( q2 − r2s) ( q4 + q2r2s + r4s2)

Answer:

c

Step-by-step explanation:

because the explanation its just c

The value of P(1.17 <= Z <= 2.26 ) is 0.1091

From the question, we have

Z value for 1.17 is 0.8790

Z value for 2.26 is 0.9881

P(1.17 <= Z <= 2.26 ) = 0.9881 - 0.8790 = 0.1091

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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The exponential model of the given data is f(t) = 30.18 × 1.06^t.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

Given that,

The average price for office space in 2004 is $30.18.

The average price for office space in 2015 is $66.85.

Suppose the average price in 2004 is taken as y₀.

The given situation can be represented in the form of exponential function f(t) = y₀b^t as,

Take t = 0 for 2004

Then,  f(0) = y₀b^0

⇒ f(0) = y₀ = $30.18.

Then, at 2015, t = 12. Substitute the respective values to get,

f(12) = 30.18 × b^12

⇒ 66.85 = 30.18 × b^12

⇒ b^12 = 66.85 / 30.18

⇒ b = 1.06

Thus in exponential form the given situation can be written as,

f(t) =30.18 × 1.06^t

Hence, the given data can be modeled in exponential function as  f(t) =30.18 × 1.06^t.

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The value of TU is 21

From the question, we have

ST=3x+3 and TU=2x+9

ST = TU

3x + 3 = 2x + 9

3x - 2x = 9 - 3

x = 6

substituting the value, we get

TU = 2x + 9

= 2 (6) + 9

= 12 + 9

TU = 21

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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The function operation (f - g)(x) of the functions f(x) = -3x² + 2x - 3 and g(x) = 2x² - 3x + 4 is -5x² + 5x - 7.

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To determine the function operation (f - g)(x), replace the function designators with the real functions and simplify.

(f - g)(x) = f(x) - g(x)

(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )

Apply distributive property to eliminate the parenthesis.

(f - g)(x) = ( -3x² + 2x - 3 ) - ( 2x² - 3x + 4 )

(f - g)(x) = -3x² + 2x - 3 - 2x² + 3x - 4

Collect and add like terms

(f - g)(x) = -3x² - 2x² + 2x + 3x - 3 - 4

(f - g)(x) = -5x² + 5x - 7

Therefore, the function operation (f - g)(x) is -5x² + 5x - 7.

Option A is the correct answer.

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Answer:

Real, Irrational

Step-by-step explanation:

5sqrt2 is NOT:

Natural (1,2,3...)

Whole (0,1,2,3...)

Integer (...-3,-2,-1,0,1,2,3...)

Rational (can be written like a ratio)

Imaginary (have the number i in it.)

It IS Irrational, will have neverending decimal with no repeating pattern.

5sqrt2 = 7.0710678119...

It IS REAL and IRRATIONAL.

The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.

Given that,

We have to calculate the monthly payment P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4% (let r=.9967).

We know that,

Formula for monthly payment is P(i(1+i)ⁿ/(1+i)ⁿ-1)

Here,

P is principal amount $75,000

n is number of months 240 months

i is interest rate 4% is 0.04

=P(i(1+i)ⁿ/(1+i)ⁿ-1)

=75,000(0.04(1+0.04)²⁴⁰/(1+0.04)²⁴⁰-1)

=75,000(0.04(1.04)²⁴⁰/(1.04)²⁴⁰-1)

=75,000(0.04(12246.20236)/(12245.20236)

=75,000(0.04×1.000081665)

=38455

Therefore, The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.

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Sandy earn 306.9 dollars in commission and 1739.1 dollars in hourly wages.

Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales.

She worked 71 hours over the last two weeks and had a total of $2,046 in sales before taxes.

The amount she will earn in her hourly wages and commission is as follows:

amount earn in commission = 15% of 2046

amount earn in commission = 15 / 100 × 2046

amount earn in commission = 30690 / 100

amount earn in commission = 306.9 dollars

Therefore,

amount earn in hourly wages = 2046 - 306.9

amount earn in hourly wages = 1739.1 dollars.

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The value of the x is 60 km and the value of the y is 70 km.

Given that a man travels x km at 60 km/h and y km at 40 km/h and the total time traveled is 11/4 i.e 2.75 h.

