The repeating decimal 0.73737373... is rational and can be expressed as the ratio of two integers, 73 and 99.
To show that the number 0.73737373... is rational, we need to express it as a ratio of two integers. Let's call the repeating decimal x.
First, we'll multiply both sides of the equation x = 0.73737373... by 100 to get rid of the decimal point:
100x = 73.737373...
Next, we'll subtract x from 100x:
100x - x = 73.737373... - 0.73737373...
Simplifying the right-hand side, we get:
99x = 73
Dividing both sides by 99, we obtain:
x = 73/99
Therefore, we have shown that the repeating decimal 0.73737373... is rational and can be expressed as the ratio of two integers, 73 and 99.
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find the value of each variable in the diagram
The value of the variables are;
x =21
y = 16. 5
How to determine the valuesFirst, we need to know the properties of a parallelogram. They include;
The opposite sides are equal.The opposite angles are equal.The consecutive or adjacent angles are supplementary, sum up to 180 degreesIf any one of the angles is a right angle, then all the other angles will be at right angle equally.Then, from the information given, we have that;
3x = 63
Make 'x' the subject of formula, we have;
x = 63/3
Divide the values
x= 21
Also,
4y - 1 = 65
collect like terms
4y = 66
y = 16 .5
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Decorative sheets of paper sell for
$0.16 per sheet. How many sheets
are sold for $7.84?
Answer:
42 sheet of paper
Step-by-step explanation:
$7.84 divided by $0.16
This equals 42
After spending 7 dollars and 84 cents, 42 sheets of paper will be sold.
If we fail to reject the null hypothesis after performing an ANOVA, it means that the between group variability _________________. a. could not be measured.
b. was bigger than the within group variability
c. was the same size as the within group variability.
d. was zero
The correct option is c. was the same size as the within group variability, because the between-group variability was not significantly larger than the within-group variability.
How do you interpret the results of an ANOVA?In ANOVA (analysis of variance), the null hypothesis assumes that the means of all groups are equal. On the other hand, the alternative hypothesis suggests that at least one of the group means is different from the others.
If we perform an ANOVA and fail to reject the null hypothesis, it means that we do not have enough evidence to conclude that the means of the groups are significantly different. In other words, the variation between the group means is not significantly larger than the variation within the groups.
This implies that the between-group variability (i.e., variation in means between different groups) is similar in magnitude to the within-group variability (i.e., variation in observations within each group).
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Which angle in the figure is a right angle?
1: ∠STU
2: ∠TSR
3: ∠TUS
4: I don't know.
Answer:
TUS
Step-by-step explanation:
The angle parallel has the square that indicates its a right angle - parallel angles have the same number
Answer:
3: ∠TUS
Step-by-step explanation:
line measures 180°
so < U + <TUS =180°................ < U = 90°
< U + <TUS =180°................ < U = 90° 90° + <TUS = 180°
< U + <TUS =180°................ < U = 90° 90° + <TUS = 180° <TUS = 90°
The mean mark obtained by 5 girls is 38. When another girl’s mark is added to the list it increases to 40. Find the mark obtained by the new girl added.
The mean mark obtained by 5 girls is 38. Mark obtained by the new girl added is 62.
Let the mark obtained by the new girl be x.
Given, the mean mark obtained by 5 girls is 38.
So, the total marks obtained by the 5 girls = 5 * 38 = 190.
When the mark of the new girl is added, the mean mark increases to 40.
So, the total marks obtained by all the 6 girls = 6 * 40 = 240.
Therefore, the mark obtained by the new girl = Total marks obtained by all 6 girls - Total marks obtained by 5 girls
= 240 - 190
= 50.
Therefore, the mark obtained by the new girl added is 60.
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5. What is the slope of the line that passes through (0, 1) and (3, 7)? A -2 B -1/2 C 1/2 D 2
The slope of the line that passes through the points (0, 1) and (3, 7) include the following: D. 2.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope) = rise/run
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope) = (7 - 1)/(3 - 0)
Rate of change (slope) = 6/3
Rate of change (slope) = 2.
Based on the data points, the rate of change is the change in y-axis with respect to the x-axis and it is equal to 2.
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Claim: Most adults would erase all of their personal information online if they could. A software firm survey of randomly selected adults showed that % of them would erase all of their personal information online if they could. Find the value of the test statistic.
The null hypothesis and conclude that the percentage of adults who would erase all of their personal information online if they could is significantly different from 50%.
The test statistic for the claim that most adults would erase their personal information online if they could.
Based on the information provided.
It seems that a software firm conducted a survey of randomly selected adults, and we need to determine the percentage and test statistic.
To calculate the test statistic, you can use the formula for a one-sample proportion z-test.
Here,
P is the sample proportion (percentage from the survey),
p is the null hypothesis proportion (0.5, as "most" implies more than 50%), and
n is the sample size (number of adults surveyed).
Once you have the percentage from the survey and the sample size, you can plug in those values into the formula to find the test statistic (z).
This value will help you determine if there's enough evidence to support the claim that most adults would erase their personal information online if they could.
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la suma de tres números consecutivos es 54.
Answer:
16, 18, 20
Step-by-step explanation:
16, 18, 20 es igual a 54, así que esa será tu respuesta.
¡espero que esto haya ayudado!
Isaac and Victorio share money in the ratio Victorio receives £6. 60 work out the difference
The difference in the amount received by Victoria and Isaac is £3.96
Data obtained from the question include:
Isaac's ratio = 2
Victoria's ratio = 5
Total ratio = 2 + 5 = 7
And, Amount Victoria receive = £6.60.
Next, we shall determine the total amount of money shared by Isaac and Victoria. This is illustrated below:
Let T be the total amount of money shared.
Victoria received = £6.60
Victoria's share =
Victoria's ratio/total ratio x total amount
£6.60 = 5/7 x T
£6.60 = 5T/7
Cross multiply;
5T = £6.60 x 7
5T = £46.2
Divide both side by 5
T = £46.2/5
T = £9.24
Therefore, the total amount shared is £9.24.
Next, we shall determine the amount received by Isaac. This is illustrated below:
Victoria's share = £6.60
Total amount shared = £9.24.
Isaac's share =?
Isaac's share = Total amount shared – Victoria's share
Isaac's share = £9.24 – £6.60
Isaac's share = £2.64
Therefore, Isaac received £2.64
Finally, we shall determine the difference between how much money Isaac and Victoria receive. This is illustrated below:
Victoria receive = £6.60
Isaac receive = £2.64
Difference = £6.60 – £2.64
Difference = £3.96
Therefore, the difference in the amount received by Victoria and Isaac is £3.96
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Complete question is,
Isaac and Victoria share money in the ratio 2 : 5 Victoria recieve £6.60
work out the difference between how much money Isaac and Victoria receive?
Karrie has 20 bags of prizes each bag has four prizes. She also has a red bag with 13. Prizes and a blue bag with the rest of the prizes. She has a total of 100 prizes how many prizes are in the blue bag write an equation use a variable for the unknown number
What is the range of the function shown in the graph below?
Answer:
{-3, -∞)
Step-by-step explanation:
The range of a function is how far the y goes up or down of a function goes.
We see the function start at -3 and go forever. So, the range of the functions is {-3, -∞)
A newsletter publisher believes that above 41% of their readers own a personal computer. Is there sufficient evidence at the 0.10 level to substantiate the publisher's claim
If the sample proportion is greater than 0.494 (i.e., if [tex]\hat{p}[/tex] > 0.494), then there is sufficient evidence to substantiate the publisher's claim that above 41% of their readers own a personal computer at the 0.10 level of significance.
To determine if there is sufficient evidence to substantiate the publisher's claim that above 41% of their readers own a personal computer, a hypothesis test can be conducted.
Let p be the proportion of readers who own a personal computer.
The null hypothesis is that p ≤ 0.41, and the alternative hypothesis is that p > 0.41.
Assuming a random sample of readers, with a sample size n, let x be the number of readers in the sample who own a personal computer.
The sample proportion, [tex]\hat{p}[/tex], is given by x/n.
Under the null hypothesis, the sampling distribution of [tex]\hat{p}[/tex], is approximately normal with a mean of 0.41 and a standard deviation of sqrt(0.41*(1-0.41)/n).
Using a significance level of 0.10, the critical value from a standard normal distribution is 1.28 (since the alternative hypothesis is one-tailed).
To conduct the hypothesis test, calculate the test statistic[tex]z = (\hat{p} - 0.41) / \sqrt{(0.41*(1-0.41)/n) }[/tex]
If z > 1.28, then the null hypothesis can be rejected in favor of the alternative hypothesis at the 0.10 level of significance.
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(a) We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take a random sample of 50 days, and record Intel's and Southwest's stock on those same days.
Thus, to determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can use a statistical analysis of the daily rate of return for each stock over a 50-day period. However, the small sample size means that we must be cautious when interpreting the results.
