Two boats leave the same dock in Cairo at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels four miles per hour. The southbound boat goes eight miles per hour. How many hours will it take them to be 66 miles apart?

The composite functions and their domains are listed as follows:

a) (f ∘ g)(x) = sin(2x/(x + 5)), domain is all real values except x = -5.

b) (g ∘ f)(x) = sin(2x)/(sin(2x) + 5), domain is all real values except x = -5 and the values of x for which sin(2x) + 5 = 0.

c) (f ∘ f)(x) = sin(sin(2x)), domain is all real values.

d) (g ∘ g)(x) = x/(6x + 5), domain is all real values except x = -5 and x = -5/6.

The composite functions are found applying the inner function as the input to the outer function, according to the rule presented as follows:

(f ∘ g)(x) = f(g(x)).

The domain is the set of values that respect all the input constraints of the inner function, of the outer function, and of the composite function.

For this problem, the functions are given as follows:

For item a, the inner function g is applied as the input to the outer function f, hence:

f(g(x)) = sin(2x/(x + 5))

The sine has no constrains, the fraction cannot have a denominator zero, hence the domain is composed by all real values except x = -5.

The other composite functions are listed as follows:

[tex]g(g(x)) = \frac{\frac{x}{x + 5}}{\frac{x}{x + 5} + 5} = \frac{x}{6x + 5}[/tex]

Domain is all real values except:

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The amount that hw must invest to achieve the goal when it will be compounded annualy is $68750

Given Information:

Principal Amount (P) = to be calculated

Rate of Interest (r) = 8 %

Time Period (t) = 6

Amount Received (A) = $110000

Number of times the interest is compounded quarterly (n) = 4

The Formula for the amount received when the principal (P) is compounded is given by,

[tex]A = P( 1 + \frac{r}{100n} )^{nt}[/tex]

Now, putting the values, we get:

[tex]110000 =P( 1 + \frac{8}{100*4} )^{4*6}[/tex]

P = $68750

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The length of i will be 531.3 inch when h is 300 inch and ∠G is 30° and ∠H is 29°.

When two straight lines or rays intersect at a shared terminal, an angle is generated. An angle's vertex is the common point of contact. The difference in direction between two lines or surfaces is defined as an angle. Angles are expressed in degrees. From a same point, the two hands draw separate sets of lines. Angle refers to these groups of lines that originate from a common point. Every minute, the two hands create various angles. In real life, one example of an angle is a clock.

Here,

∠I=180-(30+29)

=180-59

∠I=121°

h/sin H=i/sin I

300/sin 29=i/sin 121

i=300*sin 121/sin 29

i=531.3 inch

When h is 300 inches, G is 30 degrees, and H is 29 degrees, the length of I is 531.3 inches.

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Answer: y = 11

Step-by-step explanation:

Our problem: 72y - 126 = 522 + 144

1. Simplify 552 + 144 to 666

72y - 126 = 666

2. Add 126 to both sides

72y = 666 + 126

3. Simplify 666 + 126 to 792

72y = 792

4. Divide both sides by 72

y = [tex]\frac{792}{72}[/tex]

5. Simplify [tex]\frac{792}{72}[/tex] to 11

y = 11

the answer is a, -π/8

Answer:10

Step-by-step explanation:

1.20 + (4.75 × x) = 48.701.20 + 4.75x = 48.70Collect like terms 4.75x = 48.70 - 1.204.75x = 47.50Divide both side by 4.754.75x/4.75 = 47.50/4.75.x = 10

The point estimate for the lifetime of a certain type of battery is 120.1 hours.

Let X represent the battery's lifetime. X has a normal distribution with a standard deviation of 20 hours. The sample size is 50, and the average lifetime is 120.1 hours.

Calculating the mean of a sample drawn from the population yields a point estimate of the population's mean. The mean is calculated as the sum of all sample values divided by the number of values.

A single value estimate of a parameter is referred to as a point estimate. A sample mean, for example, is a point estimate of the population mean. An interval estimate provides a range of values within which the parameter is expected to fall. The population mean point estimate is sample mean and this is 120.1 hours.

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Complete question

The lifetime of a certain type of battery is known to be normally distributed with standard deviation =σ17 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 95% confidence interval for the mean lifetime for this type of battery. What is the point estimated?

The quantity of items tha must be made for supply to equal demand is 2050 items

Demand simply means a consumer's desire to buy goods and services without any hesitation and pay the price for it.

To calculate the unit of quantity Q that must be made for demand to be equal to supply, we equate the demand and supply equation.

From the question,

For Demand

From Supply,

When supply is equal to demand

Solve for P

Substitute the values of P into equation 1

Hence, the quantity of items tha must be made 2050 items.

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Step-by-step explanation:

it is totally simple : you need to put the x-value into every place of the x-variable, and then we calculate.

and then the same for the next x-value. and the next. ...

