Suppose a student takes a 10-question true-false test, but they didn't study. What's the probability they get 3 problems correct by guessing

The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

What is dilation?

A dilation is a transformation that creates an image that has the same shape as the original but is larger.

• An enlargement is a dilation that produces a larger image.

• A reduction is a dilation that produces a smaller image.

• A dilation expands or contracts the original figure.

A dilation is a stretch or a shrink in the size and location of a figure or point.

The scale factor in a dilation is the amount by which the figure is stretched or shrunk.

The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,

k, the location of the center of dilation, \((x_0,y_0)\) is

\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)

Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).

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Answer:

V≈743.25

Step-by-step explanation:

V=5

12tan(54°)ha2=5

12·tan(54°)·4·182≈743.24624

Answer:

it is 1

Step-by-step explanation:

E = midpoint

DF = DE + EF

but, DE = EF because E is the midpoint

Substitution

9x - 10 = 92 + 92

Simplification

9x - 10 = 184

9x = 184 + 10

9x = 194

x = 194/9

x = 21.55

Answer:

x³ + 9x²y + 27xy² + 27y³

Step-by-step explanation:

( x + 3y )² =

(x + 3y)(x + 3y) =

x² + 3xy + 3yx + 9y² =

x² + 6xy + 9y²

(x + 3y)(x² + 6xy + 9y²) =

x³ + 6x²y + 9xy² + 3yx² + 18xy² + 27y³ =

x³ + 9x²y + 27xy² + 27y³

Hope this helps :)

Answer:

f(-6)= -8

Step-by-step explanation:

just look at where x is -6 and y is -8 so f(-6) is -8

Hopes this helps please mark brainliest

Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

Answer:

its domain

Step-by-step explanation:

Answer:

i believe it is A- range.

Step-by-step explanation:

i took the quiz

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

The curve joining the points P1, P2, P3, and so on is called the involute of a circle.

To construct the locus of the free end of the coir for unwinding through an angle of 360 degrees, as well as the normal and tangent at any point on the curve.

Here are the steps for construction:

1. Draw a line PQ that is tangent to the circle and is equal to the circumference of the circle. This line represents the coir being unwound.

2. Divide both the circle and the tangent line into the same number of equal parts. Label these divisions on the circle as 1, 2, 3, and so on. Similarly, label the divisions on the tangent line as 1', 2', 3', and so on.

3. Draw tangents at points 1, 2, 3, and so on on the circle. Mark the points where these tangents intersect the tangent line as P1, P2, P3, and so on.

The distance from each point Pi to the corresponding point i' on the tangent line should be the same as the distance from the center of the circle to the point i on the circle.

4. The curve joining the points P1, P2, P3, and so on is called the involute of a circle. This curve represents the locus of the free end of the coir as it unwinds.

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The process involves creating an initial circle that represents the drum, then using this to draw a horizontal line that's the same length as your first circle's circumference. Divide both into segments and draw lines (tangents) from one set of segments to the other. Points along these lines represent an unwound thread and create the involute when joined up. Tangents and normals can also be drawn onto this curve.

This question pertains to the mathematical concept of a curve locus, specifically the spiral curve produced by unwinding a coir from a drum. To draw this spiral curve (or 'involute'), start by sketching a circle representing the drum (with diameter 30mm). Next, calculate the circumference of this circle and draw a horizontal line of equivalent length. Then, divide this line and the circumference of your circle into the same number of equal sections. For each section in your circle, draw a line from the point of division to an equivalent point on your horizontal line. These lines are your tangents. Mark points on these lines which correspond to the distances covered by the unwound thread. Finally, join these points to create the involute of the circle.

For the part about drawing a normal and a tangent at any point on the curve: Pick a point on the curve. Remember that the tangent at a point on an involute is perpendicular to the line from the point to the centre of the original circle. A normal at any point on a curve is simply a line drawn perpendicular to the tangent at that point.

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Answer:

height of water = 5.60 cm

Step-by-step explanation:

To solve this problem, we must first calculate the volume of water present. Since the rectangular container is completely filled, the volume of water is the same as the volume of the container.

∴ Volume of water = volume of rectangular container

                                 = length × width × height

                                 = 2 cm × 11 cm × 20 cm

                                 = 440 cm³

Therefore the volume of the water is 440 cm³.

The water is poured into a cylindrical container. Therefore, to calculate the height of the water in the cylindrical container, we can use the formula for the volume of a cylinder, and then solve for height:

Volume = \(\pi r^2 h\) = 440

             ⇒ \(\pi \times (5)^2 \times h = 440\)

             ⇒ \(25\pi \times h = 440\)

             ⇒ \(h = \frac{440}{25\pi }\)

             ⇒ h = 5.60 cm

The height of water in the cylindrical container is 5.60 cm.

