Consider the set of all sets of exactly three integers. Select all true statements about the set .(a) is infinite(b) is finite(c) is countably infinite(d), where denotes the natural numbers(e) is uncountable

Answer:

1/4

Step-by-step explanation:

2 to the power of -2 would be 1/4.

This is because 2 to the power of -1 would be 1/2. And the power of 2 would square the 2 as the denominator making it 1/4.

The reason -1 makes the 2 turn into a fraction is that to the power of 2 means 2x2, to the power of one means 2, The power of zero would therefore divide by 2 so 2/2 = 1 and so 2 to the power of -1 would be 1/2.

         [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

    What is 2 to the power of -2?

   [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

Let's look at the last property of exponents - [tex]\bold{\#7 - negative\:exponents}[/tex]

                                    [tex]\Large\text{$a^{-n}=\displaystyle\frac{1}{a^n}$}[/tex]

So if we have a number with a negative exponent, we flip it over.

According to Property #7,

      [tex]\Large\text{2^{-2}=\displaystyle\frac{1}{2^2} =\frac{1}{4}$}[/tex]

                    [tex]\rule{50}{1}\smile\smile\smile\smile\smile\smile\rule{60}{1}[/tex]

[tex]3 b(broccolis=\frac{1}{8} )=\frac{3}{8}[/tex]

[tex]4c(carrots=\frac{1}{6})=\frac{4}{6}[/tex]

Lastly:

[tex]2t(tomatoes=\frac{1}{4})=\frac{2}{4}[/tex]

Answer:

0.01%

Step-by-step explanation:

There's no need to worry about a problem like this, it's easy. All you have to do is find the area of the smaller rectangle, being 50, then find the area of the other one, 5000, and divide the smaller by the larger and transfer it to a percentage. 50/5000 = 0.01 = 0.01%

Answer:

Area=153.75 divdided by 2 = 76.88

permitere= 8 + 10.25+18.8=37.05

Step-by-step explanation:

Answer:

Acute Scalene Triangle

Step-by-step explanation:

This depends on the classification type. Because we are given both the angle measure and information on the sides, I am combining the angle and side classification.

1. In terms of angles, it's acute. All the angles are less than 90, so it makes it acute.

2. In terms of sides, it's scalene because it has no equal sides.

Answer:

D) 56 inches to 74 inches

Step-by-step explanation:

By the Empirical Rule, 99.7% of data in a normal distribution spread across ±3σ standard deviations from the mean μ.

Hence, the range maximum is μ+3σ = 65+3(3) = 65+9 = 74 inches, and the range minimum is μ-3σ = 65-3(3) = 65-9 = 56 inches

Thus, 99.7% of the population will have a height within the range of 56 inches to 74 inches

If it is enlarged by a scale factor of 2. Then the coordinates of the translated triangle will be (2, -2), (6, 0), and (2, -8).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The coordinates of a triangle are (1,-1), (3,0), and (1,-4).

If it is enlarged by a scale factor of 2.

Then the coordinates of the translated triangle

(1,-1) → (2, -2)

(3,0) → (6, 0)

(1,-4) → (2, -8)

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A force of 4.05×10⁶ N was exerted on one side of the wall.

Force is an external agent capable of changing the state of rest or motion of a particular body. It has a magnitude and a direction.

The following data were obtained from the question:

Breadth (B) = 4 m

Length (L) = 10 m

Standard pressure (P) = 101325 Nm¯²

Next, we shall determine the area of the wall. This can be obtained as follow:

Area (A) = length (L) × breadth (B)

A = 10 × 4

A = 40 m²

Finally, we shall determine the force exerted on one side of the wall as follow:

Standard pressure (P) = 101325 Nm¯²

Area (A) = 40 m²

Pressure (P) = Force (F) /Area (A)

101325 = F/40

F = 101325 × 40

F = 4.05×10⁶ N.

Therefore, a force of 4.05×10⁶ N was exerted on one side of the wall.

