Add the quotient of 120 and 60 To the quotient of 72 and 9.

The expression   -2³a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴ with no negative exponents is -a⁵b⁶/3

The given expression is -2³a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴

a and b are the variable in the expression

We have to find the expression without negative exponents

[tex]\frac{a^m}{a^n}=a^m^-^n[/tex]

-8a⁴b⁻⁵/ 24a⁷b³ × b¹⁰/a⁻²b⁻⁴

-a³/3b⁸  × a²b¹⁴

-a⁵b⁶/3

Hence, the expression with no negative exponents is -a⁵b⁶/3

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a) The population is modeled by:

[tex]y = 13,500*(1.04)^t[/tex]

b) In the year 2008, the population is  18,476

The general population equation is an exponential equation of the form:

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

Where A is the initial population, r is the rate of growth, and t is the variable, time in years.

Here we know that the initial population is 13500, the rate is 4% (or 0.04 in decimal form).

Then the equation is:

[tex]y = 13,500*(1.04)^t[/tex]

b) 2008 is 8 years after 2000, so we need to evaluate in t = 8.

[tex]y = 13,500*(1.04)^8 = 18,475.68[/tex]

we can round that to the next whole number, which is 18,476

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The solution by completing the square for the equation x² + 3x = 24 is x ≈ 3.55 or x ≈ -6.55, which is (3.55, -6.55) when rounded to the nearest hundredth. The correct answer is A).

To solve by completing the square, we need to take half of the coefficient of x, square it, and add and subtract it to both sides of the equation. Then, we can factor the left side and solve for x.

Starting with the equation

x² + 3x = 24

First, we add and subtract (3/2)² = 2.25 to both sides

x² + 3x + 2.25 - 2.25 = 24

(x + 1.5)² = 26.25

Taking the square root of both sides

x + 1.5 = ±√26.25

x = -1.5 ± √26.25

Rounding to the nearest hundredth, we get

x ≈ 3.55 or x ≈ -6.55

So the answer is (3.55, -6.55). The correct option is A).

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Step-by-step explanation:

To calculate your after-tax return on investment, we need to know your tax rate. Let's assume your tax rate is 20%.

Your total income from the salary and interest is:

$29,000 + $125 = $29,125

Your tax liability on this income is:

$29,125 * 20% = $5,825

So your after-tax income is:

$29,125 - $5,825 = $23,300

Your after-tax return on the investment is:

$125 / $23,300 = 0.0054 or 0.54%

Therefore, your after-tax return on the investment is 0.54%.

Step-by-step explanation:

y = a(x-3)(x+1)         sub in the given point to calculate 'a'

-10 = a( 1-3)(1+1)

-10 = -4a

a = 2.5

then    y = 2.5 ( x-3)(x+1)   = 2.5 x^2 -5x -7.5

The maximum salary Larry can offer a new employee per annum is $250,000.

The maximum salary conferrable on a new employee is based on projections, worked out as follows:

The gross revenue to be generated = $8 million

Annual profit margin = 15% or $1.2 million ($8 million x 15%)

Current projected expenses for the year = $6.3 million

Actual cost of an employee = $0.5 million ($8 - 1.2 - 6.3)

Maximum salary = $250,000 ($0.5 million x 50%).

Thus, based on current projections of a gross revenue of 8 million USD with a 15% annual profit margin and projected expenses of 6.3 million, the maximum salary that Larry can offer a new employee is $250,000.

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Answer:

To determine the scale factor used to create the image, we need to compare the corresponding side lengths of the original triangle ABC and the dilated triangle A'B'C'.

Let's take the side AB of triangle ABC and its corresponding side A'B' of triangle A'B'C'. The length of AB is 18-9=9 units, while the length of A'B' is 6-3=3 units. Therefore, the scale factor for the dilation from triangle ABC to triangle A'B'C' is:

scale factor = length of A'B' / length of AB = 3/9 = 1/3

So the answer is: the scale factor used to create the image is one third.

Step-by-step explanation:

The scale factor used to create the image triangle A'B'C' is 1/4.

To determine the scale factor used to create the image, we can compare the corresponding side lengths of the original triangle ABC and the resulting triangle A'B'C'.

Let's calculate the length of a side of triangle ABC and the corresponding side of triangle A'B'C':

Length of side AB in triangle ABC:

AB = √(12 - 4)² + (4 - 4)²

= 8

Length of side A'B' in triangle A'B'C':

A'B' = √(3 - 1)² + (1 - 1)²

=2

To find the scale factor, we can divide the length of the corresponding side in the image triangle (A'B'C') by the length of the corresponding side in the original triangle (ABC):

Scale factor = A'B' / AB

= 2 / 8

= 1/4

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Multiplying radical expressions √6(√2 + √6) involves multiplying the coefficients and then multiplying the radicands. Therefore, the final answer is 2√12 + 6√6.

The multiplication of two radicals can be done by using the product rule which states that the product of two radicals is equal to the product of the coefficients and the product of the radicands.

Multiplying radical expressions involves multiplying the coefficients and then multiplying the radicands.

In this case, the coefficients are 1 and the radicands are √6 and (√2 + √6). The first step is to multiply the coefficients, which is 1*1 = 1.

The second step is to multiply the radicands, which is √6*(√2 + √6).

In this case, the product of the radicands is (√2 * √6) + (√6 * √6).

This can be simplified to 2√12 + 6√6.

Therefore, the final answer is 1*(2√12 + 6√6) = 2√12 + 6√6.

In summary, multiplying radical expressions √6(√2 + √6) involves multiplying the coefficients and then multiplying the radicands. Therefore, the final answer is 2√12 + 6√6.

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The solution to the system of equations shown above is: A. More than 1 solution.

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

3y - 3x = -9   ......equation 1.

4y - 4x=-12 ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by multiple ordered pairs and as such, it has more than one solution or infinitely many solutions because the lines coincide.

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Answer:

A

Step-by-step explanation:

When shape P is enlarged by the scale factor and the centre, the new coordinates would be (2, 6), (6, 6), (0, 8), and (4, 8).

The current coordinates are:

( 1 , 3 ) ( 3, 3 ) ( 0, 4 ) and ( 2, 4 )

The new coordinates, with an expansion of 2 would be:

Point 1:

New coordinates: (1 x 2, 3 x 2) = (2, 6)

Point 2:

New coordinates: (3 x 2, 3 x 2) = ( 6, 6 )

Point 3:

New coordinates: ( 0 x 2, 4 x 2) = ( 0, 8 )

Point 4:

New coordinates: (2 x 2, 4 x 2) = ( 4, 8 )

The enlarged figure would have coordinates at  (2, 6), (6, 6), (0, 8), and (4, 8).

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39 over 80 will be the probability of getting desired outcomes.

Finding the total number of rolls that produced an odd number and dividing that by the total number of rolls will yield the experimental probability that the number rolled was odd.

80 rolls are listed as the total. We sum the frequency of the odd numbers to determine the total number of rolls that produced an odd number:

Total frequency of odd numbers = frequency of 1 + frequency of 3 + frequency of 5

= 15 + 14 + 10

= 39

the following is the experimental likelihood that the number rolled was odd:

The frequency of odd numbers divided by the total number of rolls gives the probability of rolling an odd number.

= 39 / 80

Therefore, the probability will be 39 over 80.

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The decimal time 0.8 seconds can be said as: A. Zero point eight seconds

In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number.

A decimal number is normally read by saying the whole part of it as a whole number and by individually reading out every number after the decimal point. For example, 28.79 would be read as twenty-eight point seventy nine.

Thus, the decimal 0.8 seconds can be pronounced as:

Zero point eight seconds

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Answer:

The midpoint of segment AB is: M = ((-3 + 7)/2, (3 + (-7))/2) = (2, -2)

The slope of segment AB is: m = (y2 - y1)/(x2 - x1) = (-7 - 3)/(7 - (-3)) = -1

The slope of a line perpendicular to AB is the negative reciprocal of m: m_perp = -1/m = 1

The equation of the line passing through M with slope m_perp is: y - (-2) = 1(x - 2)

Simplifying, we get: y = x - 4

Therefore, an arbitrary point P(x, y) is on the perpendicular bisector of segment AB if and only if its coordinates satisfy the equation: y = x - 4

Answer:

y = x - 4

Step-by-step explanation:

