+----------------+
| 0 | 1 | -1 |
+-----+-----+-----+
| 2 | -2 | 3 |
+-----+-----+-----+
| -3 | 4 | -4 |
+-----+-----+-----+
o o
The zero pairs are (-2, 2) and (-4, 4), and I've circled them in the model above.
To draw a model using integer chips and circle the zero pairs, start by laying out the positive and negative integer chips side by side in a line. The negative numbers should be on the left and the positive numbers should be on the right. Next, take a second line of chips, also with negative numbers on the left and positive numbers on the right, and arrange it so that the chips on the first line line up with the corresponding chips on the second line. For example, the negative 3 chip on the first line should be paired with the positive 3 chip on the second line. The same should be done for all other chips. Finally, circle any pairs of chips where the sum of the two numbers is equal to 0. This will indicate that they are zero pairs.
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2. The tables show the saturated fat content, in grams, of pizzas sold by two regional chains.
Marcello's Pizza
17 12 10 8 8 10 10 5 16 16
12 15 7 11 11 13 13 11 12 8
Pizza a Go-Go
98
7 11 9 10 8 139
12 13 6 11 10 8
Several students want to test the null hypothesis that there is no difference between the saturated
fat content in the pizza of these chains. Using a significance level of 0.05, which of the following
displays the correct test statistic, P-value, and conclusion?
(1 point)
Answers provided in image
The cοrrect answer is οptiοn B, t-statistic =1.841, p-value= 0.0748 there is nοt suffient evidence tο reject the null hypοthesis.
What is null hypοthesis?The null hypοthesis is a sοrt οf suppοsitiοn used in statistical tests, which are fοrmal prοcedures fοr drawing inferences οr taking judgements based οn evidence. Based οn a sample οf the pοpulatiοn, the hypοtheses are suppοsitiοns regarding a statistical mοdel οf the pοpulatiοn. In οrder tο distinguish between statistical nοise and scientific claims, tests, which are fundamental cοmpοnents οf statistical inference, are frequently utilised in the interpretatiοn οf scientific experimental data.
The null hypοthesis is the prοpοsitiοn under cοnsideratiοn in a test οf statistical significance. Tο evaluate the strength οf the evidence cοntradicting the null hypοthesis, the significance test is used. A claim οf "nο effect" οr "nο difference" is the null hypοthesis. Frequently, H0 is used tο represent it. The alternative hypοthesis is the assertiοn being examined in relatiοn tο the null hypοthesis. Included are symbοls H1 and Ha.
Marcellο's Pizza, Mean – 11.25, Varience- 10.1974, Standard deviatiοn – 3.1933, n- 20
Pizza a Gο-Gο, Mean – 9.6, Varience – 4.4, Standard deviatiοn – 2.0976 , n – 15
H0 - u1=u2 , Ha – u1≠u2
Test Statistics =(11.25-9.6)/ (√ {(3.1933 ×3.1933)÷20}+√{(2.097×2.097)÷15 }
=1.841
P-value = 2p (±≥1.841) ≈0.0748>0.05
Sο there is nοt sufficient evidence tο reject the null hypοthesis.
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The following table shows the number of attendees at each of the private dance events hosted by Fenel Arrangements.
Event Martha's Moonwalk Shirly's Shimmy Harry's Hoedown
# 48 33 ?
If the mean of the data set is 41 attendees, find the number of attendees at Harry's Hoedown
The number οf attendees at Harry's Hοedοwn is 42.
What is data set?A data set is a cοllectiοn οf cοnnected data. In the case οf tabular data, a data set is assοciated with οne οr mοre database tables, where each rοw alludes tο a particular recοrd in the assοciated data set and each cοlumn tο a particular variable.
Suppοse the number οf Harry's Hοedοwn attendees be "x"
Given, Mean οf the data = 41 attendees
We knοw,
Mean = sum οf οbservatiοns / number οf οbservatiοns
41 = (48+33+x) / 3
48 + 33 + x = 123
x = 123 - (48+33)
x = 42
Hence the correct answer is 42 attendees.
