Evaluate (7.62 × 105) – (8.1 × 103). Express the result in scientific notation.

Answer:

Step-by-step explanation:

Looks like the clockwise rotation of 180 degrees about the point (6,−2), followed by a translation of 9 units in a negative x-direction. That is because once it's rotated it will be at x=15 and then if you subtract -9x you will land exactly where you started

If Paige is filling her tub at a rate of 3/4 gallons every 2/3 minute, 3.375 gallons would be in the tub after 3 minutes.

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 ÷.

It is given that, Paige is filling her tub at a rate of 3/4 gallons every 2/3 minute.

We have to find gallons that would be in the tub after 3 minutes

We can utilize multiplication for the given task,

2/3 minutes = 3/4 gallons

1 minute = 3/4 × 3/2

1 minute =1.125

3 minutes = 3 × 1.125

3 minutes =3.375 gallons

Thus, if Paige is filling her tub at a rate of 3/4 gallons every 2/3 minute, 3.375 gallons would be in the tub after 3 minutes.

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Answer:

black and white striped bass

The greatest common factor amongst the three factors is 3x² as it has a degree of 2 and a coefficient greater than 1.

Sums of terms of the form k-x^n, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video. 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 (No division operation by a variable).

Here,

The polynomial=12x⁴+27x³+6x²

On simplifying,

=3x²(4x²+9x+2)

With a degree of 2 and a coefficient larger than 1, 3x² has the highest common factor of the three components.

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Answer:

Step-by-step explanation:

Aub, probability, set theory and discrete math?

Answer:

f(3)=25

Step-by-step explanation:

f(3)=11(3)-8

f(3)=33-8

f(3)=25

Answer:

f(3)=25

Step-by-step explanation:

substitute 3 into the equation for x.

f(3)=11(3)-8

11×3=33 so,

33-8=25

f(3)=25

The distance between the point (-3,7) and the line y=1/3x-2 is  11.0 units

Distance shows how long it is between a point and another

We can do this by drawing a segment that is perpendicular to the line

the given equation is 1/3x-2

The slope here is 1/3 That is slope =3

From the equation of slope=intercept form = y=mx+c

put m=3 to have

y=3x+c

From the given coordinates (-3,7)

7=3(-3)+c

7+9=c

c=16

This implies that y=3x+16

Find the line where the equation intersect  the line

⇒3x+16=1/3x-2

Rearrange the equation

8x/3=-18

Make x the subject. x=6.75

Recall that y=1/3(6.75)-2

y=2.25

The second coordinates are (6.75,2.25) and first (-3,7)

The distance is given by

d=[tex]\sqrt({X_{2}-X_{1})^{2} +(Y_{2}-Y_{1} )^{2} }[/tex]

d= √(6.75+3)²+(2.25-7)²

d=√9.75²+(-4.75)²

d=√95.0625+22.5625

d=√117.625

d=10.8455059817

Therefore the distance is 11 units

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Answer: 1/2 * 6 = 3

Step-by-step explanation:

The percentage of students who live off campus and do not have a part-time job will be 25.2%. Then the correct option is C.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

At a neighborhood school, just 60% of understudies live off the grounds. Of the people who live off-grounds, 58% of those understudies find a part-time line of work. Of the people who live nearby, 67% work part-time. The tree chart shows how the undergrads are separated into subgroups.

The number of students who live off campus and do not have a part-time job is given as,

⇒ 0.60 x (1 - 0.58) x 100

⇒ 0.252 x 100

⇒ 25.2%

The percentage of students who live off campus and do not have a part-time job will be 25.2%. Then the correct option is C.

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The APR for this loan is equal to 468%.

In Mathematics, APR is an abbreviation for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.

Mathematically, the annual percentage rate (APR) of a loan can be calculated by using this formula:

APR = [((simple interest/principal)/n) × 365] × 100

Where:

n represents the number of days.

Note: n is equal to 14 days (2 weeks).

Next, we would determine the FC for this loan as follows;

FC = $295 - $250

FC = $45.

For the two-week period, we have;

Interest = 45/250

Interest = 0.18.

