The letters in the word MATHEMATICIAN were put in a box. What is the chance of getting letter A?​

Step-by-step explanation:

To solve the equation 4e^(2x) - 1 = 13 for x, we will follow these steps:

Step 1: Add 1 to both sides of the equation to isolate the term with the exponential:

4e^(2x) = 14

Step 2: Divide both sides of the equation by 4 to isolate the exponential term:

e^(2x) = 14/4

Simplifying the right side:

e^(2x) = 7/2

Step 3: Take the natural logarithm (ln) of both sides of the equation to eliminate the exponential:

ln(e^(2x)) = ln(7/2)

By the properties of logarithms, the ln and e^(2x) cancel each other out:

2x = ln(7/2)

Step 4: Divide both sides of the equation by 2 to solve for x:

x = (1/2) ln(7/2)

Thus, the solution to the equation 4e^(2x) - 1 = 13 is x = (1/2) ln(7/2).

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

A line with slope m and that passes through the point (x₁, y₁) have the following point-slope form equation:

Furthermore, if this line passes through a second point (x₂, y₂), its slope is given by:

In this problem, the given line passes through points (6, 2) and (10, -1). So, we have:

x₁ = 6

y₁ = 2

x₂ = 10

y₂ = -1

Then, using those values to find m, we obtain:

And the equation of the line, in point-slope form, is:

Therefore, option A is correct.

Answer:

7000 cal/min

Step-by-step explanation:

It is mentioned that, Lucia is using energy at a rate of 420 kilo calories per hour ice skating

We know that,

1 kilo calories = 1000 calories

Using unitary method :

420 kilo calories = 420,000 calories

Also,

1 hour = 60 minutes

In this case, Lucia is using energy per 60 minutes =  420,000 calories. So,energy used by her per minute is :

\(E=\frac{420000}{60} =7000 calories\)

Hence, Lucia is using 7000 calories per minute.

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Answer: y=-1/4x+3

Step-by-step explanation:

==================================================

Explanation:

y = mx+b is the general form of slope intercept equations

m is the slope, b is the y intercept

The y intercept is where the graph crosses the y axis. In this case it is at (0,3) so b = 3 is the y intercept

--------------------

The slope can be found through using the slope formula

m = (y2-y1)/(x2-x1)

m = (2-3)/(4-0)

m = -1/4

Or you could note that to go from (0,3) to (4,2) we must go down 1 and over to the right 4.

slope = -1/4 = rise/run

rise = -1 means we go down 1

run = 4 means we move to the right 4

--------------------

Since m = -1/4 and b = 3, we go from y = mx+b to y = (-1/4)x+3

The matrix exponential M(t) = exp(t*A) are: M11(t) = exp(1*t)*(-1/2)*(-1/2) + exp(2*t)*(1/2)*(1/2) = (1/4)*exp(t) + (1/2)*exp(2*t)
M12(t) = exp(1*t)*(-1/2)*(1) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) - exp(t))
M21(t) = exp(1*t)*(1)*(1/2) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) + 1)
M22(t) = exp(1*t)*(1)*(1) + exp(2*t)*(1)*(1) = exp(t) + exp(2*t)

To find the matrix exponential M(t) = exp(t*A), we first need to find the eigenvectors of A corresponding to the eigenvalues X1 = 1 and X2 = 2.

For X1 = 1, we solve the equation (A - I)*v = 0, where I is the identity matrix:

(A - I)*v = (1 1; 2 2 - 1)*v = 0
RREF([A - I, zeros(2,1)])
ans =
   0    0   -1
   0    0    0

So we have the equation -v2 = 0, which means v2 can be any non-zero value. Let's choose v2 = 1, then v1 = -1/2. So the eigenvector corresponding to X1 is v1 = (-1/2; 1).

For X2 = 2, we solve the equation (A - 2*I)*v = 0:

(A - 2*I)*v = (-1 1; 2 -2)*v = 0
RREF([A - 2*I, zeros(2,1)])
ans =
   0    0   -1
   0    0    0

So we have the equation -v2 = 0, which means v2 can be any non-zero value. Let's choose v2 = 1, then v1 = 1/2. So the eigenvector corresponding to X2 is v2 = (1/2; 1).

Now we can construct the matrix exponential M(t) = exp(t*A) using the formula:

M(t) = c1*exp(X1*t)*v1*v1' + c2*exp(X2*t)*v2*v2'

where c1 and c2 are constants determined by the initial conditions. Since we don't have any initial conditions given, we can choose c1 = 1 and c2 = 0 for simplicity.

