Find the exact value using a half angle identity. Cos(-pi/8)

Answer:

57 centimeters = 57 × 0.39370078740175 = 22.4409448819 inches.

57 inches is 144.78 centimeters.

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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When r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.

The expression [3r-15] represents an algebraic expression that depends on the value of r. The condition given is that r is less than 5. To evaluate this expression, we substitute the value of r into the expression and simplify it.

Given that r is less than 5, let's substitute r = 4 into the expression:

[3(4) - 15]

= [12 - 15]

= -3

Therefore, when r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.

It's important to note that this answer is specific to the given condition that r is less than 5. If the condition changes or if r is greater than or equal to 5, the result of the expression may be different.

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Answer:

7.9.

Step-by-step explanation:

Use the Pythagorean Theorem.

√((-5)^2 + (6)^2 + (-1)^2) = √62 = 7.87 = 7.9.

Answer:

Step-by-step explanation:

7.9

Answer & Step-by-step explanation:

It is less because 2 times 3/4 is the same as 2/1 times 3/4 which is 6/4 then simplify it and you get 3/2 which then is 1 1/2.

That is why 2 times 3/4 is less than 2.

Hope that helps ;)

Answer:

circumference=28 in. after doing rounf off to the nearest hundredth

Step-by-step explanation:

The Function  f(g(x)) = g(f(x)) = x + 8.

The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).

f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8

Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8

Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,

which is x + 8.

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I think that the answer is 123

Answer:

So your Answer is B.

Step-by-step explanation:

5

There are three types of row operations:

Multiplying a row by a constant c≠0

Adding to a row a different row multiplied by a constant d

Swapping two rows

The third type is of no concern with your question.

Why the limitations on the first two types?

The idea is that row operations should be reversible, so when we perform a row operation, we can perform another one that “undoes” the effect of the previous one. The main reason is that such row operations don't change the solution set of a linear system (translated into matrix form), exactly because the operations are reversible.

Multiplying a row by 0 is not reversible: this should be clear because doing this operation on all rows will yield the null matrix and we surely lose information. Thus is disallowed.

Adding to a row itself multiplied by −1 is the same as multiplying the row by 0, so in general it is disallowed to add a row to itself multiplied by a scalar.

How do you reverse an operation of the first kind? By multiplying the same row by c−1. What for an operation of the second kind? Say we add to row i row j multiplied by d; we reverse this by adding to row i row j multiplied by −d.

The constants c and d can be anything (but for the first type c must be nonzero). Even d=0 is allowed in operations of the second kind: it is just doing nothing, which is of course reversed by doing nothing again.

Answer:

x+y=30

2x+3y=80

multiplying equation one by -3 and add equation

-3x -3y=-90

2x +3y=80

2(10)+20(3)=80

80=80

Answer:190 small packs and 4 cookies left over

Step-by-step explanation:

Add the boxes of cookies together 105+22=127

Multiply each box by 12

127 x 12=1524

Because we need to put them into smaller packs of 8 cookies

we need to divide by 8

1524÷8=190 small boxes

This is a total of 190 x 8=1520 cookies there are 4 cookies left over

7 men should be able to dig 21 wells in approximately 4.7 days.

From the question, we have the following parameters that can be used in our computation:

We can use the formula:

Number of days = (number of wells * number of days per well) / number of men.

So, we have

Number of days per well for 2 men:

11 days / 7 wells = 1.5714 days per well.

Using the above as a guide, we have the following:

the number of days for 7 men to dig 21 wells:

21 wells * 1.5714 days per well / 7 men = 4.7142days.

Hence, the number of days is 4.7 days.

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Answer:

57

Step-by-step explanation:

2x + 9y -9

2(6) + 9(6) - 9

12 + 54 - 9 = 57

good luck, i hope this helps :)

Answer:

57

Step-by-step explanation:

2*6+9*6-9=

12+54-9=

66-9=

57

Answer:

13.44

Step-by-step explanation: tax is added after payment so 12 + 5% or 100% + 12% = 112% of 12. There are many ways to solve for this, I used number line starting out because it was easiest for me, just divide 12 by 100 and put that into 1% then multiply that 1% number by 112 and you get 112%.

Answer:

Hello!!

The cost of a $12 t-shirt with 5% tax would be...

$12.60

Step-by-step explanation:

\(12\) × \(0.05=0.6\)

\($12 + 0.6=12.60\)

Hope this helps!!

Answer:

\(\displaystyle y=\frac{1}{3}x-6\)

Step-by-step explanation:

Dilation of a Line

Given a line that passes through points A(-3,-4) and B(-6,-5). We'll apply a dilation with a scale factor of 2 centered at the origin by multiplying each coordinate by 2. The points map to:

A'(-6,-8) and B'(-12,-10)

Now we find the equation of the line passing through A' and B'.

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Substituting:

\(\displaystyle y+8=\frac{-10+8}{-12+6}(x+6)\)

\(\displaystyle y+8=\frac{-2}{-6}(x+6)\)

\(\displaystyle y+8=\frac{1}{3}(x+6)\)

Operating:

\(\displaystyle y=\frac{1}{3}x+\frac{1}{3}*6-8\)

\(\displaystyle y=\frac{1}{3}x+2-8\)

\(\boxed{\displaystyle y=\frac{1}{3}x-6}\)

The confidence interval suggests that there is no significant difference in CVD risk between smokers and non-smokers, but any potential difference is likely to be small.

The given confidence interval of (-0.01, 0.04) represents a range of plausible values for the difference in the population proportion of CVD between smokers and nonsmokers, with a 95% level of confidence.

