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The mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.

The mass of a sheet of metal is directly related to its area and thickness. This means that the mass of a sheet of metal is proportional to the product of its area and its thickness. Mathematically, this can be expressed as the formula M = kAT, where M is the mass, k is a constant, A is the area and T is the thickness.In the given example of a sheet of metal with an area of 250 cm and a thickness of 1mm, we can calculate the mass of the sheet by substituting the given values into the formula: M = k(250)(1) = 200g. The constant k in this example is equal to 0.8 g/cm*mm.Therefore, the mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.

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What is the mass of a sheet of metal with an area of 250cm and a thickness of 1mm?

To fully describe a triangular prism, you would need to provide the dimensions of its triangular bases (e.g. base length and height), the length of the prism, and the length and width of the rectangular faces. Thus, option C is correct.

To find the volume of filler material required to surround the triangular prism, we need to first calculate the volume of the box and the volume of the triangular prism.

The volume of the box is given by:

[tex]8[/tex] inches ×  [tex]13[/tex] inches ×  [tex]16[/tex] inches =  [tex]1,664[/tex] cubic inches

The volume of the triangular prism is given by:

[tex](1/2) × 8[/tex] inches ×  [tex]13[/tex] inches ×  [tex]16[/tex] inches = [tex]832[/tex] cubic inches

To completely fill the box, we need to add filler material with a volume equal to the difference between the volume of the box and the volume of the triangular prism, which is:

 cubic inches— [tex]832[/tex] cubic inches   [tex]= 832[/tex] cubic inches

Therefore, the [tex]832[/tex]  Cubic inches.

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Find CD:

Let,

[tex]r_1[/tex] be a radius of Circle A

[tex]r_2[/tex] be a radius of Circle B

Given:

[tex]r=4cm.[/tex]

Circumference: [tex]2\pi r[/tex]

[tex]2\pi r_1=30[/tex]

[tex]r_1=\dfrac{15}{\pi }[/tex]

[tex]CD=D_1+D_2[/tex]

[tex]=2r_1+2rx_2[/tex]

[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]

[tex]CD=17.55cm.[/tex]

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The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.

To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.

The new value of the stock in Company A is:

[tex]4500 + (5 \times 4500) = $4725[/tex]

The new value of the stock in Company B is:

[tex]3900 + (11 \times 3900) = 4339[/tex]

The total value of the investor's stock account after the increase is:

$4725 + $4339 = $9064

To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:

($9064 - $8400) / $8400 = 0.0795

We then multiply this decimal by 100 to get the percentage increase:

0.0795 x 100 = 7.95%

Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

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The cost per square inch of the apple pie is $ 0.16.

Given that,

The diameter of the pie = 10 in

The radius of the pie = 10/2

                             = 5 inches.

Area of the pie = [tex]\pi r^{2}[/tex]

                         =  3.14 × 5²

                         = 3.14 × 25

                          = 78.5 in²

The cost of the apple pie = $ 12.85.

Therefore, the cost per square inch of the pie = 12.85 ÷ 78.5

                                                                             = $ 0.16.

Hence, the cost per square inch of the apple pie is $ 0.16.

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Answer:

J. 56

Step-by-step explanation:

The picture in this question can be a little deceiving. Each rectangular glass pane is 3 by 10 inches. This means that the picture of the 4 panes overlapping, leaves the center square open. The open area has your inner edges. The question asks for the sum of the inner and outer edges.

Every pane is 10 inches long, so the out perimeter of the figure is 40 inches because the figure has four sides. The rectangles overlap, creating 3 by 3 inch square. 3 inches off either side of a pane leaves 4 inches as the length for the edge of the inner square. Therefore, the perimeter of the inner square is 16 inches.

Outer Perimeter + Inner Perimeter = 40 + 16 = 56 inches

If the screen door spring has a spring constant of 188 N/m, then the force it exert is 54.9 N .

