Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.
What is meant by events?
In probability theory, an event is a set of outcomes or results that can occur when performing a random experiment. An event can consist of a single outcome or multiple outcomes, and it is defined as a subset of the sample space of the random experiment.
1.Rolling a dice and flipping a coin are two independent events. The probability of rolling any particular number on a dice is 1/6, and the probability of flipping heads on a coin is 1/2. Since the outcome of rolling a dice does not affect the outcome of flipping a coin and vice versa, these events are considered independent.
2.Spinning two spinners each round are independent events. The probability of each spinner landing on a particular section is fixed, and the outcome of one spinner does not affect the outcome of the other spinner. Therefore, these events are considered independent. The probability of the first spinner landing on a specific section and the second spinner landing on another specific section at the same time is the product of their individual probabilities.
3.Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. In the beginning, there are 12 S tiles and 9 M tiles in the bag. The probability of drawing an S tile is initially 12/21 or 4/7. If an S tile is drawn first, the number of S tiles in the bag decreases to 11, and the probability of drawing an M tile on the second draw becomes 9/20. Therefore, the probability of drawing an S tile and then an M tile is (4/7) x (9/20) = 18/70 = 9/35.
4.Pulling a candy, eating it, and then pulling another out of a bag are dependent events. Initially, there are a certain number of candies in the bag. After one candy is drawn and eaten, the number of candies in the bag decreases, affecting the probability of drawing a specific candy on the second draw. Therefore, these events are considered dependent.
Therefore, Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.
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GIFTS Joel has $96 to spend on at least 9 gifts for the holidays. He plans to buy puzzles that cost $8 or games that cost $12. How many of each can he buy?
Part A Create a system of inequalities that represents the constraints in the problem. Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy.
Can Joel buy 2 games and 6 puzzles and satisfy the constraints?
After answering the provided question, we can conclude that As a result, function Joel cannot satisfy the constraints by purchasing two games and six puzzles.
what is function?A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.
Part A:
8x + 12y 96
x + y ≥ 9
x ≥ 0
Part B
If Joel purchases two games and six puzzles, he will spend:
[tex]2 * $12 + 6 * $8 = $48 + $48 = 96\\8x + 12y \leq 96\\8(6) + 12(2) = 48 + 24 = 72 < 96\\x + y \geq 9\s6 + 2 = 8 < 9[/tex]
As a result, Joel cannot satisfy the constraints by purchasing two games and six puzzles.
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sara y rocio estudian lagartijas y arañas en la
universidad. si estudian 9 animales que tienen
en total 56 patas, ¿cuántas arañas y lagartijas
tienen?
Solving a system of equations we can see that they have 4 lizards and 5 spiders.
How many spiders and lizards do they have?We know that each spider has 8 legs, and each lizard has 4 legs.
Now we can define the variables:
x = number of lizards.
y = number of spiders.
We know that the total number of animals is 9, so:
x + y = 9
And the total number of legs is 56, then we can write:
4x + 8y = 56
Then we have a little system of equations:
x + y = 9
4x + 8y = 56
We can isolate x in the first equation to get:
x = 9 - y
Replacing that in the other one, we wll get:
4*(9 - y) + 8y = 56
36 - 4y + 8y = 56
4y = 56 - 36
4y = 20
y = 20/4 = 5
They have 5 spiders, and the other 4 animals must be lizards.
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what is the quotient of negative 5 over negative 15
Answer: 1/3
Step-by-step explanation:
Quotient is another word for the solution to a division problem.
So in this case the quotient is the answer to -5/-15.
When you divide a negative by another negative, you get a positive answer. The same can be said about dividing a positive number by another positive number.
So, in this case, we can change -5/-15 to 5/15.
Now we just need to simplify by finding a GCF (greatest common factor)
Both 5 and 15 shares 5 as a factor, so divide them both by 5.
Then you would get 1/3 or .33333333333333333...
