find the domain of the vector function. (enter your answer in interval notation.) r(t) = t − 1 t 1 i sin(t) j ln(81 − t2) k

For the binomial distribution, √npq formula finds the standard deviation.

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√10.24 belongs to the set of rational numbers.

Here we are given the number √10.24.

Now first we see that √10.24

= 3.2

Now as we can see that there is a number other than 0 after the decimal point here. Hence the above number cannot be classified as a natural number, a whole number, or an integer.

However, on converting 3.2 into the fractional form, we see that

3.2 = 32/10

reducing this to smallest form we get

16/5

Here we could easily represent 3.2 in the form of p/q where q is not equal to 0.

Hence p/q is a rational number.

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To write its equation in the form y is a(xh)2+k and then determine the value of the coefficient a.

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Answer:

Below

Step-by-step explanation:

Quarterly interest = .01 / 4 = .0025

periods = 4 x 3 yrs = 12

FV = 56500(1 + .0025)^12 = $ 58218 . 50

Answer:

21%

Step-by-step explanation:

Step-by-step explanation:

1) divide 134 by 106

106/134 is about 0.79

2) Multiply by 100 to find the percentage

0.79(100)= 79%

3) Subtract 79% from 100% to find the percentage difference

100%-79%= 21%

Therefore, the percent of change between 134 and 106 is 21%.

Answer:

Both are horizontal lines.

Step-by-step explanation:

See the graph.  

Y = 9  No matter what x is, y will be 9

Some points would be

(-1,9 (0,9) (1,9)

The second statement would be the equation

y = 1  

No matter what x is y is 1

Some points would be

(-1,1) (0,1) ( 1,1)

Answer:

true i think

Step-by-step explanation:

The value of the numerical expression -(5⁻⁴)(5²) will be - 1/25. Then the correct option is C.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ -(5⁻⁴)(5²)

Simplify the expression, then we have

⇒ -(5⁻⁴)(5²)

⇒ -(1/5⁴)(5²)

⇒ -(5² / 5⁴)

⇒ - 25 / 625

⇒ - 1/25

The value of the numerical expression -(5⁻⁴)(5²) will be - 1/25. Then the correct option is C.

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The required coordinate pair for W" is (2,-3)

When a point is reflected over axes, its position changes and sign of coordinates also change.

Given that, Point W is located at (-2, 3) on a coordinate plane. Point W is reflected over the x-axis to create point W'. Point W' is then reflected over the y-axis to create point W".

When a point is reflected over the x-axis, then we know,

(x, y) = (x,-y)

W(-2,3) = W (−2,−3)

And,

When a point is reflected over the y-axis, then we know,

(x, y) = (-x, y)

Therefore, W'(-2,-3) = W" (2,-3)

Hence, the coordinates of the point W" are (2,-3)

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Answer:

Step-by-step explanation:

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(a) The probability that there are no clients in the system is 0.3333

(b) The average number of customers waiting is 1.33

(c) The average number of customers in the system is 2

(d) The average time a customer spends waiting is 3.33 min

(e) The average time a customer spends in the system is 5 min

(f) The probability that arriving customers will have to wait for service is 0.6667.

Given that,

Customers of Willow Brook National Bank can conduct financial transactions at a drive-up teller window without getting out of their cars. On weekday mornings, the drive-up teller window receives 24 customers each hour, or 0.4 customers per minute, arriving at random.

Arrival rate λ = 24 customers per hour or 0.4 customers per minute

Service rate  μ​ = 36 customers per hour or 0.6 customers per minute

Utilizing the single-server drive-up bank teller operation previously mentioned, establish the following system operational characteristics:

(a) The probability that there are no clients in the system is

P₀ = 1 - λ /μ

= 1 - (24/36)

= 1/3

= 0.3333

(b) The average number of customers waiting

Lq = λ²/ [μ(μ - λ)]

= 242/[36×(36-24)]

= 1.33

(c) the average clientele using the system.

L = Lq + λ/μ  

= 1.33 + (24/36)

= 2

(d)the average length of time a consumer must wait.

Wq = λ/ [μ(μ - λ)]

= 24/[36×(36-24)]

= 0.0555 hr

= 3.33 min

(e) The average time a customer spends in the system

W = Wq + 1/μΧ

= 0.0555 + (1/36)

= 0.0833 hr

= 5 min

(f) the probability that clients who arrive will have to wait for service.

