The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?

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

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

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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Answer:

11%

Step-by-step explanation:

find the price of the shirts before markup by dividing 10800 by 400

You get 27, which you will subtract 30 by, getting you 3.

Divide this number by 27

.11

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]

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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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).

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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The linear function changes at a rate of [tex]5/4[/tex]. This implies that [tex]y[/tex] grows by [tex]5/4[/tex] units for every unit increase in [tex]x[/tex].

The graph of a linear function is a direct line. The following is the form of a linear function. a + bx = y = f(x). One independent variable one and dependent variable make up a linear function.

A linear relation on the reference system is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be expressed as f(x) => 3x - 2 since y could be substituted with f(x).

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

slope [tex]= (1 - (-4)) / (4 - 0)[/tex]

slope [tex]= 5 / 4[/tex]

Therefore, the rate of change of the function is [tex]5/4[/tex]. This means that for every [tex]1[/tex] unit increase in [tex]x[/tex], [tex]y[/tex] increases by [tex]5/4[/tex] units.

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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.

Answer:

Step-by-step explanation:

5 added with the 15 is dollars

To solve the quadratic function -3x² + 5x + 9 = 0, the formula that should be used is Option C: x = (-5 ± √133) / -6.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic formula is used to solve quadratic equations in the form of ax² + bx + c = 0, where a, b, and c are constants.

To use the quadratic formula to solve the equation -3x² + 5x + 9 = 0, we need to identify the values of a, b, and c.

In this case, a = -3, b = 5, and c = 9.

Therefore, we can use these values to plug into the quadratic formula -

x = (-b ± √(b² - 4ac)) / 2a

So the answer that can be used to find the solutions to the equation using the quadratic formula is -

x = (-5 ± √(5² - 4 × (-3) × 9)) / 2 × (-3)

Solving this equation we get -

x = (-5 ± √(25 + 108)) / -6

x = (-5 ± √133) / -6

Therefore, the solution is obtained by the equation x = (-5 ± √133) / -6.

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Answer: (-4, 5)

Step-by-step explanation:

a. q-p = 11-3 = 8, which is an even number. b. p+q = 3+11 = 14, which is an even number.

In mathematics, a prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that can only be divided evenly by 1 and itself.

There are various methods for finding prime numbers, such as the Sieve of Eratosthenes, which is a simple algorithm for generating all prime numbers up to a given limit. However, as the numbers get larger, it becomes increasingly difficult to find prime numbers, and there is no known formula for generating all prime numbers.

a. One possible example is:

p = 3

q = 11

Here, q-p = 11-3 = 8, which is an even number. However, if we add 1 to it, we get 9, which is odd but not prime (since it is divisible by 3).

b. One possible example is:

p = 3

q = 11

Here, p+q = 3+11 = 14, which is an even number. However, if we add 1 to it, we get 15, which is odd but not prime (since it is divisible by 3 and 5).

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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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Answer: -46

Step-by-step explanation:

First f-g (since its in parenthesis)

  f(x)=3x^5+6x^2-5

-  g(x)=3x^5-5x^4-15

=          0  -5x^4 +6x^2 + 10

then, sub in 2 for x

(-5x^4 +6x^2 + 10); x=2

-5(2)^4 + 6(2)^2 + 10 = -46

*can only subtract terms with the same power

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

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:

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

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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Answer:

6016920.57

Step-by-step explanation:

First, find (57)^3

= 185193

Then find (5.7)^2

= 32.49

Finally,

multiply both answers:

32.49 .  185193

= 6016920.57

Answer: 6016920.57

Step-by-step explanation:

(57)^3 = 185193

(5.7)^2 = 32.49

32.49 *  185193 = 6016920.57

Answer:

To find the area of the isosceles trapezoid, we can use the formula:

Area = ((upper base + lower base) / 2) x height

First, we need to find the height of the trapezoid. We can use the Pythagorean theorem to find the height, since the legs of the trapezoid form a right triangle with the height as the hypotenuse.

Using the Pythagorean theorem:

height^2 = leg^2 - ((lower base - upper base) / 2)^2

= 5^2 - ((16 - 8) / 2)^2

= 25 - 4^2

= 9

height = 3 cm

Now that we have the height, we can use the area formula:

Area = ((8 + 16) / 2) x 3

= 12 x 3

= 36 cm^2

Therefore, the area of the isosceles trapezoid is 36 square centimeters.

The experimental probability of rolling a number less than 4 is:

P(less than 4) = 6/12 (in fraction)

P(less than 4) = 0.5 (in decimal)

P(less than 4) = 50% (in percentage)

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

The numbers less than are 1, 2 and 3. Since six of the twelve outcome in the table are less than 4. Thus, the experimental probability of rolling a number less than 4 will be:

P(less than 4) = 6/12 (in fraction)

P(less than 4) = 0.5 (in decimal)

P(less than 4) = 50% (in percentage)

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Madison will require 88 fabric squares, rounded up to the next integer, therefore option B is the correct solution.(d).

A circle's circumference is the distance around its outside boundary.

The following formula can be used to compute it.

C = 2πr

The diameter of the circle is equal to the perimeter of the circular mirror, which is 2r, where r is the radius.

Circumference = 2 x 3.14 x 14 cm = 87.92 cm

Madison will need to cover this area with 1 cm cloth squares.

The number of fabric squares required equals the perimeter / length of each square.

87.92 cm / 1 cm = 87.92 fabric squares required

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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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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

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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Answer:

36

Step-by-step explanation:

(2 x 10)+(2 x 8) = 36

The total area is 36 cm squared.

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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Answer:

x = -60

Step-by-step explanation:

1/4x - 3 = 1/2x + 12

add three to both sides

1/4x = 1/2x + 15

subtract 1/2x from both sides

-1/4x = 15

divide by -1/4

x = -60