To rewrite y (t) = 2 sin 4pi(t) + 5 cos 4pi(t) in the form y(t) = A sin(wt + phase), you must first find the amplitude, A. Use the given
values c₁= A sin(phase) and c₂= A cos(phase), along with the Pythagorean Identity, to solve for A.

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

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Answer:

x to the 4th power+ 87x + 34

Step-by-step explanation:

Answer:

The answers will placed according to the order that they were given

6.93

15.75

17.64

6.93

Step-by-step explanation:

Answer:

1) x-2y 2) 2(13a-5)

Step-by-step explanation:

1) -1/2(-2x+4y)=2/2x-4/2y=x-2y

2) 26a-10=2(13a-5)

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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Answer:

C $0.40

Step-by-step explanation:

to find how much one pound of potatoes is, you have to divide the the cost of the bad by the number of pounds ($3.98 divided by 10 pounds)

$3.98 : 10 = $0.398 = $0.40

The expected value of the game to you is approximately $0.39.

To calculate the expected value of the game, we need to the probability of winning and losing and the corresponding payoffs.

The probability of drawing two hearts with replacement can be calculated as the product of the probabilities of drawing a heart on the first and second draws.

The probability of drawing a heart from a standard deck of 52 cards is 13/52, as there are 13 hearts out of 52 cards. Since the first card is replaced before the second draw, the probability remains the same for both draws.

Thus, the probability of drawing two hearts is (13/52) * (13/52) = 169/2704.

The payoff for winning is $12, and the payoff for losing is -$1.

To calculate the expected value, we multiply the probability of winning by the payoff for winning and subtract the probability of losing multiplied by the payoff for losing.

Expected Value = (169/2704) * $12 - (2535/2704) * $1 ≈ $0.39.

This means that on average, you can expect to win about 39 cents per game in the long run.

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"Given that they passed the test" says we're only considering the 21 students who passed the test.

There were 9 students who didn't pass the test and 7 of those didn't complete the HW.  This means that 2 students who did the HW didn't pass the test.  

Since 20 students completed the HW and 2 didn't pass the test, 18 students completed the HW and passed the test.

18/21 = 6/7 or 85.71%

Your probability is 85.71%.

1/2=1/2=1/2.is the value for the given equivalent fraction, by putting the value 3.4 in the numerators respectively

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.

For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

1/2 =    /6 =   /8.

a. Multiply numerator and denominator by 3 for equivalenting the equation    /6

Therefore,

3*3/6*3

=9/18

=1/2

therefore:1/2=1/2.

b. Multiply numerator by 4

Therefore,

4/8

=1/2.

Therefore:

1/2=1/2.

1/2=1/2=1/2.

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The factored form of the equation  P(x) = x³ + 3x² + x + 3  is P(x) = (x+1)(x² + 2x + 3).

An equation is a mathematical expression that shows that two things are equal.

One common method for finding the factored form of a polynomial equation is to use the Rational Root Theorem, which states that if a rational number a/b is a root of the polynomial equation, then (x-a/b) is a factor of the polynomial equation.

We can then use long division to divide the polynomial by the linear factor, repeat the process with the remaining polynomial, and continue this process until the polynomial is fully factored.

The polynomial equation

=> P(x) = x³ + 3x² + x + 3

can be factored as

=> (x+1)(x² + 2x + 3).

The equation P(x) = (x+1)(x² + 2x + 3) is now written as a product of two linear factors, (x + 1) and (x² + 2x + 3).

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Answer:

When you use a debit card, the funds for the amount of your purchase are taken from your checking account in almost real time. When you use a credit card, the amount will be charged to your line of credit, meaning you will pay the bill at a later date, which also gives you more time to pay.

Step-by-step explanation:

If this helps please mark as brainliest

Debit is a deduction / subtracted amount so would have a negative value ( negative sign in front of the amount)

Credit is an addition so is a positive value.

Answer: (-0.5,00)

number one i think good luck

Step-by-step explanation:

The rotation of the image given 180° clockwise around the point (-2, 1) gives the image in the second option.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

The coordinates of the given image are :

(-1, 1), (-2, 1), (-1, 4) and (-2, 4).

Point of rotation is (-2, 1).

The points are not rotated around the origin.

To make it seem like around the origin, subtract the point of rotation from the points.

So the new points are :

(1, 0), (0, 0), (1, 3) and (0, 3)

Now rotate the image with the new coordinates around the origin 180° clockwise.

Rotation is -180°, which is equivalent to rotation of 180° counterclockwise.

Coordinates (x, y) when rotated 180° clockwise becomes (-x, -y).

New coordinates after rotation about origin are :

(-1, 0), (0, 0), (-1, -3) and (0, -3).

Now add the point of rotation (-2, 1) again.

Points are :

(-3, 1), (-2, 1), (-3, -2) and (-2, -2).

Image with these points is the second option.

Hence the required image is the second option.

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The height of the antenna is approximately 5.1 feet.

1. Let's assume the height of the antenna as 'h' feet.

2. We have two angles of elevation: 5 degrees and 10 degrees.

3. When the person is 1 mile closer to the antenna, the change in the angle of elevation is 10 - 5 = 5 degrees.

4. We can use the tangent function to find the height of the antenna. The tangent of an angle is equal to the opposite side divided by the adjacent side.

