How much greater is √47 than √37?
A. Exactly 1
B. Exactly 10
C. A little less than 1
D. A little more than 3

Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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First you add 3x+x because they are like terms.

3x+x-7=10  

Your New Simplified Equation:

4x-7=10  

Now, you have to take out the -7 by adding a positive 7. Also you                          have to add +7 on the other side so add 7 to 10.

Your New Simplified Equation:

4x=17      Now, you divide both sides by 4.

Your New Simplified Equation:

x= 17/4 So, that's your answer :)

The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

What is the domain and range?

The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.

The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.

The range of a function refers to the set of all possible output values, or y-values.

To find the domain and range of functions and represent them in different formats.

To find the domain and range of a function:

The domain refers to the set of all possible input values (x-values) for the function.

The range refers to the set of all possible output values (y-values) for the function.

To represent the function as a table, you would list the input-output pairs. For example:

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

To represent the function as a mapping, you would indicate the correspondence between the input and output values.

For example:

-3     ->   -4

-1     ->     2

0     ->     0

-3    ->     5

2     ->     4

To represent the function as a graph, The x-values would be on the horizontal axis, and the y-values would be on the vertical axis.

The points (-3, -4), (-1, 2), (0, 0), (-3, 5), and (2, 4) would be plotted accordingly.

Hence, The domain and range are the set of x and values of the function are in the table.

the function as a table,

Input (x) | Output (y)

-3         |        -4

-1          |         2

0         |         0

-3         |         5

2         |         4

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The calculated volume of the model space is 1657.92 cubic inches

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

The model space made from:

The volume of the model space is calculated as

Volume = Cone + Cylinder + Hemisphere

Using the volume formulas, we have

Volume = 1/3πr²h + πr²h + 2/3πr³

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

Volume = 1/3 * 3.14 * 6² * 8 + 3.14 * 6² * 8 + 2/3 * 3.14 * 6³

Evaluate

Volume = 1657.92

Hence, the volume of the model space is 1657.92 cubic inches

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Answer: A

Step-by-step explanation:

Answer:

2(2x+1)

Step-by-step explanation:

4x and 2 are both divisible by 2.

The convolution integral is a mathematical technique used to find the inverse Laplace transform of a function. In this case, we have a function f(s) that we want to find the inverse Laplace transform of. Let's call the inverse Laplace transform of f(s) F(t).

To use the convolution integral, we first need to express f(s) as a product of two Laplace transforms. Let's call these Laplace transforms F1(s) and F2(s):

f(s) = F1(s) * F2(s)

where * denotes the convolution operation.

Next, we use the convolution theorem to find F(t):

F(t) = (1/2πi) ∫[c-i∞,c+i∞] F1(s)F2(s)e^(st)ds

where c is any constant such that the line Re(s)=c lies to the right of all singularities of F1(s) and F2(s).

In our case, we need to find the inverse Laplace transform of a specific function. Let's call this function F(s):

F(s) = 1/(s^2 + 4s + 13)

To use the convolution integral, we need to express F(s) as a product of two Laplace transforms. One way to do this is to use partial fraction decomposition:

F(s) = (1/10) * [1/(s+2+i3) - 1/(s+2-i3)]

Now we can use the convolution theorem to find the inverse Laplace transform of F(s):

f(t) = (1/2πi) ∫[c-i∞,c+i∞] F1(s)F2(s)e^(st)ds

where F1(s) = 1/(s+2+i3) and F2(s) = 1/(10)

Plugging in these values, we get:

f(t) = (1/2πi) ∫[c-i∞,c+i∞] (1/(s+2+i3))(1/(10)) e^(st)ds

Now we can simplify this integral and evaluate it using complex analysis techniques. The final answer will depend on the value of c that we choose.

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Use the convolution theorem to find the inverse Laplace transform of each of the following functions. a. F(S) = S/((S + 2)(S^2 + 1)) b. F(S) = 1/(S^2 + 64)^2 c. F(S) = (1 - 3s)/(S^2 + 8s + 25) Use the Laplace Transform to solve each of the following integral equations. a. f(t) + integral^infinity_0 (t - tau)f(tau)d tau =t b. f(t) + f(t) + sin (t) = integral^infinity_0 sin(tau)f(t - tau)d tau: f(0) = 0 Find the Inverse Laplace of the following functions. a. F(t) = 3t^ze^2t b. f(t) = sin(t - 5) u(t - 5) c. f(t) = delta(t) - 4t^3 + (t - 1)u(t - 1)

The probability that he will take one patterned and one plain T- shirt is given as follows:

p = 7/18.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in this problem are given as follows:

Hence the probability is given as follows:

p = 7/9 x 2/8 + 2/9 x 7/8

p = 28/72

p = 14/36

p = 7/18.