To determine whether Intel's stock and Southwest Airlines' stock have similar rates of return, we can conduct a statistical analysis using the sample data collected. The sample size of 50 days is relatively small, so we must be cautious when interpreting the results.
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The __________ (one word) Of two events A and B contains only those outcomes that are in both A and B
The intersection of two events A and B contains only those outcomes that are in both A and B.
The intersection of two events A and B, denoted by A ∩ B, is the set of all outcomes that are common to both A and B. In other words, it contains only those outcomes that are in both A and B.
For example, if event A is "rolling an even number on a fair six-sided die" and event B is "rolling a number greater than 3 on a fair six-sided die", then the intersection of A and B is the event "rolling an even number greater than 3 on a fair six-sided die", which contains the outcome 4 and has probability [tex]\frac{1}{6}[/tex].
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Joe completely covered a square wall using 150. 5 ft2 of wall paper without any overlap. What is closest to the side lengh of the wall in feet
Answer:
9.44 feet).
Step-by-step explanation:
To find the side length of the wall, we need to divide the total area of the wallpaper used by the number of sides. Since it is a square wall, we can assume that all sides are equal. Therefore, the total area of the wall would be 150.5 ft^2, which we can divide by 4 (for four equal sides). Thus, the side length of the wall would be approximately 9.44 feet (150.5/4 = 37.625, which is the length of one side, and 37.625/4 = 9.40625, which rounds off to 9.44 feet).
Given an array of strings words and an integer k, return the k most frequent strings.
Return the answer sorted by the frequency from highest to lowest. Sort the words with the same frequency by their lexicographical order.
We can use a priority queue to keep track of the k most frequent strings. The priority queue should be sorted by the frequency of the strings, and in case of ties, we should sort by lexicographical order.
Here's the step-by-step algorithm to solve the problem:
1. Create a hash map to count the frequency of each string in the array.
2. Create a priority queue and define a custom comparator function that compares strings based on their frequency and lexicographical order.
3. Iterate over the keys of the hash map and add each string to the priority queue.
4. Pop the top k strings from the priority queue and add them to the result array.
5. Return the result array sorted in descending order of frequency.
Here's the Python code that implements this algorithm:
```
import heapq
from collections import defaultdict
def topKFrequent(words, k):
freq = defaultdict(int)
for word in words:
freq[word] += 1
pq = []
for word, count in freq.items():
heapq.heappush(pq, (-count, word))
res = []
for i in range(k):
res.append(heapq.heappop(pq)[1])
return sorted(res, key=lambda x: (-freq[x], x))
```
In this code, we use a defaultdict from the collections module to count the frequency of each string. We then use a heap (implemented as a list) to keep track of the k most frequent strings. The -count value is used as the first element of each tuple in the heap, so that we can sort the strings by frequency in descending order. The second element of each tuple is the string itself, which is used to break ties in case of equal frequency. Finally, we sort the result array based on the frequency and lexicographical order using the sorted function and a lambda function.
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Ms. Rivera is in charge of ordering the butterfly kits again. She knows she ordered 6 cases of butterfly kits last year but can't remember how many kits come in a case. When she checks the records, Ms. Rivera finds that the school used 417 of the butterfly kits last year and had 63 left over after the festival. How many butterfly kits come in each case?
There are 80 butterfly kits in each case.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
According to the information given, Ms. Rivera ordered 6 cases of butterfly kits, so the total number of kits she ordered would be 6x.
Out of the kits ordered, the school used 417 kits, and there were 63 kits left over. So the equation representing this situation would be:
6x - 417 = 63
To find the value of "x", we can solve this equation:
6x = 417 + 63
6x = 480
x = 480/6
x = 80
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if the question is right you will be marked as branliest (guarantied)
Answer:
(a) 48 inches
(b) 3rd quarter
(c) 2nd quarter
Step-by-step explanation:
You want various descriptors of the data represented by the given box plot.
(a) MostThe greatest amount of snowfall is represented by the extreme value at the right end of the right whisker. The value there is 48 inches.
The greatest amount of snowfall is 48 inches.
(b) Most concentratedThe data is most concentrated where the limits of a quartile are closest together. Those limits are ...
Q1 — 5 to 13 (8 inch range)
Q2 — 13 to 35 (22 inch range)
Q3 — 35 to 40 (5 inch range)
Q4 — 40 to 48 (8 inch range)
The quartile with the least range is Q3. The data is most concentrated in the 3rd quarter.
(c) Most spread outAs we saw in the previous section, the second quartile has the greatest range.
The data is the most spread out in the 2nd quarter.
9) Find a11 in an arithmetic sequence where a1 = −15 and a8 = 34
10) Find the arithmetic mean of the sequence -10,___,___,___,18
The equation of line EF is y = 1 over 2x + 6. Write an equation of a line parallel to line EF in slope-intercept form that contains point (0, −2).
Answer:
y = 1/2x -2
Step-by-step explanation:
You want the equation of a line parallel to y = 1/2x +6 that contains the point (0, -2), written in slope-intercept form.
SlopeThe slope of the line you want will be the same as the slope of the line you have. That is because parallel lines have the same slope.
The equation you are given is written in slope-intercept form:
y = mx + b . . . . . . where m is the slope and b is the y-intercept
Comparing this form to the given equation, you see that ...
m = 1/2 . . . . . the slope of the line you want
InterceptThe "intercept" in the "slope-intercept" form is the value of y when x=0. The point you are given, (0, -2), tells you that y = -2 when x = 0. So, the "intercept" in your slope-intercept equation is -2.
EquationThe equation you want is the equation of a line with slope 1/2 and a y-intercept of -2.
y = 1/2x -2
The equation of the line that is parallel to line EF and passes through point (0, -2) is y = (1/2)x - 2.To find an equation of a line that is parallel to line EF and passes through point (0, -2), we need to use the fact that parallel lines have the same slope. The slope of line EF is 1/2, so the slope of the parallel line will also be 1/2.
We can start by using the point-slope form of the equation of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in m = 1/2 and (x1, y1) = (0, -2), we get:
y - (-2) = (1/2)(x - 0)
Simplifying this equation gives:
y + 2 = (1/2)x
To get this equation in slope-intercept form (y = mx + b), we can isolate y:
y = (1/2)x - 2
So the equation of the line that is parallel to line EF and passes through point (0, -2) is y = (1/2)x - 2. Note that this line intersects the y-axis at y = -2, which is the y-intercept.
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If 5^3b-1 equals 5^B -3 what is the value of B?
• -2
• -1
• 1
• 2 
Answer:
b=-1
Step-by-step explanation:
set 3b-1 and b-3 equal to each other because they have the same base which is 5.
3b-1=b-3
2b=-2
b=-1
Playing tennis and playing golf are ____________ (choose between dependent and independent)
Playing tennis and playing golf are independent activities.
What is the relationship between playing tennis and playing golf?Playing tennis and playing golf are two distinct activities that do not rely on each other for completion.
Although they share some similarities such as requiring physical stamina and hand-eye coordination, they have different sets of rules, equipment, and playing surfaces.
While playing tennis involves hitting a ball over a net to the opponent's side of the court, golf requires hitting a ball into a series of holes with as few strokes as possible.
Therefore, one can engage in either activity without having to participate in the other.
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the number 1 through 10 out in one each bag. The number 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number
Answer: 9/25
Step-by-step explanation:
What numbers do each bags have in common
5, 6, 7. 8, 9, 10 Tht's 6 numbers
the probability for each bag is the possibilities/total outcome
P(same from first bag)=6/10 = 3/5
P(same from other bag=6/10 = 3/5
Because you are looking for an "and" probability, you mulitiply
P(number from first and number from second) = 3/5 * 3/5 = 9/25
FILL IN THE BLANK. a z score must be ____ whenever it is located on the left half of the normal distribution
Answer:
A z score must be negative (-) whenever it is located on the left half of the normal distribution. This is because the left half of the normal distribution represents scores that are below the average (mean) of the distribution. A z score is a standard score that tells us how many standard deviations a particular score is from the mean. Thus, a negative z score indicates that the corresponding score is located below the mean of the distribution by a certain number of standard deviations. In contrast, a positive z score indicates that the corresponding score is located above the mean of the distribution by a certain number of standard deviations.
A fruit market equally divided 80 red apples into 8 containers, and equally divided 54 green apples into 6 containers. Natalie bought 1 container of red apples and 1 container of green apples.
Which equation could be used to find n, the total number of apples Natalie bought? pls hurry my brother is in a test is it
A.(80+54) divided by (8+6)=n
B.80x8+54x6=n
C.80 divided by 6 + 54 divided by 8=n
D. (I think this is the right one) 80 divided by 8 + 54 divided by 6=n
The equation that represents the total number of apples Natalie bought will be n = 80 / 8 + 54 / 6. Then the correct option is D.
A fruit store divided 54 green apples equally into six containers and 80 red apples equally into eight containers. One container of red and green apples was purchased by Natalie.
