We know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.
What do we mean by mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, earnings of Maya when she works for 41 hours are:
We know that Maya works for $12.00 per hour.
She's paid 1.5 times her hourly income when she works for more hours after 40 hours.
That will be: 12 × 1.5 = $18
Hence, Maya's income for 41 hours will be:
40 hours + 1 hour (Extra hour)
(12 × 40) + 18
480 + 18
$498
Therefore, we know that Maya's earnings will be $498 for working 41 hours using simple mathematical operations.
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a one-way analysis of variance experiment produced the following anova table. assume normality in the underlying populations. (you may find it useful to reference the q table). summary groups count average column 1 6 0.89 column 2 6 1.31 column 3 6 2.35 source of variation ss df ms f p-value between groups 8.65 2 4.33 16.65 0.0002 within groups 3.83 15 0.26 total 12.48 17 picture click here for the excel data file a. conduct an anova test at the 1% significance level to determine if some population means differ. multiple choice reject h0; we can conclude that some population means differ. reject h0; we cannot conclude that some population means differ. do not reject h0; we can conclude that some population means differ. do not reject h0; we cannot conclude that some population means differ. b. calculate 99% confidence interval estimates of μ1 − μ2, μ1 − μ3, and μ2 − μ3 with tukey’s hsd approach. (if the exact value for nt − c is not found in the table, then round down. negative values should be indicated by a minus sign. round your answers to 2 decimal places.) c. given your response to part b, which means significantly differ?
The confidence interval for the one-way analysis of variance experiment be, (136.27 , 163.73).
On Subtracting 1 from your sample size, we get
1000 – 1 = 999.
On Subtracting confidence level from 1, and then divide by two.
(1 – .99) / 2 = 0.005
Now, df = 999 and α = 0.005
from the table at df = 999 we got 3.274.
Divide your sample standard deviation by the square root of your sample size.
150 / √(1000) = 4.74
Now, 3.274 × 4.74 = 13.73
So, the confidence interval be,
(150 - 13.73 , 150 + 13.73) = (136.27 , 163.73)
Hence, the confidence interval for the one-way analysis of variance experiment be, (136.27 , 163.73).
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The regular price of a chair is $188.99. Determine the sale price if the regular price is reduced by 10% and the price is then reduced another 25%
The Price after reduced 2 times is $127.568
Here the explanation :
For the first reduce : multiply the regular price by 10%
188.99 x 10% =
188.99 X (10/100) = 18.899
then subtraction of this number from the regular price
188.99 - 18.899 = 170.091
The second reduce : multiply the first reduce price by 25%
170.091 X 25% =
170.091 X (25/100) = 42.523
then subtraction of this number from the first reduce price
170.091 - 42.523 = 127.568
So the latest price is $127.568
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Choose the graph for the inequality.
y≤ 2x 1
subtract 10 - 2 1/4
Answer: 7 3/4
Explanation:
Keep in mind that 2 1/4 = 2 + 1/4
10 - 2 = 8
8 - 1/4 = 7 3/4
Therefore your answer is 7 3/4
Answer:
7 3/4
Step-by-step explanation:
Take 1 away from 10 and write 10 as 9 + 1.
1 = 4/4, so 10 = 9 + 4/4 or simply 9 4/4.
Now subtract 2 1/4 from 9 4/4.
9 4/4 - 2 1/4
9 4/4
- 2 1/4
-------------
7 3/4
a sample of 1500 computer chips revealed that 69% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that 72% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.05 level to dispute the company's claim? state the null and alternative hypotheses for the above scenario.
At a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.
What is the null hypothesis in statistics?
The null hypothesis in inferential statistics states that two possibilities are the same. The null hypothesis states that the observed difference is solely due to chance. The likelihood that the null hypothesis is true can be calculated using statistical tests.
Sample size, n =1500
The sample proportion of the chips that do not fail in the first 1000 hrs of their use, [tex]\hat{p} = 0.69[/tex]
Null Hypothesis, H0: p=0.72
Alternate Hypothesis, [tex]Ha: p \neq 0.72[/tex]
Test statistic,
[tex]z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} - \frac{0.69-0.72}{\sqrt{\frac{0.72(1-0.72)}{1500}}} = -2.5877[/tex]
Critical Value,
[tex]Z_{0.05/2} =[/tex]±1.96
Now, since the absolute value of the test statistic i.e, 2.5877 is greater than the absolute value of the critical value i.e, .1.96, thus we will reject the null hypothesis.
Thus at a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.
