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In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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The value of x will be; x = 1/8

Since equation is an expression that shows the relationship between two or more numbers and variables.

We are given that  the equation  (8x-1).

Here, we need to solve for x;

(8x-1).

combine the like terms;

(8x-1) = 0

8x = 1

x = 1/8

Therefore, the solution will be as x = 1/8

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Answer:

$4

Step-by-step explanation:

15/1=60/x

x=60/15 or 4

x=$4

Hope this helps plz hit the crown :D

Answer:

$4

Step-by-step explanation:

a dozen is 12 and you need 5 dozens so it is 60 oranges. 15×4=60. therefore it is 4

step 1

Find out the measure of angle B

Applying the law of sines

substitute given values

Solve for B

The greater value of the sine is 1

so

The time for the projectile to hit the ground from the given position is 1.5 s, which is obtained using the concept of time period and velocity of a projectile.

What is a projectile?

A projectile is defined as an object that has the force of gravity as the only force occurring on it. Acceleration in the projectile motion always acts vertically.

Calculation of the time taken by projectile to hit the ground

The given parameters:

The starting velocity of the projectile, u = 48 ft / s

Height of the projectile, h = 190 ft

Model of the projectile path, h(t) = - 16(t)2 + 48t + 190          —-- 1

When the projectile hits the ground, the final velocity, v = 0

differentiating equation 1 w.r.t t, we get,

(dh(t)) / (dt) = - 32t + 48

Putting dh(t) / dt = 0, we have,

- 32t + 48 = 0

32t = 48

t = 48 / 32

t = 1.5 s

Hence, the time taken by the projectile to hit the ground is 1.5 s.

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Answer: 7?

Step-by-step explanation: 7/4 7 - 4 = 3 - 2 = 1

Answer:

j = 12

Step-by-step explanation:

\(\frac{j}{4}\) - 2 = 1 ( add 2 to both sides )

\(\frac{j}{4}\) = 3 ( multiply both sides by 4 to clear the fraction )

j = 12

Answer:

total surface area = 936 in²

Step-by-step explanation:

total surface area  = surface area of the pyramid + surface area of the cube

1.  surface area of the pyramid = 4 * area of lateral triangle side

area of lateral triangle side = 12 * 9 /

area of lateral triangle side = 54 in²

2. surface area of the pyramid = 4 * 54

surface area of the pyramid = 216 in²

3. surface area of the cube = 5 * (12 x 12)

-surface area of the cube = 720 in²

therefore, the total surface area = 216 in² + 720 in²

total surface area = 936 in²

Answer:

C

Step-by-step explanation:

Please refer to the given picture (sorry, it's a rather bad drawing.)

Anyways, we know that the cube has side lengths of 12. Since the figure is a cube, all the side lengths are 12. Let's find the surface area of the cube first.

The cube has six faces. However, we only need to do five faces because one of the faces is the face that connects the cube to the pyramid. Because of this, we won't count it towards the surface area. Therefore, the total surface area of the cube would be:

\(5(bh)\)

The bh represents the area of one face. The five multiplies that amount by five, giving us the surface area of the cube. Plug in 12 for the base and 12 for the height:

\(5(12)(12)=5(144)=720\)

Therefore, the surface area of the cube (excluding one face) is 720 square inches.

Now, find the surface area of the square pyramid. The square pyramid is composed of four congruent triangles and one square base. Again, since the square base is connecting it to the cube, we won't count it. So, we only need to find the area of the four triangles and then add it to 720.

We are given that the height of the pyramid is 9. The base of all four triangles is 12 (since the side length of the cube is 12). However, to find the area, we first need to use the Pythagorean Theorem to determine x or the actual height of one of the triangles. We won't use 9 as the height because the 9 doesn't represent the height of the triangle, but rather of the pyramid. x is essentially the hypotenuse here. Thus:

Pythagorean Theorem:

\(a^2+b^2=c^2\)

Plug in 9 for a, 12 for b, and x for c:

\(9^2+12^2=x^2\\x^2=81+144=225\\x=\sqrt{225}=15\)

Therefore, the height of the triangles is 15. Now, we can use the area formula for triangles:

\(A=\frac{1}{2} bh\)

The base is 12 and the height is 15. Thus:

\(A=\frac{1}{2}(12)(15)=6(15)=90\)

And there are four of them, so the total surface area is:

\(4(90)=360\)

Therefore, the total surface area of the composite figure (excluding the one face) is:

\((720+360)=1080\text{ in}^2\)

Answer:

no

Step-by-step explanation:

Dilatation is acutally for medicine and dilation is actually for phycology.

The solution to the equation \(cos(7x) = sin(4x+5)\)° is \(x = 7.73\)°.

To solve for x, we will use the trigonometric identity sin(θ) = cos(90° - θ) to convert the equation into an equivalent form.