Let's suppose that the time traveled for the x km is t1, time traveled for the y km is t2 and total time is T ,so by using the speed distance formula t1 & t2 will be :

t1 = x/60 and t2 = y/40 ;

T = t1 + t2;

i.e 2.75 = x/60 + y/40 ;

Multiply both sides with 120,

330 = 2x + 3y ............i

Now given that man traveled 5x km at 40 km/h and 3y km at 50 km/h in total time of 11. 7 hours. Similarly the equation for this situation will be :

T = t1 + t2;

x/8 + 3y/50 = 11.7 ;

Multiply both sides with 200, we will get

25x + 12y = 2340 .........ii

Now by simplifying the equation i and ii we will get the value of x and y which are 60 and 70 respectively.

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Answer:

The numbers in which 7 appears are. 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97, 107. So, counting all. ∴ Number of times 7 appears = 21

If function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35

The function is

f(x) = (x+3)(3x-5) - 4

We have to find the value of f(3) - f(-2) ,to find that find the value of f(3) and f(-2) separately.

The function is

f(x) = (x+3)(3x-5) - 4

Substitute the values in the equation

f(3) = (3+3)(3×3 - 5) - 4

= (6) × (9-5) - 4

= 6 × 4 -4

= 24 - 4

= 20

The value of f(3) = 20

f(-2) = (-2+3)(3×-2 - 5) - 4

= 1 × (-6-5) -4

= 1 × (-11) - 4

= -11 - 4

= -15

The value of f(-2) = -15

Then,

f(3) - f(-2) = 20 - (-15)

= 20 + 15

= 35

Hence, if function f(x) = (x+3)(3x-5) - 4, the value of f(3) - f(-2) is 35

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The area to the right of x in the normal distribution is 0.807

The normal distribution is the probability distribution that helps to find the probability for continuous variables.

For a probability x, for a normal distribution, we have that

P(X ≤ x) + P(X ≥ x) = 1

Since the area to the left of x in a normal distribution is 0.193, we require the area to the right of x.

Since P(X ≤ x) + P(X ≥ x) = 1 where

Making P(X ≥ x) subject of the formula, we have that

P(X ≥ x) = 1 - P(X ≤ x)

Given that P(X ≤ x) = 0.193

Substituting this into the equation, we have  

P(X ≥ x) = 1 - P(X ≤ x)

P(X ≥ x) = 1 - 0.193

P(X ≥ x) = 0.807

So, the area to the right of x is 0.807

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Answer:

$336

Step-by-step explanation:

[tex]\frac{280}{35} \times 42 \\ \\ =\frac{56}{7} \times 42 \\ \\ =8 \times 42 \\ \\ =\$336[/tex]

Answer:

1. I'm $3 in debt, and I spend 4 more dollars. I am now 4 dollars more in debt than I was before.

2. I'm $3 in debt, and I pay back $2 of debt. I am now $1 in debt.

Step-by-step explanation:

-Hope this helped

Answer:

Step-by-step explanation:

smaller

larger

bigger

larger

Answer:

x° = 34°

Step-by-step explanation:

First, find the interior angle supplementary to the given exterior angle 124°.

I will label it y.

124° + y° = 180°

y° = 180° - 124°

y° = 56°

Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.

x° + y° + 90° = 180°

x° + y° = 90°

x° + 56° = 90°

x° = 90° - 56°

x° = 34°

Answer:

---------------------------

The angle of elevation of the ramp to doorway of a building to the ground is found as 11°.

The ramp is the hypotenuse of a right angle triangle formed by the doorway, the ground, and the ramp.

The ramp's elevation angle is the angle Ф it makes with the ground.

Apply the tan function;

Tan Ф = length of doorway/ distance along ramp of building

Tan Ф = 1/5

Ф = 11°

Thus, the angle of elevation of the ramp to doorway of a building to the ground is found as 11°.

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Answer:

100π = 314.1592654

Step-by-step explanation:

area of a circle πr²

π×10²

10×10 =100

100×π

Answer:

density = 1.43 × 10⁻³ g/cm³

Step-by-step explanation:

We are told that oxygen gas of mass 2.23 kg has a volume of 1.56 × 10⁶ cm³, and we are told to find its density in g/cm³.

To do this we have to first convert the mass, which is given in kg, to g:

mass = 2.23 kg = 2.23 kg × 1000 [tex]\mathrm{_\frac{g}{kg}}[/tex]

                          = 2230 g

Next, we can find the density of the gas using the following formula:

[tex]\boxed{density = \frac{mass}{volume}}[/tex]

⇒ density = [tex]\mathrm{\frac{2230 \ g}{1.56 \times 10^{6} \ cm^3}}[/tex]

                 = 1.43 × 10⁻³ g/cm³

Therefore, the density of the oxygen gas is 1.43 × 10⁻³ g/cm³.

Answer:

33.8ohms

Step-by-step explanation:

10A : 13ohm

26A : 33.8ohm

Answer:

1st: One solution

2nd: Infinite many solutions

3rd: No solution

4th: No Solution

5th: One Solution

Step-by-step explanation:

1st:

The solution is (6,9)

x = 6 if a vertical line going though (6,0)

y = 9 is a horizontal line going through (0,9)

The two lines with intersect at (6,9)

2nd:

3y = 15x + 6  If you divide all the way through by 3, you get

y = 5x + 2

This is identical to the first equation given.  Since it is the same line, the answer is infinite many solutions.

3rd:

3y = x + 2  Divide all the way through by 3

y = 1/3 x + 2/3

9y = 3x + 7  Divide all the way through by 9

y = 1/3 x + 7/9

Since the slopes are the same in both equations (1/3), these line are parallel and will never intersect.

4th:

Since the slopes are both the same (2), the lines are parallel and they will never intersect, so the answer is no solution.

5th:

2y = 3x  Divide both sides by 2

y = 3/2

-5y = -10  Divide both sides by -5

y = 2x

These equations are proportional so they go through the origin.  They both have a y intercept of zero, so they intersect at (0,0).  The answer is one solution.

Equation of the line in standard form is 6x + y + 4 = 0.

Slope-intercept form of equation -> y = mx + c

Given in question,

Slope = m = -6

y-intercept = c = -4

Putting values of m and c in Slope-intercept form of equation,

y = -6x - 4

Standard form :

6x + y + 4 = 0

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The solution to the equation 5x - 5 = 15 in the replacement set is x = 4

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

5x - 5 = 15

The replacement set is given as

{0,1, 2, 3, 4}

So, we replace the variables using the elements in the replacement set

When x = 0, we have

5(0) - 5 = 15

-5 = 15 -- false

When x = 1, we have

5(1) - 5 = 15

0 = 15 -- false

When x = 2, we have

5(2) - 5 = 15

5 = 15 -- false

When x = 3, we have

5(3) - 5 = 15

10 = 15 -- false

When x = 4, we have

5(4) - 5 = 15

15 = 15 -- true

Hence, the value of the equation is x = 4

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As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.

Transformation:

Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.

Given,

Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.

Now we have to plot the graph  with the given vertices and its image after a reflection in the line y = -x .

Here reflection refers flipping of a figure.

Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)

For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:

A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)

The image of the polygon is attached below.

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The instantaneous rate of change of monthly output with respect to the number of workers is equal to 184.

The instantaneous rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity at a particular instant.

In Mathematics, the instantaneous rate of change can be calculated by taking the derivate of the function with respect to an independent variable. This ultimately implies that, the instantaneous rate of change is equivalent to the change in the derivative value at a particular instant.

Taking the derivate of the given function, we have:

Q(x) = 15,000 + 2x²

Q'(x) = d/dx(15,000) + d/dx(2x²)

Q'(x) = 0 + 2x(2)

Q'(x) = 4x.

At x = 46, we have:

Q'(x) = 4(46)

Q'(x) = 184.

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Complete Question:

The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 ≤ x ≤ 60), where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).

Q'(46) =

The answer to the algebraic expession is 10.

What is algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression.

Main Body:

We have to find the value of x²-13(x-y) at x=7 and y=4

Now substitute the value of x,y in the expression

=(7)²-13(7-4)

= 49-13(3)

= 10

Hence the answer is 10.

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Answer:

Step-by-step explanation:

You have a total of 114 legs among hippos and birds, of which there are a total of 42. You want the number of each kind of animal.

Let h represent the number of hippos. Then 42-h is the number of birds, and the total number of legs is ...

  4h +2(42 -h) = 114

Simplifying the equation gives ...

  2h +84 = 114

  2h = 30 . . . . . . subtract 84

  h = 15 . . . . . . . . number of hippos

  42 -h = 27 . . . . number of birds

There were 15 hippos and 27 birds.

The equation that represents the number of purses Paula must sell to pay for the new equipment is 5.00x = 5000.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Paula makes purses and the materials cost $2.25 per purse.

She sells them for $5.00 each now she wants to invest $5000 in some new equipment and we are assuming the no. of purses to be x.

Here the equation 5.00x - 2.25x = 5000 represents Paula's profit.

The equation that represents the no. of purses she must sell to pay for the new equipment is 5.00x = 5000.

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Answer: 5.00x - 2.25x = 5000

Step-by-step explanation: