The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to 2 decimal places
Answers
Answer:
Step-by-step explanation:
We'Re looking at a normal distribution here- let's start by drawing it out to the mean me- is 315 grams standard. Deviation is 16 point. We want to know the weight corresponding to each of these events and we can use either the appendix which i assume is a z, school table or excel so the first 1. We want the highest 20 percent up here somewhere. This is what we would call the 80 percent. It separates the bottom 80 percent from the highest 20 percent. So how do we work the well? We need to start by getting the z score for it. So how do we get that, while in excel you're going to use the norm inverse function which looks like this? So it's calls norm and then in here you just put in x, where x is your percentage and that will spit out the z score and i'm using this rather than a table, because it will give me a more exact value. So we're going to do that, and so here the percent is the 80, so it's not .8 and that spits out the z score of nort .8416 to 4 decimal places. But i'm always going to this exact score, because we now have to turn it from a z score to a piece of real data. Z score is a measure of how many standard deviations away from the mean a value is so we're. Looking for the value not .84 standard deviations, above the mean or if we write it like this x, is equal to z, sigma plus mu. So here we take our exact zedscore, because we can still just use excels, multiply it by 16 and add it on to the mean and we'll get our value of 328.447328 .47 grams to 2 decimal places for part b. We want to be middle 60 percent. Now we need to cut off points and within here where, in this interval we have 60 percent of values, which means we have 40 percent of values, not in here. So we can label our 3 sections. These 2 add up to 40 percent, so they have to be 20 percent. Each are called nor .2 and not .2, and then this middle bit here is nor .6 for the total of 100 percent point. So we need these cut off points when you, the z, scores first, and because these are equal distances away from a mine they're going to have the same z score. Just 1 is going to be positive or negative, so z is going to be equal to plus and minus. Let'S look at the lower 1. This is the 20 percent here so into this excel command. We put 20 percent nor .2 and out of it we get the z score of minus, not .8416. So it's actually very similar to the top question, because the top question asked you for the 80 percent be 80 percent. Is the upper cut off point here? 20? Is below cutoff point, so we already have the up 1, let's just calculate below 1, so we've got to be minus, nor .8416 multiplied by 16, but the standard deviation and on to the mean- and we get 301.53 and the upper cut off point is from part A so that's the middle 60 percent makes more space a part c. We want to be highest 80 percent. So now what we want is the cut off between the lowest 20 and the highest 80, which we've just got from part c part b. It'S this lower 1, here, 301.53 grams. That'S an easy! 1! Now we want the lowest 15 percent, so the lowest 15 percent is the 15 percent. So we go to our exylgamant put in the 15 for percent, so that would be no .15 and it's a z score of minus 1.036 keeping the exact value put into this formula. We multiply our z by 16, as on 315, to get 298.42 grams.
The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.
What is normal distribution?To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:
z = (x - μ) / σ
where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).
Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:
x = μ + z * σ
where z is the z-score that corresponds to the desired probability.
Event 1: The weight is less than 345 grams.
z = (345 - 360) / 9 = -1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.
x = 360 + (-1.67) * 9 = 344.03 grams
Therefore, the weight that corresponds to this event is approximately 344.03 grams.
Event 2: The weight is between 355 and 365 grams.
First, we need to find the z-scores that correspond to the two boundaries:
z1 = (355 - 360) / 9 = -0.56
z2 = (365 - 360) / 9 = 0.56
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:
0.7123 - 0.2123 = 0.5
x1 = 360 + (-0.56) * 9 = 355.16 grams
x2 = 360 + (0.56) * 9 = 364.84 grams
Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.
Event 3: The weight is greater than 375 grams.
z = (375 - 360) / 9 = 1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.
x = 360 + (1.67) * 9 = 375.97 grams
Therefore, the weight that corresponds to this event is approximately 375.97 grams.
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Related Questions
Question 2
State the probability that a randomly selected, normally
distributed value lies between
a) o below the mean and o above the mean (round to
the nearest hundredths)
b) 20 below the mean and 20 above the mean (round
to the nearest hundredths)
Answers
The probability of a randomly selected, normally distributed value lying between 20 below the mean and 20 above the mean is 0.9545 (rounded to the nearest hundredth).
