60 mi / 1 hr = ? mi / 5 hr

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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Answer:

he will pay 55.16

Answer:

After 3 minutes in the refrigerator, the temperature of the coffee will be approximately 89.6 degrees Fahrenheit

Step-by-step explanation:

To solve this problem, we can use Newton's law of cooling, which states that the rate of change in the temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings. The equation for Newton's law of cooling is:

T(t) = T_s + (T_0 - T_s) * e^(-kt)

Where:

T(t) is the temperature of the object at time t

T_s is the temperature of the surroundings

T_0 is the initial temperature of the object

k is the cooling constant

e is the base of the natural logarithm

In this case, we have:

T_s = 36 degrees Fahrenheit (temperature of the refrigerator)

T_0 = 190 degrees Fahrenheit (initial temperature of the coffee)

k = 0.12 (cooling constant)

t = 3 minutes (time elapsed)

Substituting these values into the equation, we get:

T(3) = 36 + (190 - 36) * e^(-0.12*3)

T(3) = 36 + 154 * e^(-0.36)

T(3) ≈ 89.6 degrees Fahrenheit

Therefore, after 3 minutes in the refrigerator, the temperature of the coffee will be approximately 89.6 degrees Fahrenheit.

Answer:

I think it’s B (I’m not sure if I’m right)

Step-by-step explanation:

Answer:

k=8

Step-by-step explanation:

For 2 lines to be parallel, they must have the same slope. First, let's isolate y.

5y=2x+2

y=2/5x+2/5

Now, in our second equation, we must make it so that the slope is 2/5.

5(4)=20

2(4)=k

k=8

y=8/20x+10

If you simplify that, then the slope will be 2/5.

The function h(x) =  6x² - 60x + 147 is a quadratic function, and the axis of symmetry of the function is x = 5

The equation of the function is given as:

h(x) =  6x² - 60x + 147

Differentiate the function

h'(x) = 12x - 60

Set the function to 0

12x - 60 = 0

Add 60 to both sides

12x = 60

Divide both sides by 12

x = 5

Hence, the axis of symmetry of the function is x = 5

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Answer:

X = 5 is correct

Step-by-step explanation:

just took the test on edge and got 100%

Answer:

X = 5

Step-by-step explanation:

this must form a triangle so simply using the same value of x equally in each equation.

This method is effective because it breaks down the percentage into smaller parts that are easier to calculate mentally. By finding 5% and 1% separately and then adding them together, you can quickly find the percentage that you need.To find 7% of $1000, there are various mental math methods that one can use. One of the best methods is to use a combination of the 5% and 1% methods. Here's how to do it:

Step 1: Find 5% of $1000
5% of $1000 is $50

Step 2: Find 1% of $1000
1% of $1000 is $10

Step 3: Add the two values together
$50 + $10 = $60

Step 4: Find 1% of $60
1% of $60 is $0.60

Step 5: Multiply $0.60 by 7 to get the final answer
$0.60 x 7 = $4.20

Therefore, 7% of $1000 is $4.20.

This method is effective because it breaks down the percentage into smaller parts that are easier to calculate mentally. By finding 5% and 1% separately and then adding them together, you can quickly find the percentage that you need.

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Answer:

3 solutions

Step-by-step explanation:

To solve g(x) = 2

The solutions are at the points of intersection of g(x) and y = 2

y = 2 is the equation of a horizontal line parallel to the x- axis and passing through all points with a y- coordinate of 2

If you draw the horizontal line using say (0, 2) and (2, 2)

Then g(x) intersects y = 2 at 3 places

Thus there are 3 solutions to g(x) = 2

The length of a rectangle exists 8 units more than its width. The area of the rectangle can be expressed as \($$x^4\) - 16 then the expression exists (x² + 4)(x + 2)(x - 2).

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. One or more operands, one or more operators, and one or more pairs of parentheses create an expression.

Given

L = 8 + W

Area = \($$x^4\) - 16

An expression for the width

Area = \($$x^4\) - 16

Apply exponent rules

\($=\left(x^2\right)^2-4^2$$\)

Apply Difference of Two Squares Formula: x² - y² = (x + y)(x - y)

(x²)² - 4² = (x² + 4)(x² - 4)

Factor x²- 4 = (x + 2)(x - 2)

By simplifying the above equations, we get

= (x² + 4)(x + 2)(x - 2)

The length of a rectangle is 8 units more than its width. The area of the rectangle can be expressed as x^4-16. Which expression represents the width of the rectangle?

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Answer:

The correct answer is 1/3.

Step-by-step explanation:

The reason why is because there is 3 animals. Then one beaver. So it would be 1/3.

Answer:

0.33

Step-by-step explanation:

Because they are all equal, each animal has to have the same percentage. Because there are 3 options it can land on, the denominator is 3. Because the beaver is 1 of the 3, the answer is 1/3. 1/3 is equal to 0.33 rounded so the answer is 0.33.

Answer!