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which statement(s) correctly describe the coefficient of multiple determination (r2)? select all that apply. multiple select question. it can range from 0 to 1. it can range from -1 to 1. it is the percent of explained variation. it is the same as the correlation coefficient.
The coefficient of multiple determination is describe as it ranges from
0 to 1.
As given in the question,
Explanation about coefficient of multiple determination is as follow:
Coefficient of determination is represented as the square of the correlation.In case of linear regression also, coefficient of determination is represented by the square of the correlation between two given variables.If the coefficient of determination R2 is equal to 0 then value of dependent variable cannot be predicted using independent variable.Coefficient of determination is ranges from 0 to 1.Therefore, the coefficient of multiple determination is ranges from 0 to 1.
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owns 90% of West common stock. This year, Brace generated $50,000 operating income and received $10,000 dividends from West. Brace's taxable income is: Multiple Choice $53,000 $58,000 $50,000 O $52,000
Brace's taxable income is $50,000.
It is given to us that -
Brace Inc. owns 90% of West common stock
Brace generated $50,000 operating income
and, Brace received $10,000 dividends from West
We have to find out Brace's taxable income.
Taxable income can be defined as the income (income amount) of an individual or business that federal or state government agencies use as the basis for determining the taxes owed on them.
The correct formula representing taxable income can be stated as -
A. Taxable income = Total income - Exclusions - Adjustments to income - Deductions - Exemptions.
B. Taxable income = Gross income - Adjustments to income - Deductions - Exemptions.
C. Taxable income = Adjusted gross income - (Deductions + Exemptions).
Since, it is mentioned that Brace Inc. owns 90% of West common stock, it can be determined that the stock share is more than 80%.
This implies that there will be 100% deduction in the value of taxable income since the stock share is more than 80%.
Thus, Brace's taxable income is $50,000.
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which of the following examples are vague questions? select all that apply. 1 point how much time did you spend waiting in line? do you generally prefer hot or cold?
How much time did you spend in line, question 1? is a direct response to the second question, "Do you like hot or cold?" is a vague query.
An inquiry that lacks focus on a particular subject area and is wide, ambiguous, unclear, and nebulous in nature. You won't be able to adequately analyze the data acquired at the end of the day if your survey has ambiguous questions.
You should use specific language in your survey questions, so make sure to do so. Additionally, make sure to refrain from using technical jargon and terminology that few people can normally grasp in your surveys.
Questions that are excessively general or insufficiently specified are ambiguous or vague. Generic responses that aren't pertinent to your research are frequently the outcome. Make sure your survey questions are written simply and in a way that respondents will find them simple to understand in an effort to avoid vague survey questions.
Typical Vague Questions
Do you believe our clients would advocate for us?
Are we superior to other ed-tech businesses?
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if x/3=y/9 then 9/y =
Answer:
3/x
Step-by-step explanation:
Flip them
1 1/3 = y/3 - 9, solve it. i got 13 but every calculating app i use says 31.
Answer: y=-22
Step-by-step explanation:
grant is thinking of two numbers. he says that one of the numbers is 5 times the other number and the sum of the numbers is 36. what are the numbers?
The numbers are 8 and 40, according to the given question.
What do you mean by number?
A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.
According to data in the question,
We have given information:
Sum of the numbers are 36.
The numbers are "x" and "5x";
Now, we can suggest this equation:
x+5x=48
6x=48
x=48/6
x=8
The numbers are:
x=8
5x=5(8)=40.
Therefore, the numbers are 8 and 40.
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In interval estimation, as the sample size becomes larger, the interval estimate
becomes narrower. becomes wider. remains the same, because the mean is not changing.
gets closer to 1.96.
In interval estimation, as the sample size becomes larger the interval estimate becomes narrower.
What is interval estimation?
In statistics, interval estimation is that the use of sample information to estimate associate interval of plausible values of a parameter of interest. this can be in distinction to purpose estimation, which provides one price.
Main body:
A larger sample size or lower variability can end in a tighter confidence interval with a smaller margin of error. A smaller sample size or the next variability can end in a wider confidence interval with a bigger margin of error.
Hence, as the sample size becomes larger the interval estimate becomes narrower.
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Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
A randomly chosen Endure All battery has a 10.56% chance of surviving more than 550 hours based on the z-score.
What do we mean by z-score?A Z-score quantifies how closely a value relates to the mean of a set of values.
Using standard deviations from the mean, the Z-score is computed.
