Henry recorded the number of miles he biked each day for a week. His miles were 25, 40,35, 25, 40, 60, and 75,
Enter the data into the statistics calculator,
What is the standard deviation of the miles Henry biked to the nearest tenth?

[tex]\tan(2\alpha)=\dfrac{2\tan \alpha }{1-\tan^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha}}{1-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha}{\cos^2\alpha}-\dfrac{\sin ^2\alpha}{\cos^2\alpha}}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\dfrac{2\sin\alpha}{\cos\alpha} }{\dfrac{\cos^2\alpha-\sin^2 \alpha}{\cos^2\alpha}}[/tex]

[tex]\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha}{\cos\alpha} \cdot\dfrac{\cos^2\alpha}{\cos^2\alpha-\sin^2 \alpha}\\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{2\sin\alpha\cos\alpha}{\cos^2\alpha-\sin^2 \alpha} \\\\\\\dfrac{\sin(2\alpha)}{\cos(2\alpha)}=\dfrac{\sin(2\alpha)}{\cos(2\alpha)}[/tex]

Answer:

See below.

Step-by-step explanation:

tan 2A = sin 2A / cos 2A

= 2 sinA cosA / (cos^2A - sin^2A)

Now divide top and bottom of the fraction by cos^2 A:

2 sinA cosA               cos^2A         sin^2 A

-------------------      /     -----------   -   -------------

cos^2A                      cos^2 A        cos^2 A

= 2 tan A / 1 - tan^2A).

To find the inverse of an equation just switch the places of the x and y, then solve for y like so...

(keep in mind that f(x) means the same thing as y)

original equation:

y = 4x + 8

switching x and y:

x = 4y + 8

x - 8 = 4y

[tex]\frac{1}{4}x[/tex] - 2 = y

Hope this helped!

~Just a girl in love with Shawn Mendes

George still owes $36.44 after making a payment of $37.50 on his original bill of $73.94. This is calculated by subtracting the payment from the original bill amount.

George made a payment of $37.50 on a bill of $73.94. To determine how much he still owes, we subtract the payment he made from the original bill.

Original bill: $73.94
Payment made: $37.50

To calculate the remaining balance:

Therefore, George still owes $36.44 on his bill.

Answer: There are 5 sig figs in 1.0025

Step-by-step explanation:

With significant figures, any number other then 0 is a significant figure. The two zeros are significant because they are followed by more numbers. If the number was 1.000, there would only be one sig fig.

Hope this helps!

Answer:

4000 units

Step-by-step explanation:

In 2001 the total number of marketed units= 730,000

If this number represents 50% of what was marketed in 2004, then the total number of units marketed in 2004 was:

(100/50)× 730,000=1460000

To get the number for each of the 365 days in 2004 we divide the total for 2004 by 365

1460000/365= 4000 units

Answer: 4,000 units per day.

Step-by-step explanation:

You know that in 2001 its yearly volume was 50% of its volume for 2004.

Therefore, if in 2001 the company marketed 730,000 units of its product, in 2004 the volume is:

[tex]Yearly\ volume_{(2004)}=(730,000\ units)(2)=1,460,000\ units[/tex]

Let be "x" the number of units for each of the 365 days of 2004, you can find its value by dividing  the 2004 volume by 365.

The result is:

[tex]units=\frac{1,460,000\ units}{365}=4,000\ units.[/tex]

Hello There!

I Provided Steps In The Image Attached.

Have A Great Day!

Answer:

x = -35/72

Step-by-step explanation:

3x + 1/9 = 2x - 3/8

x = -3/8 - 1/9

x = -35/72

Answer: The answer is: -5m + 2m

Step-by-step explanation:

Because -5 + 2 equals -3

Hope it helps

God bless you guy!

Final answer:

The slope of the line passing through the points (-7,2) and (5,8) is calculated using the slope formula and is found to be 0.5.

Explanation:

The student asked about the slope of the line passing through two points, (-7,2) and (5,8). To find the slope, one should use the slope formula: slope (m) = (y2 - y1) / (x2 - x1). Plugging in the values from the points, we have m = (8 - 2) / (5 - (-7)) = 6 / 12 = 0.5. Therefore, the slope of the line is 0.5.

Answer:

Step-by-step explanation:

[tex]9(2x+1)<9x-18\qquad\text{divide both sides by 9}\\\\2x+1<x-2\qquad\text{subtract 1 from both sides}\\\\2x<x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\x<-3\\\\-4<-3[/tex]

First calculate the diameter of circle.

[tex]d=8+4=12[/tex]

Now we know that diameter is equal for any two points on the arc of a circle lying opposite to each other.

