A car travels at a speed of 72 miles per hour. Write a direct variation equation for the distance, y, the car will travel in x hours. How far will the car travels in 4.5 hours?

Answer:

130 degrees.... I am pretty sure

Cus angles of a triangle add to 180 and so the inside angle is 130 and they are vertical angles so they are the same right? right?

Step-by-step explanation:

Answer:

130 degrees

Step-by-step explanation:

I first came up with the equation 30+20+?=180 (I got 180 because every angle in a triangle added up is 180), then added the 30 and 20 to get 50+?=180. I subtracted 50 from both sides and got ?=130. I know that the angle on the inside and the outside are equal because it seems like a reflection, so if the inside angle is 130 the outside angle is 130 degrees too.

Hope this helps you :)

The probability that one mouse survives less than 10 weeks is 0.6321. Hence, the correct option is (e) 0.6321

Given, The life of a type of mice (in weeks) follows exponential distribution with B (beta)=10.

Let X be the life of a type of mice (in weeks) follows exponential distribution with B (beta)=10.

The probability that one mouse survives less than 10 weeks is given by; P(X < 10)

We know that the cumulative distribution function (CDF) of an exponential distribution is given by;

F(x) = P(X ≤ x) = 1 - e^{(-x/β)}

The probability that one mouse survives less than 10 weeks is given by;

P(X < 10) = F(10)

= 1 - e^{(-10/10)}

= 1 - e^{-1}

= 0.6321

Therefore, the probability that one mouse survives less than 10 weeks is 0.6321. Hence, the correct option is (e) 0.6321.

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The two scales used in a classroom demonstration to suspend a \(10N\) weight can register a weight of \(10N\) due to the principle of equilibrium of forces.Each scale can register a weight of \(10N\) because the total weight is supported by two scales at the same time and at the same height.

When a weight of \(10N\) is suspended using the two scales, the weight pulls down on both of them by the same force. Since each scale supports half of the weight, the force exerted on each scale is \(5N\).In order to understand how the scales can register a weight of \(10N\) each, we need to take a look at the forces acting on the weight.

The weight is suspended from two scales, so it is acted upon by two forces: the force of gravity pulling it down and the upward force exerted by the scales.The two scales have a spring inside that is compressed when the weight is suspended from them.

The compression of the spring inside each scale generates an upward force that balances out the weight of the object. This results in an equilibrium of forces, with the upward force exerted by the scales balancing out the force of gravity pulling the object down. Therefore, each scale can register a weight of \(10N\) because the force exerted by each scale is equal to half the weight of the object (\(5N\)), and the two scales together can support the entire weight of the object (\(10N\)).

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Answer:

5.64 cm

Step-by-step explanation:

Required:How much more rain fell in Dubaku's town than in Elliot's town?

8 centimeters of rain fell in Dubaku's hometown

2.36 centimeters of rain fell in Elliot's hometown

We are asked to find how much more rain fell in Dubaku's town than in Elliot's town so it is calculated as the difference between the rain in both of there towns and is given by:

Difference in rain= 8-2.36

Difference in rain= 5.64 cm.

Therefore, 5.64 cm of more rain fell in Dubaku's town than in Elliot's town.

Answer:

5.64

Step-by-step explanation:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).

If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.

from the question:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.

Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.

Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.

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Answer:

a) y=0.50x+15  

b) The graph of this equation form on a coordinate plane is a line.

c) Slope  =0.50 and y-intercept = 15

Step-by-step explanation:

Let x = Number of miles driven by car

Given: The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.

a) Total cost = 0.50x+15

If y =total cost of renting the car, then y=0.50x+15   (i)

b) Above equation is similar to y= mx+c  (ii) [m = slope , xc=y-intercept] which a linear equation .

So the graph of this equation form on a coordinate plane is a line.

c) Comparing (i) and (ii)

m=0.50 , c=15

Hope this helps :)

We have a simple interest case. In this kind of situation, we have to use the next formula for simple interest:

Where:

• I is the earned interest. In this case, we have I = $200.

• P is the Principal amount (that is, the amount the man borrowed in this case). In this case, we have P = $5,000.

• R is the interest rate. In this case, we have I = 16% = 16/100.

• T is time transcurred to get the earned interest. This is the unknown value we are about to find.

