A dog ran 10 miles home. It took him 50 minutes to get there. How fast was he running? (have your answer in miles per hour)

By using the rules:

\(cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}\)

We have proven the identity. Below you can follow the demonstration.

Here you need to remember two things:

\(cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}\)

Here we have the expression:

\(\frac{1 - cos(-x)}{sec(-x) - 1}\)

By using the first rule, we can rewrite:

\(\frac{1 - cos(-x)}{sec(-x) - 1} = \frac{1 - cos(x)}{sec(x) - 1}\)

By using the second rule, we can rewrite:

\(\frac{1 - cos(x)}{sec(x) - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1}\)

Now if we multiply and divide by cos(x), we get:

\(\frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} *\frac{cos(x)}{cos(x) } = \frac{(1- cos(x))*cos(x)}{1 - cos(x)} = cos(x)\)

In this way, the identity was proven.

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Answer:

No.

Step-by-step explanation:

A function have only one output (y) for each x.  This is not true with this graph.  For example: the point (6,1) and ( 6,5) are both on the graph.  The input 6 has more than 1 output. It has the output of 1 and 5.  Since it has more than one output, it is not a function.

Answer:

5/6 quarts of water

Step-by-step explanation:

2/3 same as 4/6. 4/6 + 1/6 = 5/6

The calculated value of the probability of B is (c) 0.25

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

P(A or B) = 0.3

P(A and B) = 0.2

P(A/B) =0.8

First, we have

P(A/B) = P(A and B)/P(B)

Substitute the known values in the above equation, so, we have the following representation

0.2/P(B) = 0.8

So, we have

P(B) = 0.2/0.8

Evaluate

P(B) = 0.25

Hence, the probability of B is 0.25

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Step-by-step explanation:

0.25 = 1/4 is not reach to 1

2 is an integral number.

So, 0.25 is smaller than 2

Answer:

2/5 is equal to 0.40, which is higher than 0.25

Step-by-step explanation:

2 ÷ 5= 0.4 which is the same as 0.40

Answer:

SA = 62 cm2

Step-by-step explanation:

The surface area of the given cuboid will be 62 cm² whose dimensions are cm, 5 cm, and 2 cm.

The total surface of the cuboid = 2(LB+BH+HL)

Consider that the length, width, and height of the cuboid are L, B, and H.

The cuboid is given in the question

Which has the length, width, and height of the cuboid are 3 cm, 5 cm, and 2 cm.

The surface area of the cuboid = 2(LB+BH+HL)

Here L = 3 cm, B = 5 cm, and H = 2 cm

Substitute the values in the above formula, and we get

The surface area of the cuboid = 2(3 × 5 + 5 × 2  + 2 × 3)

The surface area of the cuboid = 2(15 + 10 + 6)

The surface area of the cuboid = 2(31)

The surface area of the cuboid = 62 cm²

Thus, the surface area of the given cuboid will be 62 cm² whose dimensions are cm, 5 cm, and 2 cm.

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Using it's formula, it is found that the standard deviation of the data-set is of 8.9.

In this problem, the data-set is: {6, 7, 5, 22, 26}.

The mean is:

\(M = \frac{6 + 7 + 5 + 22 + 26}{5} = 13.2\)

Hence, the standard deviation is:

\(S = \sqrt{\frac{(6-13.2)^2+(7-13.2)^2+(5-13.2)^2+(22-13.2)^2+(26-13.2)^2}{5}} = 8.9\)

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Answer:

38.8

Step-by-step explanation:

Because 6 is 5 and higher so it rounds up

Answer:

38.8

Step-by-step explanation:

in 38.765 the number 7 is in the tenths place so you if the number to the right of it is 5or bigger you turn the 7 into an 8

Answer:

10:21

Step-by-step explanation:

bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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Answer:

4

Step-by-step explanation:

(1+2) +( 2/3 + 3/9)

3+1=4

Answer:

A=b/2

Step-by-step explanation:

you're simplifying both ends of an equation.

Answer:

A scale drawing with a 1: 0,8 scale will have sides that measure 2.24, 1.6, and 3.2.

Step-by-step explanation:

A scale drawing refers to a drawing that has been made bigger or smaller but preserves the proportions of a drawing.

How to make the scale drawing of the sign?

The first step is to decide the scale. In this case, the best scale is 1:0.8, which means the new drawing is 0.2 smaller. This scale is ideal because this sign is slightly bigger than regular signs.

Draw the sign by multiplying each side by the scale (0,8).

Anwser: Hitler was the first person to get a 100 bomb IRL

Explenation: Took me 900 years to figure this out

To calculate Geraldo's salary after four consecutive 4% increases, we can use the formula for compound interest:

Final Amount = Initial Amount * (1 + (rate/100))^n

In this case, the initial amount is Geraldo's current salary ($40,000), the rate is the percentage increase (4%), and n is the number of consecutive increases (4).

Final Amount = $40,000 * (1 + (4/100))^4

Simplify the equation:

Final Amount = $40,000 * (1 + 0.04)^4

Final Amount = $40,000 * (1.04)^4

Now, calculate the final amount:

Final Amount ≈ $40,000 * 1.16986

Final Amount ≈ $46,794.34

After four consecutive 4% increases, Geraldo's salary would be approximately $46,794.34 per year.

Answer:

224.00 it's a good deal

Answer:

12 credits per semester

Step-by-step explanation:

she has 92 in the end but she started off with 8 so your first step is to subtract 8 from 92 which gives you 84 once you get 84 you divide that by 12 you get 7 which means she got 12 credits in each of her 7 semeters

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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If BCDE is congruent to OPQR, then DE is congruent to QR .

Congruence means the same point on two different shapes , like parallels

so BC is congruent to OP

and

DE is congruent to QR

In plain English, two objects are said to be congruent if they overlap, i.e., have the same size and shape. If two angles have the same measure, they are said to be congruent. They are congruent if the sides' lengths line up.

Two triangles are said to be congruent if their sides and angles are an exact match.

Conditions for Congruence of Triangles:

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After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer:

1900

Step-by-step explanation:

1000+900=1900

Answer:

5x+3y=-6

Step-by-step explanation:

(-3,3) (3,-7)

Slope=(-7-3)/(3-(-3))=-10/6=-5/3

y=mx+c

y=-5/3*x-2[from graph]

y=-5x-6/3

3y=-5x-6

3y+5y=-6

5x+3y=-6

Answer:

Simple random sampling  

Observational study

Step-by-step explanation:

Since in the given situation it is mentioned that department wants to test the computer virus and have to run the virus on the random selected computers so here the simple random sampling would be done and based on the simple random sampling the observational study would be done

Therefore the above represent the answer

Answer:it is simple random sampling but the collection method is not observational study I got that part wrong

Step-by-step explanation:

The solution to the given algebraic expression 3(2-4x) = 5-8x is x = 1/4

3(2-4x) = 5-8x

open parenthesis

6 - 12x = 5 - 8x

combine like terms

6 - 5 = -8x + 12x

1 = 4x

divide both sides by 4

x = 1/4

Ultimately, x = 1/4 is the answer to the algebraic expression.

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Answer:

To create a chocolate blend using 61% cocoa and 51% cocoa, 18 ounces of the 61% chocolate and an appropriate amount of the 51% cocoa are combined together. The exact amount of 51% cocoa required will depend on the desired concentration of the final blend.

Step-by-step explanation:

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

Answer: The nomenclature for steel shapes follows two standards: For wide flange, bearing pile, S-shapes, channels, and tees

tep explanation:

Answer:

Enter each answer as a fraction in simplest form, as a decimal, and as a percent. You draw one card at random from a shuffled deck of 52 playing ...

-by-step explanation: