Final answer:
In mathematics, when an operation involves an even number of signs, the result will be positive. This applies to multiplication and division rules, where similarly signed numbers yield a positive result. Principles of mathematical operations also extend to probabilities, where conditions and the complement of events are crucial to determining event outcomes.
Explanation:
If there is an even number of signs in a mathematical operation, such as multiplication or division, the solution will have a positive sign. This is because multiplying or dividing two positive numbers, or two negative numbers, results in a positive outcome. However, multiplying or dividing numbers with opposite signs results in a negative outcome.
For instance:
When two positive numbers multiply, the answer has a +ve sign, e.g., 2x3 = 6.
When two negative numbers multiply, the answer also has a +ve sign, e.g., (-4) x (-3) = 12.
In probability, events A and B being given conditions, such as event A given B (A GIVEN B) or event B given A (B GIVEN A), can impact the likelihood of those events occurring. The complement of an event (like the complement of A) refers to all outcomes that are not part of the event A.
Principles of Mathematical Operations and Probability
Understanding these principles helps solve many mathematical problems and assess probabilities, especially when working with equations with an unknown squared, which will typically result in two solutions, or when calculating the possibilities of a dice roll in probability exercises.
Sara joins a fruit of the month club. The entry cost is $25 and then she pays $18 per month. If she participates for 8 months, how much will she pay in all?
Answer:
$169
Step-by-step explanation:
Sara must pay the entry fee, and then a fee of 18$/month. if she is a member for 8 months the total paid must be
[tex]25 + 18*8 = 169[/tex]
Answer:
$169
Step-by-step explanation:
25+18m=$
m represents the months she participates for
25+18(8)=$
25+144=$
169=$
She pays $169 to be in a fruit club. Wow.
the probability of not rolling on a 2 on a 6-sided number cube is _____.
A.1/2 - B.1/3 -C.1/6 - D.5/6
Answer:
C.1/6
Step-by-step explanation:
The lifespans of zebras in a particular zoo are normally distributed. The average zebra lives 20.5years; the standard deviation is 3.9 years. Use the empirical rule (68-95-99.7%)to estimate the probability of a zebra living less than 32.2 years.
Answer:
Using the empirical rule, the probability of a zebra living less than 32.2 years is about [tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex] or about 99.85%.
Step-by-step explanation:
Roughly speaking, the empirical rule tells us that, in a normal distribution, the distance of one standard deviation from the mean, above and below it, contains approximately 68% of the observations of the normally distributed data; two standard deviations from the mean, above and below it, 95% of the data, and, finally, the distance of three standard deviations from the mean, above and below it, contains 99.7% of the data, approximately.
To estimate probabilities with this rule, we need to use, at least, two concepts: the standard normal distribution and the z-scores. A standard normal distribution is a normal distribution with mean = 0 and standard deviation = 1. It represents standardized data. This standardized data are those coming from a normal distribution and commonly called raw data. The way to standardized them is using the z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
x represents raw data. In this case, x = 32.2 years.
[tex] \\ \mu[/tex] is the population mean. In this case, [tex] \\ \mu = 20.5[/tex] years.
[tex] \\ \sigma[/tex] is the population standard deviation. In this case, [tex] \\ \sigma = 3.9[/tex] years.
Then, using [1], we "transform" the raw score into a z-score (a standardized value) and then use this to find the corresponding probability using the standard normal distribution (or the cumulative standard normal distribution to be more precise), available in any Statistics book or on the Internet.
However, applying the empirical rule, we can estimate those probabilities faster but in an approximate way.
Let us take the corresponding z-score:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{32.2 - 20.5}{3.9}[/tex]
[tex] \\ z = \frac{11.7}{3.9}[/tex]
[tex] \\ z = 3[/tex]
That is, the value z = 3 tells us the raw score 32.2 years is three standard deviations from the mean. In other words, 99.7% of the values are between z = -3 and z = 3. However, we are asked for P(z<3). The remaining area is below z = -3 and above z = 3. Since the normal distribution is symmetrical, we have to divide the remaining area by 2. That is, (1 - 0.997)/2 = 0.003/2 = 0.0015.
The area below z = -3 is, therefore, 0.0015, as well as above z = 3 or P(z<-3) = P(z>3) = 0.0015. The only area that not correspond to P(z<3) is P(z>3). As a result, we need to add the area below z = -3 (0.0015) to the value of 0.997 to finally have P(z<3).
