A road crew spread 1 1/3 tons of gravel evenly over 8 feet of road.how many tons of gravel did they spread on each foot of road?

Answer:

$145/10 = $14.50

$14.50 * 8 = $116.00

Step-by-step explanation:

Answer:

The height of the telephone pole is 14.711 m (Approx) .

Step-by-step explanation:

Let us assume that the height be x .

Let us assume that the shadow  be y .

(As the shadow is always proportional to the height .)

Thus

[tex]x\propto y[/tex]

y = kx

Where k is the constant of proportionality .

As given

if a statue that is 33 cm tall cast a shadow 83 cm long .

y = 83 cm

x = 33 cm

Put in the equation y = kx .

83 = 33k

[tex]k = \frac{83}{33}[/tex]

As given

A telephone pole cast a shadow that is 37 m .

Let us assume that the height of the telephone pole be z .

As

1m = 100cm

37m = 3700 cm

y = 3700 cm

x = z

Put in the equation  y = kx .

3700 = zk

[tex]k = \frac{3700}{z}[/tex]

Compare the value of k .

[tex]\frac{3700}{z} = \frac{83}{33}[/tex]

[tex]\frac{3700\times 33}{83} =z[/tex]

[tex]\frac{122100}{83} =z[/tex]

z = 1471.1 cm(Approx)

As

[tex]1\ cm = \frac{1}{100}\ m[/tex]

[tex]1471.1\ cm = \frac{1471.1}{100}\ m[/tex]

                       = 14.711 m (Approx)

Therefore the  height of the telephone pole is 14.711 m (Approx) .

Answer:

20.99 years . plato

Step-by-step explanation:

The time it takes for a ball thrown downwards at a velocity of 21 ft/s from a height of 255 ft to reach the ground is approximately 4.05 seconds.

The physics problem presented is a classic example of a vertically descending projectile. Here, we can use the formula of motion to find the solution. The formula is h = vt + 0.5gt², where v is the initial velocity, g is the acceleration due to gravity, and h is the height.

Since the ball is thrown downwards, the initial velocity will be negative, -21 ft/s. We're also working in feet, so the gravitational acceleration should be in feet/s², which is approximately -32.2 ft/s² (remember it's negative as it's acting downwards).

So, substituting the values into the equation, we have 255 = (-21*t) + 0.5*(-32.2)*t². Simplifying this gives us a quadratic equation: 16.1t² - 21t - 255 = 0.

The roots of this equation represent the times at which the ball will be 255 ft below its starting point. We solve the equation and get t ≈ -3.9s or t ≈ 4.05s. Clearly, time cannot be negative, so the ball hits the ground after approximately 4.05 seconds from being thrown.

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The ball thrown from a height with initial downward velocity hits the ground after 3.79 seconds. This was found by solving the quadratic equation that stems from principles of physical motion (height vs time).

The problem can be solved using the principles of kinematics in physics. The height of the ball after t seconds is given by the equation of motion, which is a quadratic equation. If we let h be 0 (height when the ball hits the ground), we can solve the equation for t.

Given: initial height = 255 feet, initial velocity = 21 feet/s, acceleration due to gravity = 32.2 ft/s² (downward); The equation of motion is: h = 255 + 21t - 16t²; We have to find the time when the ball hits the ground i.e when h=0. So, the equation becomes: 0 = 255+21t-16t².

On solving this quadratic equation, we get two roots. Assuming upward direction is positive, the negative time value reflects the time before the ball was launched and the positive value is the time it takes for the ball to hit the ground. The positive root gives us the answer, t = 3.79 s.

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 6% = 0.06

 if you want to know the total price including the tax

 multiply 15.89 x 1.06 = 16.84

If compact discs cost $15.89 each. Then the cost of each disc after 6% sales tax will be $ 16.84.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

If compact discs cost $15.89 each.

Then the cost of each disc after 6% sales tax will be

→ 1.06 × $ 15.89

→ $ 16.84

If compact discs cost $15.89 each. Then the cost of each disc after 6% sales tax will be $ 16.84.

More about the percentage link is given below.

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The probability of spinning 2 then 4: [tex]\( \frac{1}{10} \times \frac{1}{10} = \frac{1}{100} \).[/tex]

To find the probability that the first spin results in a 2 and the second spin results in a 4, we need to determine the probability of each event and then multiply them together because the spins are independent.

