How do you write 7.68 x 10^3 In standard form

Answer:

Step-by-step explanation:

39 !!!!!

Answer:

DE

Step-by-step explanation:

D)9x + 6y = 3(3x + 2y)

E)9a + 6b + 3c = 3(3a + 2b + c)

there have the same concept

3*3x equals 9x and 3*3a is 9a

Composing f(x)=2x-8 and g(x)=1/2x+4 results in the identity function, f(g(x)) = x.

To compose the two functions, we substitute g(x) into f(x) in place of x:

f(g(x)) = 2(g(x)) - 8

= 2(1/2x + 4) - 8

= x + 8 - 8

= x

Therefore, composing the two functions results in the identity function, f(g(x)) = x.

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Step-by-step explanation:

Let's call the average speed of the tortoise "t" (in meters per hour) and the average speed of the hare "h" (in meters per hour).

From the problem, we know that:

The tortoise leaves 8 minutes before the hare, so they have a 4-minute head start.

The hare crosses the finish line 4 minutes before the tortoise, so they have a 4-minute lead.

Therefore, the total time it takes for the hare to finish the race is 8 minutes less than the time it takes for the tortoise to finish the race. Let's call this time difference "dt".

The distance the hare runs is 21 meters, and the distance the tortoise runs is also 21 meters, so we have:

h * dt = 21 - t * (dt + 4 minutes)

To solve for the average speeds "t" and "h", we need to convert everything to units of hours. Let's convert 4 minutes to hours:

4 minutes = 4/60 hours = 1/15 hours

So, we can now rewrite the equation in terms of hours:

h * dt = 21 - t * (dt + 1/15 hours)

Rearranging and solving for t, we find:

t = (21 + h * dt) / (dt + 1/15)

Now, the hare runs 0.5 meters per hour faster than the tortoise, so:

h = t + 0.5

Substituting h = t + 0.5 into the equation for t, we get:

t = (21 + (t + 0.5) * dt) / (dt + 1/15)

Solving for t, we find:

t = 40/3 meters per hour

Finally, we can find the average speed of the hare by using h = t + 0.5:

h = 40/3 + 0.5 = 40/3 + 30/60 = 40/3 + 30/3 / 60 = 70/3 meters per hour

So the average speed of the tortoise is 40/3 meters per hour, and the average speed of the hare is 70/3 meters per hour

Answer:

3/2

Step-by-step explanation:

Simplify the following:

((4 + 1/5)×5)/14

((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:

((4 + 1/5)×5)/14

Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:

(((5×4)/5 + 1/5) 5)/14

5×4 = 20:

((20/5 + 1/5)×5)/14

20/5 + 1/5 = (20 + 1)/5:

(((20 + 1)/5)×5)/14

20 + 1 = 21:

(21/5×5)/14

21/5×5 = (21×5)/5:

((21×5)/5)/14

((21×5)/5)/14 = (21×5)/(5×14):

(21×5)/(5×14)

(21×5)/(5×14) = 5/5×21/14 = 21/14:

21/14

The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:

Answer:  3/2

Answer:

2

Step-by-step explanation:

2

Therefore, integral specific function f(n) you're working with will determine which interval [a, b] you choose, and there may be several distinct methods for expressing the limit as a definite integral.

A definite integral is the area beneath a curve between two defined boundaries. An is the lower limit and b is the upper bound, and baf(x)dx represents the definite integral that is the function of two variables, defined to reference the x-axis.

Here,

lim n → ∞ f (n)

You can define this limit as a definite integral over the interval [a, b], where a and b are some constants that rely on n, where f(n) is a function of n, by saying:

For , f(x) = lim n → ∞ f(n) for a ≤ x ≤ b

The maximum can then be stated as follows:

=> lim n → ∞ f(n) = ∫a^b f(x) d

The specific function f(n) you're working with will determine which interval [a, b] you choose, and there may be several distinct methods for expressing the limit as a definite integral.

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Answer:

Step-by-step explanation:

The total number of tosses is 9

The number of successes is 3

P(heads 3 times ) = 3/9

P(heads 3 times) = 1/3

Answer:

Agree

Step-by-step explanation:

Just copy and paste (without quotations): "I agree because r < -5 is just a flipped inequality of -5 > r. In other words, 'r is less than -5' is the same as '-5 is greater than r'."

Answer:

80

Step-by-step explanation:

To find the value of n when d = 3, we can use the given inverse proportionality relationship between n and d²:

n ∝ 1/d²

This can also be written as:

n = k / d²

where k is a constant of proportionality.

We are given that n = 5 when d = 12. Plugging in these values into the equation, we get:

5 = k / 12²

To solve for k, we can multiply both sides of the equation by 12²:

5 * 12² = k

k = 720

Now that we have the value of k, we can use it to find the value of n when d = 3:

n = k / d²

n = 720 / 3²

n = 720 / 9

n = 80

So, the value of n when d = 3 is 80.

Answer:

extra and not necessary stuff

Step-by-step explanation:

stuff like extra clothes and eating out a lot ...

when you do not put in the money for extra stuff in collage can keep you on track by being reminding you you don't have money for it

The option that can not be included in the cost of college is:

The income you would have earned had you not gone to college.

Option C is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

a)

The cost of tuition.

This is a part of the cost of college.

b) The cost of books required for college classes.

This is a part of the cost of college.

c) The income you would have earned had you not gone to college.