5. The opposite side is the change in height, which is h feet (since the person moved closer by 1 mile, the change in height is equal to the height of the antenna).

6. The adjacent side is the horizontal distance from the person to the antenna. We can use trigonometry to find this distance.

7. In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

  tan(5 degrees) = h / x (where x is the horizontal distance in miles)

8. Similarly, after moving closer, the tangent of the angle becomes:

  tan(10 degrees) = h / (x - 1)

9. We can solve these two equations simultaneously to find the value of h.

10. Rearranging the equations, we get:

  h = x * tan(5 degrees)

  h = (x - 1) * tan(10 degrees)

11. Setting the two expressions for h equal to each other, we have:

  x * tan(5 degrees) = (x - 1) * tan(10 degrees)

12. Solving this equation for x, we find:

  x = tan(10 degrees) / (tan(10 degrees) - tan(5 degrees))

13. Substitute the value of x back into one of the earlier equations to find h:

  h = x * tan(5 degrees)

14. Calculate the value of h using a calculator:

  h ≈ 1 * tan(5 degrees) ≈ 0.0875 miles ≈ 0.0875 * 5280 feet ≈ 461.4 feet

15. Rounded to the nearest tenth of a foot, the height of the antenna is approximately 5.1 feet.

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7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given inequality is:

x + 8 > 15

Subtracting 8 on both sides of the equation:

x + 8 - 8 > 15 - 8

x > 7

Here, 7 is not included and hence it is depicted using an open dot.

Hence, option B is the correct answer.

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The two numbers that add up to 18 and have the maximum product are 9 and 9.

We want to find two numbers that add up to 18 and that have the maximum product.

If the two numbers are X and Y:

The product is P = X*Y

And the sum must be:

X + Y = 18

Then we can write:

X = 18 - Y

Replacing that in the product we will get:

P = (Y - 18)*Y

So we have a quadratic.

Notice that the zeros are at  Y = 0 and Y = 18, then the maximum is at the vertex Y = (0 + 18)/2 = 9

Then the value of X must be:

X = 18 - 9 = 18 - 9 = 9

The two values are 9.

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By the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

The Mean Value Theorem (MVT) states that if a function ƒ(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

ƒ(x) = 2lnx - 8 is continuous on the closed interval [1, 7], since it is the sum and composition of continuous functions.

ƒ(x) = 2lnx - 8 is differentiable on the open interval (1, 7), since its derivative ƒ'(x) = 2/x is defined and continuous on (1, 7).

Therefore, the Mean Value Theorem can be applied to ƒ(x) on [1, 7]. To find the value of c, we need to solve the equation:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

Substituting the given values, we get:

2/c = [ 2ln7 - 2ln1 ] / (7 - 1)

2/c = ln7

c = 2 / ln7

c ≈ 0.909

Therefore, by the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

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Answer:

a.) one sample t test

b.) H0 : μ = 59.3

c.) H1 : μ > 59.3

d.) μ = 59.3 ; σ = 39.84

e.) xbar = 79.4 ; s = 61.36

Test statistic = 3.16

Step-by-step explanation:

Given the sample data:

49.00 49.00 49.00 49.00 49.00 63.00 63.00 63.00 63.00 63.00 199.00 199.00 199.00 199.00 199.00 38.00 38.00 38.00 38.00 38.00 48.00 48.00 48.00 48.00 48.00 49.00 63.00 199.00 38.00 48.00

Sample size, n = 30

Using calculator :

xbar from the data above = 79.4

Standard deviation = 61.359

H0 : μ = 59.3

H1 : μ > 59.3

Test statistic :

(Xbar - μ) ÷ (σ/sqrt(n)

σ = 34.83

(79.4 - 59.3) ÷ (34.83/sqrt(30))

20.1 ÷ 6.359

Test statistic = 3.16

Answer:

B. 1.64b

Step-by-step explanation:

0.33b+1b+0.31b

=1.64b

6 cos(π/2 t) is the best model for the position of the weight.

The motion of the weight on the spring can be modeled by a sine or cosine function because it oscillates back and forth around its equilibrium position.

We know that, the weight is initially pulled down 6 inches from its equilibrium position, so the function should have an amplitude of 6.

The time it takes for the spring to complete one oscillation is 4 seconds, so the period of the function is 4 seconds.

The general form of a sine or cosine function with amplitude A and period T is:

f(t) = A sin(2πt/T) or f(t)

= A cos(2πt/T)

Substituting the given values,

we get:

f(t) = 6 sin(2πt/4) or f(t)

= 6 cos(2πt/4)

Simplifying, we get:

f(t) = 6 sin(π/2 t) or f(t)

= 6 cos(π/2 t)

Therefore,

the function that best models the position of the weight is

s(t) = 6 cos(π/2 t).

So, the answer is option (D).

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Answer:

  13 slices of cheese pizza

Step-by-step explanation:

Consider grouping the slices so there are 10 pepperoni and 1 cheese in each group of 11. Then 143 slices represents 143/11 = 13 groups. Since there is 1 cheese slice in each group, ...

  13 slices of cheese pizza were sold

Answer: -3/2

Step-by-step explanation: