Find the distance from (-3,-1) to (2, 11).

Answer:25.7

Step-by-step explanation:

The probability that the one math major and one computer science major who refuse to serve together wind up on the committee together is 3/7.

The probability that the one math major and one computer science major who refuse to serve together wind up on the committee together, we can consider two cases:

Case 1: The math major who refuses to serve is selected.

In this case, we need to select 3 math majors from the remaining 4 math majors and 2 computer science majors from the 4 computer science majors who are willing to serve together. The probability of this case can be calculated as:

P(case 1) = (4 choose 3) × (4 choose 2) / (9 choose 5)

Case 2: The computer science major who refuses to serve is selected.

In this case, we need to select 3 math majors from the 5 math majors who are willing to serve together and 2 computer science majors from the remaining 3 computer science majors. The probability of this case can be calculated as:

P(case 2) = (5 choose 3) × (3 choose 2) / (9 choose 5)

To find the overall probability, we need to sum up the probabilities of both cases:

P = P(case 1) + P(case 2)

Calculating the probabilities:

P(case 1) = (4 choose 3) × (4 choose 2) / (9 choose 5) = (4 × 6) / 126 = 24 / 126 = 4 / 21

P(case 2) = (5 choose 3) × (3 choose 2) / (9 choose 5) = (10 × 3) / 126 = 30 / 126 = 5 / 21

P = P(case 1) + P(case 2) = 4/21 + 5/21 = 9/21 = 3/7

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the answer is 3x²

Step-by-step explanation:

we know that k = 3x

when we look at the actual equasion we can se that y = kx, meaning we have to multiply x by 3x which would give us 3x²

Answer:  the answer is 3x^2 three x to the power of 2

The solutions of provide logarithmic equations are present in below :

1) x = 9 ; 2) x = 0 ; 3)p = 7/9 ; 4) k= 2 ; 5) a= -1 ; 6) r = -1/2 ; 7) n = 2 ; 8) x = 1/35 ; 9) m = -2 ; 10) x = 84 ; 11) v = -6, -6 ; 12) x = -4, -7

The logarithmic number is associated with exponent and power, such that if xⁿ = m, then it is equal to logₓ m = n. That is exponential value are inverse of logarithm values. Some basic properties of logarithmic numbers:

Now, we solve each logarithm equation one by one. Assume that 'log' is the base-10 logarithm where absence of base.

1) log (5x) = log (2x + 9)

Exponentiate both sides

=> 5x = 2x + 9

=> 3x = 9

=> x = 9

2) log (10 − 4x) = log (10 − 3x)

Exponentiate both sides,

=> 10 - 4x = 10 - 3x

simplify, => x = 0

3) log (4p − 2) = log (−5p + 5)

Exponentiate both sides,

=> 4p - 2 = - 5p + 5

simplify, => 9p = 7

=> p = 7/9

4) log (4k − 5) = log (2k − 1)

Exponentiate both sides,

=> 4k - 5 = 2k - 1

simplify, => 2k = 4

=> k = 2

5) log (−2a + 9) = log (7 − 4a)

Exponentiate both sides,

=> - 2a + 9 = 7 - 4a

simplify, => 2a = -2

=> a = -1

6) 2log₇( −2r) = 0

=> log₇( −2r) = 0

using the property, log꜀a = n <=> cⁿ = a

=> ( 7⁰) = - 2r

=> -2 × r = 1 ( since a⁰ = 1 )

=> r = -1/2

7) −10 + log₃(n + 3) = −10

=> log₃(n + 3) = −10 + 10 = 0

using the property, log꜀a = n <=> cⁿ = a

=> 3⁰ = n + 3

=> 1 = n + 3

=> n = 2

8) −2log₅ ( 7x ) = 2

=> log₅ 7x = -1

=> 5⁻¹ = 7x

=> x = 1/35

9) log( −m) + 2 = 4

=> log( −m) = 2

Exponentiate both sides,

=> -m = 2

=> m = -2

10) −6log₃ (x − 3) = −24

simplify, log₃ (x − 3) = 4

=> (x - 3) = 3⁴ ( since log꜀a = n <=> cⁿ = a )

=> x - 3 = 81

=> x = 84

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

=> log₁₂ (v²+ 35) - log₁₂ (−12v − 1) = 0

Using the quotient property of logarithm,

\(log_{12}( \frac{v²+ 35}{-12v-1}) = 0 \)

\(\frac{v²+ 35}{-12v - 1} = {12}^{0} = 1 \)

\(v²+ 35 = −12v − 1\)

\(v²+ 35 + 12v + 1 = 0\)

\(v²+12v + 36 = 0\)

which is a quadratic equation, and solve it by middle term splitting method,

\(v²+ 6v + 6v + 36= 0\)