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Let 'n' be the total number of apples Natalie bought. Then the equation is given as,
n = 80 / 8 + 54 / 6
Thus, the correct option is D.
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FILL IN THE BLANK. "Test yourself
The quotient-remainder theorem says that for all integers n and d with d ≤ 0, there exist ___________ q and r such that __________ and ______________."
The quotient-remainder theorem says that for all integers n and d with d > 0, there exist unique integers q and r such that n = qd + r and 0 ≤ r < d.
In other words, any integer n can be divided by a positive integer d to yield a quotient q and a remainder r, where the remainder is always strictly less than the divisor.
The quotient q represents the number of times that the divisor d "fits" into the dividend n, while the remainder r represents the amount that is left over after we have divided n by d as many times as possible. This theorem is also known as the division algorithm or Euclidean division, and is a fundamental result in elementary number theory.
The theorem can be used to solve many problems involving integers, such as determining whether a given integer is divisible by another integer, finding the greatest common divisor of two integers, and solving linear Diophantine equations.
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How can I solve this
(D)To represent an inequality on a graph, follow these steps:
Identify the type of inequality. Is it a greater than or equal to (> or =), less than or equal to (< or =), greater than (>), or less than (<) inequality?
Rewrite the inequality in slope-intercept form, y = mx + b, if it is not already in that form.
Graph the equation of the line y = mx + b on the coordinate plane using the y-intercept (b) and the slope (m).
Choose a test point that is not on the line. You can use any point that is convenient to you.
Substitute the x and y values of the test point into the original inequality. If the inequality is true, shade the region of the graph that contains the test point. If the inequality is false, shade the region of the graph that does not contain the test point.
If the inequality is greater than or equal to, shade the region above the line. If the inequality is less than or equal to, shade the region below the line. If the inequality is greater than, shade the region above the line but do not include the line. If the inequality is less than, shade the region below the line but do not include the line.
Label the shaded region with the inequality symbol.
Remember that the line itself is included in the graph if the inequality is greater than or equal to or less than or equal to, but not included if the inequality is greater than or less than.
Which best proves why the expressions 4(x+3)+2x and 6(x+2) must be equivalent expressions?
When x-3, both expressions have a value of 30
When x-
5, both expressions have a value of 42
When x-1, both expressions have a value of 18, and when x-8, both expressions have a value of 60.
O When x-2, both expressions have a value of 15, and when x-6, both expressions have a value of 39.
Answer + Step-by-step explanation:
Two algebraic expressions are equivalent if they always lead to the same result when you evaluate them, no matter what values you substitute for the variables. To check whether a more complex expression is equivalent to a simpler expression, you can distribute any coefficients and combine any like terms on each side of the equation. Then arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent
In this case, we can see that when x-3, both expressions have a value of 30; when x-5, both expressions have a value of 42; when x-1, both expressions have a value of 18; when x-8, both expressions have a value of 60; and when x-2, both expressions have a value of 15; and when x-6, both expressions have a value of 39 https://the-equivalent.com/expressions-are-equivalent/. Therefore, we can conclude that these two expressions are equivalent
derstand and Determine Simple Probability
In a video game, the player can choose a character from 4 animal characters and 3 human characters. Players can also let the
computer randomly select a character for them.
The player will have the computer randomly select his character.
What is the probability it will pick a human character?
Enter your answer as a fraction in simplest form in the box.
Basic
7
8
9
y
x²
VÕ
L
G
The probability that the computer will pick a human character is 3/7
What is the probability?The probability that when the computer randomly selects his character, it will pick a human character is calculated using the formula below:
Probability of human character = number of human characters / total number of charactersThe number of human characters = 3
The total number of characters = 7
Let the probability of picking a human character be P(human character).
P(human character) = 3/7
Therefore, the probability that the computer will pick a human character is 3/7
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HELP
look at the picture it says what to do.
:)
The mean 5.0 (increases/decreases) by 7.0 (value of the outlier), the median 5.0 (stays the same/increases/decreases) by 0.0 (value of the outlier), and the mode is (stays the same/different) the same when the outlier is removed.
When the outlier is removed, the mean decreases by the value of the outlier (7), the median stays the same since the outlier was not part of the middle value, and the mode remains the same since there is no change in the value that appears most frequently.
Therefore, when the outlier is removed, the mean decreases by the value of the outlier (7), the median stays the same since the outlier was not part of the middle value, and the mode remains the same since there is no change in the value that appears most frequently.
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