write the following expression without negative exponents and without parentheses (-9x)^-2

The given limit is limt→0(2sin(2t)ln(2t)).  The value of the given limit is INF.

We can evaluate the above limit using L'Hospital's rule, which states that if we have a limit of the form 0/0 or ∞/∞, we can differentiate the numerator and the denominator until we get a limit that is solvable.

Now, let's differentiate the given expression with respect to t.

We have:

limt→0(2sin(2t)ln(2t))

=(limt→0(2sin(2t))) (limt→0(ln(2t))/t)...(1)

Now, let us differentiate

(limt→0(2sin(2t)))

(limt→0(ln(2t))/t) with respect to t.

Since sin(2t) = 2cos(2t),

we get:

limt→0(2sin(2t))

= limt→0(4cos(2t)) = 4....(2)

Now, let us apply L'Hospital's rule to

limt→0(ln(2t))/t.

We have:

limt→0(ln(2t))/t

= limt→0(1/t)/1

=limt→0(1/t)

=∞

Now, let us substitute the above values in (1)

limt→0(2sin(2t)ln(2t))

=(limt→0(2sin(2t))) (limt→0(ln(2t))/t)...(1)

=4×∞=INF

Hence, the value of the given limit is INF.

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Answer:

764-118=s

Step-by-step explanation:

The school has 764 students. Taking away the third graders will let you know how many are left in the other grades. Please marl brainliest.

Oh, and assuming you want the total number in each grade, 1-6? its          (764-118)%5=s

Answer:

118+s=764 is the correct answer.

According to given data, we can prove that Statement 1 is increasing function, Statement 2 is Decreasing Function, and Statement 3 is Constant Function.

1. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts sent) is y = 60x, where y is the total number of texts sent and x is the number of days. The graph of this function is increasing because as the number of days increases, the total number of texts sent also increases at a constant rate of 60 texts per day.

2. The linear function that describes the relationship between the input value (number of days) and the output value (total number of texts remaining for the month) is y = 500 - 60x, where y is the total number of texts remaining for the month and x is the number of days. The graph of this function is decreasing because as the number of days increases, the total number of texts remaining for the month decreases at a constant rate of 60 texts per day.

3. The linear function that describes the relationship between the input value (number of days) and the output value (total cost of texting each month) is y = 50, where y is the total cost of texting each month and x is the number of days. The graph of this function is constant because the cost of texting is the same regardless of the number of days.

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Answer:

all of them are linear

Step-by-step explanation:

Use the function y=ax, plug x and y into it.

I have just tried it and all of them are linear function.

The given expression can be simplified using trigonometric identities. By using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we get:

cos(pi/4-x) = cos(pi/4)cos(x) + sin(pi/4)sin(x)

Substituting the given values of cos(x) and sin(x), we get:

cos(pi/4-x) = (1/sqrt(2))(-1/2) + (1/sqrt(2))(sqrt(3)/2)

Simplifying this expression, we get:

cos(pi/4-x) = -sqrt(2)/4 + sqrt(6)/4

The given expression involves the cosine of the difference between two angles. By using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we can simplify the expression in terms of the cosine and sine of the individual angles. We are given the value of cos(x) and we can use the identity sin^2(x) + cos^2(x) = 1 to find the value of sin(x). Once we have the values of sin(x) and cos(x), we can substitute them in the above identity to get the simplified expression.

In this particular problem, we are given the value of cos(x) and the fact that x is in the second quadrant, which implies that sin(x) is positive. Using these values, we can simplify the expression to get the final answer. It is important to note that the answer is requested in exact form as a fraction, and not as a decimal approximation.

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Answer:

i need the formulas

Step-by-step explanation:

UGHHHH! I need the answers to.

The given sequence;–3.2, 4.8, –7.2, 10.8, is a geometric progression common ratio of -1.5.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

The given sequence ;

–3.2, 4.8, –7.2, 10.8, …

The common ratio

= -4.8/ 3.2

= - 1.5

The terms having a common ratio of -1.5 best describe the relationship between the successive terms in the sequence of the terms.

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Answer:

hold up lemma check

Step-by-step explanation:

M = {2, 3, 5, 7} (and possibly includes 11 if "between x and y" means to include both x and y)

N = {1, 2, 3, 4, 6, 12}

Then

M U N = {1, 2, 3, 4, 5, 6, 7, 12}

(or possibly {1, 2, 3, 4, 5, 6, 7, 11, 12})

M ∩ N = {2, 3}

We can solve this problem using a system of linear equations, have in mind the expression for simple interest:

Let x be the principal invested on the first account.

Let y be the principal invested on the second account.

We can solve the system by the method of substitution, isolate the variable y in equation (1):

Now, substitute (1) into equation (2) to get x-value:

Austin invested $16,000 on the first account.

Then, substitute the x-value in the equation (1) to get y-value:

Austin invested $14,000 on the second account.

Answer:

-7

Step-by-step explanation:

Square numbers always have two possible roots: a positive and negative root. This is because two positive numbers multiply to make a positive number and two negative numbers also multiply to make a positive number

-7 × -7 is still 49, just like 7 × 7

Hope this helps!