\(v(v + 6) + 6(v + 6)= 0\)

\((v + 6) (6 + v)= 0\)

so, v = -6, -6

12) log₉(−11x + 2) = log₉ (x²+ 30)

=> log₉ (x²+ 30) - log₉(−11x + 2) = 0

Using the quotient property of logarithm,

\(log₉(\frac{x²+ 30 }{−11x + 2}) = 0\)

\( \frac{x²+ 30}{-11x + 2} ={9}^{0} = 1 \)

=> x² + 30 = - 11x + 2

=> x² + 11x + 30 -2 = 0

=> x² + 11x + 28 = 0

Factorize using middle term splitting,

=> x² + 7x + 4x + 28 = 0

=> x( x + 7) + 4( x + 7) = 0

=> ( x + 4) (x+7) = 0

=> either x = -4 or x = -7

Hence, required solution is x = -4, -7.

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Complete question:

kuta software infinite algebra 2 logarithmic equationsSolve each equation.

1) log 5x = log (2x + 9)

2) log (10 − 4x) = log (10 − 3x)

3) log (4 − 2) = log (−5 p + 5)

4) log (4k − 5) = log (2k − 1)

5) log (−2a + 9) = log (7 − 4a)

6) 2log₇ −2r = 0

7) −10 + log₃(n + 3) = −10

8) −2log₅ 7x = 2

9) log −m + 2 = 4

10) −6log₃ (x − 3) = −24

11) log₁₂ (v²+ 35) = log₁₂ (−12v − 1)

12) log₉(−11x + 2) = log₉ (x²+ 30)

Answer:

5:3

Step-by-step explanation:

20:12

10:6

5:3

diving speed:surface speer, so u put them side by side and simplest form it

The resulting polynomial will have a degree of is \($g(h(x))$\)a polynomial that results from substituting \($h(x)$ into $g(x)$.\)\($(\text{degree of } h(x)) \times 6$.\)

To determine the degree of the polynomial $h(x)$, we need to analyze the degree of the composite polynomial \($f(g(x))g(h(x))h(f(x))$.\)

Let's break down the composite polynomial:

$f(g(x))$ is a polynomial that results from substituting $g(x)$ into $f(x)$. Since $g(x)$ is a polynomial of degree $3$ when substituted into $f(x)$ of degree $6$, the resulting polynomial will have a degree of \($6 \times 3 = 18$.\)

$g(h(x))$ is a polynomial that results from substituting $h(x)$ into $g(x)$. Since $h(x)$ is a polynomial of unknown degree when substituted into $g(x)$ of degree $3$, the resulting polynomial will have a degree of \($3 \times (\text{degree of } h(x))$.\)

$h(f(x))$ is a polynomial that results from substituting $f(x)$ into $h(x)$. Since $f(x)$ is a polynomial of degree $6$ when substituted into $h(x)$ of unknown degree, The resulting polynomial will have a degree of

\($(\text{degree of } h(x)) \times 6$.\)

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Answer:B. The number is composite. Its prime factors written as a product are (5*3^3*2^2)

Step-by-step explanation:

Since 540 is an even number, that means it can be divided by 2. This means that the number is composite.

You can keep dividing it by 2 until you can't anymore.

Once you divide 540 by 2 twice, then you get 135.

You can divide it by 5 because the ones digit is 5.

Then you get 27, which is 3 times itself 3 times.

You finally multiply the numbers you divided by, and you get 2*2*5*3*3*3, which is 5*3^3*2^2.

Analysts use financial ratios rather than absolute numbers because ratios provide a more meaningful and comparative assessment of a company's financial performance.

Ratios allow for a standardized comparison between companies of different sizes and industries, facilitating a better understanding of their financial health, operational efficiency, and profitability.

Furthermore, ratios enable analysts to evaluate a company's performance over time and benchmark it against industry averages and competitors. Some examples of commonly used financial ratios include the current ratio, return on equity (ROE), and earnings per share (EPS).

Current Ratio: The current ratio measures a company's ability to meet its short-term obligations. It is calculated by dividing current assets by current liabilities. For example, if a company has current assets of $500,000 and current liabilities of $250,000, the current ratio would be 2 ($500,000 / $250,000). A higher current ratio indicates a stronger liquidity position, suggesting the company is better equipped to meet its short-term financial obligations.

Return on Equity (ROE): ROE measures a company's profitability relative to its shareholders' equity. It is calculated by dividing net income by average shareholders' equity and multiplying by 100 to express it as a percentage. For instance, if a company has a net income of $1 million and average shareholders' equity of $10 million, the ROE would be 10% ($1 million / $10 million * 100). A higher ROE signifies better profitability and efficient utilization of shareholders' capital.

