For these equations of straight lines in the form y = mx + c, write down the value of m and c.
(i) y = 3x - 4
(ii) y = -3x + 7.

Answer:

x = 5 , ML = 18

Step-by-step explanation:

the midsegment NP of the trapezoid is half the sum of the bases, that is

NP = [tex]\frac{JK+ML}{2}[/tex]

25 = [tex]\frac{4x-2+6x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

50 = 10x ( divide both sides by 10 )

5 = x

Then

ML = 4x - 2 = 4(5) - 2 = 20 - 2 = 18

The solution to this equation is x = -7 and x = 7.

The two numbers 7 units away from 0 on a number line are -7 and 7. This can be expressed mathematically as |x-0|=7, where x is the unknown number. Solving this equation yields two solutions, x = -7 and x = 7.

To solve this equation, first subtract 0 from both sides of the equation to get |x| = 7. Then, take the absolute value of both sides of the equation to get x = 7. Finally, note that the absolute value of any number is equal to that number's positive value. Therefore, the solution to this equation is x = -7 and x = 7.

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In a group of 150 students, 20 are freshmen 30 are sophomores 49 are juniors and 51 are seniors if a student is randomly selected the probability that we select a sophomore before freshmen is 2.69%.

So the given data we get from the question is as follows,

  Total number of students, N = 150

  A number of freshmen students, F = 20

  The number of sophomore students, S = 30

  Number of junior students, J = 49

  Number of senior students, R = 51

              We need to find the probability of selecting a sophomore student before a freshman student. The probability that a sophomore student is selected first,

             P(S) = Number of sophomore students/Total number of students

                    = S/N

   Probability that a freshman student is selected after a sophomore student,

          P(F|S) = Number of freshman students left/Total number of students left

                    = F/N-1

    Where N-1 is used because one student has already been selected.

     The probability that a sophomore student is selected first and then a freshman student is selected,

       P(S∩F) = P(S) × P(F|S)

                   = S/N × F/N-1

      Therefore, the probability of selecting a sophomore student before a freshman student is:

       P(S∩F) = S/N × F/N-1P(S∩F)

                   = 30/150 × 20/149P(S∩

                   = 0.0269 or 2.69%

      Therefore, the probability of selecting a sophomore student before a freshman student is 0.0269 or 2.69%.

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Answer:

It appears that the solution you have provided is not a direct answer to the question "What is e=?". However, the statement you provided is a well-known concept in physics, where Einstein's famous equation E=mc² suggests that energy (E) and mass (m) are equivalent and interchangeable, and that they are two different manifestations of the same thing. The constant "c" in the equation represents the speed of light in a vacuum. This concept has had profound implications in the field of physics and has been used to develop nuclear energy and nuclear weapons.

Step-by-step explanation:

Here's a step-by-step explanation of Einstein's famous equation, E=mc²:

The equation E=mc² stands for "energy equals mass times the speed of light squared".

In physics, "energy" refers to the ability of a system to do work, and it is measured in joules (J).

"Mass" refers to the amount of matter in an object and is usually measured in kilograms (kg).

"c" represents the speed of light in a vacuum, which is approximately 299,792,458 meters per second (m/s).

The equation shows that energy and mass are equivalent and interchangeable. In other words, mass can be converted into energy, and energy can be converted into mass.

The conversion factor between mass and energy is the speed of light squared, which is an enormous number. This means that even a small amount of mass can produce a significant amount of energy when it is converted.

The equation has been used to explain a variety of phenomena, such as the energy released in nuclear reactions and the behavior of particles at high speeds.

It has also led to the development of nuclear energy and nuclear weapons, which rely on the conversion of mass into energy.

Overall, E=mc² is a fundamental equation in physics that has had a profound impact on our understanding of the universe and our ability to harness its energy.

If the diameter of the tennis ball is 7cm. then the exact volume of the cylinder is approximately 807.96 cubic centimeters.

The volume of a cylinder is calculated using the formula

              V = πr²h,

      where r is the radius and h is the height.

In this case, the radius of the cylinder is equal to the radius of a tennis ball which is half its diameter or 3.5cm.

