sound travels at a rate of about 1.1*10^3 feet per second. Suppose a mining company detonates a bundle of dynamite at a distance of 625 feet from a canyon wall. At the time of a detonation the miners sit safely at a distance of 2,600 feet from the dynamite. How long after detonation will the miners hear the echo of the blast off the canyon wall? Round to the nearest tenth if necessary.

The study design is best described as a case-control study.

A community uses a telephone survey to rate a representative sample of its citizens.

Diabetes is significantly correlated with obesity.

Non-experimental or observational study designs include cohort designs. In a cohort study, the participants don't already have the desired result. They are chosen based on the person's exposure status.

A case-control study is a sort of observational research in which two existent groups with outcomes that differ from one another are found and compared on the basis of a purported causal factor.

An example of an observational study design is the cross-sectional study design. In a cross-sectional study, the researcher simultaneously assesses the participants' exposures and outcomes.

Therefore, the study is a case-control study.

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Given:

The length of the rectangle is 50 yards. The perimeter is less than 180 yards.

Required:

Write the solution inequality in terms of width w.

Explanation:

Let the width of the rectangle is w.

The perimeter of the rectangle is given by the formula:

Final Answer:

The first option is the correct answer.

Lets first look at the cost per round with the 25 round pass

Take the total cost and divide by the number of rounds

$84 / 25 rounds

$ 3.36 per round

OR

They can pay 3.25 per round with the single pay

$3.25 is less than 3.36 so it is cheaper ( less per round) to pay the single round price

Option 2 $3.25 is cheaper

Given the measurements:

x1 = 10

x2 = 11

x3 = 15

x4 = 6

We're asked to find:

Which is

100+121+225+36

=482

Answer:

Step-by-step explanation:

you would cut 99 in half and make your way down until nothing left which gives you 48.985 or

49.99$ rounded

We know how many pounds are needed to cover 5000 ft^2, and we need to find how many are needed to cover 27000ft^2. To find this value, divide 27000 by 5000 and multiply the result by the weight.

27000/5000 x 18.75
5.4 x 18.75
101.25

So, we need 101 1/4 pounds of fertilizer. How many bags is that?

101.25/18.75
5.4

We'll say that since the 0.4 of a bag will still need to be used, that you need 6 bags to cover 27000ft^2.

The value of x is −61.5 . option B

An algebraic expression is simply seen as one with terms, factors, variables, coefficients, constants.

These expressions may also consist of arithmetic operations, some of which includes;

Based on the information given, we have;

−0.28x − 15.3 = 1.92

To determine the value of the variable 'x' we need to take the following steps;

collect like terms from the equation

-0. 28x = 1. 92 + 15. 3

Add like terms

-0. 28x = 17.22

Divide both side by the coefficient of x

x = 17. 22/-0.28

x = - 61. 5

Hence, the value is - 61. 5

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In parallelogram ABCD, AB = 3 cm and the diagonals AC and BD are 5.8 cm and 4.2 cm respectively. If the diagonals AC and BD intersect at O, then the perimeter of ∆AOB is 8 cm

perimeter of a triangle = length 1 + length 2 + length 3

assuming

length 1 = AB = 3 cm

length 2 = 5.8 / 2

length 3 = 4.2 / 2

Reason for length 2 and length 3 is when the diagonal of a parallelogram intersect they bisect each other. bisect means divide each other into two equal parts

substituting the values

perimeter of the triangle = 3 + 5.8 / 2 + 4.2 / 2

= 3 + 2.9 +  2.1

= 8 cm

The perimeter of the triangle formed is 8 cm

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The months will they have same number of miles. is 1.732 months.

Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. This will be expressed as y = 5132 + 525x

Lily's car has 4,789 miles on it already, and she drives 723 mile per month. This will be:

y = 4789 + 723x

x = number of months

y = miles

The number of months will be gotten by equating the equations. This will be:

5132 + 525x = 4789 + 723x

Collect like terms

198x = 343

Divide

x = 343 / 198

x = 1.732 months.

The number of months is 1.732.

The complete question is written below.

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Miranda and Lily both bought a used car on the same day. Miranda's used car has 5,132 miles on it already, and she drives 525 miles per month. Lily's car has 4,789 miles on it already, and she drives 723 mile per month. How many months will they have same number of miles.

Answer:

-3 [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Is this the problem?

1 4/9 (-2 4/7)

[tex]\frac{13}{9}[/tex][tex](\frac{-18}{7})[/tex] = [tex]\frac{-26}{7}[/tex]

-3 [tex]\frac{5}{7}[/tex]

The number of squats she did in the first week is 81 squats.

This refers to the amount of value that a thing is incremented by, in a percentage, which is over 100.

Given that she had a percentage increase by 35%

And started doing 108 squats

To find the number of squats she did during the first week would be:

100-35= 75%

75/100 * 108= 81 squats.

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The equation of the parabola, in vertex form, that represents the ball's distance, y, from the hole, x seconds after the ball is hit is

y = (-2m/s²)t² + (-2m/s)t + 6m.

Given:

Let's assume that the hole is at y = 0m, with x seconds as the time.

The vertex of the parabola can be written as (-1s, 8m) where the time variable, x, is supposed to be in seconds, while the distance variable, y, is supposed to be in meters.