Therefore, the annual percentage rate (APR) of this loan is given by;

APR = 0.18 × 52/2

APR = 468%.

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Answer:

There is no solution to this problem. It is not possible to find three numbers that form an arithmetic sequence and, when 1, 3, and 9 are added to them respectively, form a geometric sequence.

Step-by-step explanation:

To find the three numbers in the arithmetic sequence, let's call the first number in the sequence "a," the second number "a + d," and the third number "a + 2d," where "d" is the common difference between the numbers. The sum of these three numbers is:

a + (a + d) + (a + 2d) = 15

This simplifies to:

3a + 3d = 15

To find the three numbers in the geometric sequence, let's call the first number in the sequence "b," the second number "r * b," and the third number "r^2 * b," where "r" is the common ratio between the numbers. The sum of these three numbers is:

b + (r * b) + (r^2 * b) = 15 + b + (r * b) + (r^2 * b)

This simplifies to:

b(1 + r + r^2) = 15 + b + br + br^2

We are told that if 1, 3, and 9 are added to the three numbers in the arithmetic sequence, we get the three numbers in the geometric sequence. Therefore, we can set up the following system of equations:

3a + 3d = 15

b(1 + r + r^2) = 15 + b + br + br^2

Subtracting b from both sides of the second equation gives:

b(1 + r + r^2) - b = 15 + br + br^2

This simplifies to:

b(r^2 + r - 1) = 15 + br + br^2

Subtracting br and br^2 from both sides gives:

b(r^2 + r - 1) - br - br^2 = 15

This simplifies to:

b(r^2 + r - 1 - r - r^2) = 15

This simplifies to:

b(r - 1)(r + 1) = 15

Dividing both sides by (r - 1)(r + 1) gives:

b = 15 / (r - 1)(r + 1)

We are told that the three numbers in the arithmetic sequence add up to 15, so we can substitute 3a + 3d = 15 into the equation above to solve for "b":

3a + 3d = 15

b = 15 / (r - 1)(r + 1)

Substituting 3a + 3d = 15 into the equation above gives:

b = 15 / (r - 1)(r + 1)

Substituting b = 15 / (r - 1)(r + 1) into the second equation gives:

15 / (r - 1)(r + 1)(1 + r + r^2) = 15 + 15 / (r - 1)(r + 1) + 15 / (r - 1)(r + 1)*r + 15 / (r - 1)(r + 1)*r^2

This simplifies to:

15 / (r - 1)(r + 1)(1 + r + r^2) = 15 + 15r + 15r^2

Multiplying both sides by (r - 1)(r + 1) gives:

15 = 15 + 15r + 15r^2

Subtracting 15 from both sides gives:

0 = 15r + 15r^2

Subtracting 15r^2 from both sides gives:

0 - 15r^2 = 15r

This simplifies to:

-15r^2 = 15r

Dividing both sides by -15 gives:

r^2 = r

Solving for "r" gives:

r = 1 or r = 0

If "r" is equal to 1, then the common ratio between the numbers in the geometric sequence is 1, which means that the three numbers in the geometric sequence are the same. This does not satisfy the condition that the three numbers in the geometric sequence are formed by adding 1, 3, and 9 to the three numbers in the arithmetic sequence, so we can eliminate this solution.

If "r" is equal to 0, then the common ratio between the numbers in the geometric sequence is 0, which means that the three numbers in the geometric sequence are all 0. This does not satisfy the condition that the three numbers in the geometric sequence are formed by adding 1, 3, and 9 to the three numbers in the arithmetic sequence, so we can eliminate this solution as well.

Therefore, there is no solution to this problem. It is not possible to find three numbers that form an arithmetic sequence and, when 1, 3, and 9 are added to them respectively, form a geometric sequence.

For the given right triangle the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

Given that,

In a right triangle tan(P) = 0.051

And, hypotenuse = 117 cm.