Then
[tex] \\ P(z<3) = P(x<32.2) = 0.997 + P(z<-3)[/tex]
[tex] \\ P(z<3) = P(x<32.2) = 0.997 + 0.0015[/tex]
[tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex]
Thus, using the empirical rule, the probability of a zebra living less than 32.2 years is about [tex] \\ P(z<3) = P(x<32.2) = 0.9985[/tex].
In the graph below, we have a representation of the area below z = 3 or P(z<3) = P(x<32.2) is, approximately, 0.9985 or 99.85%.
Notice that using the cumulative standard normal table, as explained before, we have that P(z<3) = 0.99865.
Answer: 68, if the question asks between 16.6 and 24.4 years. 99.85, if the question asks for less.
Step-by-step explanation:
Cape Hatteras Lighthouse was built in 1870 and rises 208 feet above sea level. From the top of the lighthouse, the lighthouse keeper observes two ships along the same line of sight. The angle of depression to ship 1 is 20 and the angle of depression to ship 2 is 12.5 . For safety purposes, the keeper thinks the two ships should be at least 300 feet apart. If they are less than 300 feet apart, she will sound a warning. How far apart are the vessels? Will she sound the warning?
Answer:
The distance between them is 366.75 feet.
She doesn't need to sound a warning yet.
Step-by-step explanation:
Please see the attached files for explanation.
To find the Distance between ships, we can use trigonometry. The distance between the ships is the absolute difference between their heights above the horizontal.
To find the distance between the two ships, we can use trigonometry. Let's consider the triangle formed by the lighthouse, ship 1, and ship 2. The angle of depression to ship 1 is 20°, so the angle between the line of sight and the horizontal is also 20°. Similarly, the angle of depression to ship 2 is 12.5°, so the angle between the line of sight and the horizontal is also 12.5°.
We can use the tangent function to find the height of ship 1 and ship 2 above the horizontal. Using the formula tan(angle) = opposite/adjacent, we have: tan(20°) = height of ship 1/208 and tan(12.5°) = height of ship 2/208. Rearranging these equations, we get the heights: height of ship 1 = 208 * tan(20°) and height of ship 2 = 208 * tan(12.5°).
Now, to find the distance between the ships, we need to subtract the heights of the ships from each other. If the distance is less than 300 feet, the keeper will sound a warning. So, the distance between the ships is: distance = |height of ship 1 - height of ship 2|. If this distance is less than 300 feet, she will sound the warning.
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The sum of two negative numbers is always a negative number. Choose the correct answer below A. True B. False
Answer:
True
I hope this helps :)
Answer:
True
Step-by-step explanation:
True because there are only negative numbers in the calculation. Zero pairs are formed when a positive and a negative number are added
(x - 17.7) + 19.6 = 27.8 and an explanation
[tex](x - 17.7) + 19.6 = 27.8 \\ x - 17.7 = 27.8 - 19.6 \\ x - 17.7 = 8.2 \\ x = 17.7 + 8.2 \\ x = 25.9[/tex]
A basketball player made the following number of free throws in 8 successive games: 6, 18, 15, 14, 19, 12, 19, and 15. What is the median number of successful free throws?
Answer:
15
Step-by-step explanation:
Hello!
To find the median, all you have to do is order the number of terms in ascending order and then count to the middlemost number(s).
Arranging in ascending order:
[tex]6,\:12,\:14,\:15,\:15,\:18,\:19,\:19[/tex]
Since this is an even number, our two medians are 15 and 15.
(15 + 15) / 2 = 15.
Thus, the median of successful free throws is [tex]\boxed{15}[/tex].
please help me with this question, I am kinda desperate :( I honestly have no idea what i am doing...
if logb2=1 and logb3=1.58, evaluate the following:
logb8
Answer:
3
Step-by-step explanation:
logb(8)
logb(2³)
3 × logb(2)
3 × 1
3
Need help ASAP please!
Answer:
so f(0) = g(0) and f(2) = g(2)
Step-by-step explanation:
f(x) = g(x) where the two graphs intersect
The graphs cross at the x coordinate 0 and x coordinate 2
so f(0) = g(0) and f(2) = g(2)
Answer:
First one
Step-by-step explanation:
f(x) = g(x)
Is the point of intersection of the two graphs
(0,4) and (2,0)
Solutions are: x = 0 and x = 2
Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes. The distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes. (a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized score for Clay's marathon time. Show your work. (b) The finishing time for Kathy was 272 minutes. What proportion of women who ran the marathon had a finishing time less than Kathy's? Show your work. (c) The standard deviation of finishing time is greater for women than for men. What does this indicate about the finishing times of the women who ran the marathon compared to the finishing times of the men who ran the marathon?
