How to write an equation?

The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%

The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

x' = 51

μ = 47

σ = 4

Thus;

z = (51 - 47)/4

z = 1

From empirical formula at 1 standard deviation above the means, the probability is 68%.

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Answer:

5

Step-by-step explanation:

a+b=30

a=30-b------1

&a-b=20

a=20+b-----2

From eqn 1 and 2, we get

30-b=20+b

or, 10=2b

b=5

Now, a=20+5

a=25

Therefore, a/b=25/5

=5

Using a system of equation, the value of a/b obtained from the values of a and b calculated is 5

The system of equations:

From (1) :

a = 30 - b - - - (3)

Substituting a = 30 - b into (2)

30 - b - b = 20

30 - 2b = 20

30 - 20 = 2b

10 = 2b

b = 5

From (3) :

a = 30 - 5

a = 25

Hence,

a/b = 25 / 5 = 5

Hence, the value of a/b is 5

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The transformation above is 15 units translation upwards and to the right.

A translation moves a shape up, down or from side to side but it does not change its appearance in any other way. Translation is an example of a transformation. A transformation is a way of changing the size or position of a shape. Every point in the shape is translated the same distance in the same direction

if the x-coordinates is at x, y is at x -10 after 15 units translation to the right, x coordinates moves x + 15 while y-coordinates moves (x -10 + 15)  which is ( x + 5)

In conclusion the transformation 15 units in the positive x and y axis

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Answer:

{B} travelling costs paid in connection with a temporary work assignment

Answer:

Step-by-step explanation:

Question 1.

\(12x-4 > 5x+10\)

Move all terms containing \(x\) to the left side of the inequality.

Subtract \(5x\) from both sides of the inequality.

\(12x-4-5x > 10\)

Subtract \(5x\) from \(12x\).

\(7x-4 > 10\)

Move all terms not containing \(x\) to the right side of the inequality.

Add 4 to both sides of the inequality.

\(7x > 14\)

Divide each term in \(7x > 14\) by 7 and simplify.

The answer can be written as \(x > 2\) or (2,∞)

Question 2.

\((-4x+1)+6\geq8x +72\)

\(-4x+1+6\geq8x +72\)

Move all terms containing \(x\) to the left side of the inequality.

Subtract \(8x\) from both sides of the inequality.

\(-12x+7\geq 72\)

Move all terms not containing \(x\) to the right side of the inequality.

Subtract 7 from both sides of the inequality.

\(-12x\geq 65\)

Divide each term in \(-12x\geq 65\) by − 12 .

When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

\(\frac{-12x}{-12} \leq \frac{65}{-12}\)

The answer can be written as \(x\leq- \frac{65}{12}\)  or (−∞,−\(\frac{65}{12}\)]

Answer:

d is the answer

in think

Step-by-step explanation:

try it

Answer:

A

Step-by-step explanation:

Number of student=32

Number of girls=12

Number of boys=32-12

=20

Ratio of girls to boys=12:20

=6:10

=3:5

Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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Answer:

is it A and C ):

Step-by-step explanation:

The value of h is 8 units.

"Two triangles are similar when their corresponding sides are in proportion and all corresponding angles are equal."

For given question,

ΔBAD and ΔCBD are similar triangle.

So, their sides are in proportion.

\(\Rightarrow \frac{BA}{CB}= \frac{AD}{BD}= \frac{BD}{CD}\)                    ..................(i)

For given figure,

BD = h, CD = 4 units

Now, we find the length of the side AD.

⇒ AD = AC - CD

⇒ AD = 20 - 4

⇒ AD = 16 units

From (i),

\(\Rightarrow \frac{AD}{BD}= \frac{BD}{CD} \\\\\Rightarrow \frac{16}{h} =\frac{h}{4}\\\\ \Rightarrow 16\times 4=h\times h\\\\\Rightarrow h^2=64\\\\\Rightarrow h=8\)

Therefore, the value of h is 8 units.

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The equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The point-slope form of a line can be converted to the slope-intercept form of a line, y = mx + b, where b is the y-intercept.

The equation y - 5 = (4/3)(x - 6) can be rearranged into the point-slope form of a line by isolating the y-term and simplifying: y - 5 = (4/3)(x - 6)y - 5 = (4/3)x - 8y = (4/3)x - 3

Now, we have the point-slope form of the line with slope 4/3 and y-intercept -3.

To convert this to the slope-intercept form of a line, we simply rearrange the equation to solve for y:y = (4/3)x - 3 This is the slope-intercept form of the line, where the slope is 4/3 and the y-intercept is -3.

Thus, the equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

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Answer:

y = (1/3)x - (1/3)

(1/3)

Step-by-step explanation:

We can find the slope by subtracting Q points by P points.

(2 - (-1)) / (7 - (-2))

3 / 9

1/3 = slope

To find y intercept we can use the slope and find the difference left

y = (1/3)x

-1 = (1/3)(-2)

-1 = -(2/3)

This is not true

To make it true we must subtract -(1/3)

This means our equation is

y = (1/3)x - (1/3)

Answer:

. 0625

Step-by-step explanation:

1/2^4

or

1/16

just doing half life

Answer:

0.4

Step-by-step explanation:

35 ÷ 14 = 2.5

14 ÷ 2.5 = 5.6

5.6 ÷ 14 = 0.4

(sorry if I'm incorrect)

Answer:

Step-by-step explanation:

Let the volume of water left in the tank be w and time be t, then the required expression is:

Since w is not negative, we should add the restriction of t ≥ 0 and:

So the expression is valid for 0 ≤ t ≤ 2.5 min

Answer:

179,000-94,000=y   y=85,000

Answer:

30.39in^2 (^2 means squared)

Step-by-step explanation:

3 x 3 = 9in^2

3.1 x 6.9 =21.39in^2

9 + 21.39 = 30.39in^2

The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Answer:

330

11 choose 4

\(=\frac{11!}{4!\left(11-4\right)!}\\= 330\)

Step-by-step explanation:

The value of transformation of f (x) makes f(x) < g(x) is,

⇒ shifts the function 3 units upward.

We know that;

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Now, We have;

Functions are,

f (x) = x²

g(x) = x² +3

Hence, The value of transformation of f (x) makes f(x) < g(x) is,

⇒ shifts the function 3 units upward.

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Answer:

8^(7), which is 2097152

Step-by-step explanation:

8^(4) × 8^(3)

= 8^(4+3)

= 8^(7)

= 2097152

Answer:

The answer is 2097152.

Step-by-step explanation:

1) Use the product rule: x^a x^b = x^ a + b.

\( {8}^{7} \)

2) Simplify.

\(2097152\)

Thus, the answer will be 2097152.

Answer:

1 1/4

Step-by-step explanation:

here is the exact form if your looking for that. :)

5/4

and heres the decimal form if you are looking for that :>

1.25

Answer:

growth and .09% increase I believe

Step-by-step explanation:

Answer:

I just need points.

Step-by-step explanation:

Answer:

Step-by-step explanation:

7) ∠1  + 30 = 180                {linear pair}

            ∠1 = 180 - 30

            ∠1 = 150

8)  ∠2 = 30    {Vertically opposite angles are congruent}

9) In ΔLMN,

∠L + ∠N + ∠M = 180   {angle sum property of triangle}

50 + 30 + ∠M = 180

       80 + ∠M = 180

                ∠M = 180 - 80

                ∠M = 100°

10) Sum of exterior angle of a triangle equals to sum of opposite interior angles.

∠B + ∠A = ∠BCD

30 +   ∠A = 80

        ∠A  = 80 - 30

      ∠A = 50

3/8 or .375

You can find slope by doing rise/run (in fraction form) Rise is counting up or down spaces from one point until you hit the line of the next point. And then the run is counting over to the next point on the line. the number of spaces you counted up or down is the numerator and the run is the denominator.

Answer:

\(y=-\sqrt{x+2}-1\)

Step-by-step explanation:

Hi there!

Please take a look at the attached image. This is the parent function of the radical function.

\(y=\sqrt{x}\)

This equation represents the transformations of the parent function:

\(y=a\sqrt{b(x-h)}+k\)

a dictates vertical stretch.

b dictates horizontal stretch.

h dictates horizontal translation.

k dictates vertical translation.

If we take a look at the given graph, we can tell that the following transformations have been applied:

- reflection across x-axis (a = -1)

- translation 2 units to the left (h = -2)

- translation 1 unit down (k = -1)

Therefore, the function that represents the graph is:

\(y=-\sqrt{x+2}-1\)

I hope this helps!

The ratios will be equal if the theorem that the product of the extremes equals the product means follows.

Let us understand the equality of ratios through example. The example ratio will be -

7:10 = 21:30

In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.

Product of extremes = 7 × 30

Extremes product = 210

Product of means = 21 × 10

Means product = 210

Since the products are equal, the ratios are also equal.

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The complete question is -

Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.

Ratio = 7:10 and 21:30.

Answer:

2^40 =

1) (2^2)^20

2) (2^5)^8

3) (2^8)^5

4) (2^10)^4

Step-by-step explanation:

We know this simply because we multiply the exponent inside the parentheses by the exponenent outside the parentheses. Using this, we can simply find the numbers that have a product of 40.

Answer:

1/23

Step-by-step explanation:

The perpendicular slope will be the opposite reciprocal of the original slope so if slope of c is -23, slope of d is 1/23

Answer:

y = m x * b      equation for a straight line

When x = 0        you have b = y = 4

y = m x + 4        revised equation

When y = 0,     m = -4 / x = -4 / 2 = -2

y = -2 x + 4         or   -2 x - y = -4  

(a) is the correct answer