i need the answer for all three or atleast the bottom one pls help me

The quotient to the expression is 1/64

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: The expression 4⁻⁵ / 4⁻²

When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

Thus simplifying the expression we get

4⁻⁵ / 4⁻²

4⁻⁵× 4²

4⁻⁵ ⁺ ²

4⁻³

1/64

Thus the quotient is 4⁻³

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The cosine form of the function 10sin(wt - 40)  is 10cos(wt - 50).

The cosine form of the function 10sin(wt - 40) can be found using the identity sin(x - y) = sin(x)cos(y) - cos(x)sin(y).

By applying this identity to the given function, we can rewrite it in terms of cosine.

10sin(wt - 40) = 10(sin(wt)cos(40) - cos(wt)sin(40))

Now, we can use the fact that cos(90 - x) = sin(x) and sin(90 - x) = cos(x) to further simplify the expression.

10(sin(wt)cos(40) - cos(wt)sin(40)) = 10(sin(wt)sin(50) + cos(wt)cos(50))

Finally, we can use the identity cos(x + y) = cos(x)cos(y) - sin(x)sin(y) to rewrite the expression in terms of cosine.

10(sin(wt)sin(50) + cos(wt)cos(50)) = 10cos(wt - 50)

Therefore, the cosine form of the function 10sin(wt - 40) is 10cos(wt - 50).

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Answer:

multiply vertically

Step-by-step explanation:

Answer:

i think it's <C and <R since they're 90 degree angles, though they are small

The maximum height of the parabola approximating the given trajectory is approximately 5.22 units.

To approximate the trajectory with a parabola in the least squares sense, we need to find the best-fitting quadratic function of the form y = ax² + bx + c. We can use the method of least squares to minimize the sum of the squares of the vertical distances between the data points and the parabola.

1. Set up a system of linear equations using the given data points: (0,0), (1,3), (2,5), and (3,4).
2. Solve the system using linear algebra or other methods to find the coefficients a, b, and c.
3. Determine the maximum height of the parabola using the vertex formula: x = -b/(2a).
4. Plug the value of x back into the equation y = ax² + bx + c to find the maximum height.

Following these steps, we find that the best-fitting parabola is approximately y = -0.5x² + 2.5x + 0.5. The maximum height occurs at x = -b/(2a) ≈ 2.5, and the corresponding height is approximately 5.22 units.

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Answer:

x < -15

Step-by-step explanation:

Here is the solution:

-3x-42 > 3

Add the numbers

-3x > 45

Divide both sides of the inequation by -3 and flip the inequality sign.

x < -15

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

Answer:

Not correct .

Step-by-step explanation:

A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.

To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).

In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.

Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).

Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.

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Answer:

38

Step-by-step explanation:

If 9 workers can complete a job in 56 minutes, then it takes 36 minutes for 14 workers.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that amount of time needed to complete a job, t, varies inversely with the number of workers, w.

t=k/w

k is a constant

9 workers can complete a job in 56 minutes

t=56 and w=9

56=k/9

Apply cross multiplication

k=9×56

k=504

We need to find how many minutes would it take for 14 workers.

t=504/14

t=36

Hence, it takes 36 minutes for 14 workers.

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In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is  $1.60 more to the cab driver.

A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.

Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%

amount of gratuity = 20% 0f 32 = 6.40

The fare of the cab  + gratuity = 32 + 6.40 = 38.40

Check to the cab driver for $40 ,  implies ($40 - $38.40)= $1.60 more to the cab driver.

Hence, it is reasonable.

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To find the angle of least nonnegative measure that is coterminal with θ = -570°, we can add or subtract multiples of 360° until we get an angle between 0° and 360°.

We can start by adding 360° to -570°:

-570° + 360° = -210°

This is still negative, so we can add another 360°:

-210° + 360° = 150°

This is between 0° and 360°, so the angle of least nonnegative measure that is coterminal with θ = -570° is 150°. Therefore, 0c is 150°.