Earnings per Share (EPS): EPS indicates the profitability of a company on a per-share basis. It is calculated by dividing net income attributable to common shareholders by the weighted average number of outstanding shares. For example, if a company has a net income of $5 million and 10 million weighted average shares outstanding, the EPS would be $0.50 ($5 million / 10 million). A higher EPS implies higher profitability for each share held by investors.

Financial ratios provide valuable insights into a company's financial performance and facilitate better comparisons and analysis. Absolute numbers alone may not convey the same level of meaningful information or allow for easy comparisons between companies. Ratios allow analysts to assess a company's financial health, profitability, liquidity, efficiency, and other key aspects relative to industry peers and historical performance.

They help identify trends, strengths, weaknesses, and potential investment opportunities or risks. While absolute numbers provide essential context, ratios offer a standardized framework for evaluation and decision-making, making them a preferred tool for financial analysis.

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Answer:

y=-23/7;y=-19/7;y=-15/7

Step-by-step explanation:

when x is -2 then y is;

2(-2)-7y=19

-4-7y=19

-7y=23 divide both sides by -7

y=-23/7

when x=0 then y is;

2(0)-7y=19

-7y=19

y=-19/7

when x=2 then y is;

2(2)-7y=19

4-7y=19

-7y=15

y=-15/7

Answer:

H is E

Step-by-step explanation:

In the formula of the energy of photons "h" signifies Planck's constant.

The Planck constant, often known as Planck's constant, is a crucial physical constant in quantum physics. The mass-energy equivalency establishes the relationship between mass and frequency, and the constant establishes the relationship between a photon's energy and frequency.

In the equation energy E = h X v. The "h" there signifies Planck's constant

Planck's constant is a value, that shows the rate at which the energy of a photon increases/decreases, as the frequency of its electromagnetic wave changes.

Therefore,  in the formula of the energy of photons "h" signifies Planck's constant.

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Yes, the data provide evidence that there is a linear association between hours of television watched a week and GPA. This statement can be supported by statistical analysis of the data.

A linear association exists between two variables when the pattern of their plotted values on a scatterplot approximates a straight line. A linear association occurs when one variable increases while the other decreases. It is also known as a straight-line relationship.

The data you have asked about, which is the relationship between hours of television watched a week and GPA can be analyzed using statistical tools. The data can be graphed in a scatterplot to see whether there is a pattern between the variables. If a straight-line pattern is observed, then there is a linear association.

The statistical tools that can be used to analyze the data include the calculation of the correlation coefficient and regression analysis. The correlation coefficient is a measure of the strength of the association between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative relationship, 0 indicating no relationship, and 1 indicating a perfect positive relationship.

Regression analysis can be used to determine the equation of the line of best fit for the data. This line represents the linear relationship between the two variables. By analyzing the slope of the line, we can determine the strength of the relationship between the variables. In conclusion, yes, the data provide evidence that there is a linear association between hours of television watched a week and GPA.

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Answer:

The answer would be 6

Answer:

terminating decimal

Step-by-step explanation:

11 / 128 = 0.0859375

it is terminating because the numbers stop and don't go on forever.

The expected count for the cell corresponding to the white car in the sampling will be 204.

From the information given, the certain car model comes in four different colors, and can either have automatic or manual transmission.

The expected count for the cell corresponding to the white car will be:

= 96 × 204/384

= 51

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The modeof the data is "Singing".

In statistics, the mode refers to the value or values that appear most frequently in a dataset. It represents the peak of the frequency distribution. In the given data, we have a list of talent show acts, and we are looking for the act(s) that occur most frequently.

To find the mode(s) of the given data, we look for the value(s) that appear most frequently. Let's count the occurrences of each act:

Singing - 7 times

Dancing - 6 times

Comedy - 3 times

Poetry - 2 times

Juggling - 1 time

Magic - 1 time

From the counts, we can see that "Singing" appears the most frequently, occurring 7 times. Therefore, the mode(s) of the data is "Singing".

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The number of ways to contain 2 black card and 3 red cards are 84,500.

What is card deck?

A piece of specially made card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that has been imprinted with distinctive motifs is what is known as a playing card. Each card frequently has a finish on the front and reverse to make handling simpler.

There are 26 red card and 26 black card in a 52 card deck.

We have to find the number of ways contain 2 black card and 3 red cards.

Initial black card: 26 options

Secondly black card: 25 options

First caution: 26 options

Second warning: 25 options

Three red cards: 24 options

A total of,

26 x 25 x 26 x 25 x 24 = 10,140,000.

But since all orders are equal, we divide by the number of orders for a five card hand:

5 x 4 x 3 x 2 x 1 = 5! = 120

So,

10,40,000 / 120 = 84,500.

Hence, the number of ways to contain 2 black card and 3 red cards are 84,500.

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Answer:

The slope is 4/3

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

rearrange into slope-intercept form

3y=4x-6

y=4/3x-2

The marginal utility is the extra satisfaction derived from the consumption of a product.

Your information isn't well written. Therefore, an overview of utility will be given. The total utility is the total amount of satisfaction that a consumer derives from a product.

The marginal utility simply means the extra satisfaction that's gotten from a product when an additional unit is consumed.

The formula for marginal utility will be:

= Total utility difference/Quantity of goods difference

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The two numbers are 7/6 and 5 when the sum of two numbers is 3 more than four times the first number.

Let's call the two numbers x and y, where x is the first number and y is the second number.

The problem gives us two equations that relate the two numbers:

\(x + y = 3 + 4x\\y - x = 2y - 10\)

We can substitute the expression for y from equation 1 into equation 2:

\(y - x = 2(3 + 4x) - 10\)

Expanding the right side and simplifying, we get:

\(y - x = 6 + 8x - 10\\y - x = 8x - 4\)

Adding x to both sides:

\(y = 9x - 4\)

Substituting this expression for y into equation 1:

\(x + (9x - 4) = 3 + 4x\)

Expanding and simplifying the right side:

\(10x - 4 = 3 + 4x\)

Subtracting 4x from both sides:

\(6x - 4 = 3\)

Adding 4 to both sides:

\(6x = 7\)

Dividing both sides by 6:

\(x = 7/6\)

Substituting this value of x back into the expression for y:

\(y = 9x - 4 = 9 * (7/6) - 4 = 63/6 - 4 = 9 - 4 = 5\)

So the two numbers are 7/6 and 5.

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer: 607 items

Step-by-step explanation:

To get 607 you divide 11004 by 524 to get the percent returned. You then take that number and multiply it by 12747. Hope this helps!

the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

In mathematics, the common logarithm is the logarithm with base 10.

It is also known as the decadic logarithm and as the decimal logarithm function.

Here, we have the logarithm function as:

( log ₂ 4 )

Now, we can see that:

It has a base of 2.

So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.

Therefore, we get that, the logarithm function ( log ₂ 4 ) is not a common logarithm function as it does not have a base 10.

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Answer:

Slope: 2

Step-by-step explanation:

Answer:

C. -1 is less than x

Step-by-step explanation:

-3 < 4x + 1

-3-1 < 4x +(1 -1)

-4 < 4x

-4/4 < 4x/4

-1 < x

Step-by-step explanation:

Let alpha be the unknown angle. We can set up our sine law as follows:

\( \frac{ \sin( \alpha ) }{5 \: m} = \frac{ \sin(42) }{3.6 \: m } \)

or

\( \sin( \alpha ) = \frac{5 \: m}{3.6 \: m} \times \sin(42) = 0.929\)

Solving for alpha,

\( \alpha = arcsin(0.929) = 68 \: degrees\)

1. The given statement  is true by proving its contrapositive statement that "If n is an even integer, then n² + 2n + 4 is even."

2. The given statement is true by proving its contradiction statement that if there exist integers x and y such that 6x - 15y = 2, it leads to a contradiction.

1: To prove the statement "If n is an integer such that n² + 2n + 4 is odd, then n is odd"

By contrapositive, we need to prove that "If n is an even integer, then n² + 2n + 4 is even."

Assume that n is an even integer,

Then we can write n as n = 2k,

Where k is an integer.

We can substitute this value of n in n² + 2n + 4 to get:

n² + 2n + 4 = (2k)² + 2(2k) + 4

                  = 4k² + 4k + 4

                  = 4(k² + k + 1)

Since k is an integer, k² + k + 1 is also an integer,

And hence 4(k² + k + 1) is even.

Therefore, we have proved that if n is an even integer, then n² + 2n + 4 is even, which is the contrapositive of the original statement.

Hence, the original statement is true.

To prove the statement "There are no two integers x and y with

6x - 15y = 2" by contradiction,

Assume that there are two integers x and y such that 6x - 15y = 2,

And then show that this assumption leads to a contradiction.

Assume that there exist integers x and y such that

6x - 15y = 2.

Simplify this equation by dividing both sides by 3:

2x - 5y = 2/3

Since 2/3 is not an integer, the left-hand side of the equation must also not be an integer.

However, this is a contradiction because 2x and 5y are both integers, and the difference of two integers must also be an integer.

Therefore, our initial assumption that there exist integers x and y such that 6x - 15y = 2 is false, and the statement "There are no two integers x and y with 6x - 15y = 2" is true.

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The complete question is attached below;

Answer:

well, we know it is

y = -4 x + b

so all we need is b

5 = -4(9) + b

5 = -36 + b

b = 41

so

y = -4 x + 41