given an integer variable timer, write a statement that uses the auto-decrement operator to decrease the value of that variable by 1.

The simplified form of the expression (mp)⁶ is equal to m⁶×p⁶.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

The given expression is (mp)⁶.

We know, 2²×2² = 2⁴ but 2²×3² = (2×3)² = 6².

Therefore, (mp)⁶ = m⁶×p⁶.

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Answer:

Step-by-step explanation:

The entry "EQUIPMENT $12,000" is listed as a debit in the T-account, which means it is an increase in assets. Therefore, the correct answer is (b) increase in assets.

Answer:

x = 8

Step-by-step explanation:

To solve the equation x(x - 2) = 48 for x, we can first expand the left side:

x^2 - 2x = 48

Next, we'll add 2x to both sides to isolate x^2:

x^2 = 48 + 2x

Then, we'll subtract 2x from both sides:

x^2 - 2x = 48

Now we have a quadratic equation that we can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -2, and c = 48. Plugging these values into the formula:

x = (-(-2) ± √((-2)^2 - 4(1)(48))) / 2(1)

x = (2 ± √(4 + 192)) / 2

x = (2 ± √196) / 2

x = (2 ± 14) / 2

So the two solutions are x = (2 + 14) / 2 = 8 and x = (2 - 14) / 2 = -6.

Keep in mind that x cannot be negative in this context as it represents a measurement. Therefore, x = 8 is the only solution that has a meaningful value in this context.

Step-by-step explanation:

x(x-2)=48

Remove the parentheses

x²-2x=48

Move the constant to the left

x²- 2x - 48=0

Rewrite the expression

x² + 6x - 8x - 48 = 0

Factor the expressions

x(x+6) - 8(x+6) = 0

Separate into possible cases

(x+6) (x-8)=0

x + 6 = 0

x - 8 = 0

x = - 6 or x = 8

The coordinates of the vertices of the image include the following: (-1, 3), (-1, -1), (5, -1), and (7, 3).

In this exercise, we would have to dilate (enlarge) the coordinates of the pre-image by using a scale factor of 2 centered at the point (1, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate 1, we have;

Coordinate 1 = (2, 4)  →  (2(2 - 1) + 1, 2(4 - 5) + 5)

Coordinate 1 = (2, 4)  →  (2(-1) + 1, 2(-1) + 5)

Coordinate 1' = (-1, 3).

For coordinate 2, we have;

Coordinate 2 = (2, 2)  →  (2(2 - 1) + 1, 2(2 - 5) + 5)

Coordinate 2 = (2, 2)  →  (2(-1) + 1, 2(-3) + 5)

Coordinate 2' = (-1, -1).

For coordinate 3, we have;

Coordinate 3 = (3, 2)  →  (2(3 - 1) + 1, 2(2 - 5) + 5)

Coordinate 3 = (3, 2)  →  (2(2) + 1, 2(-3) + 5)

Coordinate 3' = (5, -1).

For coordinate 4, we have;

Coordinate 1 = (4, 4)  →  (2(4 - 1) + 1, 2(4 - 5) + 5)

Coordinate 1 = (4, 4)  →  (2(3) + 1, 2(-1) + 5)

Coordinate 1' = (7, 3).

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Answer:

It's 3

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

3540/3820 = 93%

so 7% decline

if linearly = every year decline 7%

so back in 1990, 3 years ago, the population was

p° = 3820/(1-7%)^3 =3820/.8=4749

so from 1990

p = 4749 * (1-7%)^t

2009 is 16 years from 1993

so p = 3820 * (1-7%)^16 =1196

Answer:

  A)  P(t) = 3820 -70t

  B)  2700

Step-by-step explanation:

You want a linear equation for the moose population that changed from 3820 in 1993 to 3540 in 1997, and you want the predicted population in 2009.

The slope of the linear function can be found from ...

  m = (p2 -p1)/(t2 -t1)

If we let t represent years after 1993, then this is ...

  m = (3540 -3820)/(4 -0) = -280/4 = -70

P(t) = 3820 -70t . . . . . . . . population is 3820 when t=0, 70 less each year

2009 is 16 years after 1993, so we want P(16):

  P(16) = 3820 -70·16 = 3820 -1120

  P(16) = 2700

The population is predicted to be 2700 in 2009.

Answer: 1200 dollars

Step-by-step explanation:For this question we use the formula:

principal amount x interest rate/100 x time

4000 x 6/100 x 5

4000 x 0.06 x 5

1200

Answer:

$5,387.42

Step-by-step explanation:

Use the formula:

[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}\\[/tex]

where A = amount accrued (principal + interest)
P = initial deposit

r = annual interest rate as a decimal

n = number of times compounded annually

t = number of years

Given
P = 4000
r = 6/100 = 0.06
n = 4 times a year
t = 5 years

[tex]A = 4000\left( 1 + \dfrac{0.06}{4}\right)^{4\cdot 5}\\\\A = 4000 ( 1+ 0.015)^{20}\\\\A = 4000 (1.015)^{20}\\\\A = \$5,387.42[/tex]

Answer:

y = - 3x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 3 , then

y = - 3x + c

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - 3x - 3 ← equation of line of reflection

Answer:

Step-by-step explanation:

Given that cos(60°) = 1/2, we can use trigonometric identities to find the sine, cosine, and tangent of 30°:

Sine of 30°:

sin(30°) = √[1 - cos^2(30°)] = √[1 - (cos(60°)/2)^2] = √[1 - 1/4] = √3/2.

