What is sin 45º ?
Just do the math.

There are **16,640** valid passwords. There are two cases to consider: passwords that are 5 characters long, and passwords that are 6 characters long.

**Case 1: 5-character passwords**

There are 26 choices for each of the first 3 characters, since they can be lowercase letters or digits. There are 10 choices for the fourth character, since it must be a digit. The fifth character must be different from the first three characters, so there are 25 choices for it.

Therefore, there are $26 \times 26 \times 26 \times 10 \times 25 = 16,640$ 5-character passwords.

**Case 2: 6-character passwords**

There are 26 choices for each of the first 4 characters, since they can be lowercase letters or digits. The fifth character must be different from the first four characters, so there are 25 choices for it. The sixth character must also be different from the first four characters, so there are 24 choices for it.

Therefore, there are $26 \times 26 \times 26 \times 25 \times 24 = 358,800$ 6-character passwords.

Total

The total number of valid passwords is $16,640 + 358,800 = \boxed{375,440}$.

The first step is to determine how many choices there are for each character in a password. For the first three characters, there are 26 choices, since they can be lowercase letters or digits.

The fourth character must be a digit, so there are 10 choices for it. The fifth character must be different from the first three characters, so there are 25 choices for it.

The second step is to determine how many passwords there are for each case. For the 5-character passwords, there are 26 choices for each of the first 3 characters, and 10 choices for the fourth character,

and 25 choices for the fifth character. So, there are $26 \times 26 \times 26 \times 10 \times 25 = 16,640$ 5-character passwords.

For the 6-character passwords, there are 26 choices for each of the first 4 characters, and 25 choices for the fifth character, and 24 choices for the sixth character. So, there are $26 \times 26 \times 26 \times 25 \times 24 = 358,800$ 6-character passwords.

The third step is to add up the number of passwords for each case to get the total number of passwords. The total number of passwords is $16,640 + 358,800 = \boxed{375,440}$.

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Answer

There are 36 combinations and 181440 permutations

Explanation

The number of combinations of n object taking r at a time is given by the formula;

From the question, n = 9 and r = 7, then substitute these values into the formula

The number of permutations of n object taking r at a time is given by the formula;

Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations

Therefore, there are 36 combinations and 181440 permutations

The 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).

Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.

The confidence interval of statistical data is computed using the formula:

\((\overline{x} - Z\frac{\sigma }{n},\overline{x} + Z\frac{\sigma }{n})\)

where \(\overline{x}\) is the mean, Z is the Z-score corresponding to the confidence interval, σ is the standard deviation, and n is the sample size.

In the question, the sample size (n) = 36, the mean of the sample (\(\overline{x}\)) = 28.4 mi/gallon, the standard deviation (σ) = 6 mi/gallon.

The confidence interval given to us is 98%.

Z-score corresponding to this (Z) = 2.33.

Thus, the confidence interval can be calculated as:

(28.4 - 2.33{6/√36},28.4 + 2.33{6/√36})

= (28.4 - 2.33,28.4 + 2.33)

= (26.07,30.73).

Thus, the 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).

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Answer: send a pic

Step-by-step explanation: go take a pic and come back

Answer:

15

Step-by-step explanation:

BD=AC

E is the midpoint of both lines, so BE=CE

There are 81 different ways to place 5 distinguishable balls in 3 indistinguishable boxes using combinations.

Given that in how many ways we can put 5 balls in 3 boxes if balls are distinguishable, but the boxes are not.

To find the number of ways we will use the concept of combination.

Combinations can be defined as the entire outcomes of an event where the order of outcomes does not matter.

Given Data

The number of balls is 5 balls.

The number of boxes is 3 boxes.

The balls are distinguishable, but the boxes are not distinguishable.

According to the question, the expression for the number of ways is,

P = \(\frac{n^N}{n}\)

Putting the values in the formula we get,

P = \(\frac{3^5}{3}\)

P = 81

Hence the number of the ways are 81.

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Answer:

$1080

Step-by-step explanation:

Since we have 40% off 60 percent of the price is $648 so we can make ratios

60/100=648/x

Cross multiply

60x=100(648)

60x=64800

/60.  /60

x=1080

Sales price is $1080

Hopes this helps please mark brainliest

Answer:

19

Step-by-step explanation:

Plug 3 in for (x)

You'd have: 2(3)²+1

Solve. Do parentheses first so... 3²=9

You now have: 2(9)+1

Solve

18+1 = 19

Answer:

y=113505(1+0.012)^(x)

y=120481. Answered by Gauthmath

Answer: 5

Step-by-step explanation:

From the question, we are informed that "x varies inversely with v". This means that

x = k/v

where,

k is a constant

We have to find k when x=35 when v=3

x = k/v

35 = k/3

k = 35 × 3

k = 105

Therefore when v = 21, x will be:

x = k/v

x = 105/21

x = 5

The correct formula to calculate inventory turnover is the first option:  Inventory turnover = Cost of goods sold / Average merchandise inventory

The correct formula to calculate inventory turnover is the first option: Inventory turnover = Cost of goods sold / Average merchandise inventory. Inventory turnover is a financial metric that measures how efficiently a company is managing its inventory.

It is calculated by dividing the cost of goods sold (COGS) by the average merchandise inventory. COGS represents the cost incurred by a company to produce or acquire the goods that are sold during a specific period. Average merchandise inventory is the average value of inventory held by the company over a certain time period.

By dividing COGS by average merchandise inventory, we can determine how many times the inventory is sold and replaced during that period, providing insight into inventory management efficiency.


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Answer:

Step-by-step explanation:

x=0

Answer:

Given,

y=x³ ,0≤x≤2

We have to find the surface area of the surface by rotating the curve about the x axis.

For rotation about the x axis, the surface area formula is given by-

s=2π∫ᵇₐ y√1+(y)² dx

y=x³

y'=3x²

By rotating the curve y=x³ about the x axis in the interval [0,2]

s=2π∫₀²(x³)√1+(3x²)² dx

let u=1+9x⁴

du=36x³dx

dx/36x³

Substituting u and du in the integral,

s= 2π∫₀²(x³)√u du/36x³

s= 2π∫₀²√u du

s= 2π/36.2/3[u.3/2]₀²

s= π/27[(145)³/²-(1)³/²]

s= π/27 [1746.03-1]

s= π/27 [1745.03]

s= 64.67π

s= 64.67(3.14)

s=203.06 square units.

therefore, the exact surface area is 203.06 square units.

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Answer:

      In order to find the surface area obtained by rotating the curve we need to find surface area for rotation along x axis then substituting values in the integral.                       

         Given:    y=3x, for x is in [1,125] about the y axis.

                                            y=x³ ,0≤x≤2

Lets find the surface area of the rotating curve,

Finding surface area for rotation along x-axis,

                                    s=2π∫ᵇₐ y√1+(y)² dx

                                     y=x³

                                     y'=3x²

By rotating the curve y=x³ about the x axis in the interval [0,2]

                           s=2π∫₀²(x³)√1+(3x²)² dx

                          Assuming  u =1+9x⁴

                                           du=36x³dx

                                               =dx/36x³

Substituting respective values of u and du in the integral,

                              s= 2π∫₀²(x³)√u du/36x³

                              s= 2π∫₀²√u du

                              s= 2π/36.2/3[u.3/2]₀²

                              s= π/27[(145)³/²-(1)³/²]

                              s= π/27 [1746.03-1]

                              s= π/27 [1745.03]

                              s= 64.67π

                              s= 64.67(3.14)

                              s=203.06 square units.

hence, the surface area is 203.06 square units.

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Answer:

3

Step-by-step explanation:

We can find the slope of the given line in this two way:

1) the faster is calculate -a/b where a is the number the multiply x and b is the number the multiply y. In this case we have -1/3

2) the second method is rewrite the equation in slope intercept form and find the therm that multiply x

3y = -x-15

y = -1/3x - 5

Also in this case we have -1/3

Two perpendicular lines have the the product of the their slope that is -1

So the slope that we are finding is 3

In fact = 3 x -1/3 = -1

Answer:

400,000

Step-by-step explanation:

The coordinates of the vertices of the image triangle are J'(-4, 0), K'(-2, 2), and L'(-1, 0).

To find the coordinates of the vertices of the image after dilation by a scale factor of 0.5 centered at the origin, we multiply each coordinate by the scale factor.

Let's apply the dilation to each vertex:

J' = (-8 * 0.5, 0 * 0.5) = (-4, 0)

K' = (-4 * 0.5, 4 * 0.5) = (-2, 2)

L' = (-2 * 0.5, 0 * 0.5) = (-1, 0)

Therefore, the coordinates of the vertices of the image triangle are J'(-4, 0), K'(-2, 2), and L'(-1, 0).

To graph the preimage and image, you can plot the points J(-8, 0), K(-4, 4), and L(-2, 0) on one sheet of paper to represent the preimage triangle. Then, on a separate sheet of paper, plot the points J'(-4, 0), K'(-2, 2), and L'(-1, 0) to represent the image triangle. Make sure to label each vertex accordingly.

