To divide 5472 by 81 using the shortened form of the division algorithm, what should be your first thought? Select from the drop-down menus to correctly complete the thought. "How many times does 81 divides into Choose... ?"
5
54
547
5472

Answer:

New force = 24 N

Step-by-step explanation:

The force acting on the object varies directly with the object's acceleration

i.e.

\(\dfrac{F_1}{F_2}=\dfrac{a_1}{a_2}\) ...(1)

We have,

F₁ = 40 N, a₁ = 10 m/s², a₂ = 6 m/s₂, F₂ =?

Put all the values in equation (1).

\(F_2=\dfrac{F_1a_2}{a_1}\\\\F_2=\dfrac{40\times 6}{10}\\\\F_2=24\ N\)

So, the new force becomes 24 N.

Answer: 1/3

Step-by-step explanation: slope is the difference between the y values over the difference of the x values

The slope of the line that passes through A(0,−5) and B(3,−4) will be 1/3.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The slope could be positive or negative.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope m = (-4 + 5)/(3 - 0)

m = 1/3

Hence "The slope of the line that passes through A(0,−5) and B(3,−4) will be 1/3".

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Answer:

a.375

Step-by-step explanation:

Answer: 702

Step-by-step explanation:

From the question, we are informed that the parking lot of a theater has a capacity of 1118 cars and that on Monday, the ratio of the empty parking spots to occupied parking spots is 16:27.

Based on the ratio given, the number of cars that were parked there on that day will be:

= 27/(16 + 27) × 1118

= 27/43 × 1118

= 27 × 26

= 702 cars

Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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The area of the composite shape are

1. Orange

2. Light blue

3. Purple

4. Green

5. Red

6. Yellow

7. Light green

8. Yellow

9. Dark blue

10. Pink

The area of the composite shapes are solved as follows

1. rectangles

= 7 * 3 + (15 - 7) * 1.5

= 21 + 12

= 33 square cm

2.

= 39 x 4 + 0.5(39 + 26) x (18 - 4)

= 156 + 455

= 611 square m

3.

= 12 * 15 + 0.5 x 15 x 10

= 180 + 75

= 255 square ft

4.

= 15 x 7 + 0.5 x π x 3.5 x 3.5

= 105 + 19.24

= 124.2 square cm

5.

= 0.5 x 10 x 22 - 0.5 x 6 x 12

= 110 - 36

= 74 square yd

6.

= 0.5 x π x 3 x 3 + 0.5 x 6 x 11

= 14.14 + 33

= 47.1 square m

7.

= 18 x 6 - 2 x π x 2 x 2

= 108 - 25.13

= 82.8 square m

8.

= 4 x 16 + 0.5 (16 + 10) x (8 - 4)

= 64 + 52

= 116 square cm

9.

= 18 x 8 - 4 * 0.5 x 4 x 4

= 144 - 32

= 112 square cm

10.

= [0.5 (7 + (9 + 3)) x (15 + 6 - 17)] + [(17 - 6) x (9 + 3)] + [6 x 9]

= 38 + 132 + 54

= 224 square cm

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Answer: D

Step-by-step explanation:

The first data set, D1, has values ranging from 2.1 to 5.5, while the second data set, D2, has values ranging from 3.5 to 9.4. Since there is no overlap between the ranges of values in D1 and D2, these data sets show no overlap. In contrast, data sets A, B, and C all have overlapping ranges of values.

In the case   given above, it would be better to   survey students in a class that is required rather than an elective to get a sample with the least  bias.

This is because electives   may appeal to students who already have an interest in a particular field of  science, while students in   required courses may have more varied interests and backgrounds      

 Therefore, surveying students  in preferred classes will result in a more representative sample of the school 's student body and   reduce bias.

Also , a larger sample size of required courses would provide more accurate   data to determine the areas  of science that students are most interested in.

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Answer:  

Rectangular pyramid  8 edges

Rectangular prism    12 edges

Triangular Prism   9 edges

Triangular Pyramid  6 edges

Step-by-step explanation: Faces connected at edges

Rectangular pyramid    1 Base  and 4  slanted  triangular sides

Rectangular prism    2 top and bottom bases and 4 sides

Triangular Prism   2 top and bottom triangular bases 3 rectangular sides

Triangular Pyramid    1 triangular base, 3 slanted triangular sides

The matching is as follow:

Rectangular pyramid:  8 edges

Rectangular prism:  12 edges

Triangular Prism: 9 edges

Triangular Pyramid: 6 edges

A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.