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Answer:

alternate interior angles

Step-by-step explanation:

We are looking at angles <3 and <6

which are on opposite sides of a transversal (line crossing through 2 parallel lines)

meaning that those 2 angles are congruent and are alternate interior angles are they are on the inside of this figure.

*Can we see the answer choices?  I'm not sure what they are, meaning I cannot fully help you*

Hope this helps a little! :)

Step-by-step explanation:

We know that,

\(\boxed{\sf \sin θ = \dfrac{Opposite \: side}{Hypotenuse}}\)

\(\longmapsto \sf \sin 30^{\circ} = \dfrac{x}{12}\)

\(\longmapsto \sf \dfrac{1}{2}= \dfrac{x}{12}\)

\(\longmapsto \sf \dfrac{1}{2}×12= \dfrac{x}{12}×12\)

\(\longmapsto \sf x = 6\)

Answer:

x = 6

Step-by-step explanation:

Hello!

The missing angle is 60°, and is found by subtracting 90° and 30° from 180°.

Using basic triangle theorems of a 30° - 60° - 90° triangle, we know that the leg opposite to 30°, x, is one-half of the hypotenuse.

The value of x is 6.

The leg opposite to 60° is √3 times the leg opposite to 30°.

Answer:

No, yes, yes, yes, no, no, yes, no, yes, no, no, yes

Step-by-step explanation:

Explanation is in the comments by the way.

The accrued amount of an investment is equal to the sum of the principal amount and the interest earned:

Write the expression in terms of the interest:

To calculate the interest, the first step is to determine the accrued amount after 5 years.

The savings account compounds annually, to determine the accrued amount you have to apply the following formula:

Where

A is the accrued amount

P is the principal amount

r is the interest rate expressed as a decimal value

t is the time in years

n is the number of compounding periods

The principal amount is P= $800

The interest rate of the account is 14%, to express it as a decimal value, divide it by 100

The time period for the investment is 5 years.

The account compounds annually, which means that there is only one compounding period per year, so, n=1.

Calculate the accrued amount:

After 5 years the accrued amount will be A= $1540.33

Finally, calculate the interest:

After 5 years she will have $740.33 of interest.

Given:

2.1 % loses twice a year.

So at first, the initial investment is $400.

Then first year will be,

Second year:

Hence, the correct option is Option D.

To find the roots of a third-degree polynomial, also known as a cubic polynomial, we can use a method called factoring or apply the cubic formula.

The first step is to check if there are any common factors that can be factored out. Next, we can use the rational root theorem to determine potential rational roots. By applying synthetic division or long division, we can divide the polynomial by the potential roots to see if they are indeed roots.

If a rational root is found, we can then use synthetic division to factor out the corresponding quadratic equation. Finally, we can solve the quadratic equation using methods like factoring, completing the square, or using the quadratic formula to find the remaining roots.

It's important to note that not all cubic polynomials can be easily factored or solved algebraically. In such cases, numerical methods or approximation techniques may be used to find the roots.

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To find the roots of a third degree polynomial, you can follow these steps: 1) Check for rational roots using the Rational Root Theorem. 2) Use synthetic division to divide the polynomial by a linear factor. 3) Factor the resulting quadratic equation. 4) Solve for the roots by setting each factor equal to zero.

To find the roots of a third degree polynomial, we can follow these steps:

Remember, the Fundamental Theorem of Algebra states that every polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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what is the difference between 880 an 580

The probability that the total of the two numbers is more than 32 = \(\frac{2}{5}\)

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

\(^nC_r=\frac{n!}{r!(n-r)!}\)

For given question,

We have been given five number cards.

Two of the five cards are picked at random.

Using combination formula the possible number of outcomes would be,

\(^5C_2\\\\=\frac{5!}{2!(5-2)!} \\\\=10\)

So, n(S) = 10

Let event A : the total of the two numbers is more than 32

A = {(19, 14), (19, 22), (13, 22), (14, 22)}

So, n(A) = 4

Using the formula for probability,

\(\Rightarrow P(A)=\frac{n(A)}{n(S)} \\\\\Rightarrow P(A)=\frac{4}{10}\\\\\Rightarrow P(A)=\frac{2}{5}\)

Therefore, the probability that the total of the two numbers is more than 32 = \(\frac{2}{5}\)

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Lerato spends 2 hours 30 minutes talking to her relatives during on the month of April.

The cost is 90 cents per minute, so first we need to convert the total time Lerato spent on phone calls to minutes.To do that, we can use the following calculation:2 hours 30 minutes = 2 × 60 + 30 = 150 minutesNow,

we can multiply the total minutes by the cost per minute:$150 \text{ minutes} \times 90 \text{ cents/minute} = 13500 \text{ cents} $

But we need to convert cents to Rand, so we divide by 100 (since there are 100\($150 \text{ minutes} \times 90 \text{ cents/minute} = 13500 \text{ cents} $\) cents in one Rand):$13500 \text{ cents} ÷ 100 = 135 \text{ Rand}$

Therefore,

Lerato spent 135 Rand talking to her relatives during the month of April.

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The unit tangent and unit normal vectors, T(t) and N(t), of the vector function r(t) = ⟨2t, 1/2t², t²⟩ can be found by normalizing the derivative of the function with respect to t.  the unit tangent vector T(t) is ⟨2, t, 2t⟩ / √(5t² + 4), and the unit normal vector N(t) is ⟨0, 1, 2⟩ / √5.

To find the unit tangent vector T(t), we differentiate the vector function r(t) with respect to t:

r'(t) = ⟨2, t, 2t⟩.

Next, we normalize the derivative vector to obtain the unit tangent vector:

T(t) = r'(t) / ||r'(t)||,

where ||r'(t)|| denotes the magnitude of r'(t). To find the magnitude, we calculate:

||r'(t)|| = √(2² + t² + (2t)²) = √(4 + t² + 4t²) = √(5t² + 4).

Thus, the unit tangent vector T(t) is:

T(t) = ⟨2, t, 2t⟩ / √(5t² + 4).

To find the unit normal vector N(t), we differentiate T(t) with respect to and normalize the resulting vector:

N(t) = T'(t) / ||T'(t)||.

Differentiating T(t), we get:

T'(t) = ⟨0, 1, 2⟩ / √(5t² + 4).

Normalizing T'(t), we have:

N(t) = ⟨0, 1, 2⟩ / ||⟨0, 1, 2⟩|| = ⟨0, 1, 2⟩ / √(1² + 2²) = ⟨0, 1, 2⟩ / √5.

Therefore, the unit tangent vector T(t) is ⟨2, t, 2t⟩ / √(5t² + 4), and the unit normal vector N(t) is ⟨0, 1, 2⟩ / √5.

Answer:

\(\frac{43}{k}\) times

Step-by-step explanation:

How many times Iris makes her recipe before her sugar runs out is determined by how many times \(k\) can fit into \(43\) thus making the expression \(\frac{43}{k}\).

Hope this helps :)

a) To obtain the potential pressure drop in the wellbore, we can use the hydrostatic pressure equation.

The potential pressure drop is equal to the pressure gradient multiplied by the length of the wellbore. The pressure gradient can be calculated using the equation: Pressure gradient = (density of oil × acceleration due to gravity) × sin(θ), where θ is the deviation angle of the wellbore from horizontal flow. In this case, the pressure gradient would be (48 lbm/ft^3 × 32.2 ft/s^2) × sin(15°). Multiplying the pressure gradient by the wellbore length of 6,000 ft gives the potential pressure drop.

b) To determine the frictional pressure drop in the wellbore, we can use the Darcy-Weisbach equation. The Darcy-Weisbach equation states that the pressure drop is equal to the friction factor multiplied by the pipe length, density, squared velocity, and divided by the pipe diameter. However, to calculate the friction factor, we need the Reynolds number. The Reynolds number can be calculated as (density × velocity × diameter) divided by the oil viscosity. Once the Reynolds number is known, the friction factor can be determined. Finally, using the friction factor, we can calculate the frictional pressure drop.