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The area of the shaded region of the circle is 63.24 ft²

We know that the area of a circle of radius R is given by the formula:

Area = pi*R²

Where pi = 3.14

If we have only a section of a circle defined by an angle θ, the area of that section will be:

area = (θ/360°)*3.14*R²

Here we know that the radius is 5 feet, and that AOB (the non-shaded part) is 70°, then we will have:

θ = 360° - 70° = 290°

Then the area of the shaded region is:

area = (290°/360°)*3.14*(5 ft)² = 63.24 ft²

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Using the formula shown replace r with 11 and pi with 3:

Volume = 4/3 x 3 x 11^3

Volume = 5,324 in^3

Answer: 81

Step-by-step explanation: If you add all of the numbers, then you end up getting 81.35 and 81.35 estimated to the nearest whole number is 81 because that's the closest whole number to 81.35.

Answer:

B - we can conclude that 90% confidence interval is narrower than the 95% confidence interval.

Step-by-step explanation:

The correct statement is the 90% confidence interval is narrower than the 95% confidence interval, the option is B.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that;

The four options

Now,

A confidence interval is a range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way1. The confidence level is the percentage of times you expect to reproduce an estimate between the upper and lower bounds of the confidence interval, and is set by the alpha value12.

All else being equal, a higher confidence level produces a wider confidence interval12.

Therefore, by the given mean answer will be The 90% confidence interval is narrower than the 95% confidence interval.

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Answer:

62

Step-by-step explanation:

Step-by-step explanation:

hope it is helpful to you

Answer:

B) 7....................

The solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

Given the equation in question;

|3x-7| - 7 = x

First, add 7 to both sides.

|3x-7| - 7 + 7 = x + 7

|3x-7|  = x + 7

Next, remove the absolute value term, this creates a ± on the right side of the question.

|3x-7|  = x + 7

3x-7  = ±( x + 7 )

The complete solution is the result of both the negative and positive portions of the solution.

For the first solution, use the positive of ±.

3x-7  = ( x + 7 )

3x - 7  =  x + 7  

3x - x = 7 + 7

2x = 14

x - 14/2

x = 7

For the second solution, use the negative of ±.

3x-7  = -( x + 7 )

3x-7  = -x - 7

3x + x = -7 + 7

4x = 0

x = 0/4

x = 0

Therefore, the solutions to the given equation containing absolute value term |3x-7| - 7 = x are 0 and 7.

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The value car 10 years after it has been purchased is $50,638.40.

∫x dx = (1/2)x² + C

∫e²(0.06x) dx = (1/0.06)e²(0.06x) + C = (16.667e²(0.06x)) + C

∫(x² - x - 2)/(x²(-1)) dx = ∫(x³ - x² - 2x) dx

Applying the power rule,

= (1/4)x³ - (1/3)x³ - x² + C

∫(x² + x³ - 6x) dx = (1/3)x³ + (1/4)x² - (3/2)x² + C

∫(v0 + e²(-x)) dv = v0v - e²(-x) + C

∫(-3e²(-3x) - 6x²(-1)) dx = 3e²(-3x) - 6ln(x) + C

∫(e²(2x) + 1) dx = (1/2)e²(2x) + x + C

∫(4t² - √(12t) + e²(-6x + B)) dx = (4/3)t³ - (2/5)(12t²(3/2)) + xe²(-6x + B) + C

∫(3x² + 2 + 2x + 1 + x²(-1) - x²(-2)) dx = x³ + 2x + x² + ln(x) - (-1/x) + C

Simplifying,  x³ + x² + 2x + ln(x) + (1/x) + C

∫x dx = (1/2)x² + C

move on to the next part of your question:

The value of the car after t years can be found using the formula:

P(t) = P(0) - ∫P'(t) dt

Given that P'(t) = -3,240e²(-0.09t), and P(0) = $36,000,

P(t) = 36,000 - ∫(-3,240e²(-0.09t)) dt

Integrating,

P(t) = 36,000 - ∫(-3,240e²(-0.09t)) dt

= 36,000 - (3,240/(-0.09))e²(-0.09t) + C

Simplifying further,

P(t) = 36,000 + 36,000e²(-0.09t) + C

The value of the car 10 years after it purchased, t = 10 into the formula:

P(10) = 36,000 + 36,000e²(-0.09 × 10)

Calculating the value:

P(10) = 36,000 + 36,000e²(-0.9)

=36,000 + 36,000(0.4066)

= 36,000 + 14,638.4

=$50,638.40

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The word bank to fill in the blanks in the given sentences is messenger, transcribed, nucleus, RNA, codons, ribosome, transfer, amino acid, and protein. The amino acids are added to the growing protein chain as specified by the mRNA sequence, which is read by the ribosome.