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Step-by-step explanation:

option D is correct answer

Answer:

C

Step-by-step explanation:

[tex]\text{Plug} ~(x,y) = ( 2,0)~ \text{in both equations.}\\\\3*0 = 2-2\implies 0=0\\\\0 = -2(2) +4 \implies 0=0\\\\\text{Hence x =2 and y =0.}[/tex]

If the two ends of this triangular right prism are equilateral triangles. The surface area of the prism is 74cm.

Using this formula

A=bh+L(S1+S2+S3)

Where:

L=5cm

b=4cm

h=3.5cm

S1=4cm

S2=4cm

S3=4cm

Let plug in the formula

A=4(3.5)+5(4+4+4)

A=14+5(12)

A=14+60

A=74 cm

Therefore the surface area of the prism is 74cm.

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The system of equation 2x + y = 2 y = –2x – 1 has infinitely many solutions because the coefficient of the x and y in the equations are same.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a system of equations:

2x + y = 2  …(1)

y = –2x – 1  or

2x + y = -1 ...(2)

As we can see the coefficient of the x and y in the equation (1) and (2) are same which means they infinitely many solutions.

Thus, the system of equation 2x + y = 2 y = –2x – 1 has infinitely many solutions because the coefficient of the x and y in the equations are same.

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Answer:

8.7%

Step-by-step explanation:

Well the net sales of Quarter 1 = 115 whilst the net sales of Quarter 2 = 125.

So the difference in the 2 numbers is 125-115 = 10

To find percentage change, you do 10/115 = 0.0869565217

Then, 0.0869565217 x 100 = 8.7% change to 1 decimal point.

So your percentage change is 8.7%.

The time used for the first part of the trip in minutes is 270 minutes.

Total distance travelled = 675 km

He travelled from 1pm to 9pm.

He rested for 1 hour 30 minutes. The total time used for the trip is 6 hours 30 minutes.

let

the time used for the first part of the trip = x

Therefore,

speed = distance / time

distance = 110x

the time used for the first part of the trip = 6.5 - x

distance = 90(6.5 - x)

distance = 585 - 90x

Hence,

110x + 585 - 90x = 675

20x + 585 = 675

20x = 675 - 585

20x = 90

x  = 90 / 20

x = 4.5 hours = 270 minutes

Therefore, the time used for the first part of the trip is 270 minutes.

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Answer:

x = 36.9°

Given:

opposite side: 9

adjacent side: 12

angle: x

Using tane rule:

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

Solve:

[tex]\sf tan(x) = \dfrac{9}{12}[/tex]

[tex]\sf x = tan^{-1}(\dfrac{9}{12})[/tex]

[tex]\sf x = 36.87[/tex]

[tex]\sf x = 36.9[/tex]

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve ~

since the given triangle is an right angled triangle we can use Trigonometric ratios here :

[tex]\qquad \sf  \dashrightarrow \: \tan(x) = \dfrac{9}{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \tan(x) = \dfrac{3}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: x= tan { }^{ - 1} \bigg( \dfrac{3}{4} \bigg)[/tex]

[tex]\qquad \sf  \dashrightarrow \:x \approx37 \degree[/tex]

The confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.

It is defined as an error that gives an idea about the percentage of errors that exist in the real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times{\sqrt \dfrac{p(1-p)}{n}\\[/tex]

Where   Z is the z-score at the confidence interval

            p is the population proportion

            n is the number of samples.

We have p = 68% = 0.68

n = 115

Z score for 90% confidence interval = 1.64

[tex]\rm MOE = 1.64\times{\sqrt \dfrac{0.68(1-0.68)}{115}\\[/tex]

MOE = 0.071

So the confidence interval will be:

= (0.68-0.071, 0.68+0.071)

= (0.609, 0.751)  or

= (60.9%, 75.1%)

Thus, the confidence interval at a 90% confidence level is (60.9%,75.1%) if in the end of a semester, she loaned 115 highlighters and found that 68% were not returned option (A) is correct.

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Answer:

  0.9%

Step-by-step explanation:

The percentage change is found by multiplying the fractional change by 100%. The fractional change is the change amount divided by the original amount.