Therefore, we have:

Then we have:

Now, we need to divide both sides of the equation by the product 5000(0.16) to solve for T as follows:

Answer:

\(y = -\frac{1}{3}x + 3\)

Step-by-step explanation:

Required

The graph equation

From the graph, we have:

\((x_1,y_1) = (0,3)\)

\((x_2,y_2) = (3,2)\)

First, calculate the slope (m)

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m = \frac{2-3}{3-0}\)

\(m = \frac{-1}{3}\)

\(m = -\frac{1}{3}\)

The equation is calculated as:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = -\frac{1}{3}(x - 0) + 3\)

\(y = -\frac{1}{3}(x) + 3\)

\(y = -\frac{1}{3}x + 3\)

The equation which represents the graphed function is; y = (-1/3)x + 3

By observation, the graphed line crosses the y-axis at point; (0, 3). Hence, the y-intercept is at y= 3.

Additionally, the slope of the line can be evaluated by considering the two points given;

Slope, m = (2-3)/(3-0)

Slope, m = -1/3

Hence, the equation of the line is;

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Answer:

2.5% believe.

Step-by-step explanation:

I may be wrong but heres how I solved it.

Take the 8 hours and convert it to minutes.

8 hours - 480 minutes total

12 minutes out of 480 minutes is 2.5%

Check the picture below.

Answer:

A

Step-by-step explanation:

A congruent shape is a shape that has the exact same shape and size as another. therefore, I believe that the first, second, and third pairs are congruent. If it could only be one pair, I think the last one.

An actual application of sampling theorem and aliasing in Computer Science is in digital signal processing.

In the field of digital signal processing, the sampling theorem and aliasing play a crucial role in the conversion of continuous-time analog signals into discrete-time digital signals. The sampling theorem states that in order to accurately reconstruct an analog signal from its samples, the sampling rate must be at least twice the highest frequency component present in the signal.

This process involves taking periodic samples of the continuous-time signal at regular intervals, which is known as the sampling rate.

Aliasing, on the other hand, occurs when the sampling rate is not sufficient to capture the complete information of the analog signal. It results in the folding of higher frequency components into lower frequency ranges, causing distortion or loss of information. This phenomenon is particularly relevant in computer science because many real-world signals, such as audio or video data, are continuous-time analog signals that need to be sampled and processed digitally.

In audio compression algorithms like MP3, the audio signal is first sampled at a certain rate, following the guidelines of the sampling theorem. Then, to reduce the file size, the algorithm removes the high-frequency components that are beyond the range of human hearing, utilizing the aliasing effect.

By selectively discarding these frequencies and reconstructing the signal during playback, it achieves significant compression while maintaining acceptable audio quality.

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Answer:

Total amount after 3 year = 1,157.625

Step-by-step explanation:

Given:

Amount deposit P = $1,000

Number of year n = 3 year

Interest rate r = 5% = 0.05

Find:

Total amount after 3 year

Computation:

Amount = P[1+r]ⁿ

Total amount after 3 year = 1,000[1+0.05]³

Total amount after 3 year = 1,000[1.05]³

Total amount after 3 year = 1,157.625

The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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Answer:

160 minutes or two hours and 40 minutes

Step-by-step explanation:

        First, let's divide 2 hours of total work by the 15 minutes chunks she does.

2 hours = 120 minutes

120 minutes / 15 minutes = 8

        She will have 8 sessions of studying with a break. Now we can calculate the total.

[] 120 minutes of studying

[] 8 * 5 minute break = 40 minutes of break

[] 120 + 40 = 160 minutes

Answer:

45 because it is what I think

Answer:

12

Step-by-step explanation:

Because if you see clearly that is the only answer that makes the most sense!

The value of m is the expression x⁴ + mx² + 64 a perfect square will be 16.

A perfect square trinomial formulation can be created by taking the binomial equation's squared. If and then only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is indeed a perfect square.

The equation is given below.

⇒ x⁴ + mx² + 64

Then the value of a, b, and c will be 1, m, and 64, respectively. Then the equation will be given as,

b² = 4ac

m² = 4 x 1 x 64

m² = 265

m² = 16²

m = 16

The value of m is the expression x⁴ + mx² + 64 a perfect square will be 16.

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complete question:

For what value of m is the expression x4+mx2+64 a perfect square?

Answer:

4

Step-by-step explanation:

Notice each side was increased by 4 times

You can set up a ratio of

\(\frac{new}{old}\)

then reduce or divide

The Angle Bisector Equidistant Theorem Converse (ABET Converse) states that if a point is equidistant from the sides of an angle, then it lies on the angle bisector.

To understand the ABET Converse, we first need to understand the Angle Bisector Equidistant Theorem (ABET). The ABET states that if a point lies on the angle bisector of an angle, then it is equidistant from the sides of the angle. In other words, if we draw an angle and then bisect it (i.e., draw a line that splits the angle into two equal parts), any point on that line will be equidistant from the sides of the angle. The ABET Converse simply flips this idea around. It states that if a point is equidistant from the sides of an angle, then it must lie on the angle bisector. So, if we have a point that is the same distance from both sides of an angle, then that point must lie on the line that bisects the angle.

