Which phrase describes the algebraic expression 3 x minus 4?
the sum of three times a number and four
four less than three times a number
the quotient of three times a number less four
the difference between four and three

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

1.35 is the point estimate for mean value of thickness of paint when the sample observation is taken into consideration.

The Mean Value Theorem is a crucial concept in calculus. The original form of the mean value theorem was developed in the 14th century by Parmeshwara, a mathematician from Kerela, India. Furthermore, Rolle provided a simpler model of this back in the 17th century: Rolle's Theorem, which was proved solely for polynomial observation and did not part of the calculus. The current iteration of the Mean Value Theorem was first presented in 1823 by Augustin Louis Cauchy.

The mean value theorem asserts that for a curve passing through two given points, there is one point on the curve where the tangent is parallel to the secant running through the two provided locations.

How to solve?

We are given the following sample for thickness for low-viscosity paint.

0.81 0.87 0.90 1.05 1.11 1.14 1.30 1.30 1.48 1.48 1.59 1.60 1.66 1.69 1.78 1.84.

a) Point estimate of the mean value of coating thickness.

We use the sample mean to estimate the mean value of the coating thickness.

mean= sum of all observations/total number of observations

mean=21.6/16

mean=1.35 which is the point estimate for mean value of thickness of paint.

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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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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.

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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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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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.

The 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:

__

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.

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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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

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A randomly chosen Endure All battery has a 10.56% chance of surviving more than 550 hours based on the 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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Answer: 6 ÷ 1/4 = 24

We can use the Skip, Flip, Multiply method to solve.

Since our first fraction is 6/1, we can leave it alone.

Our next fraction is 1/4, and we flip the numerator and denominator to become 4/1.

Finally, we can multiply our two new fractions.

6/1 × 4/1 = 24/1, which reduces to 24.

The required number of year at 2.5% simple interest on a quarterly basis is 4%.

if the interest rate is 8% each year, however the estimation being referred to requires a quarterly financing cost, then, at that point, the significant loan cost is 2% per quarter. The 2% per quarter is comparable to a straightforward loan fee of 8% each year

We have,

Interest in 3 months = 2.5%

So, interest in one year = 4(2.5%) = 10%

Principle amount = $700

Final amount = $980

To calculate number of years,

total interest = 980 - 700 = $280

Let number of years be t.

Then,

$280/t = 10% of $700

t = $280/$70 = 4 years

Thus, required years 4.

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Answer: y=-22

Step-by-step explanation:

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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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 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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Circumference of the circle is equal to 289.03 cm.

Number of times stone hit the ground = 345

It is the total length covered by the outer boundary of the circle.

It is always equal to  2πr .

So the distance covered in one round of the circle will be equal to 2πr .

A)The stone will hit the ground on each complete rotation.

Hence, the distance travelled each time when the stone hits the ground will be equal to its circumference.

Circumference = 2πr = 2 × 3.14 × 46 = 289.03 cm

B) The stone hits ground once, when the bicycle moves 289.03cm

    We have to calculate for 1 km = 100000cm

Number of times stone hit the ground= 100000 / 289.03 = 345.99

Now, when the stone had hit 345 times, after that it was just close of hitting, the ground so we do not count 0.99

Hence, number of times stone hit the ground = 345

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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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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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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 searchlight is   0.333 ft  deep, with the concept of the parabola equation

We will be using the equation of parabola for calculating the width of the opening here the vertex to focus is 3, so p=3

x² = 4py, where y is the width

=>x² = 4*3*y  

=>x² = 12y  ,  

=>y = x² /12

Since here the dpeth is 2 feet, been the parabola be symmetry, distributed in  two  equal parts, we get 4/2 = 2, the y axix must take (y,-2) and (y,2) now substituting the values we get

y = (2 ^ 2)/12

y = 1/3 ,Therefore the depth is equal to 0.333 ft.

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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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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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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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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.

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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Answer:

Number of ways in which a person can order a four course meal is 1440

Step-by-step explanation:

Combinations are mathematical operations that count the number of possible arrangements for a set of items where the order of the selection is irrelevant.

According to the above definition:

There were 8 different appetizer available for selection.

For each of 8 appetizer , we have the option to order any one of the 12 different main courses , giving 8×12=96 different combinations of appetizer and main courses.

Similarly , for 96 different combinations of appetizer and main courses we have the option to order 5 different vegetables and 3 different deserts , giving 96×5×3=1440

Number of ways in which a person can order a four course meal is 1440

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Answer: 24

Step-by-step explanation: there are 1000g in a kg which means 250g is 1/4 of a kg, so we need to multiply 250 and 6 by 4, so we get our answer of $24/kg of tomatoes.

Answer:

I believe the slope is 1/4

Step-by-step explanation:

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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:

Therefore, the coefficient of multiple determination is ranges from 0 to 1.

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