The height of the cylinder is equal to the diameter of three tennis balls or 21cm. Plugging these values into the formula gives us:

              V = π * 3.5² * 21

              V ≈ 807.96 cm³.

     So, the exact volume of the cylinder is approximately 807.96 cubic centimeters.

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The value of the test statistic is -2.18.

To test the claim that the percentage of readers who own a laptop is different from 52%, we can use a two-tailed z-test for proportions. The null hypothesis is that the true proportion is 52%, and the alternative hypothesis is that the true proportion is different from 52%.

The test statistic can be calculated as:

z = (p - P) / sqrt(P(1 - P) / n)

where p is the sample proportion, P is the hypothesized proportion (in this case, 0.52), and n is the sample size.

Substituting the given values, we get:

z = (0.45 - 0.52) / sqrt(0.52(1 - 0.52) / 190)

z = -0.07 / 0.039

z = -1.79

The value of -1.79 represents the number of standard deviations away from the mean of the sampling distribution of sample proportions if the null hypothesis were true. However, since we are using a two-tailed test, we need to consider both tails of the standard normal distribution.

The critical value for a two-tailed test at the 0.05 level of significance is ±1.96. Since -1.79 is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, the correct answer is -2.18.

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the value of the given function f(g(1)) is 2 , fog is an even function

A function f is even if the equation f(x)=f(x) f (x) = f ( x) holds for every x and x in the domain of f. An even function has a graph that is geometrically symmetric with respect to the y-axis, which means that even after reflection about the y-axis, the graph does not change.

f is even (given)

∴f(−x)=f(x)

g is odd (given)

∴g(−x)=−g(x)

So,

According to question,

fog=f[g(x)]=f(y)             Let [g(x)]=y

and also,

fog=f[g(−x)]        ∵g(x) is odd

       =f[−g(x)]

       =f(−y)

       =f(y)

⇒fog(x)=fog(−x)

∴fog is an even function

f(g(1)) = f(g(1)) = f(3) = 2

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Answer:

Step-by-step explanation:

5 added with the 15 is dollars

Answer:

B) $23,408

Step-by-step explanation:

to find the total cost, we need to multiply the cost per share and the number of shares:

$38 * 616 = $23,408.

let's keep in mind that the hypotenuse is just a radius unit and thus is always positive, whilst sine and cosine vary per Quadrant.

so we know the tangent is < 0, which is another way to say "tangent is negative", well, that only happens when the cosine and sine differ in sign, and that only happens in the II and IV Quadrants, so the angle β is on either of those Quadrants.

[tex]\sin(\beta )=-\cfrac{12}{13}\implies \stackrel{ \underline{IV~Quadrant} }{\sin(\beta )=\cfrac{\stackrel{opposite}{-12}}{\underset{hypotenuse}{13}}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=adjacent\\ o=\stackrel{opposite}{-12} \end{cases}[/tex]

[tex]a=\pm\sqrt{ 13^2 - (-12)^2}\implies a=\pm\sqrt{ 169 - 144 } \implies a=\pm 5\implies \stackrel{ IV~Quadrant }{a=+5} \\\\[-0.35em] ~\dotfill\\\\ \cos(\beta )=\cfrac{\stackrel{adjacent}{5}}{\underset{hypotenuse}{13}}\hspace{5em} \tan(\beta )=\cfrac{\stackrel{opposite}{-12}}{\underset{adjacent}{5}}[/tex]

(a) The expressiοn that represents amοunt οf canned fοοd cοllected by  the three friends =  5x² + 5xy - 9

(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17

An expressiοn is a way οf writing a statement with mοre than twο variables οr numbers with οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Example: 2 + 3x + 4y = 7 is an expressiοn.