This occurs in the nucleus. Second, the RNA gets translated into a sequence of amino acids. The ribosome reads the mRNA every three bases known as codons. The transfer RNA carries amino acids to the ribosome to build the protein. In the first step of the central dogma, transcription takes place. Transcription is the process of DNA being copied into RNA. The DNA is present in the nucleus of a cell.

The RNA is formed through the transcription process. mRNA is produced from the DNA molecule during transcription. mRNA stands for messenger RNA. The transcription process is divided into three stages: initiation, elongation, and termination. In the second step of the central dogma, translation takes place. In the process of translation, mRNA is translated into a protein. Amino acids are linked together to form a protein chain, which is determined by the sequence of codons in the mRNA molecule. Ribosomes are the sites of translation. Transfer RNA (tRNA) molecules carry amino acids to the ribosome. Each amino acid is attached to a specific tRNA molecule.

The amino acids are added to the growing protein chain as specified by the mRNA sequence, which is read by the ribosome.

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To determine which point maximizes the objective function, we need to evaluate the objective function at each of the given points and then compare the results. The point that produces the highest value for z will be the solution.

a. (1, 1)

z = 3(1) + 5(1) = 8

b. (2, 7)

z = 3(2) + 5(7) = 41

c. (5, 10)

z = 3(5) + 5(10) = 55

d. (6, 3)

z = 3(6) + 5(3) = 33

Therefore, the point that maximizes the objective function is (5, 10) with a value of z = 55.

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Answer

Step-by-step explanation:

The value of g(1) is approximately 0.491, obtained by integrating g'(x) and using the initial condition g(4)=0.325 to determine the constant of integration

the value of g(1) is determined by integrating the given derivative function g'(x) and evaluating it at x=1.

The initial condition g(4)=0.325 is also provided, which can be used to solve for the constant of integration.

integrating the given derivative function g'(x) involves finding the antiderivative of each term separately.

The antiderivative of 1/x is ln(x), the antiderivative of\(e^(-x) -e^(-x),\) and the antiderivative of\(cos(x^100)\) is \(sin(x^100)/100.\)

After integrating each term, we obtain g(x) = ln(x) - e^(-x) \(sin(x^100)/100.\) + C, where C is the constant of integration.

Using the initial condition g(4) = 0.325, we can substitute x=4 and solve for C.

Plugging in the values, 0.325 = \(ln(4) - e^(-4) sin(4^100)/100\) + C. By evaluating this equation, we can find the value of C.

Finally, with the constant of integration C determined, we can substitute x=1 into the function g(x) = \(ln(4) - e^(-4) sin(4^100)/100\) + C to find the value of g(1).

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In dataset 60 is the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation.

n dataset C, the data is spread more tightly around the mean than in other datasets. Accordingly, it would have a smaller standard deviation

Standard deviation is 60

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The curve at the top is more dispersed and has a greater standard deviation than the curve at the bottom, which is more concentrated around the mean and has a lower standard deviation.

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Answer:

7.8 * 10^7

Step-by-step explanation:

Group coefficients together and exponents together to multiply numbers in scientific notation.

( 7.8  *  1 )  ( 10 ^3  * 10^4)

Multiply  7.8 times 1.

7.8 * (10^3 * 10^4)

Use the power rule  a^m * a^n = a^(m+n) to combine exponents. So, add 3 and 4

7.8 * 10^7

Answer: it is - 13

Step-by-step explanation: it is -13 because it either can be less or more

Answer:the third one

Step-by-step explanation:

Answer: 3/4 hour

Step-by-step explanation: You can add 1/4 at a time to get to the 3 2/4.