So we have:

M11(t) = exp(1*t)*(-1/2)*(-1/2) + exp(2*t)*(1/2)*(1/2) = (1/4)*exp(t) + (1/2)*exp(2*t)
M12(t) = exp(1*t)*(-1/2)*(1) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) - exp(t))
M21(t) = exp(1*t)*(1)*(1/2) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) + 1)
M22(t) = exp(1*t)*(1)*(1) + exp(2*t)*(1)*(1) = exp(t) + exp(2*t)

So the matrix exponential M(t) is:

M(t) = ( (1/4)*exp(t) + (1/2)*exp(2*t)    (1/2)*(exp(2*t) - exp(t));
       (1/2)*(exp(2*t) + 1)              exp(t) + exp(2*t) )

To find the matrix exponential M(t) = exp(tA) given that the eigenvalues of matrix A are λ1 = 1 and λ2 = 2, we first need to find the eigenvectors corresponding to each eigenvalue, and then form the matrix P of eigenvectors and the diagonal matrix D of eigenvalues. Finally, we can compute M(t) using the formula:

M(t) = P * exp(tD) * P^(-1)

After finding the eigenvectors and forming the matrices P and D, compute exp(tD) by taking the exponentiation of each diagonal element:

exp(tD) = | exp(tλ1)   0      |
              | 0          exp(tλ2) |

Now, compute M(t) by multiplying P, exp(tD), and the inverse of P. The resulting matrix M(t) will have the following components:

M11(t) = exp(1*t)*(-1/2)*(-1/2) + exp(2*t)*(1/2)*(1/2) = (1/4)*exp(t) + (1/2)*exp(2*t)
M12(t) = exp(1*t)*(-1/2)*(1) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) - exp(t))
M21(t) = exp(1*t)*(1)*(1/2) + exp(2*t)*(1/2)*(1) = (1/2)*(exp(2*t) + 1)
M22(t) = exp(1*t)*(1)*(1) + exp(2*t)*(1)*(1) = exp(t) + exp(2*t)

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Answer:

- The equation that represent the cost C of renting a car and driving x miles is C = $39.11 + $0.50x

- $130 can travel 181.32 miles

Step-by-step explanation:

From the question, a rental company rents a luxury car at a daily rate of 39.34 ​$ plus​ $.50 per mile, that is

$0.50 is added to the initial $39.34 for every mile.

The equation that represent the cost C of renting a car and driving x miles is

C = $39.34 + $0.50x

Now, to determine how many miles 130$ can travel,

we will put C = $100, and determine x in the above equation

$130 = $39.34 + $0.50x

$130 - $39.34 = $0.50x

$90.66 = $0.50x

x = $90.66/$0.50

x = 181.32

Hence, $130 can travel 181.32 miles

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Answer:

Jeff Bezos, is Amazon's founder, who's one of the richest people in the world.

The federal government won't require everyone to get vaccinated.

The federal government also won't required everyone in america to carry a passport.

New York recently because the first state to have a cov id passport.

Florida banned the co vid passport.

Restraunt owners think its against peoples rights to have a co vid passport, so they won't need them there!

Theatres are requiring a passport for the vaccine, due to wanting to fill the audience.

Heinz makes more ketchup than anyone

12 billions ketchup packets will be made this year from h einz, which is enough to reach the moon and back.

astronauts had a lot of ketchup in space

1 hundred and forty miles per hour is reached on the fasted roller coaster according to genius world records.

Step-by-step explanation:

Hope this helps! Plz mark as brainliest!

Answer:

54z+88

Step-by-step explanation:

To find the perimeter, add up the length of the sides

P = 27z+ 20+ 9z+ 24+ 12z+ 30+ 6z+ 14

Combine like terms

P = 27z+9z+12z+6z+20+24+30+14

P =54z+88

The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ lim θ → 0 ( sin θ / θ ) = 1

Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.

⇒ lim θ → 0 ( sin θ / θ ) = 1

Take LHS;

⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )

⇒ lim θ → 0 ( cos θ / 1 )

⇒ ( cos 0 )

⇒ 1

⇒ RHS

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Answer:

$30

Step-by-step explanation:

12.50/5=2.50

2.50*12=30

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Answer:

124

Step-by-step explanation:

white 124, chocolate 62, strawberry 31

Answer:

5. Trend line

6. Line graph

Step-by-step explanation:

The trend line is used to estimate data on a graph.

A line graph is used to show how information changes over time.