What is the fundamental concept of probability?A number between zero and one represents the probability that an occurrence will take place. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.
We can calculate the probabilities of a randomly chosen value falling between different z-scores using the provided standard normal distribution table.
a) The probability of a value being 0 below or above the mean is the same as the probability of a value being -1 to 1 standard deviations from the mean. According to the standard normal distribution table, the probability of a z-score between -1 and 1 is 0.6827. As a result, the probability of a randomly chosen, normally distributed value falling between 0 below and 0 above the mean is 0.6827. (rounded to the nearest hundredth).
b) The probability of a value falling between 20 and 20 standard deviations from the mean is the same as the probability of a value falling between -20/10 and 20/10 standard deviations from the mean (since the standard deviation is 10). According to the standard normal distribution table, the probability of a z-score between -2 and 2 is 0.9545. As a result, the probability of a randomly chosen, normally distributed value falling between 20 below and 20 above the mean is 0.9545. (rounded to the nearest hundredth).
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place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
Answers
The correct order of the steps to test the general hypothesis is given as B, A, E, C, D, F.
A hypothesis is basically a uncertain fact that is backed by some logical and solid information. While using the hypothesis, it s important that we use the correct method to verify the credibility of the hypothesis in the system.
So, as per the given option, the correct sequence should be, B, A, E, C, D, F.
We first set up the null hypothesis and the alternative hypothesis, and then we choose the degree of significance. The next phases in hypothesis testing are choosing the test statistics and creating the decision-making rule.
When we get to a conclusion based on the hypothesis after carefully calculating and computing the hypothesis' performance, the procedure is said to be finished.
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Complete question - place the following steps in order. what is the correct order for the general procedure for hypothesis testing?
A. Select the level of significance
B. setup null and alternative hypothesis
C. Establish the decision rule
D. performance computation
E. select the test statistics
F. Draw conclusions
If the area of one side of this cube is 25 cm^2
2
, what is the area of the whole surface of the cube?
cm^2
2
Answers
Answer:
150 cm2
Step-by-step explanation:
Given side of cube's area = 25. Since Side's a square,
Edge^2 = 5^2 = 5 cm
Total surface area: 6*a² = 6*5*5 = 150 cm2
what is the domain of the function {(-1,-1),(0,1),(2,-1)}
a) (-1,1)
b) (-1,0,2)
c) (-1,0,1,2)
d) {(-1,-1),(0,1),(2,-1)}
Answers
Answer:
[tex]b) \quad(-1,0,2)[/tex]
Step-by-step explanation:
The domain is the set of all input values for a function. It can be represented as a list of values where it is countable or as a set notation
Here there are only 3 ordered pairs. The first entry in each ordered pair represents the input of the function, the second entry the corresponding output value
Looking at the first entry in all three ordered pairs we get the domain as
[tex](-1, 0 , 2)[/tex]
Ciara throws four fair six-sided dice. The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6 Work out the probability that at least one of the dice lands on an even number.
Answers
The likelihood that one or more of the dice will land on an even number is 1296.
How does probability work?The likelihood of an event is quantified by its probability, which is a number. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The likelihood of an event increasing with probability of occurrence.
According to the given information:Four 6-sided dice are rolled what is the probability that at least two dice show least 2 die the same.
For 2 of the same: 5×5×642) =900
For 3 of the same: 5×643) =120
For 4 of the same: 644) =6
Combined: 900+120+6=1026
Total possibilities: 64=1296
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The probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
We can solve this problem by finding the probability that all four dice land on odd numbers and then subtracting this probability from 1 to get the probability that at least one of the dice lands on an even number.
The probability that one dice lands on an odd number is 3/6 = 1/2, and the probability that all four dice land on odd numbers is:
(1/2) × (1/2) × (1/2) × (1/2) = 1/16
Therefore, the probability that at least one of the dice lands on an even number is:
1 - 1/16 = 15/16
So the probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
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PLS HELP FAST 20 POINTS + BRAINLIEST
Answers
Answer:
£22
Step-by-step explanation:
50% of 88=88/100 ×50=44
44÷2=25%=22
75% of £88 is deducted, so that 88-66=£22
Don't forget my Brainliestcan someone please help me asap!!! ill mark brainlistt...