Part a)
We have that,the distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes.
We want to calculate and interpret the standardized score for Clay's marathon time, if the finishing time for Clay was 289 minutes.
We use the formula:
[tex]z = \frac{x - \bar x}{s} [/tex]
we substitute the values to get:
[tex]z = \frac{289 - 242}{29} [/tex]
[tex]z = 1.62[/tex]
This means Clay's finishing time is 1.62 standard deviation above the mean finishing time.
Part b)
This time, we have that, the distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes.
We want to find the proportion of women who ran the marathon that had a finishing time less than Kathy if the finishing time for Kathy was 272 minutes.
We first calculate the z-score to get:
[tex]z = \frac{272 - 259}{32} = 0.41[/tex]
From the normal standard distribution table P(z<0.41)=0.6591.
This means 65.91% of women had a finishing time less than Kathy's finishing time.
Part c
The standard deviation of a data set tells us how far away the individual data are from the mean.
If the standard deviation of finishing time is greater for women than men, it means the finishing time for women are farther from the mean finishing time than that of men.
Using the normal distribution, it is found that:
a) His standardized score was of z = 1.6, which means that his finishing time is of 1.6 standard deviations above the mean finishing time for all men.
b) 0.6591 = 65.91% of women who ran the marathon had a finishing time less than Kathy's.
c) The higher standard deviation shows that the finishing times of the women who ran the marathon are more spread out compared to the finishing times of the men who ran the marathon.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Item a:
For men, mean of 242 minutes, thus [tex]\mu = 242[/tex].Standard deviation of 29 minutes, thus [tex]\sigma = 29[/tex].The z-score is found when X = 289, thus:[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{289 - 242}{29}[/tex]
[tex]Z = 1.6[/tex]
His standardized score was of z = 1.6, which means that his finishing time is of 1.6 standard deviations above the mean finishing time for all men.
Item b:
For women, mean of 259 minutes, thus [tex]\mu = 259[/tex]Standard deviation of 32 minutes, thus [tex]\sigma = 32[/tex].The proportion is the p-value of Z when X = 272, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{272 - 259}{32}[/tex]
[tex]Z = 0.41[/tex]
[tex]Z = 0.41[/tex] has a p-value of 0.6591.
0.6591 = 65.91% of women who ran the marathon had a finishing time less than Kathy's.
Item c:
The higher standard deviation shows that the finishing times of the women who ran the marathon are more spread out compared to the finishing times of the men who ran the marathon.
A similar problem is given at https://brainly.com/question/24855678
solve for x can anyone help me ?
Answer:
E
Step-by-step explanation:
-18x + 21 > -15
-18x > -36
x < 2
20x - 13》17
20x》40
x》2
Or is union
Union of x < 2 and x》2 is all real numbers
what's 1.12 as a fraction.
Answer:
1.12 = 28 / 25
Step-by-step explanation:
28 over 25
28
---
25
BRAINLIST please have a great day
Answer:
28/25
Step-by-step explanation:
hope this helps.
least common multiple of 4, 8 and 2
Answer:
2
Step-by-step explanation:
your welcome
Answer:
2:2,4,6,8,10,12,14,16
4:4,8,12,16
8:8,16
the LCM is 16
molly has $45 in her wallet, which is 3 times as much as her brother has
Answer:$15
Step-by-step explanation:
45 divided by 3 =15
Answer:
her brother has $15
Step-by-step explanation:
m= molly
b= brother
m=45
b= 45÷3
b=15
11. What is the area of this figure?*
12.6 cm
6.4 cm
Juanita cut her cheese into 4 equal pieces she gave 2 pieces to her brother
Answer:
She has 2 pieces left
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y = x + 5?
–2
2
Answer:
-2
or
A.
Step-by-step explanation:
on edge 2020
A researcher is investigating whether a new fertilizer affects the yield of tomato plants. As part of an experiment, 20 plants will be randomly assigned the new fertilizer and 20 will be assigned the current fertilizer. The mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be calculated. Which of the following is the appropriate inference procedure for analyzing the results of the experiment?a)A matched-pairs t-interval for a mean differenceb)A two-sample t-interval for a difference between sample meansc)A two-sample t-interval for a difference between population meansd)A one-sample t-interval for a sample meane)A one-sample t-interval for a population mean
Answer:
Correct option is (c).