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Answer:

1. don't know what you want for the first one but..

2. x=9

3. y= 8

Step-by-step explanation:

x = 1.5y

ex y=2 x=2

Answer:

50x - 99 x =79 + 31 is your answer

Step-by-step explanation:

The given expression -0.4(3x+8) is equal to the expression -1.2x - 3.2 (Option 3), but not equal to the expressions -3x - 3.2 (Option 1) or -1.2x + 3.2 (Option 4).YES

To determine if the given expression -0.4(3x+8) is equal to each of the provided expressions, let's simplify the expression and compare the results.

Here are the calculations:1. -3x - 3.2:To simplify -0.4(3x+8), we distribute -0.4 to both terms inside the parentheses:

-0.4(3x) + (-0.4)(8) = -1.2x - 3.2The simplified expression is -1.2x - 3.2.2. -1.2x - 8:

Comparing this expression to the simplified form of the given expression, we can see that they are not equal. , the answer is No.3. -1.2x - 3.2:Comparing this expression to the simplified form of the given expression, we can see that they are equal. , the answer is Yes.

4. -1.2x + 3.2:Comparing this expression to the simplified form of the given expression, we can see that they are not equal. , the answer is No.

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The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.

To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula

z = ( x- μ)/ σ

where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get

z = ( 42,000- 40,000)/ 3,000 = 0.67

Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.

thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.

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The correct question is given below-

A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?

Answer:

n = 47/3

Step-by-step explanation:

Let the number be n.  

Then tripling this number and subtracting 4 from the result is 3n - 4 = 43

This result could be solved for n as follows:

Add 4 to both sides:  3n = 47

Then n = 47/3

the monster truck needs to pull with a force of approximately 4692.9 pounds to remain unmoved at the state fair truck pull. Rounded to the nearest tenth, the answer is 4692.9 pounds.

Explanation:

To find the resultant force of the two pickups, we first need to calculate the horizontal and vertical components of the force vectors. We can use trigonometry to do this. The force exerted by the pickup pulling at a 45-degree angle can be split into its horizontal and vertical components by multiplying the force by the cosine and sine of the angle, respectively. So the horizontal component of the 3800-pound force is 3800 cos(45) = 2679. This means that the force exerted horizontally by this pickup is 2679 pounds. Similarly, the vertical component of the 3800-pound force is 3800 sin(45) = 2679.

Next, we can add the horizontal components of the two pickups together to find the total horizontal force exerted on the monster truck. The horizontal component of the 1200-pound force is simply 1200, as it is already in the horizontal direction. So the total horizontal force exerted on the monster truck is 2679 + 1200 = 3879 pounds.

We can do the same for the vertical components of the force vectors. The vertical component of the 1200-pound force is 0, as it is already in the vertical direction. So the total vertical force exerted on the monster truck is simply the vertical component of the 3800-pound force, which is 2679 pounds.

Finally, we can use the Pythagorean theorem to find the magnitude of the resultant force. The magnitude of the resultant force is the square root of the sum of the squares of the horizontal and vertical components of the force vectors. So the magnitude of the resultant force is √(3879² + 2679²) = 4692.9 pounds.

Therefore, the monster truck needs to pull with a force of approximately 4692.9 pounds to remain unmoved at the state fair truck pull. Rounded to the nearest tenth, the answer is 4692.9 pounds.

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The percentage of the sheets with no air bubbles is given as follows:

13.53%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

The mean for this problem is given as follows:

\(\mu = 2\)

The proportion of these sheets with no air bubbles is P(X = 0), hence it is given as follows:

P(X = 0) = e^-2 = 0.1353 = 13.53%.

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Answer:

c. 1/2

Step-by-step explanation:

graph goes up 1 over 2 and is positive

Answer:

130° degrees

Step-by-step explanation:

semi circle = 180°

so 13/18 of 180° = 130°

Answer:

Step-by-step explanation:

\(\dfrac{13}{18}*180=13*10 \\\\\\\)

            = 130°

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(x-3y=9\implies -3y=-x+9\implies y=\cfrac{-x+9}{-3} \\\\\\ y=\cfrac{-x}{-3}+\cfrac{9}{-3}\implies y=\cfrac{1}{3}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a likne whose slope is 1/3 and it passes through (-10 , 9)

\((\stackrel{x_1}{-10}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-10)}) \implies y -9= \cfrac{1}{3} (x +10) \\\\\\ y-9=\cfrac{1}{3}x+\cfrac{10}{3}\implies y=\cfrac{1}{3}x+\cfrac{10}{3}+9\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{37}{3} \end{array}}\)