Answers
Answer:
Step-by-step explanation:
To solve this problem, we can use the formula for the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given the length of two sides of the triangle (the legs) and we need to find the length of the hypotenuse.
Let's label the sides of the triangle:
The shorter leg is the vertical side opposite the angle marked 55 degrees, so let's call it "a".
The longer leg is the horizontal side adjacent to the angle marked 55 degrees, so let's call it "b".
The hypotenuse is the side opposite the right angle, so let's call it "c".
Using trigonometry, we can determine the value of "a" and "b":
a = b * tan(55°) (since tangent = opposite/adjacent, we solve for opposite which is "a" in this case)
a = 100 * tan(55°) = 100 * 1.428 = 142.8
b = 100
Now, we can use the Pythagorean theorem to find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 142.8^2 + 100^2
c^2 = 20484.84 + 10000
c^2 = 30484.84
c = sqrt(30484.84)
c ≈ 174.6
Therefore, the length of the hypotenuse is approximately 174.6 units (the units are not given in the problem, but we can assume they are consistent with the units used for the given values of "a" and "b").
The problem does not specify the orientation or scale of the graph, but we can assume that it is a right triangle with the angle marked 55 degrees in the upper left corner.
The vertical side (the shorter leg) of the triangle should be labeled with a length of approximately 142.8 units (assuming the units used for the problem are consistent with the values given for "a" and "b"). The horizontal side (the longer leg) should be labeled with a length of 100 units.
The hypotenuse (the side opposite the right angle) should be drawn as a diagonal line connecting the endpoints of the vertical and horizontal sides. The hypotenuse should be labeled with a length of approximately 174.6 units.
The angle marked 55 degrees should be labeled as such, and the other two angles of the triangle (the right angle and the angle opposite the longer leg) should be labeled accordingly.
The population of a certain city was 3,846 in 1996. It is expected to decrease by about 0.27% per year. Write an exponential decay function, and use it to approximate the population in 2022.
Answers
Answer:
To write an exponential decay function for this situation, we can use the formula:
P(t) = P₀e^(rt)
where:
P(t) = the population at time t
P₀ = the initial population
r = the annual rate of decrease (as a decimal)
t = time in years
We are given P₀ = 3,846 and r = -0.0027 (since the population is decreasing).
To approximate the population in 2022, we need to find t, the number of years from 1996 to 2022. That is:
t = 2022 - 1996 = 26 years
Now we can plug in the values we have:
P(t) = 3,846 e^(-0.0027t)
To find P(2022), we plug in t = 26:
P(26) = 3,846 e^(-0.0027(26))
≈ 3,200.62
Therefore, we can approximate the population of the city in 2022 to be about 3,201 people.
Answer:
3,101
Step-by-step explanation:
Please hit brainliest if this helped!
To write an exponential decay function for the population of the city, we can use the formula:
P(t) = P₀e^(-rt)
where P(t) is the population at time t, P₀ is the initial population, r is the decay rate, and e is the base of the natural logarithm.
In this problem, P₀ = 3,846 and r = 0.0027 (0.27% expressed as a decimal). We want to find the population in 2022, which is 26 years after 1996.To use the formula, we need to convert 26 years to the same time units as the decay rate. Since the decay rate is per year, we can use 26 years directly. Therefore, the exponential decay function for the population is:
P(t) = 3,846e^(-0.0027t)
To find the population in 2022 (t = 26), we substitute t = 26 into the function:
P(26) = 3,846e^(-0.0027*26) ≈ 3,101
Therefore, the population in 2022 is approximately 3,101.
Let me know if this helped by hitting brainliest! If you have any questions, comment below and I"ll get back to you ASAP.
Find the derivative of f(x) = -2x^3 by the limit process…
Answers
Answer:
f'(x) = -6x^2
f'(-5) = -150
f'(0) = 0
f'(√17) = -102
Find the value of Tan 15 without using a table or calcutator
Answers
Answer:
Step-by-step explanation:
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Given that x is a positive integer less than 100, how many solutions does the congruence x+13=55 (mod 34) have?
Answers
The congruence x + 13 ≡ 55 (mod 34) simplifies to x ≡ 12 (mod 34). There are three solutions for x less than 100 that satisfy this congruence.
The given congruence is x + 13 ≡ 55 (mod 34). Simplifying this, we get x ≡ 12 (mod 34).
We need to find the number of solutions for x that are less than 100 and satisfy this congruence.
The general solution for the congruence x ≡ 12 (mod 34) is x = 12 + 34k, where k is an integer.
The solutions that are less than 100 are obtained when k = 0, 1, or 2.
Thus, the number of solutions is 3.
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Baker School's hockey games are 60 minutes long. Nico played for 30 minutes of the last game. What percent of the game time did Nico play?
Pick the model that represents the problem.
Answers
Dude he played for 1/2 of the game half of 60 is 30.
50%.
I'm I missing something?
Elizabeth works as a server in coffee shop, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work. 25 g 20 15 10 6 0 0 l0 15 20 Tip Amounts (dollars a. Write a few sentences to describe the distribution of tip amounts for the day shown. b. One of the tip amounts was S8. If the S8 tip had been S18, what effect would the increase have had on the following statistics? Justify your answers. i. The mean: ii. The median:
Answers
a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.
b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.
a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.
b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.
ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.
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construct shear and bending diagrams for the following beams. show your equations used to create the plots. p p p p l/2 l/4 l/4 p p p l/3 l/3 l/3
Answers
The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.
To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:
Leftmost section (0 ≤ x ≤ L/4)
Second section (L/4 < x ≤ L/2)
Third section (L/2 < x ≤ 5L/12)
Fourth section (5L/12 < x ≤ 7L/12)
Rightmost section (7L/12 < x ≤ L)
We can use the equations for shear and bending moments to create the plots:
For section 1: 0 ≤ x ≤ L/4
The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.
For section 2: L/4 < x ≤ L/2
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.
For section 3: L/2 < x ≤ 5L/12
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.
For section 4: 5L/12 < x ≤ 7L/12
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.
For section 5: 7L/12 < x ≤ L
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.
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ab and bc are perpendicular lines find the value of x of 25
Answers
Answer:
If the time is 3:45 how many minutes is it slow or fast
Find the 66th derivative of the function f(x) = 4 sin (x)…..
Answers
In response to the stated question, we may state that As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.
Using the chain rule and the derivative of the sine function repeatedly yields the 66th derivative of the function [tex]f(x) = 4 sin (x).[/tex]
The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x), and this pattern repeats itself every two derivatives.
As a result, the first derivative of f(x) is:
[tex]f'(x) = 4 cos (x)[/tex]
The second derivative is as follows:
[tex]f"(x) = -4 sin (x)[/tex]
The third derivative is as follows:
[tex]f"'(x) = -4 cos (x)[/tex]
The fourth derivative is as follows:
[tex]f""(x) = 4 sin (x)[/tex]
And so forth.
[tex]f^{(66)(x)} = 4 sin (x)[/tex]
Because the pattern repeats every four derivatives, the 66th derivative is the same as the second, sixth, tenth, fourteenth, and so on.
As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).
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2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Question 1
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
Answers
Accοrding tο the data, the answers tο Questiοns 1 and 2 are: Harris shοuld anticipate spinning a sum οr less 10 apprοximately 367 times and a tοtal that is 10 οr larger apprοximately 133 times.
What are a fοrmula and an equatiοn?Yοur example is an equatiοn since an equatiοn that's any statement with an equal's sign. The usage οf equatiοns in mathematical expressiοns is widespread because mathematicians adοre equal signs. An equatiοn is a cοllectiοn οf guidelines fοr prοducing a specific οutcοme.
Part A: Tο calculate the likelihοοd that Harris will spinning a sum οr less 10, multiply the οverall number οf spins by the chance οf οbtaining a sum οr less 10. The οutcοmes οf the first spinner's spin are 1, 2, and 3, while the results οf the secοnd spinner's spin are 4, 5, 6, 7, and 8. Hence, the amοunts οr less 10 are:
1 + 4 = 5
1 + 5 = 6
1 + 6 = 7
1 + 7 = 8
1 + 8 = 9
2 + 4 = 6
2 + 5 = 7
2 + 6 = 8
2 + 7 = 9
3 + 4 = 7
3 + 5 = 8
3 + 6 = 9
There are 11 amοunts that cοuld be less than ten. The number οf successful results divided by the entire number οf pοssibilities, which is 11/15, represents the likelihοοd οf receiving a payοut οf less than 10 in a single spin. Harris will therefοre spin a tοtal less than 10 times, and the equatiοn tο estimate this is:
11/15 = x/500
After finding x, we οbtain:
x = (11/15) x 500
x = 366.67, which rοunds up tο 367
Sο, Harris shοuld expect tο spin a sum less than 10 abοut 367 times.