This is not a part of the cost of college.

d) The cost of rent for your off-campus apartment.

This is a part of the cost of college.

Thus,

The income you would have earned had you not gone to college is not a part of the cost of college.

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The complete question is:

When calculating the cost of college, which of the following should you probably not include?

a) The cost of tuition,

b) The cost of books required for college classes,

c) The income you would have earned had you not gone to college,

d) The cost of rent for your off-campus apartment.

Answer:

x=42

Step-by-step explanation:

step 1: multiply 3 to both sides of the equation to isolate x

then you get x=14x3=42

x=42

Answer:

X=42

Step-by-step explanation:

14 * 3= 42

14 = x/3

14= 42/3

divide

14=14

The 11th term of the geometric sequence 1, 4, 16,... is 4¹⁰.

A sequence is a grouping of objects in a particular order that permits repetitions. It has members, just like a set does. The length of the sequence is determined by the number of items.

Consider the geometric sequences 1, 4, 16......

For a geometric sequence a, ar, ar²,.....

Where a is the first term, and r is the common ratio of the sequence.

Then for the sequence 1, 4, 16,...

a = 1 and r = 4

The nth term of a geometric sequence is given as:

aₙ = ar⁽ ⁿ ⁻ ¹⁾

Therefore, the 11th term of the sequence will be:

a₁₁ = 1 × r¹¹ ⁻ ¹

a₁₁ = (4)¹⁰

a₁₁ = 4¹⁰

Hence, the 11th term of the sequence is 4¹⁰.

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Answer:

A equilateral

Step-by-step explanation:

hey, its equilateral because all sides of the triangle are the same length

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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The tangent at any point of a circle is perpendicular to the radius through the point of contact by showing that line PQ coincides with the radius OP.

Let us assume that we have a circle with center O and radius r.

Let P be any point on the circle .

And let Q be the point of intersection of the tangent to the circle at P and the radius OP,

To prove that PQ is perpendicular to OP.

First, we observe that OP is a radius of the circle and therefore its length is r.

Since PQ is tangent to the circle at point P,

It is perpendicular to the radius drawn from the center of the circle to point P.

As the tangent to a circle is perpendicular to the radius drawn to the point of contact.

This implies, angle QOP is a right angle.

Next, triangle OPQ is a right triangle with right angle at Q.

By the Pythagorean Theorem, we have,

OP²= OQ² + PQ²

Substituting r for OP and noting that OQ = r since Q is on the radius. we have,

⇒ r² = r²+ PQ²

Subtracting r² from both sides, we get,

⇒ PQ² = 0

This implies that PQ = 0,

In other words, that point Q coincides with point P.

PQ is a line that coincides with the radius OP.

And since angle QOP is a right angle, we can conclude that PQ is perpendicular to OP.

Therefore, it is proved that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

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The above question is incomplete, the complete question is:

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

The distance from the point to the parametric line is given as follows:

5 units.

The first step is obtaining the vector from the line L(0, 5 + 3t, 2 + t) to the point P(5,5,2), as follows:

P - L = (5, -3t, -t).

The direction vector of the line is given as follows:

(0, 3, 1).

The dot product of the vector with the direction of the line is of zero, hence:

(5, -3t, -t)(0, 3, 1) = 0

-9t - t = 0

-10t = 0

t = 0.

Thus the point on the line which we will use to obtain the distance is of:

(0, 5 + 3(0), 2 + 0) = (0,5,2).

The the distance is obtained applying the formula for the distance between two points as follows:

Distance = square root [(5 - 0)² + (5 - 5)² + (2-2)²] = 5 units.

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The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Answer:

Step-by-step explanation:

a. x is negative: x < 0

b. y is nonnegative: y ≥ 0

c. q is less than or equal to π: q ≤ π

Answer:

a.

2. x < 0

b.

2. y ≥ 0

c.

5. q ≤ π

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

a. The statement "x is negative" means that x is less than 0. Mathematically, we can represent this as x < 0.

b. The statement "y is nonnegative" means that y is greater than or equal to 0. Mathematically, we can represent this as y ≥ 0.

c. The statement "q is less than or equal to π" means that the value of q is either equal to π or less than π. Mathematically, we can represent this as q ≤ π.

Answer:

which question ?

Step-by-step explanation:

Using the uniform distribution, the standard deviation of the timeout is of 34.64 seconds.

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The standard deviation is:

\(S = \sqrt{\frac{(b - a)^2}{12}}\).

For this problem, the bounds are:

a = 0, b = 120.

Hence the standard deviation is found as follows:

\(S = \sqrt{\frac{(120 - 0)^2}{12}} = 34.64\).

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Answer:

convert 13.025 to base 10

Answer: An array is a collection of items of same data type stored at contiguous memory locations.

Step-by-step explanation: There you go dude happy to help

Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

Answer:

\(D = 72.2\ yd\)

Step-by-step explanation:

Given

\(Length\ (L)= 58\ yd\)

\(Width \ (W)= 43\ yd\)

Required

Determine the diagonal (D)

The relationship between D, L and W can be gotten using Pythagoras Theorem:

\(D^2 = L^2 + W^2\)

Substitute values for L and W

\(D^2 = 58^2 + 43^2\)

\(D^2 = 3364 + 1849\)

\(D^2 = 5213\)

Take Square root of both sides

\(D = \sqrt{5213}\)

\(D = 72.2011080247\)

\(D = 72.2\ yd\) (Approximated)