A textile factory uses a 43 liter bucket of dye per 1 roll of fabric that is 1,067 feet long. If the factory has 4 buckets of dye, can it dye 5 rolls of fabric?
The factory has 172 litres of dye available.
What is litres?Liters (also spelled litres) is a unit of volume in the International System of Units (SI). It is commonly used to measure the volume of liquids, gases, and solids that can be poured or contained in a container. One liter is equivalent to 1000 cubic centimeters (cc) or milliliters (ml), and it is roughly equal to 1.057 quarts or 0.264 gallons.
In the given question,
First, we need to find out how much dye is needed for one roll of fabric. We know that 43 liters of dye are needed for 1 roll of fabric that is 1,067 feet long. Therefore, we can say that:
1 roll of fabric = 43 liters
1,067 feet
To find out how much dye is needed for 5 rolls of fabric, we can multiply both sides of this equation by 5:
5 rolls of fabric = 5 × 43 liters
1,067 feet = 215 liters
1,067 feet
So, 5 rolls of fabric would require 215 liters of dye.
Next, we need to check if the 4 buckets of dye are enough to dye 5 rolls of fabric. Each bucket contains 43 liters of dye, so 4 buckets would contain:
4 buckets of dye = 4 × 43 liters
= 172 liters
Therefore, the factory has 172 liters of dye available.
Since 215 liters of dye are required for 5 rolls of fabric, and the factory has only 172 liters of dye available, it cannot dye 5 rolls of fabric with the given amount of dye.
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coordinate points: (-5,-3),(-7,-11),(4,-13). give the coordinate of the fourth vertex
Answer:
(6,-5)
Step-by-step explanation:
Parallel lines have the same slope.
21. In the voting for City Council Precinct 5, only of all eligible voters cast votes. What fraction of all eligible voters voted for Shelley? Morgan? Who received more votes?
All eligible voters voted for Shelley= 3/20 ,
All eligible voters voted for Morgan= 31/100, Morgan received most votes.
What is mean by multiplication?Multiplication is a mathematical operation that embodies the basic idea of numerous additions of the same number. The outcomes of multiplying two or more numbers are referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplication facilitates the process of adding the same number again.
Let's suppose Precinct 5 has 100 registered voters. There were 50 voters who participated in the election because only 50% of those who were eligible to vote actually did so.
3/10 of the votes were cast for Shelley, which translated as 3/10 x 50 or 15 votes.
With 5/8 of the vote, Morgan received 5/8 x 50 votes, or 31.25 votes. Therefore, we must round this figure down to 31 votes as we are dealing with whole voters.
We must divide the number of votes received by the total number of eligible voters in order to determine the percentage of all eligible voters who cast a ballot for Shelley: 100 eligible voters x 15 votes = 3/20.
Morgan won the most votes since she received more than Shelley.
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Please help me find the arc!
Step-by-step explanation:
Find the 360° circumference of the circle ( pi * d) then you want 90 / 360ths of that
Radius = 10 mi then d = 20 miles
Circumference = pi * 20 = 20 pi miles
90 / 360 * 20 pi = 15.7 mi
24÷6+2×9 without using a calculator
Answer:
Step-by-step explanation:
[tex]24\div 6+2\times 9 =4+18=22[/tex]
÷ and × first followed by + and -. But otherwise work left to right.
Answer: 22
Step-by-step explanation:
1.) Solve using PEMDAS.
The height of a rectangular prism is 26 inches and its base is a rectangle with an area of 6 cubic inches. What is the volume of the prism in cubic inches?
Answer choices -
A. 112 in³
B. 72 in³
C. 156 in³
D. 36 in³
Answer:
The height of a rectangular prism is 26 inches and its base is a rectangle with an area of 6 cubic inches. What is the volume of the prism in cubic inches?
Step-by-step explanation:
The height of a rectangular prism is 26 inches and its base is a rectangle with an area of 6 cubic inches. What is the volume of the prism in cubic inches?