\(cos(7x) = sin(4x+5)\) can be rewritten as \(cos(7x) = cos(90 - (4x+5))\)

Using fact that cosine function is periodic with a period of 360°, we will set angles inside the cosine functions equal to each other:

7x = 90° - (4x+5)°

Simplifying:

7x = 90° - 4x - 5°

7x + 4x = 90° - 5°

11x = 85°

x = 85° / 11

x = 7.73°.

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Answer:

Step-by-step explanation:

I would say B

Answer:

E

Step-by-step explanation:

The average rate of change of A(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ - 4, 6 ] , then

f(b) = f(6) = 6² + 2(6) + 3 = 36 + 12 + 3 = 51

f(a) = f(- 4) = (- 4)² + 2(- 4) + 3 = 16 - 8 + 3 = 11 , thus

average rate of change = \(\frac{51-11}{6-(-4)}\) = \(\frac{40}{10}\) = 4 → E

Answer:

The mass of Sun is \(65\times 10^5\) times greater than mass of Mercury.

Step-by-step explanation:

We are given that

Mass of the sun=\(M=2.13525\times 10^{30}\) kg

Mass of Mercury, \(m=3.285\times 10^{23}\)kg

We have to find how many times greater is the mass of the sun than the mass of Mercury.

Mass of sun/Mass of mercury=\(\frac{2.13525\times 10^{30}}{3.285\times 10^{23}}\)

Mass of sun/Mass of mercury\(=0.65\times 10^{30-23}\)

Using the property

\(a^x/a^y=a^{x-y}\)

Mass of sun/Mass of mercury\(=0.65\times 10^{7}\)

Mass of sun/Mass of mercury\(=65\times 10^5\)

Mass of Sun=\(65\times 10^5\) times Mass of Mercury

Hence, the mass of Sun is \(65\times 10^5\) times greater than mass of Mercury.

Answer:

The LCM of 88 and 90 is 3960.

Answer:

By the Euclidean algorithm, \(\gcd(88, 90) = \gcd(88, 2) = \gcd(0, 2) = 2\). Therefore, \(\text{lcm}(88,90) = \frac{88 \cdot 90}{\gcd(88, 90)} = \frac{88 \cdot 90}{2} = \boxed{3960}.\)

The volume of Cone A is 100π cubic ft.

The formula to calculate the volume of a cone is V = (1/3)*π*r²*h, where r is the radius and h is the height of the cone.

If we double the radius and the height of a cone, the volume of the cone will increase four times. Mathematically, this can be shown using the formula. If we double both the radius and the height, the volume will become (1/3)*π*(2r)²*(2h) which simplifies to (1/3)*π*4r²*2h. This simplifies further to 4*(1/3)*π*r²*h which is equal to 4*V, where V is the original volume of the cone.

In the given question, the volume of Cone B is 25π cubic ft. If we double the radius and the height of Cone B, the volume of Cone A will be 4*25π cubic ft or 100π cubic ft.

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Okay, here we have this:

Considering the provided equation, we are going to analize if the function is even, odd, or neither. So we obtain the following:

Since a function is even if f(-x)=f(x), then we have:

Finally we obtain that f(-x) is equal to f(x), then this mean that the function is even.

Answer:

546

Step-by-step explanation:

Surface Area = 2(lw + lh + wh)

plug in l w and h

The surface area and volume of a cube with different edge length are

When a cube with edge length 4inches ,

Surface area = 96 square inches and Volume =64 cubic inches.

Cube dilated by scale factor 0.25 ,  

Surface area = 6 square inches and Volume =1 cubic inches.

The surface area of a cube is = 6 times the area of one face.

Each face of this cube has an area equals to

= (4 inches) x (4 inches)

= 16 square inches,

So the total surface area is,

Surface area

= 6 x 16 square inches

= 96 square inches

The volume of a cube =  length of one edge cubed.

Here, the edge length is 4 inches,

Volume

= (4 inches)^3

= 64 cubic inches

When a cube is dilated by a scale factor of 0.25, all of its edges are multiplied by 0.25.

This implies,

The edge length of the image cube is

0.25 x 4 inches = 1 inch.

Surface area of the image cube =  6 times the area of one face.

Each face of the image cube has an area of

= (1 inch) x (1 inch)

= 1 square inch,

So the total surface area is,

Surface area

= 6 x 1 square inch

= 6 square inches

Volume of the image cube = length of one edge cubed.

Here, the edge length is 1 inch,

Volume

= (1 inch)^3

= 1 cubic inch

Therefore, the surface area and volume for the given dimensions are

For edge length 4inches , Surface area = 96 square inches and Volume =64 cubic inches.

For scale factor 0.25 ,  Surface area = 6 square inches and Volume =1 cubic inches.

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To multiply the polynomials (1-2t)(5t+t^2), we can use the distributive property and multiply each term in the first polynomial by each term in the second polynomial:

(1-2t)(5t+t^2) = 1(5t+t^2) - 2t(5t+t^2)

Multiplying the first term by each term in the second polynomial, we get:

5t + t^2

Multiplying the second term by each term in the second polynomial, we get:

-10t^2 - 2t^3

Combining like terms, we get:

-2t^3 - 10t^2 + 5t

Therefore, the answer is D. -2t^3 - 9t^2 + 5t.