Step-by-step explanation:
The experiment is conducted to determine whether a new fertilizer affects the yield of tomato plants.
The procedure involves randomly assigning the new fertilizer to 20 plants and the other 20 will be assigned the current fertilizer.
Then the mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be calculated.
The collected sample data will then be used to make conclusion about the population.
The researchers main aim is to determine whether the new fertilizer is effective or not, i.e. if on using the new fertilizer the yield of tomatoes increases or not.
So, the parameter under study id the difference between tow population means.
To make inferences about the experiment the researcher can construct a two-sample t-interval for a difference between population means. The confidence interval has a certain specific probability of including the true parameter value.
Thus, the correct option is (c).
The correct answer is (c) option.
The following information should be considered:
The experiment is conducted for measuring whether a new fertilizer impacts the yield of tomato plants or not After this, the mean number of tomatoes produced per plant will be recorded for each fertilizer, and the difference in the sample means will be determined. The researchers main focus is to measured whether the new fertilizer is effective or not. Thus, the parameter under study is the difference between two population means. For make inferences related to the experiment the researcher can construct a two-sample t-interval for a difference between population means. The confidence interval has a specific probability of involving the true parameter value.
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How many 2-digit numbers can be formed from the digits 1 through 8 if each digit is only used once?
Answer:
56.
Step-by-step explanation:
That is the number of permutations of 2 from 8
= 8P2
= 8!/(8-2)!
= 8!/6!
= 8 * 7
= 56.
Answer:57
Step-by-step explanation:
12
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17
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21
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24
25
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80% is best represented by which the following fractions
A. 8/100
B.4/5
C.3/4
D.8/10
Answer:
B. 4/5
Step-by-step explanation:
8/10 simplified is 4/5 so the other person is still correct.
But if there's a fraction that could be simplified, then the simplified answer would be the best answer you're looking for.
A rectangle as an area of 240 square ft the base is 15 what is the height of the rectangle
Answer:
16 ft
Step-by-step explanation:
Hi there,
The formula for the area of a rectangle is A = b*h.
So, let's start out by plugging in what we know.
240 = 15h
Now, solve for h by dividing both sides by 15
h = 16
So, the height of the rectangle is 16 ft
Hope this helps! Stay safe!
- Emily
What Is -6.75?
A natural number or
Whole # or
A integer or
Rational or
Irrational or
Real?
(Choose one)
-6.75 is a rational number since it can be expressed as a fraction of two integers. It's also a real number, but it's not a natural, whole, integer, or irrational number.
Explanation:The number -6.75 is a Rational Number. Here's why:
A Natural Number is a number that is a positive integer, which would not include -6.75 because it is negative. A Whole Number is a number without fractional components, so -6.75 isn't a whole number as it has a fractional part. An Integer is a whole number that can be positive, negative, or zero, but does not include fractions or decimals, therefore, -6.75 isn't an integer. A Rational Number is a number that can be expressed as a fraction of two integers, and since -6.75 can be written as -675/100, it falls into this category. Since all rational numbers are included in the Real Number set, -6.75 is also a real number. However, an Irrational Number cannot be expressed as a ratio of two integers, which means that -6.75 isn't irrational.
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What is f(2) of the function?
F(x)=4x+1
Answer:
9
Step-by-step explanation:
just replace the x with 2 and solve
4(2)+1
8+1
= 9
Explain why a polar curve is not always bounded.
Answer: There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(Θ)) to be an unbounded polar. An example of an unbounded curve would be r = Θ for 0 ≤ Θ.
Answer:
There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(Θ)) to be an unbounded polar.
Step-by-step explanation:
its correct on EDGE2022
The scale drawing represents an existing barn. The shortest side of the barn measures 150 meters. If a new barn that is 2/3 its size replaces the existing barn, what will be the scale of this drawing to the new barn?
The scale of the drawing to the new barn is 1:1.5.
