the quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertil- izer to estimate the variance in the pounds of impuri- ties. the sample variance was found to be 6.62. find a 95% confidence interval for the population variance in the pounds of impurities.

Using the concept of unit price, we see that;

Unit price of Brand A  = $0.3654

Unit price of Brand B = $0.3785

The better buy is Brand A

A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can then be used to compare the same type of goods sold in differing weights and amounts.

Now, we are told that brand A has a pack of 24 pencils for $8.77. Thus;

Unit price of Brand A = 8.77/24 = $0.3654

We are told that brand B has a pack of 26 pencils for $9.84. Thus;

Unit price of Brand B= 9.84/26 = $0.3785

Thus;

Unit price of Brand A  = $0.3654

Unit price of Brand B = $0.3785

Thus, brand A has the cheaper unit price and is thus the better buy.

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If she moves at a speed of 1.33 miles per minute while walking 4 miles in 3 minutes, she can cover 20 miles in 15 minutes.

A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

In 3 minutes, she walk 4 miles,

speed=distance/time

=4/3 miles/minute

distance=speed*time

=4/3*15

=20 miles

She can walk 20 miles in 15 minutes if she walks 4 miles in 3 minutes with a speed of 1.33 miles/minute.

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The value after simplifying the number 10^3(10)^4 is 10⁷.

The simplification of given number can be done through the rule of exponent -

[tex] {a}^{m} [/tex] × [tex] {a}^{n} [/tex] = [tex] {a}^{m+n} [/tex], where m and n are the powers of a.

Now, keeping the values in formula -

Value = [tex] {10}^{3} [/tex] × [tex] {10}^{4} [/tex]

Based on the rule, the simplified for these powers will be

Value = [tex] {10}^{3+4} [/tex]

Performing addition of powers on Right Hand Side of the equation

Value = [tex] {10}^{7} [/tex]

Alternatively, the numbers can be expanded and multiplied. Further write the result in scientific notation as above. However, it will a long method which is not practical for very large numbers.

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The expected profit that the contractor will earn from the sale is equal to $177600.

Whenever a contactor does sale of a certain commodities, he expects that whatever he does he earns a profit from the sales. Profit is earned when the selling price of the commodity is more than the price at which the commodity was brought by the contractor.

The expected profit from the sale is calculated as the sum of the profits multiplied by their respective probabilities. In this case, the expected profit is given by:

Expected profit = (240000.0 * 0.76) + (-20000.0 * 0.24) = 182400.0 + (-4800.0) = $177,600

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Answer:

B. Since [tex]\triangle ABC \cong \triangle DEF[/tex] by SSS and [tex]\triangle DEF \cong \triangle GHJ[/tex] by SAS, [tex]\triangle ABC \cong \triangle GHJ[/tex] by the Transitive Property of Congruence.

The congruent statement and the reason why the triangles are congruent is (b) Since AC ≅ GJ and CB ≅ JH, AB must be congruent to GH. So, ABC ≅ GHJ by SSS

From the question, we have the following parameters that can be used in our computation:

Triangles = ABC, DEF and GHJ

There are several theorems that make any two triangles to be congruent

One of these theorems is the SSS congruent theorem

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles ABC and GHJ have the same mark

AC and GJ

CB and JH

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following angles must also be congruent

AB must be congruent to GH

Hence, the congruent statement on the congruency of the triangles is (d)

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Permutation test is used to synthesize the population distribution of the statistic of interest for hypothesis testing of mean, median, and quartiles

An estimation of the population distribution—the distribution from which our observations originated—is the goal of a permutation test. We can then calculate how uncommon our observed values are in comparison to the population.

I find the permutation test to be more natural, and it only relies on the assumption of random assignment of treatment groups.

In a permutation test, you compare the observed test statistic to the distribution of values

you get when the treatment group assignments are shuffled/randomized/permuted.

The null hypothesis that two distinct groups originate from the same distribution is tested using permutation tests, also known as exact tests, randomization tests, or re-randomization tests. A permutation test can be used for hypothesis testing or significance testing (including A/B testing) without requiring any presumptions to be made about the distribution of the samples, such as that the samples must be normally distributed.

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The no. of ways or Probability can a student select 2 from each set of books = 13860

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

By multiplying the number of possibilities there are to choose books from each kind, separately, one can determine the maximum number of ways a student can choose two books from each subject.

Rule for Multiplication:

If an event A can be performed in m different ways and another event B in n different ways, then the two events together can be performed in (mn) different ways.

A combination problem is created by the various ways that math, science, and literature books might be chosen.

