The number of children x, belonging to each of eight families registering for swimming was 3,2,6,3,4,2,5,6. Find the mean, x. (Give answer correct to 2 decimal places.)

Answer:

Differentiation is used to break down the function into parts, and integration is used to unite those parts to form the original function. Geometrically the differentiation and integration formula is used to find the slope of a curve, and the area under the curve respectively.

Answer:

integration is the opposite of differentiation

Step-by-step explanation:

integration requires addition of 1 to the power and then division by the value eg

the integral of

\({x}^{2} = \frac{ {x}^{2 + 1} }{2 + 1} \\ = \frac{ {x}^{3} }{3} \)

while in differentiation, u subtract one and multiply by the value. eg

the differential of

\( \frac{ {x}^{3} }{3} = 3( \frac{ {x}^{3 - 1} }{3} ) \\ = 3( \frac{ {x}^{2} }{3} ) \\ = {x}^{2} \)

Answer:

4 batches

Step-by-step explanation:

one batch calls for:

3/4 PB

1 1/2 cup SG

1 EGG

3/.75(3/4)= 4

9/1.5(1 1/2)=6

5/1= 5

The maximum number of batches she can make before running out of ingredients is 4

Answer:

-34

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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The only set of side lengths that can form a triangle is 9, 4, 8.

Option A is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check if each of the given sets of side lengths satisfies this condition:

A.

9, 4, 8

9 + 4 > 8 ✓

9 + 8 > 4 ✓

4 + 8 > 9 ✓

All three inequalities are true, so these side lengths can form a triangle.

B.

14, 7, 6

14 + 7 > 6 ✓

14 + 6 > 7 ✓

7 + 6 > 14 ✗

The last inequality is false, so these side lengths cannot form a triangle.

C.

3, 8, 1

3 + 8 > 1 ✓

3 + 1 > 8 ✗

8 + 1 > 3 ✓

The second inequality is false, so these side lengths cannot form a triangle.

Therefore,

The only set of side lengths that can form a triangle is A. 9, 4, 8.

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The value of x is \(x=\frac{268}{3}\) = 89.33 degree.

How do you find value of x?

The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values. The letter "x" is frequently used in mathematics to denote an unknowable amount or variable. Similar to how X-rays confounded their discoverer and Malcolm X adopted the sign to stand for the lost name of his African ancestry, x also denotes the unknown in English.

x+44+x+3+x+45=360

Group like terms

x+x+x+44+3+45=360

Add similar elements: x+x+x=3 x

3 x+44+3+45=360

Add the numbers: 44+3+45=92

3 x+92=360

Move 92 to the right side

3 x=268

Divide both sides by 3

\(\frac{3 x}{3}=\frac{268}{3}\)

Simplify

\(x=\frac{268}{3}\)

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Answer:

False

Step-by-step explanation:

Since a triangle must contain 3 interior angles all adding to 180°, then there can't be more than one right angle since 2 right angles would add up to 180°.

Answer

f= 1

step by step explanation

The distance from the center of the Earth to the point where the net gravitational force is zero is one-ninth the distance from the Earth to the Moon.

Let's assume that the distance from the center of the Earth to this point is denoted as x.

Given:

Mass of the Moon (M\(_{moon}\)) = 1/81 × M\(_{earth}\)

Distance from Earth to Moon (d\(_{moon}\)) = distance on center

According to the principle of gravitational equilibrium, the gravitational force from the Earth and the gravitational force from the Moon acting on an object at that point must balance out. Mathematically, we can express this as:

F\(_{earth}\) = F\(_{moon}\)

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F \(_{gravity}\)= G × (m₁ × m₂) / r²

Where:

G is the gravitational constant (approximately 6.67430 x 10⁻¹¹m²/kg/s²)

m₁ and m₂ are the masses of the two objects

r is the distance between the centers of the two objects

Considering the gravitational forces involved:

F\(_{gravity}\)\(_{earth}\) = G ₓ (M\(_{EARTH}\)  ₓ m\(_{OBJECT}\)) / (d\(_{earth}\))²

F\(_{gravity}\) \(_{moon}\) = G ₓ (M \(_{moon}\) ₓ m\(_{object}\)) / (d \(_{moon}\))²