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Answer:
42
Step-by-step explanation:
A crow is holding a 0.11 kg clam above a rocky beach from a height of 11.5 m. What is the potential energy clam?
(show work please!!)
Answer:
The potential energy (PE) of an object is given by:
PE = mgh
where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s² near the Earth's surface), and h is the height of the object above a reference level.
In this case, the mass of the clam is 0.11 kg, the height above the beach is 11.5 m, and the acceleration due to gravity is 9.8 m/s². Therefore, the potential energy of the clam is:
PE = (0.11 kg) × (9.8 m/s²) × (11.5 m) ≈ 12.7 J
So the potential energy of the clam is approximately 12.7 Joules.
The function f(x)=4x-8 is reflected accross the y axis resulting in a new function write the equation of g(x)
a youth basketball team is made up of 7 girls and 6 boys. the coach assigns five players at a time to specific positions. how many ways can the thirteen players be assigned to the five different positions? provide your answer below:
After using the npr formula, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.
There are a total of 13 players on the youth basketball team, and there are five different positions that need to be filled. To determine the number of ways that the players can be assigned to these positions, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of players, and r is the number of positions. In this case, n = 13 and r = 5. Plugging these values into the formula, we get:
P(13, 5) = 13! / (13 - 5)!
= 13! / 8!
= (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= (13 * 12 * 11 * 10 * 9) / 1
= 154440
Therefore, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.
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20. What is the value of x to the nearest tenth? The diagram is not drawn to scale. (1 point)
x
x=14.4
x 12.7
x=3.0
x=2.2
Using similar triangle theorem, to calculate the ratios of the length, the value of x is 14.4 units
What is similar triangle theoremThe similar triangle theorem, also known as the AA (angle-angle) similarity theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar. That is, the corresponding sides of the triangles are in proportion, and the ratios of the corresponding sides are equal. In other words, if ΔABC ~ ΔDEF, then:
AB/DE = BC/EF = AC/DF
This theorem can be used to solve problems involving similar triangles, such as finding unknown side lengths or angles.
To find the value of x, we need to apply similar triangle theorem.
Taking the ratios of sides from the two triangles;
13.5 / 6.2 = x / 6.6
Cross multiply both sides and solve for x
x = (13.5 * 6.6) / 6.2
x = 14.4 units
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The height of a basketball thrown by a 6 foot tall man follows a path defined by the function h(x) = -0. 5x^{2} + 3x + 6 h(x)=−0. 5x2+3x+6, where x is the horizontal distance from where it is thrown. How far away from the basket should the player stand in order for the ball to go in the basket (10 feet high) on its way down? Show all work
Answer:
Step-by-step explanation:
Multiply both sides by 2.
Splitting the middle term, we get
In the given function the leading coefficient is negative, so the given function represents a downward parabola. It means, first the function is increasing after that the function is decreasing.
So, the value of the function is 10 at (its way up) and at (its way down.
Therefore, the player should stand 4 units away from the basket in order for the ball to go in the basket (10 feet high) on its way down.
HELP PLEASE
its math
Thank you
Answer:
Option 2
Step-by-step explanation:
For two angles to be adjacent they need to have a common side/ray and a common vertex!
Hope this helps!!!
Answer:
Step-by-step explanation:
In geometry, two angles are adjacent if they have a common side and a common vertex. In other words, adjacent angles are directly next to each other and do not overlap.
->No, the two indicated angles do not share common vertex
meters and feet are two different scales for measuring distance. Five meters is approximantly 16.41 ft, and 12 m is approximently 39.37ft. write an equation that shows the approximate distance in feet as a function of the distance in meters
Step-by-step explanation:
16.41 ft / 5 m = 'unit rate' (or conversion factor) = 3.282 ft/ m
then # ft = 3.282 ft / m * # meter (approximately )
Suppose you compile all possible samples 100 children of preschool age your school district; the expected value of (when 100) will be equal the expected value for all of the possible samples of. 25 children of preschool your schoc district- The standard error for this distribution of samples wihen 100 will be equal The standard rror for all the possible samples 100 possible samples of 25, You predict the size the standard error of sample size 25 because the standard error of M for all of the sample size of 100 relative to You #crcinterested Mucn tme childmen Spcnd actually compie possinie %mnblee sibling? weekends among thls population - 2,431 certain slzer children
You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the sampling distribution.