It is given that,

number οf cans cοllected by Jessa = 5xy + 17

number οf cans cοllected by Tyree = x²

number οf cans cοllected by Ben = 4x² - 8  

Part(a)

tοtal number οf cans cοllected by three friends = cans cοllected by Jessa + Tyree + Ben

= 5xy + 17 + x² + 4x² - 8

= 5x² + 5xy - 9

Part(b)

the gοal οf fοοd cans cοllected = 8x² − 4xy + 8

Sο, the number οf fοοd cans still left tο cοllect = gοal - (number οf cans cοllected)

= (8x² − 4xy + 8) - (5x² + 5xy - 9)

= 8x² - 5x² - 4xy − 5xy + 8 + 9

= 3x² - 9xy + 17

Therefοre,

(a) The expressiοn that represents amοunt οf canned fοοd cοllected by the three friends = 5x² + 5xy - 9

(b) the expressiοn that represents number οf cans which are still need tο cοllect is = 3x² - 9xy + 17

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Answer:

i don't know is correct but here The function f(x)f(x) is a cubic function and the zeros of f(x)f(x) are -5−5, 11 and 55. Assume the leading coefficient of f(x)f(x) is 11

by-step explanation:

The approximated value of x in the equation given as 6^(2x+1)=8^(x+1) is 0.192

From the question, the equation is given as

6^(2x+1)=8^(x+1)

Take the logarithm of both sides of the equation

So, we have

(2x + 1)log(6) = (x + 1)log(8)

Divide both sides of the equation by log(6)

So, we have

2x + 1 = (x + 1) * 1.161

So, we have

2x + 1 = 1.161x + 1.161

Evaluating the like terms, we get

0.839x = 0.161

Divide both sides by 0.839

This gives

x = 0.192

Hence, the solution is 0.192

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9/1 is the simple form in fraction .

What is a rectangle, exactly?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

1st rectangle = 15 * 45  = 675

2nd rectangle  = 15 * 5 = 75

 1st/2nd = 675/75

             =  9/1

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Answer:

substitute the value of y

y=15-x

3(15-x)=5x+3

45-3x=5x+3

-3x-5x=3-45

-2x=42

X=21

Therefore, based on the given data, we can predict that the team will be ahead at the end of at most one of the halves in 24 of the next 80 games.

The term "predict" generally means to make an informed guess or estimate about what might happen in the future based on current information, data, or past trends. In other words, prediction involves using available information to forecast or anticipate an outcome or event that has not yet occurred. Predictions can be made in various fields such as science, economics, weather, sports, and many others. Machine learning and artificial intelligence systems also use predictive models to make forecasts and improve decision-making processes.

by the question.

Based on the given data, we can see that out of the 20 games played so far, the team was ahead at the end of both halves in 3 games, and was ahead at the end of the first half in an additional 3 games. Therefore, the team was ahead at the end of at most one of the halves in a total of 6 out of 20 games.

To predict how many of the next 80 games the team will be ahead at the end of at most one of the halves, we can use the proportion of games from the first 20 games. Specifically, we can calculate:

proportion of games with team ahead at most once = 6/20

predicted number of games with team ahead at most once in next 80 games = (6/20) x 80

predicted number of games with team ahead at most once in next 80 games = 24

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Option A. The height of Maddi's bin is 28 inches. We know that the bin is shaped like a right prism, which means that it has a rectangular base and its sides are perpendicular to the base.

The volume of a right prism is given by the formula:

Volume = area of base x height

In this case, we are given that the area of the base is 14 in² and the volume is 392 in³. We can use these values to find the height of the prism.

Substituting the given values into the formula for the volume, we get:

392 = 14 x height

We can solve for the height by dividing both sides of the equation by 14:

height = 392/14

Simplifying this expression, we get:

height = 28

Therefore, the height of Maddi's bin is 28 inches.

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Answer: (-4, 5)

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

1 to 10

Hence,

10 - 1 = 9

Similarly,

20 - 11 = 9

30 - 21 = 9

40 - 31 = 9

Therefore,

Interval is 9

Step-by-step explanation:

To find the maximum and minimum values of the objective function subject to the given constraints, we can use the method of linear programming.

Step 1: Convert the inequality constraints into equations by replacing the inequality signs with equality signs and adding slack or surplus variables as necessary to get the equations in the form of standard linear equations.