When a data point's Z-score equals 0, it means that the total value of the data point is equal to the mean value.
So, the Z score is used to calculate how much the raw score deviates from the mean.
The Z score is calculated using the following steps:
z = (x - μ)/σ
We know that: x > 550 and μ = 500, σ = 40
z = 550 - 500 / 40
z = 1.25
According to the normal distribution graph:
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, a randomly chosen Endure All battery has a 10.56% chance of surviving more than 550 hours based on the z-score.
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according to a recent survey, 85% of high school sutdents own a personal media player. what is the probability that 6 out of 10 random high school students own a personal media player?
As per the binomial distribution, the probability that 6 out of 10 random high school students own a personal media player is 4%.
Binomial distribution:
The general formula to calculate the binomial distribution is written as,
P = aCx pˣ (1 - p)ᵃ⁻ˣ
Where,
x = Total number of successful trails
a = Total number of events
p = Probability of success
1 – p = Probability of failure
nCr = [n!/r!(n−r)]!
Given,
According to a recent survey, 85% of high school students own a personal media player.
Here we need to find the probability that 6 out of 10 random high school students own a personal media player.
While we looking into the given question,
Total number of student = 10
Success rate = 6
Probability percentage = 85%
When we convert this into decimal then we get the probability as 0.85.
Now, according to the binomial distribution, Substituting in values for this problem, n=10, p=0.85, and X=6 on the formula, then we get,
=> P = [10!/6!4!] x (0.85)⁶ x(1- 0.85)¹⁰⁻⁶
When we simplify this one then we get the probability as,
=> P = 0.04
When we convert this into percentage, then we get the probability as 4%.
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what is a simpler form for the radical expression 4√2401x^12y^16
Answer:
[tex]49x^{6}[/tex][tex]y^{8}[/tex]
Step-by-step explanation:
1. Factor 2401 into its prime factors
2401 = 74
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
2401 = 74
No factors remain inside the root!!
To complete this part of the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
49 = 72
At the end of this step the partly simplified SQRT looks like this:
49√(x^12y^16)
2. Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) √(x8)=x4
(3.2) √(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) √(x5)=x2•√(x)
(4.2) √(x-7)=x-3•√(x-1)
Applying these rules to our case we find out that
SQRT(x12y16) = x6y8
Combine both simplifications:
sqrt (2401x12y16) =
49x6y8
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 2 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Linear Equations w/ Distribution 2(3y-8)=8?
Answer:
Step-by-step explanation:
2(3y-8)=8
First we distribute the numbers inside the brackets, 2x3y , 2x8=
6y-16=8, then, we put the 16 on the other side which turns it positive,
6y=8+16
6y=24
y=4
Sorry for the bad explanation.
what information is missing for the interpretation of an anova if you only run an omnibus/overall anova (without any post-hoc tests)? why do we need to run follow up tests when we conduct a one-way anova?
The statistical method known as analysis of variance (ANOVA) is used to examine how different means differ from one another.
When you only run an omnibus/overall anova without any post-hoc tests, you will be unable to determine which of the groups are statistically different from each other. This is because an omnibus/overall anova simply tells you whether there is a significant difference between any of the groups, but does not tell you which groups are different. Follow up tests are needed to determine which of the groups are statistically different from each other.
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identify the explanatory variable and the response variable. a teacher wants to determine if the amount of homework given to her students can be used to predict the students' test scores.
]]The explanator variable is amount of homework given and the response variable is student's test score.
Variable:
In math variable is an alphabet which is used to represent the unknown number.
Given,
A teacher wants to determine if the amount of homework given to her students can be used to predict the students' test scores
Here we need to identify the explanatory variable and the response variable
While we looking in to the given situation, the we have identified that the two variables are used here is,
=> homework given.
=> Test score
While analyzing the variable we have identified that the explanatory variable defines the situation so it is homework given and the response variable defines the result of the scenario that is the students score.
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Dagmar borrow $19. 800 from her bank to buy a new car. If he get a 6-year loan at 4. 75% interet compounded monthly, how much doe Dagmar pay in full for the car?
Compound interest accrued at a rate of 4.75% per year, compounded once annually, on a principal of $19.80 over a period of six years, resulting in a total of $26.16 in accrued principal and interest.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). %, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
Here,
First, convert R as a percent to r as a decimal
r = R/100
r = 4.75/100
r = 0.0475 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 19.80(1 + 0.0475/1)(1)(6)
A = 19.80(1 + 0.0475)(6)
A = $26.16
Over the course of six years, compound interest accrued on a $19.80 principal at a rate of 4.75% per year, compounded once annually, for a total of $26.16 in accrued principal and interest.
