4. Solve each equation for x.
a. 3x - 12y = 27
c. 4x - k= 17
b. 6x - 7y= -2
d. kx + c = 9

The empirical formula of compound X is MnO₂.

The empirical formula of compound Y is Mn₃O₄.

We have,

To determine the empirical formulas of compounds X and Y, we need to find the ratio of the elements present in each compound.

For compound X:

The percentage of manganese (Mn) is 63.3%, which corresponds to 63.3 grams out of 100 grams.

The percentage of oxygen (O) is 36.7%, which corresponds to 36.7 grams out of 100 grams.

To find the empirical formula of X, we need to determine the ratio of Mn to O. To simplify the ratio, we can divide both values by their respective atomic masses.

The atomic mass of Mn is approximately 54.94 g/mol, and the atomic mass of O is approximately 16.00 g/mol.

For Mn: (63.3 g) / (54.94 g/mol) ≈ 1.15 mol

For O: (36.7 g) / (16.00 g/mol) ≈ 2.29 mol

The ratio of Mn to O is approximately 1.15:2.29, which simplifies to approximately 1:2.

Therefore, the empirical formula of compound X is MnO₂.

Now, let's calculate the empirical formula of compound Y using a similar approach:

The percentage of Mn in Y is 72.0%, which corresponds to 72.0 grams out of 100 grams.

The percentage of O in Y is 28.0%, which corresponds to 28.0 grams out of 100 grams.

Using the atomic masses mentioned earlier:

For Mn: (72.0 g) / (54.94 g/mol) ≈ 1.31 mol

For O: (28.0 g) / (16.00 g/mol) ≈ 1.75 mol

The ratio of Mn to O in compound Y is approximately 1.31:1.75, which simplifies to approximately 3:4.

Therefore, the empirical formula of compound Y is Mn₃O₄.

Thus,

The empirical formula of compound X is MnO₂.

The empirical formula of compound Y is Mn₃O₄.

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Step-by-step explanation:

Probabibility = 1/6 * 1/6 = 1/36 = 2.77%.

Answer:

the answer is C

Step-by-step explanation:

The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) \(\sqrt{x + 5}\)

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) \(\sqrt{\dfrac{5}{x} } +3= 17\)

\(\sqrt{\dfrac{5}{x} }= 17-3 =14\)

\(\dfrac{5}{x} }=14^2=196\)

\(x = \dfrac{5}{196}\)

9e) \(\sqrt{\dfrac{4}{x} } = 1\)

\(\dfrac{4}{x} } = 1^2\)

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) \(\sqrt{\dfrac{0.6}{36} }\)

\(\sqrt{\dfrac{0.6}{36} }\) = \(\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13\)

9h) \(\sqrt{\dfrac{4-10}{0.01} }\)

\(\sqrt{\dfrac{4-10}{0.01} }\)= √(-600) = √(-1)·√(600) = i·10·√6

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The given First Order Logic sentences are:

\(2.1 ∀x∃y(L(x,y)), \\2.2 ∃x∃y∃z(L(x,y)\\L(x,z)∧¬(y=z)\\∀w(L(x,w)⟹((w=y)∨(w=z))\)

The First Order Logic sentence \(∀x∃y(L(x,y))\) means that "for all x, there exists at least one person y such that x loves y."

So, the sentence implies that every person in the set of all people loves at least one person. The First Order Logic sentence

\(∃x∃y∃z(L(x,y)∧L(x,z)∧¬(y=z)\\∀w(L(x,w)⟹((w=y)∨(w=z)))\)

can be translated to English as follows: "There exist three people x, y, and z, such that x loves both y and z but y and z are different, and for all the other people in the world who x loves, that person is either y or z."So, we can conclude that the First Order Logic sentence

\(∃x∃y∃z(L(x,y)∧L(x,z)∧¬(y=z)\\∀w(L(x,w)⟹((w=y)∨(w=z))))\)

talks about the existence of three people, x, y, and z in the set of all people such that x loves both y and z, but y and z are different, and there is no other person who x loves except y and z.