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a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

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The monthly payments for a $35,000 car loan at 10% APR compounded monthly for 36 months are $1,129.35.

To calculate the monthly payments, we can use the formula for the monthly payment amount on a loan:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where M is the monthly payment, P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of payments (loan term in months).

In this case, P = $35,000, r = 10% divided by 12 (monthly interest rate), and n = 36.

Plugging these values into the formula:

M = 35,000 * (0.1/12 * (1 + 0.1/12)^36) / ((1 + 0.1/12)^36 - 1)

≈ $1,129.35.

Therefore, the monthly payments for the $35,000 car loan at 10% APR compounded monthly for 36 months amount to approximately $1,129.35. The correct answer is C.

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Helen deposited $1100 in a savings account with a 4.5% annual interest rate. After 7 years, if the account is compounded quarterly, weekly, or semi-annually, she would have $1614.53, $1617.92, or $1606.24, respectively.

a. To model the amount of money in Helen's savings account at the end of t years, compounded k times during the year, we can use the following formula:

A = P(1 + r/k)^(kt)

So the function to model the amount of money in Helen's savings account at the end of t years, compounded k times during the year is:

A = 1100(1 + 0.045/k)^(kt)

b. To determine the amount of money in Helen's account at the end of 7 years if it is compounded quarterly, weekly, and semi-annually, we can substitute the given values of k and t into the formula and simplify:

Compounded quarterly:

A = 1100(1 + 0.045/4)^(4*7)

A = 1100(1.01125)^28

A = 1614.53 (rounded to the nearest cent)

Compounded weekly:

A = 1100(1 + 0.045/52)^(52*7)

A = 1100(1.00086538)^364

A = 1617.92 (rounded to the nearest cent)

Compounded semi-annually:

A = 1100(1 + 0.045/2)^(2*7)

A = 1100(1.0225)^14

A = 1606.24 (rounded to the nearest cent)

Therefore, after 7 years, if Helen's account is compounded quarterly, she would have $1614.53; if it is compounded weekly, she would have $1617.92, and if it is compounded semi-annually, she would have $1606.24.

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Answer:

According to the given data, if it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6.

Step-by-step explanation:

Past studies indicate that about 60 percent of the trees in a forested region are classified as softwood.

A botanist studying the region suspects that the proportion might be greater than 0.60.

The botanist obtained a random sample of trees from the region and conducted a test of H0:p=0.6 versus Ha:p>0.6.

Therefore, he p-value of the test was 0.015, indicating the past studies.

Answer:

they are both SSS

Step-by-step explanation:

you only have information of the sides.

hope it helps :)

Answer:

sure.. 16pi

Step-by-step explanation:

use the equation

\(a = \pi \: {r}^{2} \)

\(radius = diameter \div 2\)

r = 8÷2 = 4 ft

\(a = \pi \times {4 }^{2} \)

\(a = 16 \: \pi\)

Therefore, the correct option is (d) $270.48, which represents your take-home pay after deducting the specified taxes from your earnings.

To calculate the take-home pay, we need to subtract the total amount of taxes from the earnings.

In this case, the earnings are $420 per week.

The social security tax is 7.65% of the earnings. Therefore, the amount deducted for social security tax is:

Social security tax = 7.65% * $420 = $32.13

The federal tax is 22% of the earnings. So, the amount deducted for federal tax is:

Federal tax = 22% * $420 = $92.40

The state tax is 5.95% of the earnings. Hence, the amount deducted for state tax is:

State tax = 5.95% * $420 = $24.99

To calculate the take-home pay, we subtract the total taxes from the earnings:

Take-home pay = $420 - ($32.13 + $92.40 + $24.99) = $270.48

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The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.

The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:

C = 0.0052 + 0.3(10) + 20

C = 0.0052 + 3 + 20

C = 23.0052

Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:

C' = 0.0052 + 0.3(Y + ΔY) + 20

C' = 0.0052 + 0.3Y + 0.3ΔY + 20

To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):

MPC = (C' - C) / ΔY

MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY

Simplifying the equation, we can cancel out the terms that don't involve ΔY:

MPC = (0.3ΔY) / ΔY

MPC = 0.3

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Answer:

720,000 is 719,618.4 larger than 3.6 x 106

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

step 1

\(n+2\)

step 2

\(2(n+2)\\\\=2n+4\)

step 4

\(2n+4-3\\\\=2n+1\)

if n=3

\(2(3)+1\\\\=6+1\\\\=7\)

output is 7