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Translate the following arguments into symbolic form and use the first eight rules of inference to derive the conclusion of each. Use the letters in the order in which they are listed.If clear-cutting continues in primary forests and the Endangered Species Act is not repealed, then either the Endangered Species Act will be repealed or thousands of animal species will become extinct. Clear-cutting continues in primary forests. The Endangered Species Act will not be repealed. Therefore, thousands of animal species will become extinct. (C, E, T)
According to the Endangered Species Act, selling an endangered plant is prohibited. Likewise, exploiting the habitat of an endangered animal is also a punishable act.
The Endangered Species Act is a law created for the conservation of threatened and endangered plants and animals and the habitats in which they are found. The law prohibits any act of taking and selling of any endangered Species.
Endangered Species Act will be repealed or thousands of animal species will become extinct. Clear-cutting continues in primary forests. The Endangered Species Act will not be repealed. Therefore, thousands of animal species will become extinct. (C, E, T)
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One column of numbers consists of 61, 24, and 47. When the digits of the
numbers are added together, the result is 6 + 1 + 2 + 4 + 4 + 7 = 24, and when
the digits of 24 are then added together, the end result is 2 + 4 = 6. If the
same process is performed on the numbers in a second column, what can De
concluded?
• A. If the end result from the second column is not 6, then the sum of
the numbers in the first column is not equal to the sum of the
numbers in the second column.
B. If the end result from the second column is also 6, then the sum of
the numbers in the first column is equal to the sum of the
numbers in the second column.
C. If the end result from the second column is not 6, then the sum of
the numbers in the first column is equal to the sum of the
numbers in the second column.
D. If the end result from the second column is also 6, then the sum of
the numbers in the first column is not equal to the sum of the
numbers in the
second column.
Answer:
The question is incomplete because it must content a list of choices to select the right one.
Any way, a conclusion that you can make, and that is a common one for this kind of questions, is about whether the sum of the numbers of the second column may or not be the same sum of the numbers of the first column.
The condition for the two sums be the same is that when the digits of the second column are added together the result be the same obtained for the sum of the digits of the first column. In this case that is 6.
So, the possible answer is:
If the end result from the second column is not 6, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
Step-by-step explanation:
Answer:
A. If the end result from the second column is not 6, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.
Step-by-step explanation:
You want to know the relationship between the sums of two columns of numbers if the sum of digits of the first column is 6, and the same sum of digits computation is performed on the second column.
Sum of digitsThe sum of digits of a number is the modulo-9 value of that number. When a column of numbers is added, the modulo-9 value of the sum will be the sum of the modulo-9 values of the individual numbers.
If 6 is the modulo-9 value of the sum of a column of numbers, another column of numbers will not have the same sum if its modulo-9 value is not also 6.
The description of choice A applies:
If the end result from the second column is not 6, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.__
Additional comment
Here "sum of digits" refers to the process of repeatedly summing the digits of any multi-digit number until the total is in the range 1–9. This is effectively a modulo-9 calculation.
The "modulo-9" value of a number is normally a digit in the range 0–8. For any non-zero number, the sum of digits will be a number in the range 1–9. The sum of digits calculation will give 9 instead of 0 when the modulo-9 value is 0.
Modulo arithmetic is useful for a number of purposes. One of them is checking evaluation of an expression. This process is also referred to as "casting out nines." Casting out nines is a simple time-honored method of checking arithmetic for errors, though it cannot find digit transpositions.
In a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another (T/F)?
It is true that in a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another.
ANOVA, which represents the analysis of variance, is a statistical test used to examine the distinction between the means of more than two groups.
One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.
In a one-way ANOVA scenario, the overall F value must be statistically significant for more than two of the means to be significantly different.
thus we can say that the given statement is true.
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To solve 6÷1/4, James thinks about how the distance from his home to the store is 1/4 mile and he wonders how many times he would have to walk that distance to walk 6 miles. What is the quotient of 6 and 1/4?
Answer: 6 ÷ 1/4 = 24
We can use the Skip, Flip, Multiply method to solve.
Skip:Since our first fraction is 6/1, we can leave it alone.
Flip:Our next fraction is 1/4, and we flip the numerator and denominator to become 4/1.
Multiply:
Finally, we can multiply our two new fractions.
6/1 × 4/1 = 24/1, which reduces to 24.
Answer Recap: The quotient of 6 and 1/4 is 24.