Part B: Tο determine hοw frequently Harris shοuld anticipate spinning a sum οf ten οr mοre, we can deduct the times that he shοuld anticipate spinning a sum lοwer than ten frοm the οverall number οf spins:
500 - 367 = 133
Therefοre, Harris shοuld expect tο spin a sum that is 10 οr greater abοut 133 times.
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What the values of angles B and C?
Answers
The value of b is 73° as opposite angles of congruent sides are equal in an isosceles triangle.
What dοes a math angle mean?An angle is created by cοmbining twο rays (half-lines) that have a cοmmοn terminal. The angle's vertex is the latter, while the rays are alternately referred tο as the angle's legs and its arms.
What is fundamental angle?An angle within a shape that has the shape's base as οne οf its sides is knοwn as the base angle οf a shape in geοmetry. Cοnsider the triangle in the image as an example. We can οbserve that the triangle's base side is made up οf an angle B side and an angle C side. As a result, the triangle's base angles are angles B and C.
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PLEASE HELP ME!!! Type the correct answer in each box. Use T for true and F for false.
Complete the truth table for the contrapositive of a conditional statement.
р
T
T
LL
LL
q
T
F
T
LL
P→q
T
F
T
T
~9~p
Answers
The answer will of given mathematical logic will be T F T T F respectivelly.
What fundamental ideas underlie mathematical logic?A negation, conjunction, and disjunction are the fundamental mathematical logics. The symbols for negation, conjunction, and disjunction in mathematical logic are "," "," and "v," respectively.
What is the purpose of mathematical logic?Logical proofs frequently employ mathematical logic. Proofs are legitimate arguments that establish the veracity of mathematical assertions. A series of statements make up an argument. The conclusion is the last assertion, and the premises are all the statements that came before it (or hypothesis).
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The complete truth table is shown in the below diagram.
≈ q → ≈ p: True False True True
Define the conditional statement for contrapositive?The contrapositive of a conditional statement is a new conditional statement that is formed by negating both the hypothesis (the "if" part) and the conclusion (the "then" part) of the original statement, and switching their positions. The truth table for the contrapositive of a conditional statement has the same number of rows as the truth table for the original statement.
For example, if the original statement is "If it is raining, then the ground is wet", then the contrapositive would be "If the ground is not wet, then it is not raining."
According to the given table the contrapositive of a conditional statement q and p is defines as;
True
False
True
True
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a rectangular prism with a volume of 20 in^3 is dialited with a scale facotr of 2. what is the volume of the new figure?
Answers
The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.
In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.
Volume of rectangular prism = length x width x height
20 = l x w x h
Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.
New length = 2 x l
New width = 2 x w
New height = 2 x h
Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:
Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)
Simplifying this expression, we get:
Volume of new rectangular prism = 8 x (l x w x h)
We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:
Volume of new rectangular prism = 8 x 20 in³
Volume of new rectangular prism = 160 in³
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Write a quadratic inequality represented by the graph.
Answers
Using the concept of parabola, the quadratic inequality represented by the graph can be written as:
y = x² -2x +2.
Define parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.
The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix.
The general equation for a parabola is given as:
y = a(x-h) ² + k
Now here we have:
(x,y) = (2,5)
(h,k) = (1,1)
Putting these values in the equation,
5 = a (2-1) ² + 1
a = 5-1
=4
Substituting the values:
y = (x-1) + 1
y = x² -2x +2
Therefore, the quadratic inequality can be written as: y = x² -2x +2.
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What is the meaning of "the homotopy classes of paths from x to x in a space X"?
Answers
The homotopy classes of paths from x to x in a space X refer to a set of equivalence classes of continuous paths that start and end at the same point, x, in the space X, where equivalence is defined in terms of homotopy.