I need help with this please
Answer:
This is a guess but I think it's 5 min per table.
Step-by-step explanation:
The reason being:
if we know that she has 9 tables to get to and each table can seat 4 people, we would have to multiply both numbers to find how many TOTAL people are in the restaurant during the first few hours.
9x4 = 36 people in total
then, we need to convert 3hrs into minutes to get a more accurate rep as to how much time she would spend at each table (she isn't going to spend the entire 3 hrs with only one table now, is she?)
so for this, we convert 3hrs into minutes
1 min = 60 secs
1 hr = 60 minutes
3hrs -> 60 x 3 = 180 minutes
now, to understand how many time she spends at each table, we need to figure out by dividing the # of people by the amount of minutes.
180 minutes/36 people = 5 mins per table.
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.06
and a standard deviation of 1.52
. Using the empirical rule, what percentage of American women have shoe sizes that are between 6.54
and 9.58
?
An approximate of 68% of American women have shoe sizes that are between 6.54 and 9.58.
How can empirical rule be use to find the percentage?To use the empirical rule, we need to assume that the distribution of women's shoe sizes is approximately normal. Given a mean of 8.06 and a standard deviation of 1.52, we can standardize the values of 6.54 and 9.58 by subtracting the mean and dividing by the standard deviation:
Ζ1 = (6.54 - 8.06) / 1.52
Ζ1 = -1.00
Ζ2 = (9.58 - 8.06) / 1.52
Ζ2 = 1.00
The standardized values tell us that the value of 6.54 is 1 standard deviation below the mean, while the value of 9.58 is 1 standard deviation above the mean. According to the empirical rule, about 68% of the data falls within one standard deviation of the mean. Therefore, we can say that: [tex]P(6.54 < x < 9.58) = P(-1.00 < z < 1.00) = 68%[/tex]
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help I don't understand please show work
Calculate the quantity of heat absorbed by 70 g of water that warms from 30∘C to 90∘C.
Therefore, the quantity of heat absorbed by 70 g of water that warms from 30∘C to 90∘C is 17,645.6 J (joules).
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equals sign (=). The expressions on either side of the equals sign can contain numbers, variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.
Here,
The amount of heat absorbed by a substance can be calculated using the formula:
Q = mcΔT
where Q is the amount of heat absorbed, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. For water, the specific heat capacity is 4.184 J/g⋅K.
Using the given values, we can calculate the amount of heat absorbed as follows:
m = 70 g
c = 4.184 J/g⋅K
ΔT = (90 - 30)∘C = 60∘C
Q = mcΔT
Q = (70 g) x (4.184 J/g⋅K) x (60∘C)
Q = 17645.6 J
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Need help get it correct and get braì Liszt also need steps gl
According to the information, the volume of the three-dimensional rhombus is 61.92 cm³.
How to calculate the volume of the three-dimensional rhombus?The three-dimensional rhombus is a geometric solid in the shape of a prism whose lateral faces are rhombuses and the bases are parallelograms. To calculate its volume, the area of the base must be multiplied by the height of the prism.
In this case, the height of the prism is 3 cm and the dimensions of the base rhombus are 5.2 cm wide and 8 cm long. Since the rhombus has two diagonals of equal length, its area can be calculated using the formula (major diagonal x minor diagonal) / 2.
First, the length of the diagonals of the base rhombus must be calculated using the Pythagorean theorem, since its width and length are known:
major diagonal = √(5.2/2)^2 + 8^2 = √(13.04 + 64) = √77.04 = 8.78 cmminor diagonal = √(5.2/2)^2 + 3^2 = √(13.04 + 9) = √22.04 = 4.69 cmThen, the area of the base rhombus can be calculated:
area = (major diagonal x minor diagonal) / 2 = (8.78 cm x 4.69 cm) / 2 = 20.64 cm²Finally, the volume of the prism can be calculated:
volume = base area x height = 20.64 cm² x 3 cm = 61.92 cm³Therefore, the volume of the three-dimensional rhombus is 61.92 cm³.