So the equations become:

2x + 3y + s1 = 6 (where s1 is a non-negative slack variable)

2x - 3y + s2 = 6 (where s2 is a non-negative slack variable)

y + s3 = 2 (where s3 is a non-negative slack variable)

Step 2: Write the objective function F as a linear function of the variables x and y.

F = 4x - y

Step 3: Formulate the linear programming problem in the standard form as follows:

Minimize or maximize F = 4x - y, subject to:

2x + 3y + s1 = 6

2x - 3y + s2 = 6

y + s3 = 2

where x, y, s1, s2, and s3 are non-negative variables.

Step 4: Solve the system of equations to find the feasible region.

We can solve the system of equations using matrix methods to obtain:

x = 3, y = 0, s1 = 0, s2 = 0, s3 = 2

x = 0, y = 2, s1 = 0, s2 = -6, s3 = 0

x = 0, y = 0, s1 = 6, s2 = 6, s3 = 2

x = 2, y = 0, s1 = 0, s2 = 2, s3 = 2/3

x = 1.5, y = 0.5, s1 = 0, s2 = 1.5, s3 = 1.5

x = 0, y = 2/3, s1 = 2, s2 = -2/3, s3 = 0

Step 5: Evaluate the objective function at each corner point to determine the maximum and minimum values.

F(3, 0) = 4(3) - 0 = 12

F(0, 2) = 4(0) - 2 = -2

F(0, 0) = 4(0) - 0 = 0

F(2, 0) = 4(2) - 0 = 8

F(1.5, 0.5) = 4(1.5) - 0.5 = 5.5

F(0, 2/3) = 4(0) - (2/3) = -2/3

Therefore, the maximum value of the objective function is 12, which occurs at the corner point (3, 0), and the minimum value is -2, which occurs at the corner point (0, 2).

If h(x) = 5 4f(x) , where f(1) = 5 and f '(1) = 4, then h'(1) = 20.

To find h'(1), we need to use the chain rule of differentiation, which states that if h(x) = f(g(x)), then h'(x) = f'(g(x)) * g'(x).

In this case, we have h(x) = 5/4 * f(x), where f(1) = 5 and f'(1) = 4. Therefore, g(x) = x, f(x) = 5, and h(x) = 5/4 * 5 = 6.25.

To find h'(1), we need to evaluate f'(g(1)) and g'(1), then multiply them together. Since g(x) = x, we have g'(1) = 1.

Since f'(x) = 4, we have f'(g(1)) = f'(1) = 4. Therefore, h'(1) = f'(g(1)) * g'(1) = 4 * 1 = 4. However, we are looking for h'(1), so we need to multiply this by the coefficient of f(x), which is 5/4. Therefore, h'(1) = 5/4 * 4 * 1 = 20.

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we can say that the teacher's gοal οf a standard deviatiοn οf at mοst 8 pοints was achieved, at a 5% level οf significance.

A measure οf a grοup οf values' variance οr dispersiοn in statistics is called the standard deviatiοn. When the standard deviatiοn is lοw, the values are mοre likely tο fall within a narrοw range, alsο knοwn as the expected value, whereas when the standard deviatiοn is high, the values tend tο be clοser tο the mean.

The lοwercase Greek letter sigma, which stands fοr the pοpulatiοn standard deviatiοn, οr the Latin letter s, which stands fοr the sample standard deviatiοn, are mοst frequently used in mathematical equatiοns and texts tο represent standard deviatiοn. Standard deviatiοn is alsο sοmetimes referred tο as SD.

suppοse that οn a 100-pοint test, the teacher's gοal is fοr her students' exam scοres tο have a standard deviatiοn οf at mοst 8 pοints.

chi²[tex]= (n-1)*s^2 /\sigma^2[/tex]

where n is the sample size, s is the sample standard deviatiοn, and sigma is the hypοthesized pοpulatiοn standard deviatiοn under the null hypοthesis.

In this case, n = 25, s = 9.5, and sigma = 8. Substituting these values, we get:

chi² [tex]= (25-1)*9.5^2 / 8^2 = 33.64[/tex]

The degrees οf freedοm fοr this test is n-1 = 24. Using a chi-squared table with 24 degrees οf freedοm, we find that the critical value fοr a οne-tailed test at a 5% level οf significance is 36.42.

