b/15)
Since the number of games must be an integer, we can see that 2a/13 + b/15 must be a divisor of 1170. The possible values of 2a/13 + b/15 are:
2/13 + 78/15 = 72/5
4/13 + 72/15 = 56/5
6/13 + 66/15 = 44/5
8/13 + 60/15 = 32/5
The only divisor of 1170 among these values is 72/5, which corresponds to a = 26 and b = 312. Therefore, the number of games played in the round is:
number of games = 1170 / [(2a/13) + (b/15)]
= 1170 / [(2*26/13) + (312/15)]
= 195
As a result, 195 games have been played in the competition.
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2. when conducting a hypothesis test, the hypothesis that illustrates what we really think is going on in the population is called the hypothesis. an. analytical b. hypothetical c. null d. theoretical e. alternative
shawna is going out of town for the day, so she asks a friend to watch her 3 dogs. she wants to leave 12 of a pound of food for each dog. if a can of dog food has 0.75 pounds of food, how many cans should shawna leave?write your answer as a whole number, decimal, fraction, or mixed number. simplify any fractions.
Shawna wants to make sure her three dogs are fed and cared for when she leaves town for the day. She intends to give each of her dogs 12 ounces of food to achieve this. She must therefore leave a total of 36 ounces of food (3 dogs x 12 ounces of food per dog). 36 ounces are equivalent to 2.25 pounds of food because 16 ounces make up one pound.
There are 0.75 pounds of food in each can of dog food. We must divide 2.25 by 0.75 to find the quantity of dog food Shawna should leave for her companion. 3 dog food cans are the end outcome.Shawna ought to give her buddy three cans of dog food so that she can feed her dogs.
Shawna may make sure her dogs have enough food and are well cared for while she is away by leaving adequate food for them. Shawna may put any fears or concerns about her pets' welfare to rest by leaving ample food and clear directions.
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