What is the homotopy about?In other words, for any two paths, there exists a continuous transformation (called a homotopy) between them such that the endpoints remain fixed. Two paths are said to be homotopic if they can be continuously deformed into each other while keeping their endpoints fixed. The set of all paths that are homotopic to each other forms an equivalence class.
The homotopy classes of paths from x to x are important in algebraic topology, as they provide a way to study the topological structure of a space by analyzing the properties of the paths within it. They can also be used to define higher algebraic structures such as the fundamental group and higher homotopy groups.
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Change the following equation of a line into slope-intercept form.
y + 4 = 2x
Answers
Answer:
Step-by-step explanation:
[tex]y=2x-4[/tex] (slope-intercept form is [tex]y=mx+b[/tex] where m=gradient
and b is where line intercepts y-axis)
0.0125 inches thick
Question 4
1 pts
The combined weight of a spool and the wire it carries is 13.6 lb. If the weight of the spool is 1.75 lb.,
what is the weight of the wire?
Question 5
1 pts
Answers
In linear equation, 11.85 pounds is the weight of the wire.
What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Total weight of pool having 16 wires =13.6 pounds
Weight of the pool =1.75
Therefore the weight of the wire alone = 13.6 - 1.75
= 11.85 pounds
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to calculate the workload of a resource that serves different flow unit types, one must know which of the following?
Answers
The workload of the resource is 20.5 units.
To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.
For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:
Workload = (10*2 + 8*1 + 5*3) / 2
= 41 / 2
= 20.5 units
Therefore, the workload of the resource is 20.5 units.
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Complete question
What are the flow unit types that the resource is serving?
mathematicians divide the world of numbers into at least seven subsets. list seven subsets and define each
Answers
Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.
Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".
Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".
Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".
Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".
Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.
Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".
Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".
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For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).
Answers
Answer: (f⋅g)(1) = 10.
Step-by-step explanation:
To find (f⋅g)(x), we need to multiply the two functions f(x) and g(x) together. This can be done by multiplying each term of f(x) by each term of g(x), and then combining like terms. We get:
(f⋅g)(x) = f(x) * g(x)
= (-7x+3) * (3x^2 - 4x - 1)
= -21x^3 + 28x^2 + x - 3x^2 + 4x + 1
= -21x^3 + 25x^2 + 5x + 1
To find (f⋅g)(1), we can substitute x=1 into the expression for (f⋅g)(x):
(f⋅g)(1) = -21(1)^3 + 25(1)^2 + 5(1) + 1
= -21 + 25 + 5 + 1
= 10
Therefore, (f⋅g)(1) = 10.
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The point on the parabola y=x^2 that is closest to the point (1,0) is (_______,_______). The distance between the two points is ________.
you can use Newtons's Method or Bisection to help but you don't have to.
Answers
Answer:Approximately
(0.58975,0.34781)
Step-by-step explanation:
If (x,y) is a point on the parabola, then the distance between (x,y) and (1,0) is:
√(x−1)2+(y−0)2=√x4+x2−2x+1
To minimize this, we want to minimize
f(x)=x4+x2−2x+1
The minimum will occur at a zero of:
f'(x)=4x3+2x−2=2(2x3+x−1)
graph{2x^3+x-1 [-10, 10, -5, 5]}
Using Cardano's method, find
x=3√14+√8736+3√14−√8736≅0.58975
y=x2≅0.34781
My little cousin needs help with this can anyone help please.
I’m busy with my tests and I don’t have the time to explain.
Answers
Answer:
I don't knowI am sorry I will let someone else answer
Step-by-step explanation:
At a community college, a survey was taken to determine where students study on campus. Of the 250 students surveyed, it was determined that
170 studied in the library
135 studied in the cafeteria
76 studied in both the library and the cafeteria
How many studied in library or cafeteria (including both)?
Answers
Answer:
Step-by-step explanation:
To find the number of students who studied in the library or cafeteria (including both), we need to add the number of students who studied in the library and the number of students who studied in the cafeteria, but we need to subtract the number of students who studied in both the library and cafeteria to avoid counting them twice.
So, the number of students who studied in library or cafeteria is:
170 + 135 - 76 = 229
Therefore, 229 students studied in the library or cafeteria (including both).