Since we are looking for the point where the net gravitational force is zero, we set these two forces equal to each other:

G × (M\(_{earth}\) × m\(_{object}\)) / (d\(_{earth}\))²   =     G × (M \(_{moon}\) × m\(_{object}\)) / (d \(_{moon}\))²

Canceling out the common factors of G and m\(_object}\), and substituting the given values:

(M\(_{earth}\) × 1) / (d\(_{earth}\))² = (M \(_{moon}\) × 1) / (d \(_{moon}\))²

Rearranging the equation:

(d\(_{earth}\))²/ (M\(_{earth}\)) = (d \(_{moon}\))² / (M \(_{moon}\))

Taking the square root of both sides:

d\(_{earth}\) / √(M \(_{moon}\))) = d_moon / √(M \(_{moon}\))

Substituting the given values:

d\(_{earth}\) /√(M\(_{earth}\)) = d\(_{moon}\) / √(1/81 × M\(_{earth}\))

Simplifying further:

d\(_{earth}\)  / √(M\(_{earth}\)) =d\(_{moon}\)  / (1/9 × √(M\(_{earth}\)))

Multiplying both sides by √(M\(_{earth}\)):

d\(_{earth}\) = (1/9) × d\(_{moon}\)

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Answer:

-5/4

Step-by-step explanation:

Let \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(0,-1)\). The slope of the line would be:

\(\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}\)

Answer: -5/4

Step-by-step explanation:

To find the slope between two points, you can use the formula:

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

slope = (4 - (-1))/(-4 - 0)

slope = (4 + 1)/(-4)

slope = 5/-4

Therefore, the slope between the two points is -5/4.

Answer:

A 9

B 4.5

C 4.5

D 2.25

Step-by-step explanation:

I need to be 20 letters long so ya

color : 40p + 50f + 90

b&w : 15p+20f + 45

p = 26

f = 45

[substitute the values given]

color : 40(26) + 50(45) + 90

b&w : 15(26)+20(45) + 45

[solve the equation]

color : 3380

b&w : 1335

[subtract to see how much ink is saved]

3380 - 1335 = 2045

Answer:

the answer is the first one, Cara multiplied only 4 and 7 together and did not multiply 4 and 13

Step-by-step explanation:

if you look through the question you can see that Cara evaluated the (-4)^2 correctly because a negative multiplied by a negative gives you a positive thus (-4)*(-4)= 16, then next you can see that Cara subtracted 2 from 6 correctly because (6-2)= (4), and last but not least Cara did multiply 2 by 4 correctly because 2*4 or 2(4) =8 so as you can see the answer is the first one

Answer:

A is correct answer

Step-by-step explanation:

The equation that represent a linear function is y = 1 / 4 x - 1.

A linear function is a function that represents a straight line on the coordinate plane. In other words, a linear function is a function with either one or two variables without any exponents.

Linear function can be express in slope intercept form as follows:

y = mx + b

where

Therefore, the linear equation in the option is as follows:

y = 1 / 4 x - 1

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The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°

Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.

From the diagram shown:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

20 + 105 + ∠Z = 180

∠Z = 55°

Since triangle XYZ and triangle GHI are similar, hence:

∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°

The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°

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Answer: 2.0431

Step-by-step explanation:

\(\log_{8} 70=\frac{\log 70}{\log 8} \approx 2.0431\)

C. Unique solution. The system of linear equations have a unique solution because the equations are consistent and have the same number of variables and equations.

The given system of linear equations is x+2y=3 and 2x+4y=15. To determine whether the system of linear equations have no solution, infinitely many solution or unique solutions, we need to solve the system of equations. Firstly, we expand and simplify both equations to get x+2y=3 and 2x+4y=15. Then, we compare the coefficients of the equations to determine if the system of equations is consistent, inconsistent or dependent. Since the equations are consistent and have the same number of variables and equations, we can solve the system of equations. By isolating the variables and using the substitution method, we can solve the system of equations to get x=3 and y=3. This means that the system of linear equations have a unique solution.