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Answer:

1/4 = 2/8 = 3/12 = 4/16 = 5/20

These fractions are equivalent to your number

the probability that at least 3 phones are defective in a random sample of 37 phones is approximately 0.7889

To calculate the probability that at least 3 phones are defective in a random sample of 37 phones, we can use the binomial probability formula. The formula for the probability of at least a certain number of successes in a binomial distribution is:

P(X ≥ k) = 1 - P(X < k)

Where:

P(X ≥ k) is the probability of at least k successes

P(X < k) is the probability of less than k successes

In this case, "success" refers to a defective phone, and the probability of a phone being defective is 11% or 0.11. The sample size is 37 phones.

To calculate the probability, we need to sum up the probabilities of having 3, 4, 5, ..., up to 37 defective phones. We can use this formula:

P(X < k) = Σ (n choose i) * p^i * (1 - p)^(n - i)

Where:

n is the sample size (37)

i is the number of defective phones (ranging from 0 to k-1)

p is the probability of a defective phone (0.11)

Let's calculate the probability:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the formula above, we can calculate each term:

P(X = 0) = (37 choose 0) * 0.11⁰ * (1 - 0.11)³⁷

P(X = 1) = (37 choose 1) * 0.11¹ * (1 - 0.11)³⁷

P(X = 2) = (37 choose 2) * 0.11² * (1 - 0.11)³⁵

Now, let's calculate each term and sum them up:

P(X = 0) = (1) * (1) * (0.89)³⁷ = 0.0134

P(X = 1) = (37) * (0.11) * (0.89)³⁶ = 0.0613

P(X = 2) = (666) * (0.11)² * (0.89)³⁵ = 0.1364

Finally, calculate the probability:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.0134 + 0.0613 + 0.1364

= 0.2111

P(X ≥ 3) = 1 - P(X<3)

= 1 - 0.2111

=  0.7889

Calculating this value, the probability that at least 3 phones are defective in a random sample of 37 phones is approximately 0.7889

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Answer:

2 and 3

Step-by-step explanation:

Let us start by representing the first consecutive number with x. In a similar sense, the next consecutive number would be x+1. According to the given question, we can write the following equation:

\(x+x+1=3x-1\)

Solving for the equation by isolating the term containing x, we have:

\(2x+1=3x-1\\2x+2=3x\\\fbox{x=2}\)

Since we have designated x as the first consecutive integer, the other integer we are looking for is x+1, or \(\fbox{3}\) .

I hope this helps! Let me know if you have any questionss :)

Answer:

6x

Step-by-step explanation:

2x × 2= 4x

x +x = 2x

4x+ 2x = 6x

58 min/day  rate did she practice in minutes per day.

What is  time?

1 day = 2030 min ÷ (5 weeks × 7 days)

1 day = 2030 ÷ 35

1 day = 58 minutes

rate = 58 min/day

Therefore, 58 min/day  rate did she practice in minutes per day.

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Answer:

perpendicular slope = - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x - 3y = 63 ( subtract 3x from both sides )

- 3y = - 3x + 63 ( divide through by - 3 )

y = x + 21 ← in slope- intercept form

with slope m = 1

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{1}\) = - 1

Jose can plow 7.5 acres of land in an hour. it will take Jose 12 minutes to plow 1.5 acres of land.

To calculate how long will it take Jose to plow 1.5 acres of land, we can use the following steps:

1: Determine the number of acres Jose can plow per minute. Dividing 7.5 acres by 60 minutes will give us the number of acres Jose can plow in 1 minute:7.5 ÷ 60 = 0.125 acres/minute

2. Determine the number of minutes it will take Jose to plow 1.5 acres of land. To calculate the number of minutes, we can divide the number of acres by the acres Jose can plow in 1 minute: 1.5 ÷ 0.125 = 12 minutes

Therefore, it will take Jose 12 minutes to plow 1.5 acres of land.

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The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.

According to the statement

We have given that the there is a algorithm which is used to data cleanup problem of removing 0 values from a data set, and scans a list from left to right and copies every legitimate value into a new list.

and we have to explain about that algorithm.

So,

Here we given that the algorithm copies and paste the values in the new files then

the algorithm is called the copy over algorithm.

So, The copy over algorithm is a a single specimen of something that occurs in a multiple edition, such as a book, article, etc. a matter to be reproduced in print or an imitation or reproduction of an original.

So, The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.

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The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.

In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.

The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.

By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.

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m > 650 miles

A mileage over 650 miles makes company A cheaper than B.

1) Gathering the data

Company A

$127 (unlimited mileage)

Company B

$75 + 0.08m

2) To find out the mileage that makes Company A cheaper than Company B, we can write out the following:

3) Hence when we drive over 650 miles the Company A becomes cheaper than B.

The probability that in a random sample of 5, exactly 3 germinate, is given as follows:

0.3125 = 31.25%.

The binomial distribution formula gives the probability of obtaining a number of successes in a fixed number of independent trials, in which each trial has only two possible outcomes (success or failure) and the trials are independent.

The mass probability formula is defined by the equation presented as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters, along with their meaning, are defined as follows:

The parameter values for this problem are given as follows:

n = 5, p = 0.5.

Hence the probability is given as follows:

P(X = 3) = 5!/(3! x 2!) x (0.5)³ x (0.5)² = 0.3125 = 31.25%.

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The following line of code in Python calculates the probability P(t > 0.115) for a Student's t-distribution with mean 0, standard deviation 1, and 49 degrees of freedom:

import scipy.stats as stats

1 - stats.t.cdf(0.115, df=49)

The cdf function calculates the cumulative density function (CDF) of the t-distribution, which gives the probability that the random variable (t-statistic) is less than or equal to a given value. To find the probability that it is greater than a given value, we subtract the CDF from 1.

Standard deviation is a statistical measure that calculates the amount of variation or dispersion of a set of data values. It represents how far the data points in a set deviate from the mean.

A low standard deviation indicates that the data points are close to the mean, while a high standard deviation indicates that the data points are more spread out.

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Answer:

D

Step-by-step explanation:

Answer:

y - 5 = -7(x - 8)

Step-by-step explanation:

We can immediately adapt y - k = m(x - h) as follows:  replace m with -7, h with 8 and k with 5, obtaining:

y - 5 = -7(x - 8)

This is the desired equation in point-slope form.

Answer: 19

Step-by-step explanation:

The expressions are equivalent and help us find the product of two numbers, which are 30 and 2. This principle can be applied to solve complex equations. Here option A is the correct answer.

The two expressions, \(\left(30-2\right)\left(30+2\right) & 30^{2}-2^{2}\), are equivalent due to the distributive property of multiplication over addition. By simplifying both expressions, we can see that they both evaluate to the same value of 868.

To find the product of two numbers, we can use the fact that \(30^{2}-2^{2}\) is equal to (30+2)(30-2). This can be derived from the identity \((a+b)(a-b) = a^{2}-b^{2}\), where a and b are any real numbers.

Therefore, we can conclude that the two numbers whose product is being calculated are 30 and 2. We can check this by multiplying 30 and 2, which gives us 60, and verifying that (30+2)(30-2) = 32*28 = 896, which is equal to the product of 30 and 2 added to the square of 2, i.e., \(30 \times 2+2^{2} = 60+4 = 64\).

In conclusion, the expressions \(\left(30-2\right)\left(30+2\right)\) and \(30^{2}-2^{2}\) are equivalent and help us find the product of two numbers, which are 30 and 2. This mathematical principle can be applied to many other problems in algebra and can be a useful tool for solving complex equations and problems.

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Complete question:

The expressions \(\left(30-2\right)\left(30 2\right)\) and \(30^{2}-2^{2}\) are equivalent and can help us find the product of two numbers. which two numbers are they?

A - 30, 2

B - 30, 4

C - 4, 39

D - 5, 32

Answer:

(3,3)

Step-by-step explanation:

multiply the bottom equation by -2 to cancel out the x's

-2(2x+3y=15)

-4x-6y=-30

line the two equations up

4x+2y=18

-4x-6y=-30

subtract downwards

-4y=-12

divide by -4

y=3

plug y in for one of the equations

4x+2(3)=18

4x+6=18

4x=12

x=3

hope this helps!

Answer:

B

Step-by-step explanation:

plug in 1 for x and 4 for y

4 + 4 = 4(1+1)

8 = 8

Plug in 2 for x and 8 for y

8+ 4 = 4(2+1)

12 = 12

====================================================

Explanation:

3/13 = 15/65 after multiplying top and bottom by 5

2/5 = 26/65 after multiplying top and bottom by 13

Let's say there are 65 marbles in the bowl. That would mean 15 of them are red (since 15/65 reduces to 3/13) and 26 are blue. That gives 15+26 = 41 so far. Leaving 65-41 = 24 marbles that must be green.

The probability of selecting a green marble is 24/65. Once that first green marble is taken out, it is not replaced. We have 65-1 = 64 marbles left, 15 of which are red. The probability of picking red on the second selection is 15/64.

Multiply the fractions mentioned:

(24/65)*(15/64)

(24*15)/(65*64)

360/4160

9/104

As n approaches infinity, this ratio approaches 1. Therefore, the series diverges by the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of the (n+1)th term to the nth term is less than 1, then the series converges. Using this test, we can see that the absolute value of the ratio of the (n+1)th term to the nth term is:

|((-9)ⁿ⁺¹ * (2(n+1) + 1)!)/((-9)ⁿ * (2n + 1)!)|

Simplifying this expression, we get:

|(-9) * (2n + 3) * (2n + 2)/(2n + 1)(2n + 2)(-9)|

Which simplifies further to:

|2n + 3|/(2n + 1)

In summary, we used the ratio test to determine the convergence/divergence of the given series. The test involves taking the absolute value of the ratio of the (n+1)th term to the nth term and finding the limit as n approaches infinity.

If the limit is less than 1, the series converges; if the limit is greater than 1, the series diverges; and if the limit is equal to 1, the test is inconclusive and another test must be used. In this case, the limit was equal to 1, so we concluded that the series diverges.

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The correct answer is (4x^3 - 8x^2 )

Solve by using Foil's Method

Multiply (x - 3)(4x^2)

Begin, by multiplying together, the first terms of binomial

= x * 4x^2 = 4x^3

Now, multiply the last term of binomial.

= -3 * 4x^2 = -12x^2

Sum up the partial products starting from the first to last product from the first to last product and collect it:

=(4x^3 - 8x^2 )

Now, Let us know

What is Foil's Method ?

FOIL a mathematical series of steps used to multiply two binomials.

By definition we have the meaning of FOIL is given by:

F: First

O: Outer

I: Inner

L: Last

Binomial is simply an expression that consist of two variables or terms separated by either the addition sign (+) or subtraction (-).

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Answer:

$24.

Step-by-step explanation:

I multiplied 4 by 7 to get 28. Then I multiplied $28 by three weeks and got $84. Since $84 is more than I owe I subtracted $84 by $60 and got $24. I would give my friend $60 and keep $24. Hope this helps! Have a great day!

Answer:

D

Step-by-step explanation:

7.3+(-7.3)

hope that help

Answer:

Step-by-step explanation:

-4.5+4.4+0.1=0

A. =0.1

B. =-13.3

C. =0

D. =0