Evaluate f(x)=2x^2+5x-17 find f(-1)
the digits 1, 2, 3, 4, 5, 6, 7, and 9 are used to form four two-digit prime numbers, with each digit used exactly once. what is the sum of these four primes? (a) 150 (b) 160 (c) 170 (d) 180 (e) 190
The sum of four prime numbers is 190
The correct answer is an option (e)
In this question, we have been given the digits 1, 2, 3, 4, 5, 6, 7, and 9 are used to form four two-digit prime numbers, with each digit used exactly once.
We need to find the sum of these four primes.
For a 2 digit number to be prime, the units digit cannot be even or 5 as it would be divisible by either 2 or 5.
So unit digits are 1, 3, 7, 9
and the tens digits are :2, 4, 5, and 6.
the prime numbers in the 20s : 23, 29.
the prime numbers in the 40s: 41, 43, 47
the prime numbers in the 50s: 53, 59
the prime numbers in the 60s: 61, 67
There are many ways the set of 4 primes can be created
The sum would be,
(2 +4 +5 +6)×10 +(1 +3 +7 +9)
= 170 +20
= 190
Hence, the sum is 190
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instruction in image
3) 85 + x = 125
x = 125 - 85
x = 40
4) 88 + 4x + 8 + 5x + 3 = 180
add like terms
9x + 99 = 180
9x = 180 - 99
9x = 81
x = 9
m<A =
5x + 3 =
5(9) + 3 =
45 + 3 = 48
Which inequality represents the sentence? the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6. â€""3.2n 1.5 less-than-or-equal-to 8.6 â€""3.2n 1.5 greater-than-or-equal-to 8.6 â€""3.2 1.5n less-than-or-equal-to 8.6 3.2 1.5n less-than-or-equal-to 8.6
Inequality (C) -3.2 + 1.5n ≤ 8.6 correctly represents the sentence "the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6."
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
Both mathematical phrases, equations, and inequalities are created by connecting two expressions.
The equal sign (=) indicates that two expressions in an equation are believed to be equivalent.
The symbols >, <, ≤ or ≥ indicate that the two expressions in inequality are not always equal.
So, the sentence we have is:
the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6
Which can be written in inequality as:
-3.2 + 1.5n ≤ 8.6
Therefore, inequality (C) -3.2 + 1.5n ≤ 8.6 correctly represents the sentence "the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6."
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Correct question:
Which inequality represents the sentence?
the sum of negative 3.2 and 1.5 times a number is a maximum of 8.6.
a. -3.2n + 1.5 less-than-or-equal-to 8.6
b. -3.2n - 1.5 greater-than-or-equal-to 8.6
c. -3.2 + 1.5n less-than-or-equal-to 8.6
d. -3.2 - 1.5n less-than-or-equal-to 8.6
PLES HELP ME June knits scarves and hats for kids in her community. She has knitted six less than twice as many hats as scarves, and she has made a total of 78 items. How many hats has she knitted?
) assuming the sample mean and standard deviation are indicative of the class as a whole, in what range does the empirical rule predict that approximately 68% of the class will rank you? ,
Assuming the sample mean and standard deviation are indicative of the class as a whole, the range your class might rank you is from 3 to 9.
What is the sample mean?
The term "Sample Mean" describes the average value of a sample of data taken from a sizable population of data. If the sample size is large and the statistical researchers select random population fragments, it is an effective tool for determining the population mean.
When the sample is large and representative, the estimate of the population mean, which is the average value across the entire population, is more likely to be close to the population mean.
Solution Explained:
So, we know sample mean = 3 and standard deviation = 6
And according to the empirical rule, 68% of the data is within the first standard deviation.
So,
6 - 3 = 3
6 + 3 = 9
Therefore the range of rank for you is from 3 to 9.
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the living standard in country x doubles in 12 years. what is its average annual growth rate roughly?
A country will roughly double its gdp in twelve years if its annual growth rate is 5.8 using the rule of 70.
The rule of 70 is used to determine the time it takes a country to double it growth rate.
To double in 12 years =70/12 = 5.8
Therefore, A country will roughly double its gdp in twenty years if its annual growth rate is 5.8 using the rule of 70.
A measure of the rise in the value of an investment or revenue stream over the course of a year is the annual growth rate, often known as the "simple growth rate" or "average annual growth rate (AAGR)".
The formula for calculating annual growth rate divides the total value of annual growth at the beginning of the year by the total value of that growth at the end of the year.
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