1. Probability of spinning a 2 on the first spin:

  Since there is 1 section labeled '2' out of 10 sections in total, the probability of spinning a 2 on the first spin is [tex]\( \frac{1}{10} \)[/tex].

2. Probability of spinning a 4 on the second spin:

  Similarly, there is 1 section labeled '4' out of 10 sections in total, so the probability of spinning a 4 on the second spin is also [tex]\( \frac{1}{10} \)[/tex].

Now, to find the probability of both events happening (the first spin resulting in a 2 and the second spin resulting in a 4), we multiply the probabilities of each event:

[tex]\[ P(\text{first spin = 2}) \times P(\text{second spin = 4}) \][/tex]

[tex]\[ = \frac{1}{10} \times \frac{1}{10} \][/tex]

[tex]\[ = \frac{1}{100} \][/tex]

So, the probability that the first spin results in a 2 and the second spin results in a 4 is [tex]\( \frac{1}{100} \)[/tex].

The one-way ANOVA or one – way analysis of variance is used to know whether there are statistically substantial dissimilarities among the averages of three or more independent sets. It compares the means between the sets that is being examined whether any of those means are statistically pointedly dissimilar from each other. If it does have a significant result, then the alternative hypothesis can be accepted and that would mean that two sets are pointedly different from each other. The sum of squares within for this ANOVA​ procedure is 680. The answer is letter D.

The percentage of the scores are between 75.8 and 89 can be calculated using z-scores.

The percentage of the scores between 75.8 and 89 is 95%.

Given:

The mean is [tex]m=82.4[/tex].

The standard deviation is [tex]\sigma =3.3[/tex].

Calculate the Z- score for 75.8.

[tex]Z(75.8)=\dfrac{(75.8-82.4)}{3.3} \\Z(75.8) = -2[/tex]

Calculate the Z- score for 89.

[tex]Z(89)=\dfrac{(89-82.4)}{3.3}\\Z(89)=2[/tex]

Calculate the percentage of the scores are between 75.8 and 89.

[tex]P(75.8<X<89)=P(-2<Z<2)\\P(75.8<X<89)=P(Z<2)-P(Z<-2)\\[/tex]

Refer the z-table, put the value,

[tex]P(75.8<X<89)=0.9772-0.0227\\P(75.8<X<89)=0.9545[/tex]

Thus, the percentage of the scores between 75.8 and 89 is 95%.

Learn more about z-score here:

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To evaluate the solid e which lies between two cylinders and a plane, one would typically set up a triple integral in cylindrical coordinates. This involves translating the given boundaries from rectangular coordinates into cylindrical coordinates to account for the radial, angular, and vertical dimensions of the solid.

This question pertains to the evaluation of a solid, denoted as e, that is located between the two cylinders x^2 + y^2 = 1 and x^2 + y^2 = 16. These cylinders are located above the xy-plane and below the plane z = y + 4. The evaluation of such a solid requires the application of integral calculus. Typically, in such cases we would set up a triple integral by converting rectangular coordinates into cylindrical coordinates (r, theta, z).

Given the specifics of the solid, the radial path r would vary between sqrt(1) and sqrt(16), which is between 1 and 4. The angular path theta would cover the full circle, thus varying between 0 and 2π. The z-coordinate would be bounded below by the xy-plane (0) and above by the plane z = y + 4.  Please note that you would need to convert the z-boundary into cylindrical coordinates as well.

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Final answer:

The point estimate of the true proportion of all lightbulbs that last more than 500 hours is approximately 0.634, calculated using the sample data of 291 out of 459 lightbulbs lasting more than 500 hours.

Explanation:

To find a point estimate of the true proportion of all lightbulbs that last more than 500 hours, we use the sample data provided. Out of 459 randomly selected lightbulbs, 291 lasted more than 500 hours.

The point estimate is calculated by dividing the number of successes in the sample by the total number of trials. In this case, the point estimate (p-hat) would be 291 divided by 459, which gives us an estimate of the true proportion.

The calculation would be as follows:

The point estimate for the true proportion of all lightbulbs that last more than 500 hours is approximately 0.634.

Answer:

The correct answer is 0.123 cm.

Step-by-step explanation:

Each kilometer has 1000 meters and each meter has 100 centimeters.

Hence each kilometer has 1000×100=100000=105 centimeters.

Therefore, 1.23×10−6 kilometer will have

1.23×10−6×105=1.23×10−6+5=1.23×10−1 or 0.123 centimeters