Note: This question is incomplete. Here is the complete information:
Find the volume of the prism
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please explain hw you got the answer
For the given statements f(-x) = -4|x| - 5x^3 = -f(x), we can conclude that f(x) is an even function.
What is even and odd function?A function that fulfils f(-x) = f(x) for any x inside the function's domain is said to be even. The graph of an even function displays reflected y-axis symmetry geometrically. The even functions [tex]f(x) = x^2 and f(x)[/tex] = cos are two examples (x).
A function is considered odd if it meets the condition f(-x) = -f(x) for all x inside its domain. An odd function's graph displays origin rotational symmetry geometrically. Odd functions include such like [tex]f(x) = x^3 and f(x) = sin (x).[/tex]
The given function is [tex]f(x) = -4|x| + 5x^3.[/tex]
An even function is a function that satisfies f(-x) = f(x).
For the function:
[tex]f(-x) = -4|-x| + 5(-x)^3[/tex]
[tex]f(-x) = -4|x| - 5x^3[/tex]
[tex]f(x) = -4|x| + 5x^3[/tex]
Since[tex]f(-x) = -4|x| - 5x^3 = -f(x)[/tex], we can conclude that f(x) is an even function.
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Solve the inequalities. Show each solution as an interval on the number line. 23−x >19
Step-by-step explanation:
23-x >19
make x the coefficient by subtracting 23 from both sides
23-23 - x > 19 - 23
-x > -4
Divide both sides by -1, thus making the sign to change
-x / -1 > -4/-1
x < 4
Hannah invested $4,000 in a savings account that earned 2% interest compound quarterly.She determined that if she dose not withdraw or deposit any more money,the value of the account at the end of 3 years will be $4,244.83.What error did Hannah make in her calculations? What will the account balance be after 3 years?Explain.
Hannah made an error in her calculations by using simple interest instead of compound interest. To find the balance of a savings account with compound interest, you need to take into account the effect of compounding, where the interest earned is added to the principal and then earns interest as well.
To calculate the actual balance of the account after 3 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the ending balance of the account
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested
In this case, we have:
P = $4,000
r = 2% = 0.02
n = 4 (since interest is compounded quarterly)
t = 3
Plugging in these values, we get:
A = $4,000(1 + 0.02/4)^(4*3) = $4,493.72
Therefore, the actual balance of the account after 3 years with compound interest is $4,493.72.
Hannah's calculation of $4,244.83 was based on using the formula for simple interest, which only takes into account the initial investment and the annual interest rate, but not the effect of compounding.
Answer:
Her account balance after 3 years is $4,246.71
Step-by-step explanation:
In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations
Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.
Mathematically, the amount A earned on a compound interest is calculated as
A = P
where A is the account balance after the number of years which is what we want to know
P is the initial amount invested which is $4000
r is the interest rate which is 2%(2/100 = 0.02) according to the question
n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)
t is the number of years which is 3
We plug the values into the question;
A = 4000(1 + 0.02/4)^(3)(4)
A = 4000(1+0.005)^12
A = 4000(1.005)^12
A = $4,246.71
P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations
Paula Williams uses her vehicle primarily for pleasure. She has $50- deductible comprehensive, $50-deductible collision, 100/200 bodily injury, and $25,000 property damage coverage. Because of her excellent driving record, her driver-rating factor is 1.00. Her vehicle is classified as D, 14. What is her annual base premium? What is her annual premium?