-2

-2×-2 + 9 = 4 + 9 = 13

0

-2×0 + 9 = 0 + 9 = 9

2

-2×2 + 9 = -4 + 9 = 5

4

-2×4 + 9 = -8 + 9 = 1

Answer:

(2x+1)(3x+4)

Step-by-step explanation:

6x² + 11x + 4

multiply the first and last term

i.e (6x²)(4) = 24x²

find two terms that multiplies to give 24x² and when added would give 11x

¶ 8x and 3x

Therefore; 6x² + 11x + 4

6x² + 8x + 3x + 4

2x(3x + 4) + 1(3x + 4)

Answer; (2x + 1)(3x + 4)

The value of h in the parallelogram is 4 feet

The area of the parallelogram = b × h

Where b is the base of the parallelogram

h is the height of the parallelogram

One side of the parallelogram = 6 feet

The second side of the parallelogram = 8 feet

If the base of the parallelogram is 6 feet

The area = 6 × h

If the base of the parallelogram is 8 feet

Then the area of the parallelogram = 8 × 3

= 24 square feet

In both cases the area will be equal, then the equation will be

6h = 24

h = 24 / 6

h = 4 feet

Hence, the value of h in the parallelogram is 4 feet

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True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

Given,

In the question:

To see the graph :

Mark all the statement that are true.

Now, According to the question:

From the graph,

Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".

Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.

Hence, True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

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Unit rate of (1 /5 barrel) / (1/2hour) is equals to (2/5) barrels /hour.

What is unit rate?

"Unit rate is defined as the representation of the ratio of the two different units with value of the denominator equals to 1."

According to the question,

Given,

1/5 barrel/1/2 barrel

⇒ (1/2) hour = (1/5) barrel

⇒ 1 hour = (2/5) barallel

⇒ (2/5) barrel per one hour.

Therefore,

Unit  rate of given value is rewritten as

2/5 barrel/hour

hence option b is correct.

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Your question is incomplete. Please find the missing content below.

Rewrite 1/5 barrel 1/2 hour as a unit rate.

A. 2 1/2 barrel/hour

B. 2/5 barrel/hour

C. 10 barrels/hour

D. 1/10 barre./hour

Answer:

$235.20

Step-by-step explanation:

the tax :

[tex] \frac{12}{100} \times 210 = 25.20[/tex]

total cost :

$210 + $25.20 = $235.20

The numbers arranged in increasing order are D < C < A < E < B.

We are given a set of five numbers. The numbers are represented by the variables A, B, C, D, and E. The numbers need to be calculated. The numbers are solved below.

A = 2*1/2*4*1/6 = 2/3 = 0.667

B = 12*128 = 1,536

C = 1*8*1/5² = 8/25 = 0.32

D = 4*(-1)/2*(-1)*8*(-1) = -16

E = 3*√2*4*1/4 = 3√2 = 4.24

We need to arrange the numbers in increasing order. Ascending order refers to the arrangement of numbers in increasing order, from least to greatest. The numbers in ascending order are given below :

-16 < 0.32 < 0.667 < 4.24 < 1,536

The increasing order of the corresponding variables is : D < C < A < E < B.

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The sample space in regard to the vacations is 24

Choice of 3 destinations: Cozumel (C), Jamaica (J), or Grand Caymans (G) =

3C1

A choice of 2 types of rooms: balcony (B) or inside view =  2C1

And a choice of 4 types of excursions: water sports (W), horseback riding (H), parasailing (P), or zip-lining (Z) = 4C1

Choosing only one of each, the sample space in regard to the vacations

Sample space = choice of destination x choice of room x choice of water sports

= 3C1 x 2C1 X 4C1

= 3 x 2 x 4 = 24

Therefore,  the sample space in regard to the vacations is 24

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The expected value of their repair costs is $41.50.

Given the probability of failure as 0.5%, this can be illustrated as 0.005.

The cost of repair is given as $300.

The expected value of the company will be:

= Earnings - [(Cost × P(failure)]

= 43 - (300 × 0.005)

= 43 - 1.50

= 41.5

The value is $41.50.

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Complete question

company estimates that 0.5% of their products will fail after the original warranty period but within 2 years of the purchase, with a repair cost of $300. The company offers an extended two-year warranty.

If a consumer does not purchase the extended warranty, then the consumer will need to pay $43 for any necessary repairs. What is the expected value of their repair costs?

The coordinates of T' are, T'(-3, -1).

What is rotation?

A rotation is a transformation in which each point of a preimage is turned through a predetermined angle and direction around a fixed point. The center of rotation is the fixed point. The term for the amount of rotation is the angle of rotation, and it is expressed in degrees. Measure the specified angle in the anticlockwise direction using a protractor.

Given: Triangle RST has vertices R(1, 1), S(1, 4), and T(3, 1).

We have to find the coordinates of T' after counterclockwise rotation of 180°.

Since, The rule for a rotation by 180° about the origin is (x, y) → (−x, −y).

So, the coordinates R(1, 1), S(1, 4) and T(3, 1) changes to R'(-1, -1), S'(-1, -4) and T'(-3, -1).

Therefore, the coordinates of T' are T'(-3, -1).

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Answer:

Step-by-step explanation:

the correct answer is A.

because if Kay has 5 pencils and it is given to Merry 1, it means that Kay still has 4 pencils.

If Clara lives 12 floors above Darren, Clara lives on the 16 floor while Darren lives on the 4 floors.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Given that Darren and Clara reside in a towering structure, this is expected. Twelve stories above Darren, Clara resides. One day, Darren climbed the stairs from his apartment to Clara's and went to see her. He was halfway up, on the eighth floor.

Suppose Darren and Clara live on x and y number of floor respectively.

If Clara lives 12 floors above Darren.

x-y=12

If in halfway he is on the 8th floor the total number of floors in the building will be 16.

As a result, we can say that Clara lives on the 16 floors while Darren lives on the 4 floor.

Thus, if Clara lives 12 floors above Darren, Clara lives on the 16 floors while Darren lives on the 4 floors.

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Answer:

The y-intercept is when $x=0$ so $y=32\frac{ft}{s}*0-\frac{1}{2}*9.8*0^2=0$, so the ball starts on the ground. The maximum height is when $v=0$, so $0=32\frac{ft}{s}-9.8t$ and solving for $t$ we get $t=\frac{32}{9.8}=3.265s$, and plugging this back in for $y$ we get $y=32\frac{ft}{s}*3.265s-\frac{1}{2}*9.8*3.265^2=156.205 ft$. So the ball will be at its maximum height of 156.205 ft at 3.265 seconds.

Step-by-step explanation:

The $y$-intercept is $-1$.  The maximum height of the baseball is when $y=0$; that is when $x=\ln(4)$.  Here is a sketch of the path.

From the $y$-intercept, we see that the baseball starts at height $y=-1$.  It reaches a maximum height at $x=\ln(4)$; that is, $y=0$.  From there, it falls and reaches the ground at $x=2\ln(4)$; that is, $y=-1$ again.

Answer:

y(3xy-2x+1)

Step-by-step explanation:

I'm pretty sure it'd be y(3xy-2x+1).

Answer:

3xy²-2xy +y

Step-by-step explanation:

15x²y³-10x²y² +5xy² = 5xy(3xy²-2xy +y)

then

5xy(3xy²-2xy +y) / 5xy = 3xy²-2xy +y

Answer:

1 and 3

Step-by-step explanation:

discriminant = 16 - 4 * 1 * 3 = 16 - 12 = 4

x1 = (4 + √4)/2 = (4+2)/2 = 6/2 = 3

x2 = (4 - √4)/2 = (4-2)/2 = 2/2 = 1

The side x of the right triangle is 235.72 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be found using trigonometric ratios or Pythagoras theorem depending on the sides and angles given.

Hence, let find the value of x in the combine right triangles.

Therefore,

tan 28 = opposite / adjacent

tan 28 = 105 / l

cross multiply

l = 105 / tan 28

l = 105 / 0.53170943166

l = 197.479781832

l = 197.50

tan 70 = 105 / a

a = 105 / tan 70

a = 38.2168804325

a = 38.22

Therefore,

x = 197.50 + 38.22

x = 235.72 units

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a) The maximum height of the ball is 100 feet.

b) The velocity of the ball on its way up is +16 feet per second.

c) The velocity of the ball on its way down is - 16 feet per second.

A free fall is an uniformly accelerated motion experimented by a particle due to the effects of gravity. The position of the ball (s) in time (t), in seconds, is described by a quadratic equation.

a) First, we find the maximum height reached by the ball:

s(t) = 80 · t - 16 · t²

16 · t² - 80 · t + s(t) = 0

Then, by using the discriminant:

(- 80)² - 4 · 16 · s(t) = 0

64 · s(t) = (- 80)²

s(t) = 100 ft

b) Second, find the function velocity by derivatives:

v(t) = 80 - 32 · t

Third, find the time related to the position s(t) = 96 ft:

s(t) = 80 · t - 16 · t²

100 = 80 · t - 16 · t²

16 · t² - 80 · t + 96 = 0

Then, by quadratic equation:

t = 3 s or t = 2 s.

Fourth, evaluate the function velocity:

v(2) = 80 - 32 · 2

v(2) = 16

v(3) = 80 - 32 · 3

v(3) = - 16

The velocity of the ball when s(t) = 96 ft on its way up is 16 feet per second.

c) The velocity of the ball when s(t) = 96 ft on its way down is - 16 feet per second.

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The distance it should take my classmate to ride the bicycle at each speed to burn 575 calories would be = 13.2m for first speed and 11.3m for the second speed.

A fitness program is defined as the program that is adequately organised for the purpose of maintaining proper healthy calories.

The period he plans to ride the bicycle for a day = 60minutes.

For the first speed,

8 cal/ min = 11mph

To convert to hour,

8 × 60 =480

He burns 480cal per hour in 11mph speed

If 480cal = 11 mph

575 cal = X

make X the subject of formula;

X = 575×11/480

X = 6325/480

X = 13.2 m

For the second speed;

12.75 cal/ min = 15mph

To convert to hour,

12.75 × 60 =765cal

He burns 765cal per hour in 11mph speed.

If 765cal = 15mph

575 cal = y

make y the subject of formula;

y = 575 × 15/765

y = 8625/765

y = 11.3 m

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