Answer:

12

Step-by-step explanation:

100;lol

The value of 10x + 3, when x satisfies the equation 5x + 6 = 10, is 11.

To find the value of 10x + 3, we first need to solve the equation 5x + 6 = 10 for x. Then, we can substitute the obtained value of x into 10x + 3 to find its value.

Let's solve the equation 5x + 6 = 10:

5x = 10 - 6

5x = 4

x = 4/5

Now, substitute the value of x into 10x + 3:

10(4/5) + 3

(40/5) + 3

8 + 3 = 11

Therefore, the value of 10x + 3, when x satisfies the equation 5x + 6 = 10, is 11.

Complete Question:

If 5x+6=10, what is the value of 10x+3?

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Answer:

What are we suppose to do here

Step-by-step explanation:

I could help i just need a explanation on how to do it

or what u want me to do

The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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Answer:

f(8)=-161

Step-by-step explanation:

f(x) = -3x^2 + 3x + 7

f(x) = -3x2 + 3x + 7

f(8)= -3(8)^(2) + 3(8) + 7= -192+24+7=-161

Answer:

f(8) = -161

Step-by-step explanation:

The question is asking us to evaluate the function.

In this problem, the function is:

\(\large{\textsf{$ f(x) = -3x^2 + 3x + 7 $}\)

Plug in 8 for x:

\(\large\text{$ f(8) = -3(8)^2 + 3(8) + 7 $}\)

Simplify.

\(\large\text{$ f(8) = -3 * 64 + 24 + 7 $}\)

\(\large\text{$f(8) = -192 + 31 $}\)

\(\large\text{ f(8) = -161}\)

Therefore, f(8) = -161.

The constant of proportionality from the number of boxed lunches to the total cost, in dollars and cents is 8.15 dollars, or 8 dollars and 15 cents.

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilise numbers with fixed or definite values, such as 2, 2, 0.083, etc.

Given that A company orders boxed lunches from a deli. Assume the cost of each packed lunch is the same. The proportional relationship between the number of boxed lunches ordered, b, and the total cost in dollars and cents, c, can be represented by the equation C = 8. 15b.

We have to determine the constant of proportionality from the number of boxed lunches to the total cost, in dollars and cents

The equation c = 8.15b represents the total cost of the boxed lunches

c represents the total cost

b represents the number of boxed lunches

To find the total cost of multiple items, you generally multiply the cost of a single item by the number of items there are.

Using this, we can find the cost per item is 8.15 dollars, or 8 dollars and 15 cents.

Therefore the constant of proportionality from the number of boxed lunches to the total cost, in dollars and cents is 8.15 dollars, or 8 dollars and 15 cents.

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Answer:

The profit function P(x) is defined as the difference between the revenue function R(x) and the cost function C(x): P(x) = R(x) - C(x). Substituting the given functions for R(x) and C(x), we get:

P(x) = (-31.72x^2 + 2030x) - (-126.96x + 26391) = -31.72x^2 + 2156.96x - 26391

To find the maximum profit, we need to find the vertex of this quadratic function. The x-coordinate of the vertex is given by the formula x = -b/(2a), where a = -31.72 and b = 2156.96. Substituting these values into the formula, we get:

x = -2156.96/(2 * (-31.72)) ≈ 34

Substituting this value of x into the profit function, we find that the maximum profit is:

P(34) = -31.72(34)^2 + 2156.96(34) - 26391 ≈ $4,665

The selling price of the dog food is given by the revenue function divided by x: R(x)/x = (-31.72x^2 + 2030x)/x = -31.72x + 2030. Substituting x = 34 into this equation, we find that the selling price of the dog food should be set to:

-31.72(34) + 2030 ≈ $92

So, the maximum profit of $4,665 can be made when the selling price of the dog food is set to $92 per bag.

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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The clearance required from the edge of the roadway to comply with the Super elevation and Side Friction Factor Design (SSD) criteria is 1.68 inches.

To determine the clearance required from the edge of the roadway to comply with the Super elevation and Side Friction Factor Design (SSD) criteria, we need to calculate the maximum lateral displacement of the vehicle as it travels through the curve.

The lateral displacement is given by the following formula

d = V^2 / (g * R)

where:

V = design speed = 50 mph

g = gravitational constant = 32.2 ft/s^2

R = radius of curvature = 1400 ft

Substituting the values, we get

d = (50 mph)^2 / (32.2 ft/s^2 * 1400 ft)

= 0.056 ft = 0.67 inches

Therefore, the maximum lateral displacement is 0.67 inches.

According to the American Association of State Highway and Transportation Officials (AASHTO) Green Book, the minimum desirable clearance from the edge of the roadway to an obstruction is 2.5 times the maximum lateral displacement.

So, the clearance required from the edge of the roadway to comply with the SSD criteria is

Clearance = 2.5 × 0.67 inches = 1.68 inches

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