How many three-letter "words" can be made from 10 letters "FGHIJKLMNO" if repetition of letters (a) is allowed? Your answer is (b) is not allowed? Your answer is

Answer:

which side are you looking for, SOHCAHTOA

OPPOSITE

tan50.34=x÷180

x=180×1.2062(tan50.34)

x=2117.116

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

Answer:

allpes=1.8; grapes=1.85

Step-by-step explanation:

1. if to suppose the price of the apples is 'a' and the price of the grapes is 'g', then on the first day was earned 24*a+16*g=72.8 (1-equation) and on the second day 30*a+25*g=100.25 (2-equation);

2. if to solve these two equations as the the system of equations, then a=1.8 euro/kg and g=1.85 euro/kg

The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer: ya

Step-by-step explanation:

Answer:

1. x  =  − 7  +  2 y

2. x  =  1  −  2 y /3

Step-by-step explanation:

Answer:   [1]    x + 2y = 7

  [2]    3x - 2y = -3

Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine them.

Exact Form:

188

5

Decimal Form:

37.6

Mixed Number Form:

37

3

5

hope this helped have a nice day! :)

Answer:

Step-by-step explanation:

(124+64) /5

= 188/5

Answer is = 37.5

The domain of the given function is; (0, 2)

The range of the given function is; (-2, 6)

We want to evaluate the function f(x) = 4x - 2 for x = 0, 1 and 2.

Step 1;

f(0) = 4(0) - 2

f(1) = 4(1) - 2

f(2) = 4(2) - 2

Step 2;

f(0) = 0 - 2 = -2

f(1) = 4 - 2 = 2

f(2) = 8 - 2 = 6

The domain is the set of all possible input values which is (0, 2)

The range is the set of all possible output values which is (-2, 6)

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The p-value of the test hypothesis is given as follows:

0.8449.

Before obtaining the p-value for the test of the hypothesis, we must obtain the test statistic, which is the division of the sample estimate by the standard error, hence:

t = -1.75/7.12

t = -0.245.

Considering a right-tailed test, as we are testing if the mean is greater than a value, with t = -0.245 and 35 - 1 = 34 df, the p-value is given as follows:

0.8449.

(using a t-distribution calculator).

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Answer:

15,103.05

Step-by-step explanation:

Total amount in the saving account after 5 years in which the  annual interest, compounded continuously, is $15,103.85.

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

\(A=P\times\left(1+\dfrac{r}{100n}\right)^{nt}\\\)

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

$13,000 is deposited into a savings account with an annual interest rate of 3% compounded continuously.

The amount in account after 5 years can be calculated with the above formula as,

\(A=13000\times\left(1+\dfrac{3}{12\times100}\right)^{12\times5}\\A=15101.02\)

The total amount in the saving account after 5 years in which the  annual interest, compounded continuously, is $15,103..85.

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\(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\) is the possible root

What is a root ?

Mathematicians refer to a number as having a root if it can be multiplied by itself to give the original number. The square root of 49, for instance, is 7, as 77=49. 7 is referred to as the square root of 49 in this instance because it takes 49 to multiply 7 by itself twice. Considering that 333=27, the cube root of 27 is 3.

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfill the equation. In other words, if f() = 0, then x = is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

3x^4 -10x^3 -9x^2 + 40x - 12

=\(\left(3x-1\right)\frac{3x^4-10x^3-9x^2+40x-12}{3x-1}\)

=\(\left(3x-1\right)\left(x^3-3x^2-4x+12\right)\)

= \(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\)

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Answer:

(100/500) *200 =40%

Step-by-step explanation:

The Volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.

The volume of each bead, the volume of a sphere using its diameter. The formula for the volume of a sphere is given by:

V = (4/3) * π * r^3

where V is the volume and r is the radius of the sphere.

Given that the diameter of each bead is 1.5 millimeters, we can calculate the radius as half of the diameter:

r = 1.5 mm / 2 = 0.75 mm

Now, we can substitute the value of the radius into the volume formula:

V = (4/3) * π * (0.75 mm)^3

Using the value of π ≈ 3.14 and performing the calculations:

V ≈ (4/3) * 3.14 * (0.75 mm)^3

V ≈ (4/3) * 3.14 * 0.421875 mm^3

V ≈ 1.767 mm^3 (rounded to the nearest tenth)

the volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.

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The unit of the rate of change is (b) dollars per month

From the question, we have the following parameters that can be used in our computation:

The table of values

Where we have

y = total amount in dollars

x = number of months

The rate of change is calculated as

Rate  = y/x

substitute the known values in the above equation, so, we have the following representation

Rate = total amount in dollars/number of months

So, we have

Unit = dollars per month

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Answer:

violence figer in the past two years

Answer:

58cups

Step-by-step explanation:

Given the equation for the line as c = 2t - 89

If the temperature is 74 degrees, then we can find the number of cups at this temperature;

Substitute t = 74 unti the expression

x = 2(74) - 89

c = 147 - 89

c = 58cups

Hence the number of cups of lemonade is 58cups

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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So, the total interest earned over 35 years at 9% interest would be approximately $150,652.20.

An interest rate is the amount of money that a lender charges a borrower for the use of borrowed money. It is typically expressed as a percentage of the amount borrowed and can be fixed or variable. Interest rates are set by central banks or other financial institutions and can vary based on a range of factors such as inflation, economic growth, and the creditworthiness of the borrower. In general, higher interest rates make borrowing more expensive, while lower interest rates make borrowing cheaper.

To calculate the monthly deposit required to achieve $300,000 in 35 years at 9% interest, we can use the following formula:

\(PMT = (FV x r) / ((1 + r)^n - 1)\)

where PMT is the monthly payment, FV is the future value (which is $300,000), r is the monthly interest rate (which is 9% / 12 = 0.0075), and n is the number of payments (which is 35 years x 12 months per year = 420).

a) Plugging in these values into the formula, we get:

\(PMT = (300000 x 0.0075) / ((1 + 0.0075) ^{420} - 1) = $355.89\)

So, you would need to deposit approximately $355.89 per month to achieve a retirement fund of $300,000 in 35 years at 9% interest.

b) To calculate the total interest earned, we can subtract the total amount deposited ($355.89 x 420 = $149,347.80) from the future value ($300,000):

\(Total interest = $300,000 - $149,347.80 = $150,652.20\)

So, the total interest earned over 35 years at 9% interest would be approximately $150,652.20.

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Given that triangle ABD= traingle CDB then;

side AB= DC and

side AD = BC

thus equate side AB and DC as;

7y =3y +20

collect like terms as;

7y-3y = 20

4y = 20

y= 20/4 = 5

Answer:

i want to drive alone but i am 15 and need to be 17

Step-by-step explanation:

Answer: No

Step-by-step explanation:

There's no noticeable pattern.

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

Compositions are binary operators between two functions: f - Former function, g - Latter function.

f ° g (x)

Where the input of the former function is the output of the latter function. By a brief observation, we find the following relationships in accordance with the two tables:

Case I

f(x):

0 → 1

g(x):

1 → - 2

Case II

f(x):

1 → 0

g(x):

0 → 1

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

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Answer:

5th term: -10

Step-by-step explanation:

To find the nth term in the sequence, you can substitute n into the equation:

d(n) = 6 - 4(n - 1)

Since we want the 5th term, we substitute 5:

d(5) = 6 - 4(5 - 1)

d(5) = 6 - 4(4)

d(5) = 6 - 16

d(5) = -10