Answer:

=-1/6

Step-by-step explanation:

-1/2 + (3/4 * 4/9)

3/4 * 4/9 = 12/36

12/36 simplify to 1/3

-1/2 + 1/3 = -1/6

The 9th term of the geometric sequence is 64.

The formula for the nth term of a geometric sequence is:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

In this case, we are given that:

a6 = 8

r = 2

n = 9

To find the 9th term, we need to plug in the values into the formula:

a9 = a1 * r^(9-1)

We don't know a1, but we can find it using the 6th term:

a6 = a1 * r^(6-1)

8 = a1 * 2^5

a1 = 8 / 2^5

a1 = 8 / 32

a1 = 1/4

Now we can substitute a1 and r into the formula for the 9th term:

a9 = (1/4) * 2^(9-1)

a9 = (1/4) * 2^8

a9 = (1/4) * 256

a9 = 64

Therefore, the 9th term of the geometric sequence is 64.

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Answer:

$34.37.

Step-by-step explanation:

To calculate Daniel's local income tax withholding, we first need to determine his taxable income. To do this, we subtract the value of his exemptions from his yearly income: $41,300 - (4 x $900) = $37,500.

Next, we need to convert the local tax rate of 4 3/4% to a decimal by dividing it by 100: 4 3/4% = 0.0475.

Finally, we can calculate Daniel's local income tax withholding by multiplying his taxable income by the local tax rate: $37,500 x 0.0475 = $1,793.75.

To find the amount of local income tax that should be withheld from Daniel's weekly earnings, we simply divide his total local income tax by the number of weeks in a year: $1,793.75 / 52 = $34.37. Therefore, Daniel's local income tax withholding from his weekly earnings should be $34.37.

The domain are all of the x-values that are located on the x-axis of a cartesian coordinate while the range all of the y-values that are located on the y-axis of a cartesian coordinate.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

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There are 10 ways to choose a president and a vice president from a group of 5 people.

To choose a president and a vice president from a group of 5 people, we can first choose any 1 person to be the president. Once we have chosen the president, we can then choose any of the remaining 4 people to be the vice president. This gives us 5 * 4 = 20 ways to choose a president and a vice president. However, since the order in which we choose the president and vice president does not matter, we need to divide this number by 2 to get 20 / 2 = 10 ways.

Here is another way to think about it. There are 5! = 120 ways to order the 5 people. However, since the president and vice president cannot be the same person, we need to divide this number by 2! to account for the fact that the order in which we choose the president and vice president does not matter. This gives us 120 / 2! = 10 ways to choose a president and a vice president from a group of 5 people.

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Answer: 3/2

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that Y'X'=3 and YX=2, so the scale factor is 3/2.

Answer:

200.96 units^2

Step-by-step explanation:

50.24/Pi = 16 (diameter)

16/2=8 (radius)

area = Pi(r^2)

area = 3.14(8^2) = 200.96 units^2

Answer:   same

Step-by-step explanation:

Amongst the options circle shape from the Clade Race would be considered plesiomorphic.

A primitive or ancestral character state is called plesiomorphy or known as a plesiomorphic character), and a shared plesiomorphy is called a symplesiomorphy. For example, let us take an example of hair. It is a unique mammalian character that evolved with the evolution of mammals.

The term apomorphy means a specialized or derived character state which is plesiomorphy. It refers to a primitive or ancestral trait. An same as autapomorphy, it is a derived trait that is unique to one group, while a same as synapomorphy is a derived trait shared by two or more groups.

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Answer:

No question is asked, but Company P is less expensive than company M.

Step-by-step explanation:

See attached image.

The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

According to the statement

There is a region where the range of values of the independent variables in the data used to estimate the regression model.

AND

Those region is called EXPERIMENTAL REGION

So, Experimental region is called a those region in which the region within which we can make valid predictions and doesn't go outside of the bounds of the data we were provided.

So, The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

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Increasing the sample size has an effect on the standard error, but other factors determine whether the increased sample size will increase or decrease the standard error.


The standard error is a measure of the variability of the sample mean. When the sample size is increased, the standard error generally decreases because a larger sample size provides more precise estimates of the population mean. However, other factors such as the variability of the population and the sampling method used can also affect the standard error.

For example, if the population variability is high, increasing the sample size may not have a significant impact on reducing the standard error. On the other hand, if the population variability is low, increasing the sample size can lead to a substantial decrease in the standard error.

In summary, increasing the sample size generally decreases the standard error, but the magnitude of this effect depends on other factors such as population variability and sampling method.

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