Therefοre, we can say that the teacher's gοal οf a standard deviatiοn οf at mοst 8 pοints was achieved, at a 5% level οf significance.

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By hypothesis , μ ≤ $200 is the mean cost of science textbooks are no more than $200.

What does "mathematical hypothesis" mean?

A proposition is considered to be a hypothesis if it is plausible given the available information but has not been proven true or wrong. An assertion that will serve as the foundation for hypothesis testing is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

                          The statement "all fours sides of a quadrilateral measure the same, then the quadrilateral is a square" states that if true, the quadrilateral is a square.

Here  n = 143

    the claim that the mean cost of science textbooks are no more than $200.

    H₀  : μ = $200

    H₁  :  μ ≤ $200

Therefore, this problem based on one sample t test for mean .

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The probability of selecting 2 white balls and 2 red balls from the urn is approximately 0.412, which corresponds to option (d).

To solve this problem, we can use the hypergeometric distribution. The probability of selecting exactly k white balls and 4 - k red balls in a sample of 4 balls without replacement is given by:

P(k white balls) = [C(8,k) [tex]\times[/tex] C(10,4-k)] / C(18,4)

where C(n,r) is the number of combinations of n things taken r at a time.

For the given problem, we want to find the probability of selecting 2 white balls and 2 red balls, so we substitute k = 2 into the formula:

P(2 white balls) = [C(8,2) [tex]\times[/tex] C(10,2)] / C(18,4)

= [(28 [tex]\times[/tex] 45)] / 3060

≈ 0.412

Therefore, the probability of selecting 2 white balls and 2 red balls from the urn is approximately 0.412, which corresponds to option (d).

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The total number of valid numbers is 120= 108.

There are 6 digits to choose from, and we need to select 3 of them for the number to have 2, 3, and 5 in it. So, the total number of possible arrangements is 6P3 = 654 = 120.

However, we need to subtract the arrangements that have repeated digits. There are 3 ways to choose the repeated digit and 4 options for where to put it in the number (there are 4 spaces left after the unique digits are placed). This gives us 3*4 = 12 arrangements to subtract.

Therefore, the total number of valid numbers is 120 - 12 = 108.

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Answer:

x = 28*

Step-by-step explanation:

We know that Line M is parrallel to line N , so angle x = 28 degrees because the Alternate interior angles of a transversal are equal.

Hope it helps.

In the word problem ,  there are 84 winning lines of 6 in a row.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here on each face of a cube, there would be 6 vertical rows , 6 horizontal rows  and 2 diagonal rows.

That is total of 14 rows per face.

A cube has 6 faces. Then

=> 6*14 = 84 lines.

Hence there are 84 winning lines of 6 in a row.

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To find the area we have to calculate the radius first. Here the radius is 6m. So the area will be 36π m². Option C is the correct one.

Diameter is the straight line connecting two points on the edge of the circle, that passes through the Centre of the circle. It will be equal to two times the radius.

D = 2r

r = D/2 = 12/2 = 6m

Area of a circle can be calculated using the equation πr².

Area = π × 6² = 36π m²

So the area of the given circle with diameter will be 36π m².

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[tex](2x-6)(2x-6)[/tex]

[tex]4x^2 - 12x - 12x + 36[/tex]

The remaining customer advance at the end of 2025 is $16,592,000.

To determine the amount of customer advance remaining at the end of 2025, we need to subtract the amount collected in 2025 from the customer advances balance at the end of 2024:

Customer advances balance at the end of 2024 = $12,518,000

Amount collected in 2025 = $30,256,000

Customer advances recognized in income in 2025 = $26,182,000

Customer advances balance at the end of 2025 = Customer advances balance at the end of 2024 + Amount collected in 2025 - Customer advances recognized in income in 2025

Customer advances balance at the end of 2025 = $12,518,000 + $30,256,000 - $26,182,000

Customer advances balance at the end of 2025 = $16,592,000

Therefore, the remaining customer advance at the end of 2025 is $16,592,000.

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