Suppose you compile all possibilities samples of 100 children of elementary school age in your school district; the expected value of M (when n = 100) will be equal to the expected value of M for all of the possible samples of 25 children of elementary school age in your school district.
1. All possible samples of 100 children of elementary school age in your school district; the expected value of M (when n = 100) is 11.03 the expected population mean:
E(μ) = 11.03
2. The standard error of M for this distribution of samples when n = 100 will be equal to 1.964
σ/√n = 19.64/ √100 = 1.964
3. The standard error of M for all the possible samples of 100 is twice (2 times) the standard error of M for all of the possible samples of 25.
σ/√n= 19.64/√25 = 3.928 = 2( σ/√n = 19.64/√100=1.964)
4. As both the sample has a same population with different sample size, therefore we can predict the standard error on the basis of sample observation. large sample size lower stanadrd error and vice versa.
If you were interested in how much time children spend reading on weekdays among this population of 2, 431 children, would you actually compile all possible samples of a certain size, Option: No
5. If we are traying to know the reading habit of 2431 children, we do not actually compile all possible sample rather we use some specific sample on the basis of sampling distribution.
You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the sampling distribution.
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Q: Suppose you compile all possible samples of 100 children of preschool age in your school district; the expected value of M (when n = 100) will be equal to the expected value of M for all of the possible samples of 25 children of preschool age in your school district. The standard error of M for this distribution of samples when n = 100 will be equal to The standard error of M for all the possible samples of 100 is the standard error of M for all of the possible samples of 25. You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the If you were interested in how much time children spend with siblings on weekends among this population of 2,431 children, would you actually compile all possible samples of a certain size? ОО Yes No
4.02 Lesson check ! (3)
The given sequence 22, 12, 2, -8 is arithmetic, and the common difference is -10.
How to determine if the sequence is arithmetic?An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference, and if k is that common difference, we can write the recursive formula as:
a(n) = a(n - 1) + k
Here we have the sequence:
22, 12, 2, -8
Taking the differences between consecutive terms we get:
12 - 22 = -10
2 - 12 = -10
-8 - 2 = -10
The differences are all equal, then this is an arithmetic sequence, and the common difference is -10.
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For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. 32.f(x)=x3−2x2−29x−423x2−7x−20
From the given data, the vertical intercept, vertical asymptotes and slant asymptote are 2, -5/3 and 4, y = x² - 5x + 13 respectively.
To find the horizontal intercepts, we need to set f(x) = 0 and solve for x:
x³ - 2x² - 29x - 42 / (3x² - 7x - 20) = 0
We can factor the denominator using the quadratic formula:
3x² - 7x - 20 = (3x + 5)(x - 4)
Now, we can write the function as:
f(x) = (x³ - 2x² - 29x - 42) / (3x + 5)(x - 4)
To find the vertical intercept, we need to set x = 0:
f(0) = -42/(-5)(-4) = 2.1
To find the vertical asymptotes, we need to find the values of x that make the denominator equal to zero:
3x + 5 = 0 or x - 4 = 0
Solving for x, we get:
x = -5/3 or x = 4
Therefore, the vertical asymptotes are x = -5/3 and x = 4.
To find the horizontal or slant asymptote, we need to look at the degree of the numerator and denominator. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, there is a slant asymptote, which we can find by dividing the numerator by the denominator:
x³ - 2x² - 29x - 42 / (3x + 5)(x - 4) = (x² - 5x + 13) + (-2x - 2) / (3x + 5)(x - 4)
The slant asymptote is the line y = x² - 5x + 13.
Now, we can sketch the graph of the function. The graph will approach the vertical asymptotes at x = -5/3 and x = 4. The function will intersect the x-axis at x = -2, x = 3, and x = 7. The function will intersect the y-axis at y = 2.1. The graph will approach the slant asymptote y = x² - 5x + 13 as x approaches infinity or negative infinity.
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Whoever gives a step by step explanation gets brainliest!
Answer: 54 cubic yd^2
Step-by-step explanation: The volume formula for a cube is [tex]s^3[/tex] where s represents a side length.
To get the side length to solve for the surface area just do
[tex]\sqrt[3]{27} =3[/tex]
Which means that the side length is equal to 3
Now plug it into the surface area formula [tex]6s^2[/tex]
[tex]6(3)^2[/tex]
[tex]6(9)\\[/tex]
=54!
Answer:
54 yards^2
Step-by-step explanation:
Volume of a cube = side x side x side or [tex]s^3[/tex]
[tex]s^3 = 27yards^3[/tex]
s = [tex]\sqrt[3]{27}[/tex]
s = 3
Surface Area of a cube = A [tex]= 6 * s^2[/tex]
= [tex]6 * (3)^2[/tex]
= [tex]6 * 9[/tex]
=[tex]54[/tex][tex]yards^2[/tex]
Hope this helps!
Brainliest is much appreciated.
Solve each system of equations:
1. Y = x2
y = 4x - 4
solution:
2. Y = -x2 + 2x - 4
y = 3x - 2
solution:
3. Y = x2 - 3x - 5
y = -2x + 1
solution:
1) The solution is (2, 4).
2) The solutions are (-1, -5) and (2, 4).
3) The solutions are (3, -5) and (-2, 5).
1) Y = x^2 and y = 4x - 4
Substitute y from the second equation into the first equation to get:
x^2 = 4x - 4
Simplifying and rearranging:
x^2 - 4x + 4 = 0
(x - 2)^2 = 0
x = 2
Substitute x = 2 into the second equation to get:
y = 4(2) - 4 = 4
Therefore, the solution is (2, 4).
2) Y = -x^2 + 2x - 4 and y = 3x - 2
Substitute y from the second equation into the first equation to get:
-x^2 + 2x - 4 = 3x - 2
Simplifying and rearranging:
-x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1 or x = 2
Substitute x = -1 into the second equation to get:
y = 3(-1) - 2 = -5
Substitute x = 2 into the second equation to get:
y = 3(2) - 2 = 4
Therefore, the solutions are (-1, -5) and (2, 4).
3) Y = x^2 - 3x - 5 and y = -2x + 1
Substitute y from the second equation into the first equation to get:
x^2 - 3x - 5 = -2x + 1
Simplifying and rearranging:
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3 or x = -2
Substitute x = 3 into the second equation to get:
y = -2(3) + 1 = -5
Substitute x = -2 into the second equation to get:
y = -2(-2) + 1 = 5
Therefore, the solutions are (3, -5) and (-2, 5).
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Which line is perpendicular to the line y = -3x + 2
Answer:d
Step-by-step explanation:
The graphs below show the speed of a car over four different time periods. Which graph indicates the car slowing down and then stopping?
Answer:
(D)
Step-by-step explanation:
You want the graph that shows speed decreasing to zero.
Slowing"Slowing down" means speed is decreasing. On a graph of speed that is indicated by a negative slope.
StoppedWhen an object is stopped, its speed is zero. On a graph of speed, points on the horizontal axis indicate the speed is zero.
GraphThe attached graph shows the speed of a car that is slowing to a stop.
Select the correct answer.
Suppose Jared makes a down payment to obtain a loan for a new car. Which statement is true?
Interest charged for the loan will be calculated based on the price of the car minus the down payment.
Interest charged for the loan will be calculated based on the price of the car plus the down payment.
Jared won’t be charged interest on the loan because he made a down payment.
Interest charged for the loan will be calculated based on the price of the car, regardless of the down payment.