= 1 - P₀

= 1 - 0.3333

= 0.6667

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Answer: $1632 is his total annual premium for health insurance

Step-by-step explanation:

85*.60=$51

His employer pays $51 per month

you would multiply 51 by 12 to get the employers amount and them multiply 85 by twelve then you would add the two to get the total which should be his annual premium amount

$51*12 months=612

$85*12=1020

1020+612=1632

Answer: 9 weeks

Step-by-step explanation:

Let x be the number of weeks

So the equation will be

1497 - 83x < 750

Subtract 1497 on both sides

-83x < -747

x < 9

So the answer is 9 weeks

The distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85 is  479.97

The base cost of the rental is said to be 49.95 dollars + 1.19 per mile

The cost of the gas is $3.89. The mileage of the truck is 18 miles

There would be an extra cost of

$3.89/18 per mile.

= 0.216111

In x miles we would have the equation that is written as:

C(x) = 49.95 + (1.19 + 0.21611)x

C(X) = $724.85 this is the total cost. Hence we would have

$724.85 =  49.95 + 1.19x + 0.21611x

$724.85 -   49.95 = 1.40611x

674.9 = 1.40611x

divide through by 1.40611

674.9 / 1.40611 = x

x = 479.97

The distance traveled is  479.97

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The simplified expression of the statement is -41.66

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

negative 17 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 4 squared minus 4 and 7 tenths

Rewrite properly

So, we have

(-17 - 3.7 + 9.15)/5 * 4² - 4.7

Evaluate the sum and the difference in the expression

So, we have

-11.55/5 * 4² - 4.7

Evaluate the exponent and the quotient

-2.31 * 16 - 4.7

So, we have

-36.96 - 4.7

Evaluate

-41.66

Hence, the solution is -41.66

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If an object travels according to a distance function, d(t), and d' (c) < 0, then at t = c we know that the velocity is positive.

The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function depending on one of its variables. The most prominent example is velocity, which is the rate of change of displacement with respect to time. Differentiation is used to calculate the rate of change of values in real time. For example, if we want to find the velocity of an automobile, we may use differentiation.

Here,

if first derivative is < 0 then, the value is positive.

If an item moves according to a distance function, d(t), and d' (c) <0, we know that the "velocity is positive" at t = c.

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A valid conclusion is that;

Inferences can be made about all the golf balls produced on that day, and the conclusion can be made that new-style golf balls travel farther than the original-style of golf ball for this golf pro.

An inference is defined as a conclusion that is reached based on certain pieces of evidence

In this sample research, we can see that randomization and replication conditions  are met. This s because the balls are randomly selected and as such, the distance of the new ball can be compared to the distances of the original ball.

Therefore, a valid conclusion is written as;

Inferences can be made about all the golf balls produced on that day, and the conclusion can be made that new-style golf balls travel farther than the original-style of golf ball for this golf pro.

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Answer: wait how much was her allowance

Step-by-step explanation:

As per the Pythagoras theorem, the ratio of the short side to the long side of this rectangle is (√5 - 1)/ 2

In math Pythagoras theorem is defined as the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

Here we have given that the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal.

And we need to find is the square of the ratio of the short side to the long side of this rectangle

While we looking into the given question we have identified that the short side of the rectangle be a and let the long side of the rectangle be b.

Therefore, the diagonal, according to the Pythagorean Theorem, is

√(a²+b²)

Now we can write the equation:

a / b = b /√ a² + b²

Then we have to find the square of the ratio of a to b.

Let us consider the answer, be k.

When we squaring the above equation,

a²/ b² = b² / a² + b² = k

When we solve this one then we get the value of  k = 1.

Now we have to Multiply each side of the equation by k,

=> k² = 1 - k.

And then adding each side by k,

k² + k − 1 = 0.

Now, we have to Solving for k using the Quadratic Formula,

= > k = -1 ± √[1² − 4(1)(−1)] / 2

=> k = -1±√5/2

As we know that the ratio of lengths and diagonals of a rectangle cannot be negative.

Therefore, the resulting value is √5 - 1/2

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Rev is seeking independent contractors with extensive experience in audio transcription and translation. After the projects are finished, they frequently grade the work of the employees. One needs to be quick on the keyboard, attentive, comprehend appropriate punctuation, have a solid command of language and spelling, be able to pick up the format of the transcription, and be a critical thinker in order to work with them on a consistent basis. These are the characteristics Rev is seeking for in a freelancer.

Rev.com generally serves as a liaison between businesses and freelancers. One of the jobs that may be done from home carefully screens all of its applicants. The business ensures that they only employ the best individuals for their workforce. It strives to provide independent contractors with a setting where they may develop and display their talents. They can socialize with other independent contractors as a result.

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The expressions have, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given that the expression ;

T(h) = h (2h + 1)²(h - 11)² and D(x) = 3x⁴ - 27x²

Now for the first expression T(h) = h (2h + 1)²(h - 11)²

Simplifying, the expression;

T(h) = h (2h + 1)²(h - 11)²

Degree of the highest polynomial of above expression is 5.

To find end behavior, we will find the factors of expression;

T(h) = h (2h + 1)²(h - 11)²

Here, h = 0,  (2h + 1)² = 0 , (h - 11)²= 0

h= 0 , h = -1/2 , -1/2 and h = 11 , 11

Multiplicity of -1/2 is 2 and 11 is 2.

End behavior, given expression has 2 pair of repeated roots.

And  (2h + 1)² ≥ 0 , (h - 11)²≥ 0

So the expression behavior depends on the term h alone.

And also it is an even polynomial.

So the graph of expression varies to infinity term for both positive and negative.

Zeros of the polynomial are  h = 0, -1/2 , -1/2, 11 , 11.

Sketch 1,

Now for the second expression D(x) = 3x⁴ - 27x²

Simplifying, the expression;

D(x) = 3x⁴ - 27x²

Degree of the highest polynomial of above expression is 4.

To find end behavior, we will find the factors of expression;

D(x) =3x²(x+3)(x−3)

Here, x = 0,0, 3,-3.

Multiplicity of 0 is 2.

End behavior, it is an odd polynomial. So the graph of expression varies to positive infinity.

Sketch 2,

Therefore, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

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Answer: which triangle ;/

Step-by-step explanation:

The expected value of x for the awarded 3 points for each coin that lands with heads faceup is 27/8.

In this instance, we are informed that:

The probability of each of them is calculated as:

Situation 1: No heads

That implies that all three coins must land on the tail.

Thus, there is only one method to accomplish this. While the whole range of potential outcomes is;

= 2x 2x 2

= 8

via the product rule (because each coin has two alternative outcomes).

The result is:

P(x =0) = 1/8

Situation 2: One head

Single head means three points, or X = three.

Total outcomes possible = 8,

Single head can occur in 3 different ways, as other two needs to be strictly tails.

Thus,

P(x = 3) = 2/8

Situation 3: Two heads

Two heads equals 3+3 = 6.

X = 6

8 outcomes are possible in total.

Single tail means two heads. Three separate scenarios can lead to a single tail.

Therefore,

P(x = 6) = 2/8

Situation 4: Three heads

Three heads signifies that X = 9 or 3+3+3 = 9 points.

8 outcomes are possible in total.

Three heads means there is only one way to do it and no tail.

Thus,

P(x = 9) = 1/8

As a result, the expectation of X is determined as follows:

E(x) = 0. 1/8 + 3. 2/8 + 6. 2/8 + 9. 1/8

E(x) = 27/8

Therefore, 27/8 is the expected value of X.

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Part (c) is the correct option i.e. The total dealer's cost is $16588.36.

What is Percentage ?

Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given, Cost paid for car's options = 82 % $3,098 = $2540.36

           Cost paid for base price = 85 % $15,480 = $13158.

           Destination charge = $890

∴ The total dealer's cost will be :

 = Cost paid for car's options +  Cost paid for base price +  Destination charge

=  $2540.36 + $13158 + $890

= $16588.36.

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Answer: $164

Step-by-step explanation:

25*7=175

175+12.5

226.50-187.50

5*25=125+39

Jones family payed $164

Answer:

1/3 * [tex]4\pi[/tex] * h = 207, h = 155.25[tex]\pi[/tex]

Step-by-step explanation:

Since we know the area of the base is [tex]4\pi[/tex], that means the volume of the cone is:

1/3 * [tex]4\pi[/tex] * h

If we substitue, we get:

1/3 * [tex]4\pi[/tex] * h = 207

(This is the answer! If you want to solve, go below)

Now, we just solve

[tex]4\pi\\[/tex] * h = 621

h = 621/[tex]4\pi\\[/tex]

h = 155.25[tex]\pi[/tex]

Answer:

[tex]\sqrt{4100}[/tex]

Step-by-step explanation:

Step 1 Substitute Using Pythagorean Theorem:

x = [tex]\sqrt{50^2+40^2}[/tex]

Step 2 Solve:

[tex]50^2=2500[/tex]

[tex]40^2=1600[/tex]

Therefore,

[tex]\sqrt{50^2+40^2}=\sqrt{4100}[/tex]

The number of red balls Luke has at the start is 47.

blue ball per day = 2

red ball per day = -3 ('-' ve sign as he is loosing them)

let the number of red balls be represented by r

let the number of blue balls be represented by b

after 5 days

b+ 10 = r -15 -(i)

After 9 days

b + 18 =2(r-27)-(ii)

subtracting (i) from (ii)

b + 18 - b - 10 = 2r - r - 54 +15

8 = r - 39

r = 39 + 8

r = 47

The number of red balls Luke has at the start is 47

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The interpretation of -600 is (a) the slope of the function and the change in distance remaining, in meters per minute, of riding the bus

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

f(t) = -600t + 12000

A linear equation is represented as

y = mx + c

Where

Slope = m

When the equations are compared, we have

m = -600

This means that

Slope = -600

So, the interpretation of -600 is the slope

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