Rectangular pyramid have one Base and 4 slanted triangular sides

Rectangular prism have 2 top and bottom bases and 4 sides

Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.

Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.

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Answer:

=15.5

Step-by-step explanation:

1/2b x h

12b x 10=155

12b=155/10=31/2

b=31/2 divided by 12

=15.5

Answer:

3rd choice and 5th choice

Step-by-step explanation:

79m + 248 = 880

79m is $79 being charged per month

248 is the initial fees

880 is how much he has spent

we can now solve the equation to find how many months he has been subscribed for

79m = 632

m = 8

The transformation from Figure 1 to Figure 2 is a translation of 6 units to the right. This can be seen by comparing the x-coordinates of corresponding points in both figures, which have all increased by 6 units. So, the correct option is A).

To see that the transformation from Figure 1 to Figure 2 is a translation of 6 units to the right, we can compare the coordinates of corresponding points in both figures

The x-coordinate of the point (-6, 5) in Figure 1 is -6. In Figure 2, this point is at position (6, 5), which has an x-coordinate of 6. The x-coordinate of the point has increased by 6 units, indicating a translation to the right.

Similarly, the x-coordinates of all the other points have also increased by 6 units, indicating a translation to the right.

The y-coordinates of the points have not changed, which means there is no vertical translation or reflection.

Therefore, the transformation from Figure 1 to Figure 2 is a translation of 6 units to the right. So, the correct answer is A).

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Answer:

0.54

Step-by-step explanation:

Answer:

0.54

Step-by-step explanation:

calculator. easy.

With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.

Given that:

Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.

We need to know how many servings of 3/4 cup can be obtained from 13 cups.

now we need to divide 13 by 3/4

=13 ÷ 3/4  

= 13 × 4/3

= 52/3

= 17\(\frac{1}{3}\)

With one third of a serving remaining, there are 17 servings total.

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The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

\(b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2\)

Roots of quadrant equation have Samsame sign if product of roots >0.

\(\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0\)

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

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The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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Answer:

c

Step-by-step explanation:

sorry if it is wrong

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

242pi or about 760.266cm

Step-by-step explanation:

V=pi5.5^2 times 8

V=30.25pi times 8

V=242pi

V is about 760.266cm

Answer:

242pi or  760.266cm

Step-by-step explanation:

Answer: 61.1

Step-by-step explanation:

\(\begin{array}{l}\frac{6.11}{0.1}\\\\=\ \left(\frac{6.11}{0.1}\right)\cdot10\\\\=\ \frac{61.1}{1}\\\\=\ 61.1\end{array}\)

Answer:

Step-by-step explanation:

Answer: 91

Solution:

From

\(\frac{a+b+c}{3} =50\)

Therefore, a+b+c = 150

Fromb=30 so, a+c = 120

Because a < b so, a < 30

Because b < c so, c > 30

We want the least possible value of c

so, a needs to be the greatest value possible

Therefore, a = 29

From a+c = 120

Therefore, c = 120-29=91

Answer:

(-8,6)

Step-by-step explanation:

SOOO the x coordinate would be the average  of the two coordinates or (-6-10)/2 or -16/2 or -8.

the same for the y

(4+8)/2 = 6

so the midpoint is (-8,6)

The original price of the luxury car was $73,000.

The equation is in the form of y = mx + b.

The y represents the value of the car

The x represents the number of years since its purchase

The m represents the depreciation rate per year

The b represents the original value of the car.

From this, we see that the depreciation rate per year is -2,500. To find the original value of the car, we set x = 0 and solve for y:

y = -2,500(0) + 73,000

y = 73,000.

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Answer:

Step-by-step explanation:

D=90°

E=147°

F= 33°

Answer:

60%

Step-by-step explanation:

i dont know how to give an explanation on this, my teacher just said the other day in class that 780 is 60% of 1300.

I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Ultimately, the specific goal for Atlas will depend on its unique circumstances, financial position, and growth objectives.

Setting a realistic goal for Atlas to reduce outstanding amounts each month depends on various factors, including the company's financial situation, industry norms, and specific objectives. However, a common approach is to aim for a consistent reduction in outstanding amounts over time while considering practical limitations and sustainability.

One possible goal could be to target a percentage reduction in outstanding amounts each month. This could be based on factors such as historical data, industry benchmarks, and the company's financial capabilities. For example, Atlas could set a goal of reducing outstanding amounts by 5% each month.

Alternatively, Atlas could establish a specific dollar amount as a target for reduction. This could be based on the company's financial goals, cash flow projections, and outstanding debt levels. For instance, Atlas could aim to reduce outstanding amounts by $10,000 each month.

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