Answer:

The formula for calculating Principal amount would be P = I / (RT) where Interest is Interest Amount, R is Rate of Interest and T is Time Period.

Answer: 361

Step-by-step explanation:

Answer:

this can not be solved by X cause the equation is not equal to anything

Step-by-step explanation:

Answer:

  shifted down 4 units

Step-by-step explanation:

You want to know the effect on the graph of changing y=2x+2 to y=2x-2.

The constant in the equation y=2x+2 is the y-intercept. The line described by this equation crosses the y-axis at y=2.

When the equation is changed to y=2x-2, the y-intercept changes from +2 to -2, a shift down of 4 units. The shifted line has the same slope as the original, so is parallel to it.

The effect on the graph is to move it down 4 units.

Answer:

$20 - (14/100 * $20) = $17.20

Step-by-step explanation:

The sale price can be calculated by multiplying the original price by the discount percentage (which is 14/100 since the price is discounted by 14 out of 100):

Sale price = Original price - Discount amount

= Original price - (Discount percentage * Original price)

= $20 - (14/100 * $20)

= $20 - $2.80

= $17.20

So, the expression that gives the sale price is:

$20 - (14/100 * $20) = $17.20

Answer:

$1.50

Step-by-step explanation:

3 boxes = $4.50

1 box= $4.50÷3

1box= $1.50

Answer:$1.50

Step-by-step explanation:

The factors of the given expression are 2av² and (2av³-9).

The given expression is 4a²v⁵-18av².

The factors are the polynomials which are multiplied to produce the original polynomial.

2av²(2av³-9)

Therefore, the factors of the given expression are 2av² and (2av³-9).

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The magnitude of the vector r is 16.4 m (approx). The magnitude of the new vector r' is 32.8 m (approx).

Part A:

The direction of the vector r is given by the angle θ that it makes with the x-axis as shown below.

As per the given data,x-component of vector r = r_x = 14 my-component of vector r = r_y = −8.5 m

Let's calculate the magnitude of the vector r first using the Pythagorean theorem as follows:

r = √(r_x² + r_y²)

r = √((14 m)² + (-8.5 m)²)

r = √(196 m² + 72.25 m²)

r = √(268.25 m²)

r = 16.4 m (approx)

Thus, the magnitude of the vector r is 16.4 m (approx).

Now, let's calculate the direction of the vector r, which is given by the angle θ as shown in the above diagram:

θ = tan⁻¹(r_y / r_x)

θ = tan⁻¹((-8.5 m) / (14 m))

θ = -30.1° (approx)

Thus, the direction of the vector r is -30.1° (approx).

Part B: We have already calculated the magnitude of the vector r in Part A as 16.4 m (approx).

Therefore, the magnitude of the vector r is 16.4 m (approx).

Part C:If r_x and r_y are doubled, then the new components of the vector r' are given by:

r'_x = 2

r_x = 2(14 m)

= 28 m and

r'_y = 2

r_y = 2(-8.5 m)

= -17 m.

Let's calculate the magnitude of the vector r' first using the Pythagorean theorem as follows:

r' = √(r'_x² + r'_y²)

r' = √((28 m)² + (-17 m)²)

r' = √(784 m² + 289 m²)

r' = √(1073 m²)

r' = 32.8 m (approx)

Thus, the magnitude of the new vector r' is 32.8 m (approx).

Now, let's calculate the direction of the vector r', which is given by the angle θ' as shown in the below diagram:

θ' = tan⁻¹(r'_y / r'_x)

θ' = tan⁻¹((-17 m) / (28 m))

θ' = -29.2° (approx)

Thus, the direction of the new vector r' is -29.2° (approx).

Part D:We have already calculated the magnitude of the new vector r' in Part C as 32.8 m (approx).

Therefore, the magnitude of the new vector r' is 32.8 m (approx).

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Answer:

always

Step-by-step explanation:

i hope this helps you!

Answer:

Always

Explanation:

I hope this helped and good luck!

\(\bold{H \: e \: l \: l \: o \: !}\)

Let's solve by step-by-step~

\(\sf{\frac{3w \: + \: 8}{2} \: = \: 25}\)

Step 1: Multiply both sides of 2.

\(\sf{\frac{3w \: + \: 8}{2} \: = \: 25}\)

\(\sf{(\frac{3w \: + \: 8}{2}) \: * \: (2) = (25) \: * \: (2)}\)

\(\sf{3w \: + \: 8 = 50}\)

Step 2: Subtract 8 from both sides.

\(\sf{3w \: + \: 8 \: - \: 8 \: = 50 \: - \: 8}\)

\(\sf{3w = 42}\)

Step 3: Divide both sides by 3.

\(\sf{\frac{3w}{3} = \frac{42}{3}\)

\(\sf{w = 14}\)

Hope It Helps~

Answer:

B

Step-by-step explanation:

$20-$11.29= 8.71 change he wil get back

Answer:

2.83 seconds

Step-by-step explanation:

In the given equation, h represents the height (in feet) of the rock above the river at time t seconds after it is dropped, and the equation is h = -16t^2 + 128.

