Explain why the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.

This follows from the identity

[tex]\cot(x) = \dfrac1{\tan(x)} = \tan(90^\circ - x)[/tex]

The overall product is 1 because

[tex]\tan(10^\circ) \tan(80^\circ) = \cot(80^\circ) \tan(80^\circ) = 1[/tex]

[tex]\tan(20^\circ) \tan(70^\circ) = \cot(70^\circ) \tan(70^\circ) = 1[/tex]

[tex]\tan(30^\circ) \tan(60^\circ) = \cot(60^\circ) \tan(60^\circ) = 1[/tex]

[tex]\tan(40^\circ) \tan(50^\circ) = \cot(50^\circ) \tan(50^\circ) = 1[/tex]

Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:

Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.

Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:

Set up a proportion using the corresponding parts

10/8 = 4/x

Solve the proportion using cross products to find x:

10x = (8)(4)

10x = 32

x = 32/10

x = 3.2 cm

The missing length is 3.2 cm.

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Answer:

Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.

Step-by-step explanation:

21 % is the answer.

Problem is that the height of this plant 6.3 and 7.8 cm

P (6.3 <x< 7.8)

12 -5 = 7cm

7.8 - 6.3 = 1.5cm

1.5 / 7 = 0.21

=21%

Probability is a field of mathematics that deals with the numerical description of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the impossibility of the event and 1 indicating certainty.

Probability is a measure of the likelihood that an event will occur. Many events cannot be predicted with absolute certainty. You can only predict the probability that an event will occur.

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[tex]\frac{25}{4}[/tex] of the games was a tie.

To find what fraction of the games was a tie:

Total game played = 25

Win 16 lose 5 total = 21

So, tie matches = 4

The fraction will be 25/4.

Therefore, [tex]\frac{25}{4}[/tex] of the game was a tie.

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Complete question:

A soccer team played 25 games last season they won 16 games, lost 5 games, and tied the rest what fraction of the games was a tie?

Answer:

Option D is correct

Step-by-step explanation:

there were no corn muffins sold.

Answer:

No corn muffins were sold at the bake sale :)

Step-by-step explanation:

Lets go thru each answer choice to see why it is incorrect/correct :)

A.

A is incorrect because more cookies were sold than muffins! that is why A is incorrect :)

B.

This calls for adding! lets do that now :)

Chocolate chip: 5

Oatmeal: 1

Peanut: 3

6 + 1 + 3 = 10

10 < 11

10 is not greater than 11 so B is incorrect!! :)

C.

We need to add again so lets do that now!

Corn: 0

Muffin: 2

2 + 0 = 2

2 < 3

2 is less than 3 so C is incorrect!! :)

D.

It is true that 0 corn muffins were sold at the bake sale so D is our answer!! :D

Have an amazing day!!

Please rate and mark brainliest!!

A certain journey by train takes 5 hours at the speed of 45 km/h. What will be the speed of the train to complete the same journey in 3 hours?

Answer:

Journey taken time 5 hour at speed of 45km/hr

So,

 1 hour=45/5=9km/hr

Therefore,3 hour=(9x3)km/hr.

(please mark me brainliest if my answer was good)

The polynomial expression that represents the profit of selling x tablets is 10x - 100

profit = revenue – cost

= (100 + 30x) - (20x + 200)

= 100 + 30x - 20x - 200

Profit = 10x - 100

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Using the unit circle, the coordinates of the terminal point corresponding to [tex]\theta = 120^\circ[/tex] is: (-0.5, 0.866).

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

In this problem, the angle is of [tex]\theta = 120^\circ[/tex], hence:

Hence the terminal point is:

(-0.5, 0.866).

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Triangle ABC is dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle ABC has vertices at A(-3, -1), B(2, -2) and C(-1, -4). It is then dilated by a scale factor of 5 to get A'(-15, -5), B'(10, -10) and C'(-5, -20)

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The total number of bars of kitkat Mr hassell had in total is 3 1/2 bars

Total bars of KitKat = 6 × 3/4

= (6×3)/4

= 18/4

= 9/2

= 4 1/2 bars

Number of bar remaining after eating 1 bar = 4 1/2 - 1

= 3 1/2 bars

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The z value for the probability in the standard normal table is 1.29.

In this question,

Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.

The value of probability is 0.80

A standard normal random variable is between -z and +z, So

P(-z < 0 < z) = 0.80

⇒ 2P(0 < z) = 0.80

⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]

⇒ P(0 < z) = 0.40

From the standard normal table, z value for the probability 0.40 is

⇒ z = 1.29

Thus P(0 < 1.29) = 0.40

Hence we can conclude that the z value for the probability in the standard normal table is 1.29.