Answer:

14

Step-by-step explanation:

Answer:

75 dollars.

Step-by-step explanation:

Each person costs 25 dollars and p=3 we just put this into a equation.

25 × 3 = 75

C = 75

a. The chi-square statistic is not significant at the α level of .01.

b. The chi-square statistic is significant at the α level of .05.

a. With a chi-square statistic of 3.86 and a critical value of 6.63 at α level of .01, we can compare the two values.

Since 3.86 < 6.63, this means that the chi-square statistic is not significant at the α level of .01.

In other words, the result is not statistically significant and we fail to reject the null hypothesis.

b. With a chi-square statistic of 67.81 and a critical value of 3.84 at α level of .05, we can again compare the two values.

Since 67.81 > 3.84, this means that the chi-square statistic is significant at the α level of .05.

In other words, the result is statistically significant and we reject the null hypothesis.

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Answer:

0,3, and 6.

Explanation:

The second derivative of the function f is given below:

To find the x-coordinate of the point of inflection, set the second derivative of the function equal to zero and solve for x.

The x-coordinates of the point of inflection are 0,3, and 6.

There are 104 cars in the parking lot.

According to statement there are between 90 and 115 cars on the lot.

So, {X| 90 < x < 115} (This renders an infinite solution set finite)

AND exactly one eight of them have a sticker on the back, so the total number of cars must be evenly divisible by eight.

X ∈ {96, 104, 112,}

AND exactly one fourth of the cars are green, so the number of cars must be evenly divisible by 4. Here all above written numbers are divisible by 4. So, find the mean to calculate the number of cars in the parking lot.

x = (96+104+112)/3

x = 104

There are 104 cars in the parking lot.

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Answer: 19

Step-by-step explanation:

Answer:

1. 20/3 or 6 2/3

2. 0.4

3. 11

4. 11

5. They are both similar

Hope this helps!

Answer/Step-by-step explanation:

i. No. of hours Martine works per week = 33.5 hours

If she does this for 36weeks in a year, she works the following hours in a year:

33.5 hrs × 36 weeks = 1,206 hours

Rounding of to 1 significant figure (first non-zero digit counting from left to right is the first significant figure) = 1,000 hours

Thus:

33.5 × 36 = 1,000

ii. Martine earns £263 per week, in a year (36 weeks), she'd earn:

263 × 36 = 9,468 ≈ £10,000 (rounded to 1 s.f)

iii. Overtime = £8.35 per hour

To save to pay £900 for a holiday, she needs to do the following number of overtime:

900 ÷ 8.35 = 107.784431 ≈ 100 hours (rounded to 1 s.f)

Answer:

F type connector

Step-by-step explanation:

Use an F-type connector for broadband cable connections that use coaxial cable.

The F connector is a coaxial RF connector commonly used for "over the air" terrestrial television, cable television and universally for satellite television and cable modems,

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The statements that are true based on the midpoint given in the question include:

In geometry, the midpoint simply means the middle point of a line segment. The midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

Also, it should be noted that the midpoint bisects the segment.

In this case, m∠P + m∠Q + m∠R = 180°. This is because the sum of the angles in a triangle will be equal to 180°. Also, PT, QU, and RS intersect at the same point.

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Complete question:

Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.

Next, draw PT, QU, and RS.

Which statements are true?

m∠Q = m∠R

The length of QU is half the length of RP.

m∠P + m∠Q + m∠R = 180°

QU ≅ RS

PT, QU, and RS intersect at the same point.

The sum of the lengths of QU and RS is equal to the length of PT.

The work of earth scientists plays a crucial role in benefiting engineers and people all over the world in several ways.

Here are some key areas where their work is valuable:

Natural Resource Exploration: Earth scientists study the Earth's composition, structure, and processes, enabling them to locate and assess valuable natural resources such as minerals, fossil fuels, and groundwater. This information is vital for engineers involved in resource extraction, as they can use it to plan and execute efficient and sustainable extraction methods. The availability of these resources directly impacts various industries, economies, and people's access to energy and materials.

Environmental Management and Sustainability: Earth scientists study the environment and its complex interactions, including the atmosphere, hydrosphere, biosphere, and geosphere. This knowledge is crucial for engineers and policymakers involved in environmental management and sustainability. Earth scientists provide information about climate change, natural hazards, pollution, and ecosystem dynamics, which helps engineers design infrastructure, buildings, and systems that are resilient, environmentally friendly, and mitigate potential risks.

Geological Hazard Assessment and Mitigation: Earth scientists play a significant role in assessing and mitigating geological hazards such as earthquakes, volcanic eruptions, landslides, and tsunamis. By studying tectonic activity and geological processes, they can identify high-risk areas and provide valuable data for engineers to design structures and infrastructure capable of withstanding these hazards. This knowledge saves lives and minimizes damage by improving building codes, designing robust infrastructure, and implementing early warning systems.