__

  change in height = 100/11013 × 100% ≈ 0.0090802 × 100% ≈ 0.9%

Answer:

i think the answer is (-4,2)

Step-by-step explanation:

The range of the graph is the set of output values, and the range is (d) (-infinity,infinity)

From the graph in the complete question, we can see that the output values (i.e. the y values) extend indefinitely on both sides of the graph

This means that the range of the graph is the set of all real numbers.

This in other words means that (-infinity,infinity)

Hence, the range of the graph is (d) (-infinity,infinity)

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Answer:

2.99924 in

Step-by-step explanation:

Volume of a cone

V = pi x r^2 x h/3

So to solve this problem you plug in the number we already have which is the volume and the height

103.62 = pi x r^2 x 11/3

28.26 = pi x r^2

28.26/pi = r^2

[tex]\sqrt{\frac{28.26}{\pi } }[/tex] = r ≈ 2.99924

The probability that the news and weather report Is NOT on will be 0.8. Then the correct option is J.

Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.

A radio station reports news and weather, every 20 minutes for 4 minutes.

If the radio is turned on at a random time.

Then the probability that the news and weather report Is NOT on will be

P = 1 - 4/20

P = 1 - 0.20

P = 0.8

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Answer:

The correct option is "an angle measure with an arc length equal to one radius length"

When finding radians, use this formula below.

Degrees × π/180

Answer:

40

Step-by-step explanation:

The number of sides also represents the number of angles.

Now, to find the measure of one angle we will need to find the sum of angles first and to do that, we use this very simple formula:

(n-2)*180 (n is the count of interior angles)

7*180 = 1260 and to find the measure of one angle we divide the sum with the number of angles:

1260/9 = 140

now, since the sum of an interior angle and an exterior angle is 180:

180-140 = 40 is the size of one exterior angle

There's an easier way too, just divide the sum of exterior angles by the number of angles

360/9 = 40

The area of the walkway itself is π[(y + 4)²- (y - 4)²] the radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4

An equation is an expression that shows the relationship between two or more numbers and variables.

Area of circle = π * radius²

The area of the walkway itself = π(y + 4)² - π(y - 4)² = π[(y + 4)²- (y - 4)²)

The area of the walkway itself is π[(y + 4)²- (y - 4)²] the radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4

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Answer:

The answer is (x + 10)² + (y – 7)² = (4)².

Step-by-step explanation:

Here, a = (-10), b = 7 and r = 4.

So,

(x – a)² + (y – b)² = r²

[x – (-10)]² + (y – 7)² = (4)²

(x + 10)² + (y – 7)² = (4)²

Thus, The standard equation of the circle with the centre of (-10, 7) and a radius of 4 is

(x + 10)² + (y – 7)² = (4)².

Answer:

V=14.12 in³

Step-by-step explanation:

This is a tough one. To find the volume, you'll need the followimg equation:

[tex]\frac{4}{3} \pi {r}^{3}[/tex]

The 3 next to the R is an exponent. An exponent involves multiplying the radius by itself. So it would look like this: 1.5×1.5×1.5

Next, you must multiply the result by 3.14. So it would be 3.375×3.14. And finally, you must multiply that result by 4 and divide by 3. So 10.59×4 to get 42.36 then divide that by 3. 42.36 divided by 3 is 14.2. (Answer can vary from time to time and you may need to round up)

Answer:

The number closest to 300 would end up being 310!

Step-by-step explanation:

Answer:

2461.848 bushels

Step-by-step explanation:

67 tonnes x 36.744 bushels/ 1 tonnes

= 2461.848 bushels

2.5 quarts will be needed to paint the wall on the right.

The product of length and breadth.

Area of rectangle=  length * breadth

Area of first wall = l * b

= 12*7

= 108 st. ft.

Area of 2nd wall

= l*b

=18*10

=180 sq. ft.

If 1.5 qt required to paint the 108 sq. ft. area

For 1 sq ft, paint would be need= 1.5/108

For 180 sq ft paint needed = 1.5*180/108

                                            = 2.5 qt

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