1617.0 , is her annual premium.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
A = p(r)t,
where t = years that have passed,
A = amount of money after t years,
p = principal amount of money, and
r = rate of growth (interest plus 1)
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sin(alpha-beta), sina=(11)/(12)in the II quadrant, Cos(beta)=(15)/(17) in quadrant IV, sin(alpha-beta)=
Answer:
Step-by-step explanation:
To find sin(alpha-beta), we can use the trigonometric identity:
sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)
We are given that sin(alpha) = 11/12 in the second quadrant and cos(beta) = 15/17 in the fourth quadrant. We can use the Pythagorean theorem to find sin(beta):
sin^2(beta) + cos^2(beta) = 1
sin(beta) = sqrt(1 - cos^2(beta))
sin(beta) = sqrt(1 - (15/17)^2)
sin(beta) = sqrt(1 - 225/289)
sin(beta) = sqrt(64/289)
sin(beta) = 8/17 (since sin(beta) is positive in the fourth quadrant)
Now we can plug in the values we know into the identity:
sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)
sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)
We still need to find cos(alpha), which we can do using the Pythagorean identity:
sin^2(alpha) + cos^2(alpha) = 1
cos(alpha) = sqrt(1 - sin^2(alpha))
cos(alpha) = sqrt(1 - (11/12)^2)
cos(alpha) = sqrt(23/144)
Now we can substitute this value into the expression for sin(alpha - beta):
sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)
sin(alpha - beta) = (11/12)(15/17) - sqrt(23/144)(8/17)
sin(alpha - beta) ≈ 0.210
Therefore, sin(alpha - beta) is approximately equal to 0.210.
Need help on this question please!
please check the image and help
After answering the provided question, we can conclude that Mean = (13 + 13 + 11 + 10 + 8) / 5 = 11 for Condition 3 (Loud Noise). 2.28 is the standard expression deviation.
what is expression ?An expression in mathematics is a collection of representations, digits, and transnational corporations that imitate a statistical correlation or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, growing influence, division, but instead exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To compute the experiment summaries, we must first compute the mean and standard deviation for each condition:
Mean = (15 + 13 + 14 + 12) / 4 = 13.5 in Condition 1 (Low Noise).
1.5 is the standard deviation.
Mean = 19 in Condition 2 (Medium Noise).
3 is the standard deviation.
Mean = (13 + 13 + 11 + 10 + 8) / 5 = 11 for Condition 3 (Loud Noise).
2.28 is the standard deviation.
Condition 1 (Low Noise) Condition 2 (Medium Noise) Condition 3 (Loud Noise)
------------------------ --------------------------- ------------------------
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
| | | | | | | | | | |
------------------------ --------------------------- ------------------------
Median = 13.5 Median = 19 Median = 11
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Write an equation for each linear relationship. Describe the graph of the linear
relationship. State the slope and y-intercept.
Therefore , the solution of the given problem of equation comes out to be slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0).
Explain equation.Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could analyze data provided by y + 7, split 12 into two parts, and create y + 7.
Here,
This linear relationship's expression can be found by first determining the slope using the following formula:
=> slope = (y-change) / (change in x)
=> slope = (2 - (-2)) / (4 - 0) = 4/4 = 1
Consequently, the line's inclination is 1. We can now determine the equation using the point-slope form of a line's equation:
=> y - y1 = m(x - x1)
where (x1, y1) is a location on the line and m denotes the slope. We have a choice between the two points provided, so let's use (0, -2):
=> y - (-2) = 1(x - 0)
=> y + 2 = x
By taking 2 away from both edges, we arrive at:
=> y = x - 2
slope = (0 - (-4)) / (1 - (-3)) = 4/4 = 1
=> y - y1 = m(x - x1)
=> y - (-4) = 1(x - (-3))
=> y + 4 = x + 3
=> y = x - 1
A line with a slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0), represents the graph of this linear connection.
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You are given a t-statistic of -0.38. Write a short paragraph on whether the t-statistic means
that there are differences between two groups. It is up to you decide how to name the two groups
in your paragraph.
we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.
What is the t-statistic?
A t-statistic is a test statistic that is used to determine if there is a significant difference between two groups based on their means.