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Rosa is providing home-based tutoring.

What is Home-based tutoring?

Therefore, Rosa is providing home-based tutoring.

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The length of the side QR in the task content can be determined as; 12.22cm.

It follows from the task content that 2 lengths and one included angle are given in the task content. It therefore follows that the length of side QR can be evaluated by the cosine rule as follows;

QR² = 13² + 4² - (2×4×13×cos70)

QR = √149.4

QR = 12.22cm

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The price of the turkey based on the percentage given is $15.81.

It was stated that the cost is $15.50 but that there was a 2% increment in price.

Therefore, the new price will be:

= $15.50 + (2% × $15.50)

= $15.50 + $0.31

= $15.81

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The differentiation of the stated series expansion of  f term-by-term to obtain the corresponding series expansion for the stated derivative of f is  [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)Xⁿ⁻¹

f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ

⇒ f'(x) = d/dx [[tex]\sum_{n=0}^{\infty}[/tex](-1)ⁿ 3ⁿXⁿ]

= [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿ d/dx (xⁿ)

= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿ(nxⁿ⁻¹)

= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿnxⁿ⁻¹

= [tex]\sum_{n=1}^{\infty}[/tex] ((-1)ⁿnxⁿ⁻¹)3ⁿ

= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)xⁿ-1

In mathematics, differentiation is used to calculate rates of change. In mechanics, for example, velocity is the rate of change of displacement (with regard to time).

The acceleration is the rate of change of velocity (with respect to time).

They are employed in many fields, including

They can be used to represent:

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Full Question:

Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f.

If f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ

Answer:

standard deviation sign is σ

mean sign is x , and sometimes it have a hyphen directly above x.

Step-by-step explanation:

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list. To find the mean, add up all the values in the set. Then divide the sum by how many values there are.

The symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.

A cone has a circular base. So, the answer to your question is B for circle.

The Slope of the line :

[tex]m=-\frac{1}{5} \approx-0.2[/tex]

Using small, whole integer coordinates, it is simple to manually determine a line's slope. The formula becomes more effective if the coordinates are given greater or decimal values.

Because all horizontal lines have the same y-coordinates, it is important to note that all of them have a gradient of zero. In the slope formula's numerator, this will produce a zero. A vertical line, on the other hand, will have an arbitrary slope because the x-coordinates are constant. When applying the formula, this will lead to a division by zero error.

slope = (y₂ - y₁) / (x₂ - x₁)

Using the two points P=(2,3) and Q=(-3,4) as your input, determine the slope.

P=(x1,y1) and Q=(x2,y2) are two points on a line, and the slope of that line is given by :

                                 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

we have that:

                        [tex]x_{1}=2, y_{1}=3, x_{2}=-3, y_{2}=4[/tex]

Fill in the blanks in the slope calculation,

                                    [tex]m=\frac{(4)-(3)}{(-3)-(2)}\\\\=\frac{1}{-5}\\\\=-\frac{1}{5}[/tex]

Reaction:  the slope of the line is =[tex]m=-\frac{1}{5} \approx-0.2[/tex]

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The function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)

The equation is given as:

f(x) = 2(0.35)^x

The reflection of a function over the y-axis is :

f'(x) = f(-x)

So, we have:

f(-x) = 2(0.35)^(-x)

From the list of options, we have

h(x) = 2(0.35)^(-x)

Hence, the function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)

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The polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2

The GCF is given as:

GCF = 5z

This means that the polynomial can be represented as:

P(z) = GCF * Another factor

We can make use of the following function

P(z) = 5z * (z - 1)

Expand

P(z) = 5z^2 - 5z

Rewrite as:

P(z) = -5z + 5z^2

Hence, the polynomial is P(z) = 5z * (z - 1) and the equivalent forms are P(z) = 5z^2 - 5z and P(z) = -5z + 5z^2

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Answer:

[tex]y = \frac{1}{4} x + 9[/tex]

Step-by-step explanation:

All lines take the form

[tex]y = mx + c[/tex]

Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.

To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:

[tex]y = \frac{1}{4} x + 9[/tex]

Answer:

1. (x + 8)(x + 3)

2. (x - 9)²

Step-by-step explanation:

Given trinomials:

1. [tex]x^2+11x+24[/tex]

2. [tex]x^2-18x+81[/tex]

..................................................................................................................................................

When factoring trinomials of the form ax² + bx + c:

..................................................................................................................................................

1) x² + 11x + 24

Step 1: Multiply the leading coefficient (1) and the last term (24).