Answer:
Interest charged for the loan will be calculated based on the price of the car minus the down payment.
Step-by-step explanation:
Plato
A small country emits 150,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 0.5% per year for the next 5 years. In the first year of the agreement, the country will keep its emissions at 150,000 kilotons and the emissions will decrease 0.5% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 5 year period, to the nearest whole number?
Rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.
What is percentage ?Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". For example, 50% is equal to 50/100, which simplifies to 0.5. Percentages are often used to express proportions or ratios in a way that is easier to understand. For instance, if there are 20 red balls and 80 blue balls in a bag, we could say that the ratio of red balls to blue balls is 1:4, or we could express this as a percentage by saying that 20% of the balls are red and 80% are blue.
According to given information :To calculate the total carbon emissions over the 5-year period, we need to calculate the emissions for each year and then add them up.
Starting with the current emission level of 150,000 kilotons, the emissions in each of the next 5 years will be:
Year 1: 150,000 kilotons (no reduction)
Year 2: 150,000 * (1 - 0.005) = 149,325 kilotons
Year 3: 149,325 * (1 - 0.005) = 148,654 kilotons
Year 4: 148,654 * (1 - 0.005) = 147,987 kilotons
Year 5: 147,987 * (1 - 0.005) = 147,323 kilotons
To get the total emissions over the 5-year period, we add up the emissions for each year:
150,000 + 149,325 + 148,654 + 147,987 + 147,323 = 743,289 kilotons
Therefore, rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.
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Answer:742537
Step-by-step explanation: I did the math, and this is the correct answer
(Explain) the probability of the following event happening: rolling a 9 on a number cube with sides labeled 1-6.
Choose one of the following:
impossible, less likely, somewhat likely, highly likely, or certain
Answer:
Step-by-step explanation:
Impossible. Using simple logic skills, the only possible outcomes from rolling a dice are 1,2,3,4,5,6. Hence, rolling a 9 is an impossible outcome.
If the bunny ran from −81 to 81 with average speed of 18 units per minute then, the distance is ?
units and it ran for ?
minutes.
Answer:
162 and 9
Step-by-step explanation:
The distance he ran for is from - 81 to 0 and to 81
81 +81 = 162 units
Time spent =distance/speed
Time = 162/ 18 = 9mins
Find the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker. The probability is (Round to six decimal places as needed.)
The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.
The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is given by 0.0032. Probability is a concept of Mathematics. It is a measure of the likelihood of an event taking place. The concept of probability is very essential in the study of Mathematics. It helps us in determining the chance of occurrence of an event.What is the formula for probability?The probability of an event is represented by a number between 0 and 1. A probability of 0 indicates that the event is impossible while a probability of 1 indicates that the event is certain to happen.
The formula for probability is given by;Probability (P) = Number of favourable outcomes/ Total number of outcomes.The given event is to find the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker.In a deck of cards, there are 13 clubs. Out of these, we have to select 4 cards. This can be done in (13C4) ways. Similarly, one card can be chosen from each of the remaining three suits. This can be done in (13C1) * (13C1) * (13C1) ways.
Therefore, the total number of ways in which we can choose 7 cards is given by (52C7).Thus, the required probability is given by;Probability = Number of favourable outcomes/ Total number of outcomes.Number of favourable outcomes = (13C4) * (13C1) * (13C1) * (13C1)Total number of outcomes = (52C7)Probability = Number of favourable outcomes/ Total number of outcomes= [(13C4) * (13C1) * (13C1) * (13C1)]/ (52C7)= 0.0032 (rounded to 6 decimal places).Therefore, the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.
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The value of a second-hand car is £8000
Each year it loses 20% of it value at the start of this year. work out its value an year ago
pls pls help quick
Answer:
£10,000
Step-by-step explanation:
100%-20%= 80% --> 0.8
£8000 divided by 0.8 = £10,000
On his 25th birthday, Matthew started an annuity for his retirement. He deposits $630 each month into an account earning 8% annual interest compounded monthly. He determines that he will be able to retire once he has $1,000,000 in his retirement account. Determine how old Matthew will be when he is able to retire.