Explanation:To find the scale of the new barn compared to the existing barn, we can use the ratio of their sides. Let's call the shortest side of the new barn x meters. The ratio of the lengths of the shortest sides of the new and existing barns is given as 2/3. Setting up the proportion, we have 2/3 = x/150. Cross-multiplying, we find x = (2/3) * 150 = 100 meters. Therefore, the shortest side of the new barn measures 100 meters. The scale of the drawing to the new barn can be determined by dividing the length of the shortest side of the drawing by the length of the shortest side of the new barn. Let's call the scale factor y. We have y = 150/100 = 1.5. Therefore, the scale of the drawing to the new barn is 1:1.5.
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There are 30 students in Mrs. Taylor's kindergarten class. If there are twice as many students with blond hair as with blue eyes, 6 students with blond hair and blue eyes, and 3 students with neither blond hair nor blue eyes, how many students have blue eyes?
Answer:
11
Step-by-step explanation:
Let e represent the number of students with blue eyes. Then the number of students with blond hair is 2e. The total number of students is ...
3 + e + 2e -6 = 30
We subtracted 6 because the expressions e and 2e cause the 6 students with both blond hair and blue eyes to be counted twice.
3e = 33 . . . . add 3 and simplify
e = 11
11 students have blue eyes.
In the given problem, using the logical reasoning to deduce from the given facts, it can be determined that there are 10 students in Mrs. Taylor's class that have blue eyes.
Explanation:To find out how many students in Mrs. Taylor's kindergarten class have blue eyes, we need to use the information given in the problem and make a series of logical deductions.
First, we know that there are twice as many students with blond hair as with blue eyes. Let's say the number of students with blue eyes is x. This implies that the number of students with blond hair is 2x.
We also know that there are 6 students with both blond hair and blue eyes. So, those students are included in both of our previous counts. Therefore, we need to subtract 6 from each count to get the number of students with only one of those attributes.
So far, this gives us x - 6 students with only blue eyes and 2x - 6 students with only blond hair. We know that there are 3 students with neither attribute, so the total number of students is (x - 6) + (2x - 6) + 6 (students with both attributes) + 3 (students with neither attribute) = 30.
Adding these together gives us 3x = 30, so x = 30/3 = 10. Therefore, there are 10 students with blue eyes.
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how old am i if 500 reduced by 4 times my age is 184
Answer:
79 years old
Step-by-step explanation:
Let's say your age is x.
The problem says "500 reduced by 4 times my age is 184", so we convert this to math:
- "4 times my age" ⇒ 4 * x = 4x
- "500 reduced by" ⇒ 500 - (something)
- "500 reduced by 4 times my age" ⇒ 500 - 4x
- "is 184" ⇒ = 184
- "500 reduced by 4 times my age is 184" ⇒ 500 - 4x = 184
Now, we simply solve for x:
500 - 4x = 184
4x = 500 - 184 = 316
x = 79
Thus, you are 79 years old.
Hope this helps!
Grace earns $5 each times she walks her neighbor's dog. She walks the dog 5 times in one week. Then she spends $7 on a book and $9 on a building set. Write an equation to represent how much money Grace has left, m.
Answer:
$5 (5) - ($7+$9)=m
$25 - $16 =m
Step-by-step explanation:
$5 (5) - (7+9)=m
$25 - 16 =m
The equation to represent how much money Grace has left is:
m = $25 - $7 - $9
m = $25 − $16
m = $9
How do we represent the event in the form of an equation?Grace earns $5 for each dog walk.
She walks the dog 5 times in one week, so she earns 5 walks * $5/per walk = $25.
She spends $7 on a book and $9 on a building set, so she spends a total of $7 + $9 = $16.
To find out how much money Grace has left, m, we subtract her total spending from her earnings.
So, the equation to represent how much money Grace has left is:
m = $25 − $16
m = $9
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One hundred and 50 people were asked whether they like to see comedies or dramas and whether or not I buy popcorn from for the movie out of 90 people that like comedies they bought popcorn day or 40 people that said they do not buy popcorn
Answer: a) 0.6, b) [tex]\dfrac{4}{15}[/tex]
Step-by-step explanation:
Since we have given that
Total number of people were surveyed = 150
Number of people that like comedies they bought popcorn that day = 90
Number of people that said they do not buy popcorn = 40
So, Probability of getting who like comedies and bought popcorn = [tex]\dfrac{90}{150}=\dfrac{3}{5}=0.6[/tex]
Probability of getting who said they do not buy popcorn = [tex]\dfrac{40}{150}=\dfrac{4}{15}[/tex]
Hence, a) 0.6, b) [tex]\dfrac{4}{15}[/tex]
i need the steps for 38