As a result, the total number of choices can be calculated as follows: (Number of math books chosen) x (Number of scientific books chosen) x (Number of literature books selection)

= C ( 7,2) * (12,2) * (5,2)

= C (7*6/2!) * (12*11/2!) * (5*4/2!)

= 21 * 66* 10

= 13860

The no. of ways or Probability can a student select 2 from each set of books = 13860

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In percent, the fraction [tex]\frac{1}{9}\\\\[/tex] can be calculated as 11.11%.

A percentage is a common way to represent statistical data, and it is usually used to indicate one-hundredth, with the symbol "%." To calculate the percentage, it is given by:

Percentage (%) = value ÷ total value multiplied by 100%

In conclusion, the percentage of a fraction [tex]\frac{1}{9}\\\\[/tex] is 11.11%.

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Answer:

x = 8/3

y = 10/3

Step-by-step explanation:

We add (1) and (2) to get 3x = 8. This means that x = 8/3. We substitute it back into (1) to get 8/3 + y = 6 which shows that y = 10/3

The isotopes in the set I are [tex]^{14} _{7} B[/tex] and [tex]^{15} _{7} C[/tex] and set II are [tex]^{20} _{10} E, ^{21} _{10}F[/tex] and [tex]^{22} _{10} G[/tex].

Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.

Isotopes are elements with the same atomic number but different mass.

In this case, the elements in set I- B and C has the same atomic number 7 but had different mass numbers and the elements in set II- E, F and G had the same atomic number 10 and different mass numbers, therefore they are known as isotopes.

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Answer:

-4/7

Step-by-step explanation:

The slope of the given line is [tex]\frac{3-(-4)}{4-0}=\frac{7}{4}[/tex].

Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-4/7[/tex].

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

We have,

Let's first find the slope of the given line passing through (4, -3) and

(0, -4):

slope = (change in y) / (change in x)

= (-4 - (-3)) / (0 - 4)

= (-4 + 3) / (-4)

= -1 / (-4)

= 1/4

The slope of the given line is 1/4.

Now, to find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope:

[tex]slope_{perpendicular} = -1 / slope[/tex]

= -1 / (1/4)

= -4

Therefore,

The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.

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Answer:

0.0474

Step-by-step explanation:

mean = \mu = 0.8

Using the Poisson probability formula,

P(X = x) = (e-\mu * \mux ) / x!

P(X > 2) = 1 - P(x \le 2)

= 1 - P(x = 0) - P(x = 1) - P(x = 2)

= 1 - (e^-0.8 * 0.80 ) / 0! - (e^-0.8 * 0.8^1 ) / 1! - (e^-0.8 * 0.8^2 ) / 2!

=  0.0474

So, the answer is 0.0474

If two men refuse to serve together we can choose in a) 1275 ways. If b) 2 women refuse to serve together we can choose in 110 ways and if c) 1 man and 1 woman refuse to serve together then we can choose in 750 ways.

a)

Here we can get 3 cases.

The first man is elected

The second man is elected

Neither f the 2 is included

In the first 2 cases, we need to choose 4 men from 7 while in the third case we need to choose 4 men from 6.

Therefore we get

⁷C₄ X ⁶C₄  +  ⁷C₄X ⁶C₄  +  ⁶C₄X ⁶C₄

35 X 15  +  35 X 15  +  15 X 15

= 1275 ways

b)

Just like before we will have 3 cases here.

Here we will have to choose 4 women from 5 for the first 2 cases and 4  from 4 for the third case. Hence we get

⁵C₄ X ⁸C₄  +  ⁵C₄ X ⁸C₄  +  ⁴C₄ X ⁸C₄

= 50  +  50  +  10

= 110 ways

c)

Here we will have 3 cases again

The man is included

The woman is included

neither is included

Therefore we will get

⁸C₄ x ⁵C₄  +  ⁷C₄ X ⁶C₄  +  ⁷C₄ X ⁵C₄

= 10 X 5  +  35 X 15  +  35 X 5

= 750 ways

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The partial derivative dy/dx at x = e is given as follows:

[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]

The function in this problem is defined as follows:

y = tan(u).

The function y is a function of the variable u, which is a function of the variable v, which is a function of variable x, then the function of variable x can be written as follows:

[tex]y = \tan{\left(\ln{x} - \frac{1}{\ln{x}}\right)}[/tex]

Then, applying the chain rule, the derivative is the derivative of the outer tangent function multiplied by the derivative of the inner ln function.