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The corresponding areas under the curves for y = 2x-x² in the interval [1, 2] and y = x³-6x²+8x in the interval [0, 4] are 2/3 unit² and 0 unit²

Given:

1. y = 2x-x² in the interval [1, 2]

2. y = x³-6x²+8x in the interval [0, 4]

In order to find  the area under the curve for these functions for the given intervals, we will take the integral of the functions and use the intervals as upper and lower limits: Thus:

y = 2x-x² in the interval [1, 2]  will be:

\(\int\limits^2_1 {2x-x^{2} } \, dx = \left[\frac{ 2x^2}{2}-\frac{ x^3}{3}\right]_1^2\)

                   \(= \left[x^{2} -\frac{ x^3}{3}\right]_1^2\)

Substitute the value of the upper and lower limits into x:

               =  [2²- 2³/3] - [1²- 1³/3]

              =   [4 - 8/3] - [ 1 - 1/3]

              =   [4/3] - [2/3]

              = 2/3 unit²

y = x³-6x²+8x in the interval [0, 4] will be:

 \(\int\limits^4_0 {x^{3} -6x^{2} + 8x } \, dx = \left[\frac{ x^4}{4}-\frac{ 6x^3}{3}+\frac{ 8x^2}{2}\right]_0^4\)

                               \(= \left[\frac{ x^4}{4}- 2x^3+4x^2\right]_0^4\)

                              = [4⁴/4 - 2(4)³ + 4(4)²] - [0⁴/4 - 2(0)³ + 4(0)²]

                              =  [ 64 - 128 + 64] - [0 - 0 -0]

                              = 0 unit²

Therefore, the areas under the curves y = 2x-x² in the interval [1, 2]

and y = x³-6x²+8x in the interval [0, 4] are 2/3 unit² and 0 unit² respectively

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Answer:

I think it's- creeper awwww man. What was that?

Answer:

173.83

Step-by-step explanation:

An octagon has 8 sides (octa-, right, like octopus)

"regular" means all the sides are the same length.

The apothem is given, 7.243, it goes from the center to the middle of a side, at a right angle. See image. Make a triangle. Use area formula for triangle.

A = 1/2bh

Multiply by 8, bc there are 8 of these identical triangles.

OR, use the area formula for an n-sided regular polygon:

A = 1/2asn

see image.

Answer:

\(P(Green\ and\ Green) = \frac{25}{144}\)

Step-by-step explanation:

Given

\(Green=5\)

\(Blue = 7\)

Required

\(P(Green\ and\ Green)\)

This is calculated as:

\(P(Green\ and\ Green) = P(Green) * P(Green)\)

Since, it is a probability with replacement, we have:

\(P(Green\ and\ Green) = \frac{Green}{Total} * \frac{Green}{Total}\)

So, we have:

\(P(Green\ and\ Green) = \frac{5}{12} * \frac{5}{12}\)

\(P(Green\ and\ Green) = \frac{25}{144}\)

The value of above expression in simplest radical form :

Solution is in attachment !

The radical form is \(8i\sqrt{6}\).

We have the following information available from the question is:

Simplify the question into simplest radical form:

4i√−24

Now, According to the question:

4i√−24

We know that , the value of:

\(i^2=-1\)

Factors of 24 is 2× 2× 2 × 3

We can write this:

\(4i\sqrt{i^2.2.2.2.3}\)  (dot sign indicates the multiplication sign)

then,

\(4i . 2i \sqrt{6}\\ \\8i\sqrt{6}\)

Hence, The radical form is \(8i\sqrt{6}\)

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The primitive function for \(f(x) = 4e^{2x} + e^{-x}\) is given by it's indefinite integral.

To calculate it, recall:

\(\frac{d}{dx}e^{ax}=ae^{ax}\)

\(\int c f(x)dx = c\int f(x)dx\)

Let's begin

\(\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\\)

\(F(x) = 2e^{2x}-e^{-x} +c\)

To find the costant, we just need to use the fact that \(F(0)=2\)

\(F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3\)

Therefore,

\(\boxed{F(x) = 2e^{2x} - e^{-x} -3 }\)

The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800

Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.

Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.

The inequality that represents the situation becomes as;

25x + 65y ≤ 800

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Answer: D

Step-by-step explanation:

Hope it helps

Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)