[tex]\implies 1 \times 24 = \boxed{24}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (11).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:24 & \sf Sum\:of\:factors\\\cline{1-2} 1, 24\ \| -1, -24 & 25\ \| -25 \\\cline{1-2} 2, 12\ \| -2, -12 & 14\ \| -14 \\ \cline{1-2} 3, 8\ \| -3, -8 & 11\ \| -11 \\\cline{1-2} 4, 6 \ \| -4, -6 & 10\ \| -10 \\\cline{1-2}\end{array}[/tex]

[tex]\implies 3x+8x=11x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2+3x+8x+24[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2+3x)}^x+\overbrace{(8x+24)}^8\ \ \textsf{[ Factor out $x$ and $8$. ]}[/tex]

[tex]\implies x\overbrace{(x+3)}^{\textsf {Factor out}}+8(x+3)[/tex]

[tex]\implies \boxed{(x+8)(x+3)}[/tex]

The factored form of the given trinomial is [tex](x+8)(x+3)[/tex].

..................................................................................................................................................

2) x² - 18x + 81

Step 1: Multiply the leading coefficient (1) and the last term (81).

[tex]\implies 1 \times 81 = \boxed{81}[/tex]

Step 2: Find the product factors that sum up to the middle term's coefficient (-18).

[tex]\begin{array}{| c | c |}\cline{1-2} \sf Factors\:of\:81 & \sf Sum\:of\:factors\\\cline{1-2} 1, 81\ \| -1, -81 & 81\ \| -81 \\\cline{1-2} 3, 27\ \| -3, -27 & 30\ \| -30 \\ \cline{1-2} 9, 9\ \| -9, -9 & 18\ \| -18 \\\cline{1-2}\end{array}[/tex]

[tex]\implies (-9x)+(-9x)=-18x[/tex]

Step 3: Rewrite the polynomial with those factors, replacing the middle term.

[tex]\implies x^2-9x-9x+81[/tex]

Step 4: Factor by grouping.

[tex]\implies \overbrace{(x^2-9x)}^x+\overbrace{(-9x+81)}^{-9}\ \ \textsf{[ Factor out $x$ and $-9$. ]}[/tex]

[tex]\implies x\overbrace{(x-9)}^{\textsf {Factor out}}-9(x-9)[/tex]

[tex]\implies (x-9)(x-9)[/tex]

[tex]\implies \boxed{(x-9)^2}[/tex]

The factored form of the given trinomial is [tex](x-9)(x-9)\ \textsf{or}\ (x-9)^2[/tex].

The distance between the skate and point X is 16 feet

Given that the distance between point X and kite is 12 feet

and the distance between stake and kite is 20 feet

We need to find the distance between the stake and point X

Here,

Perpendicular = 12 feet

Hypotenuse = 20 feet

Base = ?

According to Pythagoras Theorem

(Hypotenuse)² =  (Perpendicular)²+(Base)²

(20)² = (12)² + (Base)²

∴ (Base)² = 400 - 144

∴ (Base)² = 256

∴ Base = 16 feet

Hence the distance between the Point X and the stake is 16 feet

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The nth term of a sequence exists 2n2² - 4n+4 is 36.

The order of operations exists as a rule that describes the right sequence of measures for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).

[tex]$2*8*2^{2} - 4*8+4[/tex]

Follow the PEMDAS order of operations

Calculating the exponents, we get 2² = 4

[tex]= 2*8*4 - 4*8+4[/tex]

= 64-32 +4

= 36

Therefore, the nth term of a sequence that exists 2n2² - 4n+4 is 36.

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Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

Xmax = -b/2a

Xmax = -10/2(-1)

Xmax = 5.

Thus, the maximum height on the vertical axis is given by:

h(x) = -x² + 10x + 9.5

h(5) = -(5)² + 10(5) + 9.5

h(5) = -25 + 50 + 9.5

h(5) = 34.5 feet.

Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.

Also, the spray reaches all the way to the ground at about:

Maximum distance = √34.5 + 5

Maximum distance = 10.87 feet.

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Complete Question:

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away​

Answer:

2×sqrt(2) = 2.828427125...

Step-by-step explanation:

x = "a positive number"

x + 56/x = x³

x² + 56 = x⁴

x⁴ - x² - 56 = 0

(x² + 7)(x² - 8) = 0

this is true only for

x² = -7

or

x² = 8

x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.

x² = 8 means

x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...

Answer: 47°

Step-by-step explanation:

Answer:

60 kilograms

Step-by-step explanation:

Answer: 9,-9

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

9x9=81