A value of 0 suggests no difference in CVD risk between the two groups Since the interval contains both positive and negative values, we cannot conclude with certainty whether the difference is statistically significant or not.

However, the fact that the interval is relatively small suggests that any difference in CVD risk between smokers and nonsmokers is likely to be small in magnitude.

Therefore, the best interpretation of the interval is that there is no strong evidence to suggest a significant difference in the risk, but any potential difference is likely to be small.

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_____The given question is incomplete, the complete question is given below:

In a large study designed to compare the risk of cardiovascular disease (CVD) between smokers and nonsmokers, random samples from each group were selected. The sample proportion of people with CVD was calculated for each group, and a 95 percent confidence interval for the difference (smoker minus nonsmoker) was given as (−0.01, 0.04). Which of the following is the best interpretation of the interval?

Step-by-step explanation:

the h stands for height of the cuboid

Answer:

[see below]

Step-by-step explanation:

In the formula for volume of a rectangular prism, the 'h' means the height of the prism given.

V = Length * Width * Height

If you mean what h means algebraically:

\(V = lwh\\\\\frac{V=lwh}{lw}\\\\\frac{V}{lw}=h\\\\\boxed{h= \frac{V}{lw}}\)

Hope this helps.

In the given options, none of them have inequality sign ≤ and ≥,  so the given inequalities do not have solid line in its solution graph.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement.

The boundary line for the inequality is drawn as a solid line if the points on the line itself do satisfy the inequality, as in the cases of ≤ and ≥. It is drawn as a dashed line if the points on the line do not satisfy the inequality, as in the cases of < and >.

Hence, in the given options, none of them have inequality sign ≤ and ≥,  so the given inequalities do not have solid line in its solution graph.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The rate of interest is 73%.

What is the annual rate?

The term annual percentage rate of charge refers to the interest rate for an entire year rather than just a monthly fee or rate as applied on a loan, mortgage loan, credit card, etc. It can also be referred to as a nominal APR or an effective APR. It is an annual rate of a finance charge.

Given that 1 dollar to grow to X dollars in 2 years is given by the formula X = (1+r) ².

A dollar to triple in 2 years.

Thus putting X = 3 in X = (1+r) ²

3 = (1+r) ²

Take square root on both sides:

√3 = 1 + r

Subtract 1 from both sides:

r = √3 - 1

r = 0.73

r = 73%

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Answer:

I am not understanding the question ok

Answer:

Step-by-step explanation:

Triangles AEB and CED are congruent as per SAS theorem since two sides are congruent and included angles are same as vertical angles

Answer: AD = 11 cm

DC = 12 cm

Step-by-step explanation:

Answer: 4.3 mi

Step-by-step explanation:

From Oxford, getting to Kingswood takes 7.5mi, and getting to Norwood takes 11.8mi.  Thus, simply do 11.8-7.5 to get 4.3mi.

Hope it helps <3

Answer:

45

Step-by-step explanation:

translation :

140% of x = $63

x = $63 ÷ 1.4

x = $45

FUN FACTS :

interesting: 100% means double that number or times 2

if a price is $20 & it increases 100% in price that means its $20 times 2 or $40

percent means per 100

cent means 100 in latin

that's why the decimal moves 2 spaces

for the 2 zeros in 100

chatgpt

The second inputs are -16 , -10 , -4, 2 ,8   an integer.

What in math is an integer?

     x                                      y = 6x - 4                                                      (x,y )                                                                                                                        

  -2                                           6 * -2 - 4                                         ( -2 , - 16)

______________________________________________________

   - 1                                          - 1 * 6 - 4                                         ( -1 , -10 )

________________________________________________________

   0                                           0 * 6 -4                                            ( 0 , -4)

________________________________________________________

     1                                          6 * 1 - 4                                             ( 1 , 2)

________________________________________________________

    2                                           6 * 2 - 4                                          ( 2 , 8 )

_______________________________________________________

the second inputs are -16 , -10 , -4, 2 ,8

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The complete question is -

Find five solutions of the equation. Select integer values for x, starting with - 2 and ending with 2. Complete the table of values below y =6x-4 (x,y) Complete the table to the right by typing an integer for the first input and an ordered pair for the second input. х y = 6x-4 (x,y) -2 - 1 0 1 2 Use two of the given points to graph the equation. Click to enlarge graph

Answer:

Mean: 60

Step-by-step explanation:

First of all, in order to find the mean, one must add all the numbers together (61,55,66,58,50,70), which would give a total of 360.

After that, divide that total by the quantity of numbers (in other words, the total number of numbers, which in this case is 6). So, you would have to divide 360 by 6 leading to an answer of 60(the mean, which in other words is like finding the average).

Using proportions, it is found that 375 products are produced with 15 workers in 5 hours.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that the rule of three are given as follows:

1000 products - 20 workers - 10 hours.

x products - 15 workers - 5 hours.

The measures are direct proportional, hence:

\(\frac{1000}{x} = \frac{20}{15} \times \frac{10}{5}\)

\(\frac{1000}{x} = \frac{40}{15}\)

Applying cross multiplication:

40x = 15(1000)

x = 15(1000)/40

x = 375.

375 products are produced with 15 workers in 5 hours.

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The amount of tea that is left after the student has drank is; ⁴/₅d mL

In word problems on fractions, what we do is that we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

For example;

4/7 of a number is 84. Find the number.

Since 4/7 of a number = 84

The, the Number = 84 × 7/4

Number = 147

Now, in this question, we are given;

Quantity of tea in cup = d ml

Amount of tea a student takes out to drink = ¹/₅ of the quantity in the cup.

Thus;

Amount of tea left = d - ¹/₅d

Amount of tea left = ⁴/₅d

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