The force exerted by the screen door spring can be calculated using Hooke's law,

The Hooke's Law states that the force exerted by a spring is directly proportional to its spring constant and the amount it is stretched.

The formula for "Hooke's-law" is ⇒ F = kx

Where F is = force exerted by spring, k is = spring constant, and x is = amount spring is stretched.

In this case , the spring constant(k) = 188 , the distance stretched(x) = 292m ;

Substituting the values,

We get,

⇒ F = (188 N/m)(0.292 m)

⇒ F = 54.896 N

⇒ F ≈ 54.9N

Therefore, The force exerted by the screen door spring is approximately 54.9 N.

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Answer:

P(0,2), Q(3,5), R(3,0)

Step-by-step explanation:

Answer:

-16²+1,000 > 300  [After an edit in the original expression, as noted below).

Step-by-step explanation:

The equation d = -16² +1,000 tells us the height above ground, d, of the object after t seconds.  When t = 0 seconds, the ball has not been dropped yet, but the equation tells us that d = 1,000 at t = 0.  That means the object starts at 1,000 feet above ground.

We want the time it takes for the object to reach any height greater than 300 feet above ground.  This is a tad (metric for just a tiny bit) unexpected, since even at time of 0 the object is greater than 1,000 feet.

Looking at the answer options, note that the left side of the inequalities is -16^2+100.  I will assume the 4th option has a typo:  the f^2.  It should read the same as the others.  

      -16^2+100 is the distance, d.  So to help us think this through, let's rephrase the answer options in terms of distance, d:

1)    d<300

2)   d≤300

3)   d≥300

4)   d>300

   The question asks "We want the time it takes for the object to reach any height greater than 300 feet above ground."

Option 4 says d>300, or height greater than 300.  That is the inequality that matches the question.  [Note:  It did not say greater than or equal to (option 3).]

The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale

Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.

Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.

The formula for calculating the magnitude of an earthquake based on its amplitude is:

Magnitude = log10 (Amplitude) - 3

where the amplitude is measured in microns.

Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:

Magnitude = log10 (100,000) - 3

Magnitude = 5 - 3

Magnitude = 2

Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.

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The value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2 is Option B: 11.8.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

To find the value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2, we substitute these values into the expression and simplify -

Substitute the values x = 4 and y = 2 into the expression -

1.3(x + 2) - (y - 6)

= 1.3(4 + 2) - (2 - 6)

Apply the addition and subtraction operation -

= 1.3(6) - (-4)

Apply the multiplication operation -

= 7.8 + 4

= 11.8

Therefore, the value of the expression is 11.8.

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Absolutely, Jada's response is right. A square is a quadrilateral with four equal-length sides. A quadrilateral is a square if all four sides measure 5 cm.

Unfortunately, there is no alternative form Jada could have drawn that meets the requirement of all four sides measuring 5 cm. Every other quadrilateral with four equal-length sides is likewise a square. If Jada had drawn a quadrilateral with one or more sides of varying lengths, the specified criterion would not have been met. As a result, the only design Jada could have sketched that meets the requirement of having all four sides measure 5 cm is a square. It is worthwhile to investigate the properties of quadrilaterals and how they connect to the conditions presented in the problem. A quadrilateral is a four-sided polygon. Quadrilaterals come in a variety of shapes, including squares, rectangles, parallelograms, trapezoids, and kites. Certain quadrilaterals have unique qualities, such as opposing sides that are parallel or all angles that are right angles. The criterion in the provided problem is that all four sides of the quadrilateral measure 5 cm.

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The difference in the loudness of sound when the two teams score is about 14.77 decibels

Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.

We can use the fact that the loudness of sound is measured in decibels (dB) and that the dB scale is logarithmic.

Let's assume that the loudness of the sound when the away team scores is x decibels. Then the loudness of the sound when the home team scores a touchdown is 30 times as great, which means it is 30x decibels.