Water Resources Management: Earth scientists study the distribution, quality, and availability of water resources, including surface water, groundwater, and glaciers. Their research helps engineers and water resource managers make informed decisions regarding the sustainable use and management of water. They can assess water availability, predict droughts and floods, identify pollution sources, and develop strategies for efficient water allocation, treatment, and conservation, benefiting agricultural, industrial, and domestic water users.

Geotechnical Engineering: Earth scientists provide valuable insights into soil and rock properties, geologic formations, and subsurface conditions. This information is crucial for geotechnical engineers who design foundations, tunnels, dams, and other structures. Earth scientists' understanding of the Earth's materials and their behavior helps engineers ensure stability, prevent landslides, manage soil liquefaction risks, and make informed decisions during construction projects.

Climate Change and Adaptation: Earth scientists contribute significantly to our understanding of climate change and its impacts. Their research helps engineers and policymakers develop strategies for climate change adaptation and mitigation. Earth scientists provide data on changing weather patterns, rising sea levels, melting glaciers, and ecosystem shifts, allowing engineers to design infrastructure, coastal defenses, and urban planning that account for future climate scenarios, protecting people and minimizing the impacts of climate change.

In summary, the work of earth scientists is vital for engineers and people worldwide as it provides critical knowledge about the Earth's resources, environmental dynamics, geological hazards, water management, geotechnical aspects, and climate change. This information supports engineers in making informed decisions, designing sustainable infrastructure, protecting lives and property, and ensuring the well-being and resilience of communities across the globe.

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To represent the cost, in cents, of mailing a letter weighing between 0 and 3 ounces using a piecewise-defined function, we can break it down into different weight intervals and calculate the cost for each interval.

Here's the piecewise-defined function P(x):

P(x) =

37 for 0 ≤ x ≤ 1

37 + 26(x - 1) for 1 < x ≤ 2

37 + 26(2 - 1) + 26(x - 2) for 2 < x ≤ 3

For weights between 0 and 1 ounce (inclusive), the cost is a constant 37 cents.

For weights between 1 and 2 ounces (exclusive), the cost is 37 cents for the first ounce plus an additional 26 cents for each additional ounce or fraction of an ounce.

For weights between 2 and 3 ounces (inclusive), the cost is 37 cents for the first ounce, 26 cents for the second ounce, and an additional 26 cents for each additional ounce or fraction of an ounce.

Note that the upper and lower bounds of each interval are inclusive, except for the upper bound of the previous interval, ensuring that there are no gaps or overlaps in the weight ranges.

Please keep in mind that this function is specific to the given cost structure and weight intervals stated in the problem.

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The value of variable x=4 units in the given figure.

A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. The side opposite to the right angle is called the hypotenuse, while the other two sides are called the legs or catheti. The lengths of the legs and the hypotenuse of a right triangle are related by the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

From the given figure;

Tan60°=p/1

p=1.732 units

The smaller triangle is right angle

h²=p²+b²

h=√1²+1.732²

h=2units

In the bigger triangle, angle subtended by base is 60 (vertically opposite angle)

Using the trigonometric function

Cos60°=2/x

1/2=2/x

x=4units

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Answer:

0---22.5   and    21---36

Step-by-step explanation:

you will always have 21 free CDs so you can put a closed circle on 21 then you can have a max of 15 CDs (180/12) soo put another closed circle on 36

now time for tapes, which is easier, the minimum is 0 and the max is 22.5. Now put closed circles on each and you're done. Except that .5 might get you in trouble, use your own discretion on rather to leave it on the .5 or round. I don't know what your teacher is looking for so I will let you decide.

Answer:

Hope it helps

Step-by-step explanation:

1: B

2: B

3: D

4: C

5: A

The finding that average IQ has increased steadily over the 20th century is referred to as the Flynn effect.

The Flynn effect is the observation that the average IQ has risen continuously over the 20th century.The Flynn effect is what?The Flynn effect is the finding that IQ levels in the general population rise over time and across generations.

For instance, during the past century, IQ scores have continuously risen in industrialised nations by about 3 points every decade. James R. Flynn, a political scientist from New Zealand who first observed this pattern, created the phrase "Flynn effect" in 1987.

The Flynn effect is significant because it demonstrates that IQ levels are not constant but can alter due to environmental factors. It also emphasises how challenging it is to define and assess intelligence, particularly when contrasting populations from various historical periods or cultural backgrounds.

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Answer:

D

Step-by-step explanation:

20x + 12 x =14x +30

20x - 14x = 30-12

6x= 18

6x/6 = 18/6

x = 3

so xs =3