[tex]12=x+4[/tex]

Now just simply solve for x.

[tex]

12=x+4 \\

12-4=x+4-4 \\

\boxed{x=8} \\

[/tex]

Hope this helps.

r3t40

The form of linear equation that describes line is:

[tex]y=sx+n[/tex]

First we must calculate the slope.

[tex]s=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{2-(-3)}{4-2}=\dfrac{5}{2}[/tex]

Now it looks a bit more like this:

[tex]y=\dfrac{5}{2}x+n[/tex]

All we need now is to put in y and x from one point doesn't matter which. I'll pick A.

The equation now looks like this:

[tex]-3=\dfrac{5}{2}\cdot2+n[/tex]

Solve for n.

[tex]

-3=5+n \\

n=-8

[/tex]

And finally write the equation.

[tex]f(x)=\dfrac{5}{2}x-8[/tex]

Hope this helps.

r3t40

Answer:

Here is the answer.

x= 1/2(7+3i√3) and 1/2(7-3i√3)

In order to change from 35 to 62, we have to add 27. So, the question becomes: which percentage of 35 is 27?

To answer this question, we set this simple equation

[tex]27 = 35\cdot\dfrac{x}{100}[/tex]

And solving for x we have

[tex]x = \dfrac{2700}{35} \approx 77.14[/tex]

So, if you change from 35 to 62, you have an increase of about 77%

The percentage change is 77.14%

The following information can be gotten from the question:

Old number = 35

New number = 62

Increase in number = 62 - 35 = 27

Percentage change will be:

= (Increase in number / Old number) × 100

= 27/35 × 100

= 2700/35

= 77.14%

In conclusion, the percentage change is 77.14%

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Answer:

B 70

Step-by-step explanation:

7 |H| + 4 G

H = -6  and G = 7

| H| = 6

7*6 + 4*7

42+28

70

Answer:

see explanation

Step-by-step explanation:

Given

3x - y = 2

Substitute y = x - 1 into the equation

3x - (x - 1) = 2

3x - x + 1 = 2 ← simplify left side

2x + 1 = 2 ← required equation after substitution

Given.

3x - y = 2

Substitute x - 1 for variable y.

3x - x - 1 = 2 ← Resulting equation

Answer:

(-2, 18), (0, 10), (2, 2)

Step-by-step explanation:

All you do is plug each coordinate into the equation to confirm the authentication.

I am joyous to assist you anytime.

Answer:

(-2, 18), (0, 10), (2, 2)

Step-by-step explanation:

You're welcome ;)

Amount of money spent per day = $1800

Cost of overhead expenses per day for labor and materials = $9

Selling price of each camera = $18

a. Let us assume the number of cameras manufactured per day = x dollars

Then

Cost of cameras sold in 1 day = 18x

So

18x = 1800 + 9x

18x - 9x = 1800

9x = 1800

x = 200

From the above deduction, we can conclude that the number cameras sold per day is 200

b. Daily selling amount of 250 cameras = 250 * 18

                                                              = 4500 dollars

Daily manufacturing price of 250 cameras = 1800 + (9 * 250)

                                                                   = 4050 dollars

Then

Daily profit = 4500 - 4050

                 = 450 dollars

Answer:

[tex]\large\boxed{(f+g)(x)=-x^2+3x-3}[/tex]

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\f(x)=-x^2-3\\\\g(x)=3x\\\\\text{Substitute:}\\\\(f+g)(x)=(-x^2-3)+(3x)=-x^2+3x-3[/tex]

Answer:

- 1280

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

here a₁ = - 10 and r = 2, hence

[tex]a_{8}[/tex] = - 10 × [tex]2^{7}[/tex] = - 10 × 128 = - 1280

Answer:

It's choice D.

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

= 3x - 2 + x^2 + 1

= x^2 + 3x - 1.

Answer:

D. x^2+3x-1

Step-by-step explanation:

You have:

f(x) = 3x-2

g(x)= x^2 +1

Then:

(f+g)(x)=f(x)+g(x)

(f+g)(x)=(3x-2)+(x^2+1)

(f+g)(x)=3x-1+x^2 (-2+1=-1)

(f+g)(x)=x^2+3x-1 (ordering terms)

Answer:

40.35

Step-by-step explanation:

First find the discount

97 * 60%

97 *.6 = 58.2

Subtract the discount to find the new price

97-58.20 =38.80

Next find the tax

38.80 * 4%

38.80 * .04

1.55

We add the tax to the sales price

38.8+1.55

40.35

Answer:

[tex]s=4w+12[/tex]

Step-by-step explanation:

Let

s -----> the number of stamps

w ----> the number of weeks

we know that

The linear equation that represent this situation is

[tex]s=4w+12[/tex] ----> equation of the line into slope intercept form

where

the slope m is equal to [tex]m=4\ stamps/week[/tex]

the y-intercept b is equal to [tex]b=12\ stamps[/tex] ---> (the initial value)

Answer:

-2

Step-by-step explanation:

If the lines are parallel, the slopes are the same.