Matthew who started an annuity on his 25th birthday by depositing $630 monthly into an account earning 8% annual interest compounded monthly will become 55 years old when the retirement account will be $1,000,000.
What is an annuity?An annuity involves a series of payments made periodically.
The annuity attracts an interest rate compounded periodically.
Compounding involves charging interest on accumulated interest and the principal for each compounding period.
I/Y (Interest per year) = 8%
PV (Present Value) = $0
PMT (Periodic Payment) = $630
FV (Future Value) = $1,000,000
Results:
N = 368.641 months
= 30 years and 9 months
Sum of all periodic payments = $232,470
Total Interest = $767,530
Matthew's current age = 25 years
55 years old (25 + 30)
Thus, Matthew will be 55 years old when his retirement (annuity) account grows to $1,000,000.
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Sam and terry contribute money to buy 2 litre tub of juice in the ratio of 2:3 calculate the amount of juice each one received after sharing in the ratio of 2:3
Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in the ratio of 2:3.
To solve this problem, we need to use the concept of ratio and proportion.
Let's first find the total amount of money contributed by Sam and Terry. Since the ratio of their contributions is 2:3, we can write:
Total contribution = Sam's contribution + Terry's contribution
Let's assume that Sam contributed $2x and Terry contributed $3x. Then, we have:
Total contribution = $2x + $3x = $5x
Now, we know that the total contribution is equal to the price of the juice, which is not given in the problem. So, let's assume that the price of the 2-litre tub of juice is $10. Then, we have:
Total contribution = Price of juice = $10
Therefore,
$5x = $10
Solving for x, we get:
x = $2
So, Sam contributed $4 and Terry contributed $6.
Now, to find the amount of juice each one received, we need to share the 2-litre tub in a ratio of 2:3.
The total ratio is 2+3 = 5.
So, Sam will receive 2/5 of the juice and Terry will receive 3/5 of the juice.
Therefore, Sam will receive (2/5) × 2 litres = 0.8 litres of juice, and Terry will receive (3/5) × 2 litres = 1.2 litres of juice.
In conclusion, Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in a ratio of 2:3.
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7. (01. 03 MC)
Stephen's current hourly pay is $9. 45. If he receives a 5% hourly pay increase each year, what will his hourly pay be in two years? (4 points)
O $9. 92
O $10. 25
$10. 42
O $11. 00
Stephen's hourly pay will be $10.42 in two years, calculated by plugging the principal amount of $9.45, the rate of interest of 5%, and the number of times interest is compounded per year of 1 into the compound interest formula.
Stephen's current hourly pay is $9.45. In order to calculate his hourly pay in two years time, we need to use the compound interest formula. The formula is A = P (1 + r/n)^nt, where A is the amount after n years, P is the principal or initial amount, r is the rate of interest, and n is the number of times interest is compounded per year. In this case, the principal is $9.45, the rate of interest is 5%, and the number of times interest is compounded per year is 1. Plugging these into the formula yields A = 9.45(1 + 0.05/1)^2*1, which equals $10.42. That means Stephen's hourly pay will be $10.42 in two years.
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Please I need help. Using y=k/x, you get k=1.5. So applying this, the first two are correct and in inverse proportion, however the last one doesn’t seem to work. Please help
Answer:
The last one doesn't work because s and t aren't inversely proportional. If they were inversely proportional, k would remain constant.
Willie’s Widgets has created a demand function for its widget, where q is the quantity demanded and p is the price of one widget.
Q = -112p + 4,500
Let E = 3.00q + 18,000, and find the total expense if 2 widgets are produced.
The total expense for producing 2 widgets is $18,006.00.
How to find the total expense for producing 2 widgets?To find the total expense for producing 2 widgets, we need to find the total revenue from selling 2 widgets and then subtract the total expense of producing them.