A t-statistic with an absolute value greater than 1.96 indicates statistical significance at the 0.05 level of significance.
In this case, the t-statistic is -0.38, which is less than the absolute value of 1.96.
This means that the difference between the means of the two groups is not statistically significant at the 0.05 level of significance.
Without information on the specific groups being compared, it is not possible to make definitive conclusions about the differences between them based solely on the t-statistic.
Hence, we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.
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Sheila manages a team of editors at a publishing company. To help determine deadlines, she developed a model based on past
projects. In the model below, x represents the number of pages which require editing, and y represents the total number of days required to complete the editing.
y = 1/85x
The linear equation that models the number of days it will take Sheila's team to edit x pages, y = (1/85)·x indicates that the correct statement is option C.
C. Her team can edit 85 pages in one day
What is the slope-intercept form of linear equations?The slope-intercept form of linear equations is; y = m·x + c, where the coefficient m is the slope and c is the y-intercept.
The parameters of the model, y = (1/85)·x are;
x = The number of pages that require editing
y = The number of days required to complete the editing
Therefore, the model is in the slope and intercept form of a linear equation, where;
1/85 = The slope
The y-intercept is zero
The slope indicates that 85 pages can be edited in one day, therefore the number of days to edit 170 (2 × 85) pages is 2 days
Similarly, when the number of days, y = 1, and the number of pages to be edited, x = 1, we get;
y = (1/85)·x
1 = (1/85)·x
x = 1/(1/85) = 85
The number of pages that can be edited in one day is 85 pages
The correct statement is therefore;
C. Her team can edit 85 pages in one day
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Sam is practicing long track speed skating at an ice skating rink. The distance around the rink is 250 yards. He has skated around the rink 7 times so far.
How many more yards does he need to skate around the rink to complete 3 miles?
Answer:
There are 1760 yards in one mile and the rink is 250 yard in perimeter.
This means 3 miles is 5280 yards.
If Sam has already gone around the whole rink 6 times, that means he was traveled a total of 1500 yards.
Sam has 3780 more yards to travel 3 miles.
This means he needs to do 15.12 more laps around the rink. Or 16 if you are rounding.
Mrs. Hernandez
minutes delivering
spends 41.25
mail in a
neighborhood. It takes her 10
minutes to deliver mail to her first five
houses. After that, it takes Mrs.
Hernandez 1.25 minutes to deliver
mail to each of the remaining
houses. Determine how many
houses still need their deliveries from
Mrs. Hernandez.
Answer:
30
Step-by-step explanation:
41.25-10=31.25
31.25/1.25=25
25+5=30
Hope this helps!
Last year the city of Goose Pimple, Vermont, paid an average of $3,261 per employee in health care costs (including insurance and additional claims). This year the city management decided that they will contract with Grimms Health Maintenance Organization. At the end of the year they would like to know if they have saved any money. They take a sample of 50 and find a sample mean of $3,015 with a standard deviation of $1,745. Present a hypothesis, a null hypothesis, and evaluate the hypothesis.
The answer of the given question based on the hypothesis the answer is the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis.
What is Hypothesis?A hypothesis is an educated guess or prediction that is used to explain an observation or set of observations. It is a proposed explanation or possible answer to a research question or problem that is based on prior knowledge, experience, and research. In science, a hypothesis is often tested through experiments or observations to determine if it can be supported or rejected by the evidence.
Hypothesis:
The city of Goose Pimple, Vermont, hypothesizes that contracting with Grimms Health Maintenance Organization will result in a significant reduction in health care costs per employee.
Null Hypothesis:
The null hypothesis is that there is no significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.
Evaluation:
To evaluate the hypothesis, we will perform a one-sample t-test. The test statistic is calculated as:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Assuming a significance level of 0.05, we will reject the null hypothesis if the calculated t-value is greater than the critical t-value.