The given data can be shown in the diagram as follows,

From the diagram it can be written as,

tan(P) = 0.051

=> P = 2.9°

Then, ∠Q = 180° - (90° + 2.9°)

                = 87.1°

Now, Sin(P) = p/117

        => Sin(2.9°) = p/117

        => p = 117 × Sin(2.9°)

                = 5.9

Similarly, Cos(P) = q/117

            => Cos(2.9°) = q/117

             => q = 117 × Cos(2.9°)

                      = 116.85

Hence, the measure of the remaining angles are 2.9° and 87.1° and the remaining sides are 5.9 cm and 116.85 cm respectively.

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Answer: Yes, it is linear expression

Step-by-step explanation:

The equation is y=mx + b

Here we have 7x, which we have the slope

We don't see the y-intercept, so it is 0

The correct option for the given problem is  the statistic is biased which is (e) option.

The central limit theorem states that in the event that you have a populace with mean μ and standard deviation σ and take adequately enormous irregular examples from the populace with substitution , then, at that point, the conveyance of the example means will be roughly regularly circulated.

By using above central limit theorem establishes that for a proportion p in a sample of size n.

The expected value is μ = p

The standard error is s = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

Now, in this problem the expected d value is different from the expected of μ = p.

Thus,  the statistic is biased, and the correct option is E.

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Correct question:

A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. What property does d hat exhibit?

A. The sampling distribution of d hat is normal.

B. The sampling distribution of d hat is binomial.

C. The sampling distribution of d hat is uniform.

D. d hat is unbiased.

E. d hat is biased.

Answer:

  3)  260 ft

Step-by-step explanation:

You want the perimeter of a rectangle 55 ft by 75 ft.

The equation for the perimeter of a rectangle is ...

  P = 2(L +W)

For the given rectangle, the perimeter is ...

  P = 2(75 ft +55 ft) = 2(130 ft) = 260 ft

Maya needs 260 feet of fencing to put fence around her rectangular yard.

The number of dollars that should be bought and sold to have the profit of $10 is 8.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the buying and selling rates of U.S. dollar ($) in a day are - Rs 115.25 and Rs 116.5 respectively. Let the dollars bought be illustrated as x.

This will be:

116.5x - 115.25x = 10

1.25x = 10

Divide

x = 10 / 1.25

x = 8

The number is 8.

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Answer:

  3 solutions

Step-by-step explanation:

You want to know the number of solutions (zeros) of the cubic function ...

  f(x) = -x³ -32x² +12x +40

Any 3rd-degree polynomial function has 3 zeros. (This is the fundamental theorem of algebra.)

Descartes' rule of signs says the one sign change in the coefficients (--++) means there is one positive real root. On its face, this means there will be 0 or 2 negative real roots.

The value of f(0) is positive (40), and the value of f(-1) is negative (-3), so there must be two negative real roots. (F(x) is positive for very large negative x, so there must be two x-intercepts for x < 0.)

A graph shows the roots to be irrational. The three real roots are approximately ...

__

Additional comment

The "steps" are to find the degree of the polynomial. It is 3, so there are 3 zeros. It is not complicated.

What is more complicated is finding their values. The checks we described above can tell whether there are 1 or 3 real roots. (An odd-degree polynomial always has at least 1 real root.) A graph is helpful for finding whether the roots are real or complex, rational or irrational.

Here, any rational roots must be integer divisors of the constant term, 40. We know the root between 0 and -1 is irrational, so all of them are.

The above root values were obtained by Newton's Method iteration, starting from the approximate values shown on the graph.

He might use the equation y = (3/2) x to determine how much flour he required for the cake.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, etc.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.

According to our question-

Accordingly, we require 2.3 cups of sugar for every cup of flour.

It also means that you need 3 1/2 cups of flour for every cup of sugar.

Therefore, if x cups of sugar and y cups of flour, respectively, are used:

y = (3/2) x.

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The Number of Ballon bouncer games played is 11.

What is  number ?

A number is a numerical unit of measurement and labelling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words can be used to represent numbers in language.

The expression for the number of ballon bouncer games played at the arcade is : 2 + 3b = 35

Let :

Glimmer arcade, g = $2 per game

Ballon bouncer, b = $3 per game

Total game tokens = 35

Her spending could be represented using the expression :

2 + 3b = 35 ; b = number of ballon bouncer games played

2 + 3b = 35

3b = 35 - 2

3b = 33

b = 33/3

b = 11

Therefore, the Number of Ballon bouncer games played is 11.

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Answer:

  (a)  The value 550 represents the initial balance in the account, which means the account started with $550.

Step-by-step explanation:

You want the meaning of 550 in the simple interest expression 687.5 = 550(1 + 0.05t).

The formula for computing the amount A of an account earning simple interest at annual rate r on its initial balance P for t years is ...

  A = P(1 +rt)

Comparing this formula to the given equation, we see ...

  687.5 = 550(1 +0.05t)

The initial balance (starting amount) was 550.

It takes 1 second  for the ball to reach its highest point.

Acceleration of gravity is the acceleration by which earth pulls

objects towards itself. Acceleration is the rate of change of speed.

Given,

The initial velocity of the ball = 16 feet/second

The initial height of the ball = 10 feet

The ball will first travel upward with an initial velocity of 16 feet/second

and the ball will reach a height of x feet from the point of release. After

that the ball will travel a total downward distance of (10+16) = 26 feet.

At highest point, velocity=0.

Applying, v = u + at

                0 = 16 + (-16)t

                t = 16/16

                t = 1 second

Hence, the ball will take 1 second to reach the highest point.

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Plot only the portion between x of -2 to 3.  See the attached graph.

To find the gas unit used in baking of cookies, we plug the values into the given equation: g = t, g = 12. Thus, the gas unit used is 12.

Organic gas usage or production is measured in "gas units." It is frequently employed to estimate the price of natural gas for a predetermined time period, such as a month or a year.

British thermal units (BTUs), a measure of the energy content of natural gas, are the industry standard for quantifying this fuel. One BTU is the amount of heat necessary to raise the temperature of one pound of water by one degree Fahrenheit.

To compute the gas unit for a given time period, the total amount of natural gas used or generated is first converted into BTUs.

How to solve?

To find the gas unit used, we plug the values into the given equation:

g = t, g = 12. Thus, the gas unit used is 12.

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Answer: y= -14.25/19.25

Step-by-step explanation:

−3.5(8.5+5.5y)=−15.5 can be write as

-29.75 - 19.25y= -15.5  

-19.25y = 14.25

y= -14.25/19.25

Answer:

3(n+4)=18

Step-by-step explanation:

Answer:3(n+4)=18

Step-by-step explanation:

The sum of 4 and a number is 4+n

Three times the sum of 4 and a number is 3(4+n)

is means equal sign

3(n+4)=18

The water levels in reservoirs A and B, which initially had 34 million gallon and 38 million gallon water, respectively, will be equal after 13.3 months.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. No, a mathematical equation cannot be solved since it lacks the "equal to" sign $(=)$, but it can be simplified. Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Here,

Let the number of months be x.

34-0.8x=38-1.1x

1.1x-0.8x=38-34

0.3x=4

x=40/3

x=13.33 months

After 13.3 months, The reservoir A and reservoir B will have same amount  of water when initially they have 34 million gallon water and 38 million gallon water respectively.

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plug in -10 for x in -x^2

-1(-10)^2 =

10^2 = 100

A. y = - (4/3)x + 4.

y = - (4/3)x - 1.

No solution.

B. y = 4x - 5.

y = - 2x + 7.

one solution.

C. 2x + 3y = 8

4x + 6y = 17.

No solution.

D. y = 5x - 15.

y = 5(x - 3).

Infinitely many solutions.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

We'll graph each system of equations, If they intersect at one point they have one solution, if they are parallel to each other they have no solution and if they are coinciding with each other they have infinitely many solutions.

y = - (4/3)x + 4.

y = - (4/3)x - 1.

These are parallel lines no solution.

y = 4x - 5.

y = - 2x + 7.

These lines intersect at (2, 3) one solution.

2x + 3y = 8

4x + 6y = 17.

They are parallel to each other.

y = 5x - 15.

y = 5(x - 3).

These are coinciding lines if we distribute the terms hence infinitely many solutions.

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