The total revenue from selling 2 widgets is simply the price per widget times the quantity demanded at that price. Since the price is not specified in the problem, we can use the demand function to find it.
We know that the quantity demanded when 2 widgets are produced is:
q = 2
So we can solve the demand function for p:
q = -112p + 4,500
2 = -112p + 4,500
-112p = -4,498
p ≈ 40.16
Therefore, the price per widget is approximately $40.16.
The total revenue from selling 2 widgets at this price is:
revenue = price × quantity demanded
revenue = $40.16 × 2
revenue = $80.32
Now we need to find the total expense of producing 2 widgets. The problem gives us an expression for the total expense:
E = 3.00q + 18,000
Substituting q = 2, we get:
E = 3.00(2) + 18,000
E = $18,006.00
Therefore, the total expense for producing 2 widgets is $18,006.00.
Finally, we can calculate the profit as the difference between the revenue and the expense:
profit = revenue - expense
profit = $80.32 - $18,006.00
profit ≈ -$17,925.68
Since the profit is negative, Willie's Widgets would not make any profit from producing 2 widgets at this price. They would lose money.
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8. Theo went to a bakery on Saturday morning. He bought a cup of hot chocolate and some bagels. The hot
chocolate cost $3.50 and each bagel costs $0.75 each.
(a) Write a linear function, that models the total cost, c, in dollars, of Theo's order based on the number of
bagels, b, he buys.
(b) Explain what the statement below means in the context of the problem.
c(6)=8
a) The total cost, c, in dollars, of Theo's order based on the number of
bagels, b, he buys is: c = 0.75b + 3.5
b) The statement c(6) = 8 represents that the number of bagels bought was 6 which resulted in a total cost of $8
How to solve Linear Equation Word Problems?The general expression for a linear equation in slope intercept form is:
y = mx + b
Where:
m is slope
b is y-intercept
a) Let the number of bagels bought be b
Cost of each bagel = $0.75
Cost of chocolate = $3.50
Thus:
Total cost is:
c = 0.75b + 3.5
b) c(6)=8
This means the number of bagels bought was 6 which resulted in a total cost of $8
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Use the central limit theorem(CLT) to compute the expected amount of sampling error with a sample size of 25 for the population with a mean of μ= 16 and a standard deviation of σ= 5 show work.
The expected amount of sampling error with a sample size of 25 is 1.
The Central Limit Theorem (CLT): What is it?According to the Central Limit Theorem (CLT), a statistical theory, regardless of the population distribution's form, the distribution of sample means tends to resemble a normal distribution as sample size grows. This indicates that the distribution of the means of multiple samples of the same size taken from a population will be roughly normal. Since it enables us to utilise normal distribution features to draw conclusions about a population even when the population distribution is unknown or non-normal, the CLT is crucial to statistics.
Given that, μ= 16 and σ= 5.
The formula for the standard error of the mean (SEM) is:
SEM = σ / √(n)
SEM = 5 / √(25)
SEM = 1
Hence, the expected amount of sampling error with a sample size of 25 is 1.
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For what value of C is the function one-to-one?
(1,2) (2,3) (3,5) (4,7) (5,11) (6,C)
For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.
The basic definition of a one-to-one function is the mapping of two sets. If each element in the range of a function g matches precisely one in the domain of g, then the function g is one-to-one. 1-1 is another way to represent one-to-one. A function or formula, such as f() connects the values of two variables in such a way that the values of the first variable's elements determine the values of the second variable in exactly the same ways.
We have:
{(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)}
We can see the number of the 2nd position is prime and in sequence so, we can easily determine that 2, 3, 5, 7, 11, and next will be 13.
For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.
When every element in a function's range and domain match exactly one another, the function is said to be one-to-one. 1-1 is also used to indicate one-to-one. A function or formula, such as f() links the elements and values of one variable to those of another in such a way that the elements of the first variable exactly predict the elements of the second variable.
The complete question is-
For what value of c is the function one-to-one?
{ (1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c) }
a)2
b) 5
c)11
d)13
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