Cosine of 30°:

cos(30°) = √[1 - sin^2(30°)] = √[1 - (√3/2)^2] = √[1 - 3/4] = √1/4.

Tangent of 30°:

tan(30°) = sin(30°) / cos(30°) = (√3/2) / (√1/4) = √3.

So, the sine of 30° is √3/2, the cosine of 30° is √1/4, and the tangent of 30° is √3.

For this data, the median is the best indicator of central tendency.

The correct option is B.

A summary measure called a measure of central tendency, also known as a measure of central or a measure of central placement, aims to summaries the entirety of a set of data using a single number that corresponds to the middle or central of its distribution.

The mean, median, mode, and the midpoint are the four indicators of central tendency. The arithmetic mean of the maximum and minimum values in a data set is used here to define the midpoint or mid-extreme of a set of statistical data values.

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I understand that the question you are looking for is:

A researcher is measuring the amount of time needed to solve a set of anagrams for a sample of n = 15 students. However, one of the participants fails to solve the problems so the researcher has an undetermined score. What is the best measure of central tendency for these data?

a) the mean

b) the median*

c) the mode

d) central tendency cannot be determined for these data

The total cash due at signing is $3,700 at the local dealership..

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

The total cash due is calculated as:

Down payment: $1,800

Security deposit: $400

Acquisition fee: $300

Total: $1,800 + $400 + $300

Apply the addition operation, and we get

= $3,700

Thus, the total cash due at signing is $3,700.

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Answer: 4x+2x+12x+9x+10x

Step-by-step explanation: The simplified expression is 37x. I didn't put an equal sign because that makes it an equation. The perimeter is the sum of all sides. All sides are given except one which can be solved using 12x because it is 2x less than that value or 10x.

The value of the unknown variable in the equation is -16

Linear equations are equations that has a leading degree of 1.

Given the linear equation below

-2 = 2 + v/4

We need to calculate for the unknown variable 'v'

Subtract 2 from both sides

-2-2 = v/4

-4 = v/4

Swap

v/4 = -4

Multiply both sides by 4

v = -4 8 4

v = -16

Hence the value of the unknown variable from the equation is -16.

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Part C: The ordered pair (0, 150) represents the initial value in the table. The initial value represents the altitude of the airplane when it started descending, i.e., the altitude of the airplane before it began its descent.

Part D: The rate of change in this equation is -5, which is the coefficient of x. The rate of change represents the decrease in altitude, in feet, per minute as the airplane descends for a landing. In other words, the altitude decreases by 5 feet for every minute that the airplane descends.

Yes the statement of my cousin that rotations, translations, and reflections will result in the congruence of corresponding lines, line segments, and angles is true

Yes, this is true. Congruence refers to the idea that two geometric figures are identical in size and shape. Translations, rotations, and reflections are rigid motions that preserve distances and angles, meaning that corresponding lines, line segments, and angles in the figures will remain congruent after the transformation.

This is because these transformations only involve shifting, rotating, or flipping the figure, but not changing its shape or size.

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Answer:

see explanation

Step-by-step explanation:

calculate slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

consider the slope of the middle dotted line

with (x₁, y₁ ) = (- 3, - 4) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line

m = [tex]\frac{-2-(-4)}{3-(-3)}[/tex] = [tex]\frac{-2+4}{3+3}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

consider the slope of the line of reflection ( the solid line )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (- 2, 3) ← 2 points on the line

m = [tex]\frac{3-0}{-2-(-1)}[/tex] = [tex]\frac{3}{-2+1}[/tex] = [tex]\frac{3}{-1}[/tex] = - 3

note the product of the slopes = [tex]\frac{1}{3}[/tex] × - 3 = - 1

indicating the lines are perpendicular to each other

a) The function is increasing on the following interval: (3, ∞).

b) The function is not decreasing on any interval of it's domain.

c) The function is not constant on any interval of it's domain.

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Answer:

$12,581.53

Step-by-step explanation:

The balance of an account after having interest compounded annually can be represented using the equation:

[tex]A = P(1 + r)^{t}[/tex]

where [tex]A[/tex] is the final balance, [tex]P[/tex] is the principal (starting amount), [tex]r[/tex] is the rate of interest, and [tex]t[/tex] is the number of years that interest is applied.

We can plug the given values into this equation and solve for [tex]A[/tex].