To find the perpendicular bisector of the line segment AB, we first need to find the midpoint of AB. The midpoint M can be found using the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) = A and (x2, y2) = B

M = ((-3 + 7)/2, (3 - 7)/2) = (2, -2)

The slope of AB can be found using the slope formula:

m = (y2 - y1)/(x2 - x1)

m = (-7 - 3)/(7 - (-3)) = -10/10 = -1

The slope of the perpendicular bisector of AB is the negative reciprocal of the slope of AB. So, the slope of the perpendicular bisector is:

m_perp = 1/m = -1/-1 = 1

Now we have the midpoint M and the slope of the perpendicular bisector. We can use the point-slope form of a line to find the equation of the perpendicular bisector.

y - y1 = m(x - x1)

where m = 1 and (x1, y1) = (2, -2)

y + 2 = 1(x - 2)

y = x - 4

Therefore, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector of segment AB with endpoints A(-3, 3) and B(7, -7) is:

y = x - 4

-2 to -4 = multiply by 2

-4 to -12 = multiply by 3

-12 to -48 = multiply by 4

-48 to -240 = multiply by 5

Our next three terms will require us to multiply by 6, then 7, then 8.

-240 x 6 = -1440

-1440 x 7 = -10080

-10080 x 8 = -80640

Answer: C

Hope this helps!

Answer:

C

Step-by-step explanation:

multiply by 2     then by  3     then by  4   then by 5

   then by   6     then by  7   then by  8

Answer:

[tex]m = \frac{ - 2 - 3}{5 - 1} = - \frac{5}{4} [/tex]

Answer:

the answer is B) 24.

Step-by-step explanation:

To find the lateral surface area of the triangular prism, we need to find the perimeter of the base and then multiply it by the height of the prism.

Looking at the net, we can see that the base is a triangle with sides of length 3 cm, 4 cm, and 5 cm. So the perimeter of the base is:

3 cm + 4 cm + 5 cm = 12 cm

The height of the prism is given as 2 cm. Therefore, the lateral surface area is:

12 cm x 2 cm = 24 cm²

So the answer is B) 24.

IF THIS HELPED, CAN YOU PLEASE GIVE 5⭐? thank you

Answer:

a polygon has ten sides and it is known as decagon

Answer: (READ IT ALL PLS)

56.8

Convert  56.8

☆*: .｡. ``.｡.:*☆

5680

Step-by-step explanation:

I'm not really sure, Because I don't get the

way you explained it. But I hope it helps.

: )

The number that is 1.5 standard deviations below the mean is approximately 0.631.

Standard deviation is a measure of the amount of dispersion in a set of data. It measures how much the data values deviate from the mean of the data set. A smaller standard deviation indicates that the values tend to be close to the mean, while a larger standard deviation indicates that the values are more spread out from the mean. Standard deviation is commonly used in statistical analysis to measure the spread of a data set and to help identify outliers.

To find the number that is 1.5 standard deviations below the mean, we first need to calculate the mean and standard deviation of X.

The mean is:

μ = Σ(x * f) / n = (0*3 + 1*15 + 2*30 + 3*27 + 4*11 + 5*7 + 6*7) / 100 = 2.77

The variance is:

σ^2 = Σ[(x - μ)^2 * f] / (n-1)

=  [(0-2.77)^2*3 + (1-2.77)^2*15 + (2-2.77)^2*30 + (3-2.77)^2*27 + (4-2.77)^2*11 + (5-2.77)^2*7 + (6-2.77)^2*7] / (100-1)

= 2.0346

The standard deviation is:

σ = [tex]\sqrt{2.0346}[/tex] = 1.426

Now we can find the number that is 1.5 standard deviations below the mean:

2.77 - 1.5(1.426) = 0.631

Therefore, the number that is 1.5 standard deviations below the mean is approximately 0.631.

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Answer:

take a photo of the question so I can answer it please

The formula for the curved surface area of a cylinder is given by:

Curved Surface Area = 2 × pi × radius × height

where pi is the mathematical constant approximately equal to 3.14, radius is the distance from the center of the circular base to the edge of the cylinder, and height is the distance between the two circular bases of the cylinder.

Given, the radius of the cylinder is 7 cm and the height is 2 cm, we can substitute these values in the above formula to find the curved surface area:

Curved Surface Area = 2 × (22/7) × 7 cm × 2 cm

= 2 × 22 × 2 cm^2

= 88 cm^2

Therefore, the curved surface area of the cylinder is 88 square centimeters.

I'm sorry to disturb but can you please mark me BRAINLEIST if this ans is helpfull

An equation that shows the cost of a pack of test tubes, t, in terms of the cost of a set of beakers is 10t = b - 4.

An equation with t and b that describes this situation is 8t + 12b = 348.

An equation that shows this substitution is 8t + 12(10t + 4) = 348.

The value of b is equal to $27.4.

The amount of money which the school paid for a set of beakers is $27.4 and $2.34 for a pack of test tubes.

In order to write a linear equation to describe this situation, we would assign variables to the cost of a pack of test tubes and the cost of a set of beakers respectively, and then translate the word problem into a linear equation as follows:

Since a pack of 10 test tubes costs $4 less than a set of nested beakers, a linear equation which can be used to model the cost of a pack of test tubes with respect to the cost of a set of beakers is given by;

10t = b - 4    .....equation 1.

For t and b, a linear equation which can be used to model the total cost is given by;

8t + 12b = 348      .....equation 2.

By making b the subject of formula in equation 1, we have;

b = 10t + 4

By substituting the value of b, we have;

8t + 12(10t + 4) = 348

8t + 120t + 48 = 348

128t = 300

t = 2.34

b = 10(2.34) + 4

b = 27.4

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Answer:

The ratio 56 to 35 = 8 to 5 = 8/5

Check the picture below.

[tex]2x+3=\cfrac{(176-2x)-47}{2}\implies 4x+6=(176-2x)-47 \\\\\\ 4x+6=129-2x\implies 6x+6=129\implies 6x=123 \\\\\\ x=\cfrac{123}{6}\implies x=\cfrac{41}{2}\implies x=20\frac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ 2\left( \frac{41}{2} \right)+3\implies 41+3\implies 44^o\impliedby \measuredangle MNO[/tex]

The surface area of the cube with a side length of 5.5 yards is 181.5 square yards.

To find the surface area of a cube with a side of 5.5 yards, we need to add up the areas of all six sides of the cube.

The formula for the surface area of a cube is

SA = 6s²

where SA is the surface area and s is the length of the side.

Substituting s = 5.5 yards into the formula, we get

SA = 6(5.5)²

SA = 6(30.25)

SA = 181.5 square yards

Therefore, the surface area of the cube is 181.5 square yards.

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maximillian walks 0.6 mile each day. He would walk 60 miles in =60/0.6 = 100 days

Answer:

He will have 60 miles in 100 days

Step-by-step explanation:

You only have to divide 60 by 0.6

[tex]60 / 0.6=100[/tex]

Hope This Helps :)

Pls Brainliest...

Answer:

The GCF is 12. ^^

Step-by-step explanation:

Answer:

12(1+5)

Step-by-step explanation:

The gcf of 12 and 60 is 12. This is because both are divisible bt 12. 12/12=1 and 60/12 is 5. Since, they're both divisible by 12, take out the 12, and multiply it by it's factors. Since 12x1= 12 and 12x5=60, it would be 12(1+5)

The area of the new shape formed by the two rectangles is calculated to be equal to 71 square centimeters.

The new shape will have a square region of 3 cm by 3 cm covered from one of the rectangles which will be under, so the area of the new shape is calculated as follows:

area of one identical rectangle = 8 cm × 5 cm

area of one identical rectangle = 40 cm²

area of the square region under = 3 cm × 3 cm

area of the square region under = 9 cm²

Area of the new shape = 40 cm² + (40 cm² - 9 cm²)

Area of the new shape = 40 cm² + 31 cm²

Area of the new shape = 71 cm²

Therefore, the area of the new shape formed by the two rectangles is calculated to be equal to 71 square centimeters.

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The value of x is given as follows:

x = 7.

Similar triangles are triangles that share these two features listed as follows:

Considering the similar triangles, the equivalent side lengths are given as follows:

Hence we apply the proportional relationship among the equivalent side lengths to obtain the value of x as follows:

8/14 = (2x - 2)/3x

14(2x - 2) = 8(3x)

28x - 28 = 24x

4x = 28

x = 7.

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