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Answer:

volume = 337.2 ft³

Step-by-step explanation:

volume = base x height = 84.3 x 4 = 337.2 ft³

Answer:

\(\huge\boxed{\text{Multiply the denominator by 2, or}}\\\\\huge{\boxed{\text{divide the percentage by 2}}}}\)

Step-by-step explanation:

Because there is no fraction or percentage given, simply follow this rule to divide a portion by 2.

Hope it helps :) and let me know if you want me to elaborate(solve with fraction)

Answer:

(a)  See attachment.

(b)  r = 0.8765 (4 d.p.)

(c)  Strong positive correlation.

(d)  See explanation.

Step-by-step explanation:

Correlation measures how closely two variables are linked.

When creating a scatter plot with bivariate data:

Plot a scatter diagram using the data from the given table and the following variables.

(See attachment).

The correlation coefficient (r) measures the strength of the linear correlation between two variables.

Using a calculator and the given data, calculate r:

As r is close to +1, this suggests that the data has a strong positive correlation.  

This suggests that the metabolic rate increases as the body mass increases.

We cannot use a regression line to predict a value of the explanatory variable. Therefore, as the body mass is the explanatory variable, we cannot say that a person's body mass will increase if their metabolic rate increases.  However, we can say that according to the scatter plot and correlation coefficient, it is highly likely that a person's metabolic rate increases as their body mass increases.  

Remember to apply caution when using values of of x outside the range of the original data to predict corresponding values of y, as these predications can be unreliable since there is no evidence that the relationship is true for all values of x.

Answer:

  3

Step-by-step explanation:

The quadratic formula is used to solve a quadratic equation in standard form, based on the values of the coefficients.

The standard-form quadratic ax² +bx +c = 0 has solutions given by the quadratic formula:

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

For the quadratic 3x² +4x -2 = 0, we have a=3, b=4, c=-2 and the formula gives ...

  \(x=\dfrac{-4\pm\sqrt{4^2-4(3)(-2)}}{2(3)}=\dfrac{-4\pm\sqrt{16+24}}{6}\\\\x=\dfrac{-4\pm 2\sqrt{10}}{6}=\dfrac{-2\pm\sqrt{10}}{3}\)

The denominator in the solution is 3.

Answer:

The answer is x=(-2±√10)/3

Step-by-step explanation:

Answer:

136 1/2 cubic inches

Step-by-step explanation:

Volume is equal to length times width times height.

For width and height, use the decimal version of the mixed fractions to make calculations easier.

5 1/4 = 5.25

6 1/2 = 6.5

4 x 5.25 x 6.5 = 136.5, or 136 1/2

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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The theoretical probability that the coin will land tails up is 1/2 = 0.5 or 50%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

In this problem, we have a fair coin, meaning that in any throw, the coin is equally as likely to land in one of the two outcomes, which are heads up or tails up.

Hence the probability is given as follows:

p = 1/2 = 0.5 = 50%.

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Ally will be able to cover 285 miles for the trip

Ally wants to rent the car for one day

The rents costs $35 and $0.35 per mile

Ally has $134.75 to spend for the trip

The number of miles Ally can drive for the trip can be calculated as follows

134.75 - 35

= 99.75

99.75/0.35

= 285

Hence Ally will be able to drive 285 miles for the trip  

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Answer:

10t + 400 would be the answer.

Step-by-step explanation:

every hour, there would be 10 gallons added to the pool, so time should be the letter "t" in the equation.

Also, there's already 400 gallons of water existing in the pool, so we need to add 400 gallons.

Therefore, 10t + 400 would be the answer.

Answer:

first of all who deleted my answer considering the fact that is was correct and i answer it first The answer is B

Step-by-step explanation:

hope this helps -_-

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

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The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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Answer:

-3, -3

Step-by-step explanation:

Given data;

The given inequality is 9>x.

The all values of x for which x is less than 9.

Thus, x=2 and x=5 are the solution of the given inequality.

Answer:

.6 goes into 12.66 21.1 times

Answer : 5x+3

There are no like terms

PLEASE GIVE ME AS BRAINLIEST

Answer: x=70, y=30

Step-by-step explanation:

The standard deviation of the number of free throws that Chauncey Billups will make in tonight's game is approximately 0.726.

To calculate the standard deviation of free throws that Chauncey Billups will make in tonight's game, we need to use the following formula:

Standard Deviation (σ) = √(n * p * (1 - p))

where n is the number of trials (free throws) and p is the probability of success (making a free throw).

In this case, n = 6 (as Billups shoots six free throws) and p = 0.894 (as his career free-throw percentage is 89.4%).

Substituting the values into the formula, we get:

Standard Deviation (σ) = √(6 * 0.894 * (1 - 0.894))

Calculating this expression, the standard deviation is approximately 0.726.

Therefore, the standard deviation of free throws that Chauncey Billups will make in tonight's game is approximately 0.726.

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Answer:

x = 6

Step-by-step explanation:

5x-3 = 2x+15

5x-2x-3 = 15

5x-2x = 15+3

3x = 15+3

3x = 18

\( \frac{3x}{3} = \frac{18}{ 3} \)

\(x = 6\)