c) To calculate the in-situ oil velocity, we need to consider the total volume of the pipe, including both oil and gas. The total pipe volume is calculated as the pipe cross-sectional area multiplied by the wellbore length. Subtracting the gas volume from the total volume gives the oil volume. Dividing the oil volume by the total time taken by the oil to flow through the pipe (converted to seconds) gives the average oil velocity.

d) The flow regime of the two-phase flow can be determined based on the oil and gas mixture properties and flow conditions. Common flow regimes include bubble flow, slug flow, annular flow, and mist flow. These regimes are characterized by different distribution and interaction of the oil and gas phases. To determine the specific flow regime, various parameters such as gas and liquid velocities, mixture density, viscosity, and surface tension need to be considered. Additional information would be required to accurately determine the flow regime in this scenario.

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Answer:

1) 8

2) 11

3) 15

Step-by-step explanation:

1) x - 3

2) x

3) x + 4

x-3+x+x+4 = 34

3x + 1 = 34

3x = 34-1

x = 33/3

x = 11

The required numbers are 8, 11, and 15.

Given that,
The sum of the three numbers is 34. The first is 3 less than the second, while the third is 4 more than the second. Find the numbers is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Let the three numbers be x, y and z
The Sum of the number is 34,
x + y + z = 34   - - - - -(1)

The first is 3 less than the second,
y = x + 3

The third is 4 more than the second.
z = y + 4
z = x + 7

Put y and z in equation 1
x + x +3 +x +4 = 34
3x = 24
x = 8

Now
Second number =
y = x + 3
y = 8 + 3 = 11

Third number
z = x + 7
z = 8 + 7
z = 15

Thus, the required number are 8, 11, and 15.

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Answer:

y = x + 3

y = 3x + 1

Step-by-step explanation:

This does it in two equations.

y = x + 3 and  y = 3x + 1 equation will send 2 different lines through the coins to capture them

using the slope intercept equation,

y = mx + b

m = slope

b = y-intercept

let's pick 2 coordinate from the graph,

(-2, 1)(-1, 2)

m = 2 - 1 / -1 - (-2)  = 1 / 1 = 1

1 =  -2 + b

b = 3

Therefore,

y = x + 3

let check for another equation that will work for another line. Let's use the coordinates (-1, -2)(0, 1) to find slope.

Therefore,

m = 1 - (-2) / 0 - (-1) = 3 / 1 = 3

y = 3x + b

1 = 3(0) + b

b = 1

y = 3x + 1

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Answer: 1

\((\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1\)

Step-by-step explanation:

Answer:

(-3, 2)

Step-by-step explanation:

x + y = -1      =          x = -1 - y

-3( -1 -y ) -4y = 2

4 + 3y - 4y = 2

-y + 4 = 2

-y = -2

y = 2

x + 2 = -1

x = -3

Answer:

The bass player is 65 inches tall.

Step-by-step explanation:

15 inches is 20% of 75, so the monitor reduces their height by 20%. 13 is 20% of 65, so the bass player must be 65 inches tall.

The probability of rolling a sum of 10 is \(\frac{1}{18}\)

as we know that total number of outcomes for a dice is equal to six raised to the power times the dice is rolled

that is,  total number of outcomes = \(6^{2} = 36\)

also, the sum can be equal to 10 in only two cases, (6,4) and (5,5)

according to the formula

Probability = \(\frac{favorable events}{ total number of outcome} = \frac{2}{36} = \frac{1}{18}\)

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Question:

You roll a fair six-sided die and record the result X. You roll the die again and record the result Y. What is the probability of rolling a sum of 10?

Answer:

See attached photo for work

Step-by-step explanation:



When dividing 210 by 3.5 using long division, the quotient is 60.

Dividing is a fundamental mathematical operation that involves splitting a quantity or set of items into equal parts. It is the inverse of multiplication, where one number, called the dividend, is separated into smaller portions or groups by another number, known as the divisor. The result is called the quotient. Division is denoted by the symbol "/", ÷, or ":".

When dividing 210 by 3.5 using long division, we start by dividing 2 by 3.5 which gives us 0 as the quotient. We then bring down the next digit, 1, and divide 21 by 3.5 which gives us 6 as the quotient. Finally, we bring down the last digit, 0, and divide 0 by 3.5 which gives us 0 as the quotient. Therefore, 210 divided by 3.5 is equal to 60.

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