The difference in loudness between the two scenarios is given by the difference in decibels:

difference in decibels = 10 log (30x/x) = 10 log 30 = 14.77

Therefore, the difference in the loudness of sound when the two teams score is about 14.77 decibels

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The probability that no one gets a hole on the sixth hole is given as follows:

0.9534 = 95.34%.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

The holes are independent, hence the probability of no one getting a hole in the sixth hole is P(X = 0), thus:

P(X = 0) = (1 - 1/3709)^175

P(X = 0) = 0.9534 = 95.34%.

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Answer:

y = - [tex]\frac{5}{2}[/tex] x - 1

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 )

calculate m using the slope formula

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

with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table

m = [tex]\frac{-6-9}{2-(-4)}[/tex] = [tex]\frac{-15}{2+4}[/tex] = [tex]\frac{-15}{6}[/tex] = - [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then

c = - 1

y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line

Answer:

He is now selling only one product and making less money because he is not selling other TVs.

Step-by-step explanation:

So if you read the paragraph, you get to the point where he says only making and selling the television model that makes the most money. If you think about it if they only sell one product, the other products they used to sell aren't being sold and they are making less money. I hope this helps!

Therefore , the solution of the given problem of standard deviation comes out to be he average difference between the population mean and the sample mean is 6.

Variance is a measure of variation used in statistics. The average difference between the gathering and the mean is calculated using the photo of that figure. By comparing each number to the mean, it incorporates those data points into the calculations on their own, in contrast to many other legitimate measures of variable. Variations could result from deliberate errors, unrealistic expectations, or changing economic or commercial circumstances.

Here,

For a group of n = 4, the standard error of the mean (SEM) is as follows:

=> SEM = α/√(n)

=> 24/√(4) = 12

Therefore, for n = 4 scores drawn at random from the population, the average difference between the population mean and the sample mean is 12.

b. The SEM for a group of n = 9 is:

=> α/√(n) = 24/√(9)

=> 8; SEM = α

Therefore, for n = 9 scores drawn at random from the population, the average difference between the population mean and the sample mean is 8.

c. The SEM for a sample of 16 is as follows:

=> α / √(n) = 24 / √(16) = 6;

=>  SEM =α

Therefore, for n = 16 scores drawn at random from the population, the average difference between the population mean and the sample mean is 6.

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The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.

The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:

[tex]F(x) = P(X ≤ x)[/tex]

The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,

[tex]F(x) = ∫-∞ x f(u) du[/tex]

Where f(u) is the probability density function.

For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]

Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.

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Complete question:

What is the cumulative distribution function for a continuous random variable x?

The height, in meters, where the pumpkin lands on the hill is 4.9 meters.The equation for the height of the hill is y = 0.9x.

This equation can be rearranged to solve for x, giving x = y/0.9. The equation for the height of the pumpkin is y = -0.1x² + 4.9x. Substituting the x value from the previous equation into the equation for the height of the pumpkin gives y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying this equation gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill.

The equation for the height of the hill is y = 0.9x, which describes the incline of the hill. This equation can be rearranged to solve for x, giving x = y/0.9. This equation can then be used to substitute into the equation for the height of the pumpkin, which is y = -0.1x² + 4.9x. When the x value from the previous equation is substituted into the equation for the height of the pumpkin, the equation simplifies to y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying further gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill. This can be verified by substituting 4.9 for y in the equation for the height of the hill, which gives x = 4.9/0.9 = 5.4. This value can be substituted into the equation for the height of the pumpkin, which gives y = -0.1(5.4)² + 4.9(5.4) = 4.9, verifying the result.

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Answer:

plot the point at 1

Step-by-step explanation:

Answer:

£602.84 in New York

Step-by-step explanation:

London Cost:

Converting pound to dollars:

£800 * 1.41 = $1128

Paris cost:

Converting euro to pounds:

€880/1.16 = £759

Converting pound to dollars again:

£759 * 1.41 = $1070

New york cost:

$850

The lowest price is in new york which is:

$850/1.41 = £602.84

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