When the rock reaches the river, its height above the river will be zero. So, we can set h = 0 in the equation and solve for t:

0 = -16t^2 + 128

Dividing both sides by -16, we get:

t^2 = 128/16

t^2 = 8

Taking the square root of both sides, we get:

t = ±√8

Since time cannot be negative, we take the positive square root:

t = √8 ≈ 2.83 seconds

Therefore, it will take the rock approximately 2.83 seconds to reach the river.

Answer:

x = 15

Step-by-step explanation:

The two angles form a straight line so they add to 180 degrees

3+6x   + 5x+12 = 180

Combine like terms

11x+15 = 180

Subtract 15 from each side

11x+15-15 =180-15

11x = 165

Divide by 11

11x/11 =165/11

x =15

If f(4) = 7 then the inverse of the function f⁻¹(7) is 4.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

f(4) = 7

According to inverse function property,

if f(x) = y, then f⁻¹(y) = x

The inverse of function,

f⁻¹(7) = 4

The inverse of the function f(4) = 7 is f⁻¹(7) = 4.

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Without the sample size (n) for each case, it is impossible to compute the correlation coefficient (r). Please provide the sample size to obtain accurate results.

A.) Using the formula r = σxy / (σx * σy), we get r = 2815 / (125 * 149) = 0.8420.
B.) Using the formula r = (Σxy - (Σx * Σy) / n) / sqrt((Σx^2 - (Σx)^2 / n) * (Σy^2 - (Σy)^2 / n)), we get r = (194.94 - (24.8 * 53.4) / 5) / sqrt((91.10 - (24.8)^2 / 5) * (454.44 - (53.4)^2 / 5)) = 0.9954.
C.) Using the same formula, we get r = (556472 - (5819 * 581) / 5) / sqrt((5648339 - (5819)^2 / 5) * (66495 - (581)^2 / 5)) = 0.97 D.) Using the same formula, we get r = (8853 - (58 * 638) / 5) / sqrt((886 - (58)^2 / 5) * (91530 - (638)^2 / 5)) = -0.9942.
To compute the correlation coefficient r, we use the formula:
r = (nΣxy - ΣxΣy) / √((nΣx² - (Σx)²)(nΣy² - (Σy)²))
For each case:
A) n is not given, so we cannot compute r.
B) n is not given, so we cannot compute r.
C) n is not given, so we cannot compute r.
D) n is not given, so we cannot compute r.
Without the sample size (n) for each case, it is impossible to compute the correlation coefficient (r). Please provide the sample size to obtain accurate results.

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If the radius of ice cream scoop is 1.75 cm and radius of cone is 1.75cm , then

(a) the volume of the scoop is  22.437 cm³ ;

(b) the height of cone to fit in ice cream is 7cm  .

The shape of the ice cream scoop is a whole sphere ,

the radius of ice cream scoop = 1.75cm ;

the radius of the cone is = 1.75cm ;

Part(a) ;

the volume of the ice cream scoop can be calculated by using the formula for Volume of sphere ;

So , the volume of ice cream scoop is = (4/3)×(3.14)×r³ ;

substituting the radius of sphere = 1.75 cm ;

we get ;

Volume =  (4/3)×(3.14)×(1.75)³

= 22.437

So , the Volume of the sphere is 22.437cm³ .

Part(b) ;

If the ice cream melts and fits in the cone ,

then the volume of sphere and cone should be equal ;

⇒ 22.437 = (1/3)×(3.14)×r²×h

substituting the radius of cone = 1.75cm ;

we get ;

22.437 = (1/3)×(3.14)×(1.75)²×h

22.437 = (1/3)×(3.14)×(1.75)²×h

22.437 = 3.205 × h

So , h = 22.437/3.205

h = 7.0006

h ≈ 7cm .

So , the height of the cone is 7cm .

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Answer: The correct answer is the Law of Large Numbers

Step-by-step explanation:

Imagine flipping a coin. There is a 50% likelihood that you would get tails. However, it doesn't happen all the time. If you flipped it just a few times, you could get all tails and have 100% tails.

However, if you experimented a lot of times (a large number), you almost certainly wouldn't get all tails. You would get close to 50%. That is the main point of the law.

The more trials you do, the more likely you will get close to the theoretical value.

Nicole would have $73,036.70 - $56,772.25 = $16,264.45 more money than Bentley after 14 years at the given interest rate.

Simple interest refers to an interest rate where the interest is just calculated on the principal sum of money. For the duration of the loan or investment, the interest rate is only applied once to the principal sum. On the other hand, compound interest is a type of interest where the interest is computed using both the principal and the interest from prior periods. After each compounding period, the interest rate is applied to the newly created balance.

The compound interest is given as:

\(A = P * e^{(rt)}\)

Substituting the given values:

\(A = 29000 * e^{(0.0541 * 14)} = $73,036.70\)

Now, after 14 years:

\(A = P * (1 + r/100)^t\)

Substituting the values:

\(A = 29000 * (1 + 0.04885)^{14} = $56,772.25\)

Hence, Nicole would have $73,036.70 - $56,772.25 = $16,264.45 more money than Bentley after 14 years

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