[tex]P = \$10,000[/tex]     [tex]r = 4.7\%[/tex]     [tex]t = 5[/tex]

[tex]A = 10,000(1 + 4.7\%)^{5}[/tex]

[tex]A \approx \$12,581.53[/tex]

So, Sally's balance in an account that had $10,000 before being compounded for 5 years at an interest rate of 4.7% is $12,581.53.

Answer: They are equal to one another.

1/5 is equal to 2/10.

First we must find a common denominator that both 2 and 10 can be divided by. 2 is a number that both are divisible by. So we must divide 2/10 by 2,leaving 1/5. This means that the number are equal to one another. So neither are greater than the other.

I hope this helps & Good Luck <3!!

The required critical points of f is (0, 0) and the function f does not have a local maximum nor local minimum.

The critical points of a function f are the points in the domain where the partial derivatives of f are equal to 0 or are undefined. To find the critical points of f, we can find the partial derivatives of f with respect to x and y, and set them equal to 0:

df/dx = -2x

df/dy = 2y

Setting df/dx equal to 0, we have:

-2x = 0

So, x = 0.

Setting df/dy equal to 0, we have:

2y = 0

So, y = 0.

Thus, the only critical point of f is (0, 0).

To show that f does not have any local maximums nor any local minimums at the critical point (0, 0), we can check the second partial derivatives of f at this point:

d²f/dx² = -2

d²f/dy² = 2

d²f/dxdy = 0

At (0, 0), d²f/dx² is negative and d²f/dy² is positive, which indicates that f is a saddle point at (0, 0). This means that f does not have a local maximum nor a local minimum at (0, 0).

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The following statements is true: (c) if a trapezoid is also a kite, then it must be a parallelogram and others (a),(b) &(d) are false.

The following is a list of true and false statements regarding the relationship between kites, parallelograms, rhombi, and trapezoids:

(a) False. If a kite is also a parallelogram, it does not necessarily mean that it is a rhombus. A rhombus is a type of parallelogram with equal sides, while a kite is a specific type of quadrilateral with two pairs of equal-length sides.

(b) False. If a trapezoid is also a parallelogram, it does not necessarily mean that it is a rhombus. A rhombus is a type of parallelogram with equal sides, while a trapezoid is a type of quadrilateral with exactly one pair of parallel sides.

(c) True. If a trapezoid is also a kite, then it must be a parallelogram. A kite is a specific type of quadrilateral with two pairs of equal-length sides, which automatically makes it a parallelogram.

(d) False. If a rhombus is also a trapezoid, it does not necessarily mean that it is a kite. A kite is a specific type of quadrilateral with two pairs of equal-length sides, while a rhombus is a type of parallelogram with equal sides.

In conclusion, it's important to understand the definitions and properties of each type of quadrilateral to determine if a statement about their relationship is true or false.

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Answer:

Step-by-step explanation:

Write all of the multiples of ten between 67 and 113

   70 80 90 100 110

 all of these will be divisible by 2...just need to find the one(s) divisible by 6

        only    90

Answer:

Step-by-step explanation:

Part A:

x = # of days

R:  1 hr + 3/4 hr/day(x)

J:  4 hr + 1/2 hr/day(x)

1 + 3/4x = 4 + 1/2x

3/4x - 2/4x = 3

1/4x = 3

x = 12 days

After 12 days of practicing (not including the first Saturday), they each will have practiced 10 hours

Part B:

Saturday plus 12 more days →

Saturday 1-Sun 2- Mon 3-Tues 4-Wed 5-Thurs 6-Fri 7-Sat 8-Sun 9-Mon 10-Tues 11-Wed 12-Thursday

They both will have practiced 10 hours on the second Thursday after they started on Saturday

On each roll of a 6-sided die, we have 6 possible outcomes.

Then if we roll it twice, we will have 36 outcomes.

The outcomes where the sum is 4 are:

roll 1     roll 2    sum

1             3           4

3            1            4

2           2           4

Son in 3 out of 36 outcomes the sum can be 4, then the probability opf rolling a sum of 4 is given by the quotient:

P = 3/36

P = 1/12

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[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+2}=y ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (4)^2-4(2)(2)\implies \text{\LARGE 0}\qquad \stackrel{\textit{two real positive solutions}}{\textit{two x-intercepts}}[/tex]

Answer:

2

Step-by-step explanation:

To divide 1 7/11 by 2 1/2, you first have to convert both numbers to have a common denominator. The smallest common denominator between 11 and 2 is 22. So, you convert 1 7/11 to be 2 14/22, and convert 2 1/2 to be 11/22. Then, you can divide 2 14/22 by 11/22 which gives 2.

4a - 8 + 4a - 8 + 4a - 8 = 180°

The sum of interior angle of triangle is 180°

12a - 24 = 180°

12a = 204

[tex]a = \frac{204}{12} \\ [/tex]

a = 17°