The inner function is of:

[tex]\ln{x} - \frac{1}{\ln{x}}[/tex]

Which has a derivative of:

[tex]\frac{1}{x} + \frac{1}{x\ln^2{x}}[/tex]

The outer tangent function has a derivative of:

-sec²(x).

Then the complete derivative is of:

[tex]\frac{dy}{dx} = -\sec^2{\left(\ln{x} - \frac{1}{\ln{x}}\right)} \times \left(\frac{1}{x} + \frac{1}{x\ln^2{x}}\right)[/tex]

At x = e, the numeric value of the derivative is given as follows:

[tex]\frac{dy}{dx}(e) = -\sec^2{0} \times \frac{2}{e}[/tex]

[tex]\frac{dy}{dx}(e) = -\frac{2}{e}[/tex]

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The value of a=12

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equals to symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex]\frac{a}{15}=\frac{4}{5}[/tex]

or, 5a=4*15

or, a= 4*15/5

or, a= 12

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The number of party popper she bought is 32 and the number of balloons she bought is 18.

The first step is to form a system of equations using the information provided in the question.

0.20x + 0.50y = $20 equation 1

x + y = 52 equation 2

The solution using the elimination method :

Multiply equation 2 by 0.20

0.20x + 0.20y = 10.40 equation 3

Subtract equation 3 from equation 2 :

0.30y = 9.60

Divide both sides of the equation by 0.30

y = 9.60 / 0.30

y = 32

The solution using the substitution method:

Make x the subject of the formula in equation 2

x = 52 - y equation 3

Substitute for x in equation 1 :

0.20(52 - y) + 0.50y = $20

10.40 - 0.20y + 0.50y = $20

Combine similar terms together

0.50y - 0.20y = $20 - $10.40

0.30y = $9.60

y = 9.60 / 0.30

y = 32

x = 50 - 32

x = 18

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Principal will be $1000

Given values

Simple interest, SI= $800

Interest rate, R=8%

Time, T=10 months

Principle, P= Y

As we know;

[tex]Simple Interest, SI=P×R×T[/tex]

By substituting the values, we get

$800= Y ×8% ×10

$800=0.8Y

$800÷0.8= Y

$1000=Y

Thus the above response is correct.  

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The chi-square goodness-of-fit test is a statistical test that is used to determine whether a sample comes from a population with a specific distribution. There are a few conditions that must be met in order to use this test:

1. The data must be collected from a random sample. This ensures that the sample is representative of the population, which is necessary for the test to be valid.

2. The data must be categorical. This means that the observations must fall into distinct categories, rather than being continuous or ordinal.

3. The expected frequencies for each category should be at least 5. This ensures that the chi-square test statistic is approximately normally distributed, which is necessary for the test to be valid.

4. The data must be independent. This means that the outcome of one observation should not influence the outcome of another observation.

If these conditions are not met, the chi-square goodness-of-fit test may not be appropriate. In such cases, it may be necessary to use a different statistical test.

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Answer:

  x = 3

Step-by-step explanation:

You want to know how to solve 2x +3 = 9.

A solution is an equation of the form ...

  x = constant

You can get a clue to the solution process by considering what happens to the variable. Here, ...

The solution process reverses these operations, starting with the last one first. The properties of arithmetic and equality are used.

We can undo the addition of 3 by adding -3 to both sides of the equation.

  2x +3 -3 = 9 -3

  2x +0 = 6 . . . . . . . . . . . adding 3 and its additive inverse gives zero

  2x = 6 . . . . . . . . . . . . . 0 is the additive identity element, so 2x+0 = 2x

We can undo the multiplication by multiplying by the multiplicative inverse of 2. That is, we can multiply by 1/2.

  (1/2)2x = (1/2)6

  1x = 3 . . . . . . . multiplying 2 and its multiplicative inverse gives 1

  x = 3 . . . . . . 1 is the multiplicative identity element, so 1x = x

Please note that multiplying by 1/2 is the same thing as dividing by 2. That is, multiplication and division are inverse operations.

The solution is x = 3.

It is wise to check that the solution you found makes the equation be true.

  2x +3 = 9

  2(3) +3 = 9 . . . . . substitute for x

  6 + 3 = 9 . . . . . . . true

__

Additional comment

This solution process works for just about any "solve for ..." situation, if an algebraic solution is possible. In high school math, you are introduced to just about every kind of equation we know how to solve. The list is fairly short.

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here's two, I used mathday but day with a w

Step-by-step explanation:

good website for it and it gives good explanation! Gl

Answer:

blip

Step-by-step explanation:

blipgg

Answer:

Step-by-step explanation:

following the rule of the Pythagorean triple the answer is yes

Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle

The probability of rolling a number greater than 5 or doubles will be 0.78.

       P(A)  =  n(A)/n(S)

        where -

       n(A) = Number of outcomes favorable to event A.

        n(S) = Total number of outcomes.

We have two dices are rolled.

The sample space for sum greater than 5 will be 26. For doubles, we will add 2 pairs (1, 1) and (2, 2) to 26 to get a total sample space of 28. Remaining doubles are already in 26. So, the probability of rolling a number greater than 5 or doubles will be -

P(A) = 28/36 = 0.78

Therefore, the probability of rolling a number greater than 5 or doubles will be 0.78.

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[Question in english -

From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]

Therefore, the limitations census of entire population can be described in  major points like  it can be Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable and further more

A key component of the U.S. Federal Statistical System, the United States Census Bureau, or Bureau of the Census, is in charge of gathering information on the population and economy of the United States.

Here,

Therefore ,the limitations of generalizing census findings back to the entire population are:-

The homeless population is underrepresented in the findings even though every home is required to complete a census report. This is because they are frequently impossible to reach, interview, and count.

People who do not speak either English or Spanish as their first language and whose primary language is one of those two are more likely to be overlooked in the census.

Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable.

The population fluctuates constantly, so it is unlikely that the population on the day the census results are released would closely resemble the population as described in the census.

Those who entered the country illegally but intend to stay do not submit a report.

Therefore , there are 5 major limitation described above .

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On solving the provided question, we got to know that, Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Compared to mixers, the dealer sold twice as many food processors.

Let M be the quantity of mixers sold.

Therefore, 2M is the quantity of food processors sold.

A total of 60 of the three appliances were sold by the dealer.

M + 2M = 3M

Thus, 3M is a representation of the whole sales of mixers and food processors.

60 appliances were purchased in total, thus 60 - 3M equals the quantity of blenders purchased.

Everything was sold by the merchant for a total of $4,200.

We get: (30)(M) + (120)(2M) + (50)(60 - 3M) = 4,200

30M + 240M + 3000 - 150M = 4200

130M + 3000 = 4200

120M = 1200

M = 10

The retailer so sold 10 mixers.

This indicates that the vendor sold 20 food processors and 30 food processors.

Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

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10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

percentage, a relative value indicating hundredth parts of any quantity.

The formula for quarterly compound interest formula:

[tex]A=P(1+\frac{r}{4} )^{4t}[/tex]

P is the principle amount

t is time

r is rate of interest

A is final amount

[tex]1750=1000(1+\frac{0.0575}{4} )^{4t}[/tex]

[tex]1750=1000(1+0.0144)^{4t}[/tex]

[tex]1750=1000(1.0144)^{4t}[/tex]

Divide both sides by 1000

[tex]1.75=1.0144^{4t}[/tex]

Take log on both sides

log1.75=4tlog1.0144

0.243=4t(0.006)

0.243=0.024t

Divide both sides by 0.024

t=10.12

t=10 years

Hence, 10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

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Simple probability is the calculation of an outcome or the chance of an event ever happening.

18.65% probability that the person is from Washington

Two events, A and B.

[tex]P(B/A)=\frac{P(B)*P(A/B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Arrived by train.

Event B: From Washington.

15% are from Washington

This means that [tex]P(B)=0.15[/tex]

12% of the attendees from Washington came to the conference by train.

This means that [tex]P(A/B)=0.12[/tex]

Probability of arriving by train:

6% of 60%(from California), 17% of 25%(from Oregon) or 12% of 15%(from Washington). So

[tex]P(A)=0.06*0.6+0.17*0.25+0.12*0.15=0.0965[/tex]

If an attendee is selected at random and found to have arrived by train,

[tex]P(B/A)=\frac{0.15+0.12}{0.0965} =0.1865[/tex]

=0.1865

18.65% probability that the person is from Washington

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−32i is the answer if you use DeMoivre's theorem to find (1−i)^10.

A formula for determining the powers of complex numbers is provided by De Moivre's theorem. It might be easier to comprehend de Moivre's theorem if we first look at what happens when we multiply a complex number by itself. This illustrates how the argument is multiplied by two and the absolute value is squared when squaring a complex number.

One of the most important and useful theorems in the study of complex numbers is DeMoivre's Theorem, which combines trigonometry with complex numbers. It's also helpful to find relationships between trigonometric functions at different angles. The name of the theorem pays homage to the well-known mathematician De Moivre, who made several contributions to mathematics, notably in the areas of probability theory and algebra. Attached below is the answer.

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