Population mean = $3,261 (given)
Sample mean = $3,015
Sample standard deviation = $1,745
Sample size = 50
t = (3015 - 3261) / (1745 / sqrt(50)) = -2.58
Using a t-table with 49 degrees of freedom (sample size - 1) and a significance level of 0.05, the critical t-value is ±2.009.
Since the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis. This means that there is not enough evidence to suggest that there is a significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.
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Sketch the algebra-tile shape at right on your paper. Write an expression for the perimeter of the shape. Then find the perimeter for each of each of the given values of x.
A sketch of the algebra-tile shape is shown in the image attached below.
An expression for the perimeter of the shape is 4x + 4.
The perimeter for each of the given values of x are 32 units, 26 units, and 13.33 units respectively.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangular shape can be calculated by using this mathematical expression;
P = 2(L + B)
Where:
P represent the perimeter of a rectangle.B represent the breadth of a rectangle.L represent the length of a rectangle.Based on the sketch of the algebra-tile shape, an expression for its perimeter is given by:
Perimeter of the shape = 4x + 4
When x = 7 units, the perimeter of the shape can be calculated as follows;
Perimeter of the shape = 4(7) + 4
Perimeter of the shape = 32 units.
When x = 7 units, the perimeter of the shape can be calculated as follows;
Perimeter of the shape = 4(5.5) + 4
Perimeter of the shape = 26 units.
When x = 7 units, the perimeter of the shape can be calculated as follows;
Perimeter of the shape = 4(7/3) + 4
Perimeter of the shape = 13.33 units.
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Jason conducted a survey amongst his friends to determine the amount of hours they watch TV each week. Here is the table that Jason found.What statement is NOT true about the frequency chart?
Only 3 people did not watch TV each week.
The largest group of people were the ones who watched 1 hour per week.
70% of the people spent less than 1 hour watching TV a week
30% watch 2 hours or more on TV a week
The incorrect statement is Only 3 people did not watch TV each week.
What is the frequency?
The frequency of a repeated event is its number of instances per unit of time. It differs from angular frequency and is sometimes referred to as temporal frequency for clarification. One event occurs per second when measuring frequency in hertz.
Here, we have
Given: Jason conducted a survey among his friends to determine the number of hours they watch TV each week.
We have to determine which statement is NOT true about the frequency chart.
We concluded that the incorrect statement is Only 3 people did not watch TV each week.
Hence, the incorrect statement is Only 3 people did not watch TV each week.
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If mWC = 108° and m/U = 37°, find mLQ.
The measure of angle mLQ is 125°. we got the answer with the concept of inscribed angle in the figure .
what is inscribed angle?
An inscribed angle is an angle formed by two chords in a circle that have a common endpoint on the circle. In other words, the endpoints of the angle are on the circle, and the angle "opens up" inside the circle. The measure of an inscribed angle is equal to half the measure of the arc that it intercepts.
In the given question,
We know that the measure of angle mWC is 108° and the measure of angle m/U is 37°. Since angle QCU is an inscribed angle that intercepts arc CQ, its measure is equal to half the measure of arc CQ. Similarly, angle LUW is an inscribed angle that intercepts arc WL, so its measure is equal to half the measure of arc WL.
We can use these facts to set up the following equation:
mLQ = (mCQ / 2) + (mWL / 2)
We can find the measures of arcs CQ and WL by subtracting the measures of angles QCU and LUW from 360°, respectively. Therefore:
mCQ = 360° - 2mQCU
= 360° - 2(mWC - m/U)
= 360° - 2(108° - 37°)
= 182°
mWL = 360° - 2mULW
= 360° - 2(m/U + mWC)
= 360° - 2(37° + 108°)
= 68°
Substituting these values into the equation for mLQ, we get:
mLQ = (mCQ / 2) + (mWL / 2)
= (182° / 2) + (68° / 2)
= 125°
Therefore, the measure of angle mLQ is 125°.
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