Since the green line has a slope of -2, the red line has a slope of -2

Answer:

the answer is c and e

Step-by-step explanation:

just took it

The datasets that have outliers are (c) 16, 32, 38, 39, 41, 42, 58, (d) 17, 23, 28, 31, 39, 45, 75 and (e) 18, 30, 34, 38, 43, 45, 68

Data sets are simply collections of related data elements

Outliers are data elements that are relatively far from other data elements in the dataset

If a value is too small or too high from other elements, then the dataset has an outlier

By the method of observation, we can conclude that the following datasets have outliers

Hence, the datasets that have outliers are (c), (d) and (e)

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A bar graph is most suitable for comparing data across different categories or groups, as each bar corresponds to a particular group and the height or length of the bar shows the quantity of data for that group.

The type of data that is best represented by a bar graph is generally data that is being compared across different categories or groups, which corresponds to option A. This is because each bar in a bar graph represents a particular group or category, and the height or length of the bar corresponds to the quantity of data for that group. For example, if you conducted a survey to find out the favorite fruit of students in a class and the choices were apples, bananas, oranges, and grapes, a bar graph would be a suitable way to present this categorical data.

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Answer:

Step-by-step explanation:93.75

Follow below steps;

To solve for the dimensions of the picture whose length is 22.75 inches shorter than twice the width and has a perimeter of 116.5 inches, we first need to set up equations based on the given information.

Step 1: Set up the equations

Let w represent the width of the picture. Then, the length will be 2w - 22.75 inches.

Since the perimeter of a rectangle is given by the formula P = 2l + 2w where l is the length and w is the width, we can substitute the expressions for length and width to get the perimeter equation:

116.5 = 2(2w - 22.75) + 2w

Step 2: Solve for width

Expanding the perimeter equation we get:

116.5 = 4w - 45.5 + 2w

Combining like terms:

116.5 = 6w - 45.5

Adding 45.5 to both sides:

116.5 + 45.5 = 6w

162 = 6w

Divide both sides by 6 to find w:

w = 162 / 6

w = 27 inches

Step 3: Find the length

Now we calculate the length using the width (w = 27):

Length = 2w - 22.75

Length = 2(27) - 22.75

Length = 54 - 22.75

Length = 31.25 inches

So, the dimensions of the picture are a width of 27 inches and a length of 31.25 inches.

Answer:

D

Step-by-step explanation:

It isn't the most efficient way to solve the problem, but the other 3 are incorrect.

expression (2 x 2 + 4 x - 7)(x) + (2 x 2 + 4 x 7)(-3)  is equivalent to (2 x 2 + 4 x - 7)(x-3).

solving this we will get the valve of Y if x is given.

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Answer:

When Harold wrote his equation, the point he used was (7, 0) ⇒ the third answer

Step-by-step explanation:

* Lets look to the equation to find the correct answer

- He used the point-slope form is y – y1 = m(x – x1), where m is the

 slope of the line , (x1 , y1) are the coordinates of the point which

 the line passes through it and (x , y) are the coordinates of any

 general point on the line

- Lets solve the problem

- Harold correctly wrote the equation y = 3(x – 7)

∵ y - y1 = m (x - x1)

∵ y = 3 (x - 7)

- By comparing between the two equations

∴ y1 = 0

∴ m = 3

∴ x1 = 7

- He used the point (x1 , y1)

∴ Harold used the point (7 , 0) to write the equation

∴ The answer is when Harold wrote his equation, the point he used

   was (7, 0)

ANSWER

When Harold wrote his equation, the point he used was (7, 0).

EXPLANATION

The point-slope form is given as

[tex]y-y_1=m(x-x_1)[/tex]

The equation Harold wrote correctly is:

[tex]y = 3(x - 7)[/tex]

This is the same as:

[tex]y - 0= 3(x - 7)[/tex]

Comparing to point-slope form, we have

[tex]x_1=7 \: \: and \: \: y_1=0[/tex]

Hence the point is (7,0)

When Harold wrote his equation, the point he used was (7, 0).

The top right one, because for every argument there is only one corresponding value.