The ball reaches the hole at x = 1s, so we have point (1s, 0m)

The vertex of the parabola y = ax² + bx + c is known to be at

x = -b/2a,

So, -1 = -b/2a

We have the following equations,

8m = a(-1s)² + b(-1s) + c

0m = a*(1s)² + b(1s) + c

-1s = -b/2a

b = 2a × 1s

Substituting the value of b in the equations and simplifying them,

8m = a×1s² - 1s×2a×1s + c

⇒ 8m = a( 1s² - 2s²) + c = -a×1s² + c.

0m = a×1s² + 1s×2a×1s + c

⇒ 0m = a(1s² + 2s²) + c = a×3s² + c

Deriving the value of c from the second equation we put it in the first equation,

c = - a×3s²

The first equation is as,

8m = -a×1s² - a×3s² = -a×4s²

a = 8m/-4s² = -2m/s²

From the value of a we can calculate the values of b and c.

c = -a×3s² = -(-2m/s²)×3s²= 6m.

b = 1s×2a = 1s×(-2m/s²) = -2m/s.

Then the equation is:

y = (-2m/s²)t² + (-2m/s)t + 6m

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Answer:

a = 3 , b = - 18

Step-by-step explanation:

2 - [tex]\frac{x+1}{x-2}[/tex] - [tex]\frac{x-4}{x+2}[/tex]

express as a fraction with common denominator (x - 2)(x + 2)

= [tex]\frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)}[/tex]

= [tex]\frac{2(x^2-4)-(x^2+3x+2)-(x^2-6x+8)}{x^2-4}[/tex]

= [tex]\frac{2x^2-8-x^2-3x-2-x^2+6x-8}{x^2-4}[/tex]

= [tex]\frac{3x-18}{x^2-4}[/tex]

compare to [tex]\frac{ax+b}{x^2-4}[/tex]

with a = 3 and b = - 18

Answer:

$73

Step-by-step explanation:

From the given function, it is found that:

a. A reasonable domain for the function is of 0 ≤ d ≤ 11.

b. The y-intercept of the graph represents that the initial radius of the algae is of 7 mm.

c. The average rate of change between the 4th and the 11th day of the function means that the radius of the algae grew by an average of 0.64 mm a day.

The function is modeled according to the following rule:

f(d) = 7(1.06)^d

In which:

When the biologist concluded her study, the radius of the algae was approximately 13.29 mm, hence the upper bound of the domain is found as follows:

[tex]13.29 = 7(1.06)^d[/tex]

[tex](1.06)^d = \frac{13.29}{7}[/tex]

[tex]\log{(1.06)^d} = \log{\left(\frac{13.29}{7}\right)}[/tex]

[tex]d\log{1.06} = \log{\left(\frac{13.29}{7}\right)}[/tex]

[tex]d = \frac{\log{\left(\frac{13.29}{7}\right)}}{\log{1.06}}[/tex]

d = 11.

The smallest possible number of days is of 11, hence a reasonable domain for the function is:

0 ≤ d ≤ 11.

The y-intercept of the graph represents that the initial radius of the algae, as it is calculated when d = 0, hence it's value is given by:

[tex]f(0) = 7(1.06)^0 = 7[/tex]

The average rate of change of a function is given by the change in the output divided by change in the input, hence:

r = (13.29 - 8.84)/(11 - 4) = 0.64 mm a day.

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It will be a horizontal line

The variance of the sample mean is 12/35 = 0.3429.. This is a result of uniform distribution.

The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive.

According to the question, we have

Sample size (n) = 36; uniform continuous distribution has a maximum of 14 and a minimum of 2.

The notation for the uniform distribution is

X U(a,b), where  a=  the lowest value of x  and  b=  the highest value of x. The probability density function is f(x) = 1/(ba ) fo axb .

b = 14 and a = 2.

Variance in uniform distribution = (b-a)² / 12.

Put the value of a and b, 

Variance = ( 14-2)²/12 = 12

Sample variance is used to calculate the variability of sample sets.

The variance of the sample means = variance / (sample size- 1) 9= (b-a)²/ (n-1)

= 12/35= 0.342

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Answer:2,523

Step-by-step explanation:

Answer:

0.30 dollar

Step-by-step explanation:

333.33 points == 1 dollar

: 333.33

1 points == 0.003 dollar

* 100

100 points == 0.30 dollar

Answer:

A,B,C

Step-by-step explanation:

Using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².

In the given shaded region there is one rectangle and one triangle.

First, find the area of the shaded rectangle.

Now find the area of the shaded triangle.

So, the Area of the triangle is:

Therefore, the total area of the shaded region is:

Therefore, using the area of triangles and rectangles, we know that the area of the shaded region is 255cm².

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Hello!

The ratio between pig and other animals

 ==> looks like   [tex]\text{number of pigs}: \text{ number of other animals}[/tex]

Since there are 8 pigs and 11 other kind of animals

 ⇒ the ratio is ⇒ 8: 11

Hope that helps!

Answer:

Remember, a positive and a negative while being added is always a negative outcome, so when you add -29.03 + 26.5, you get -2.53

After the 90° rotation, Block C will resemble this in some ways (see the image below).

So, rotate block C by 90°:

Block C will look somewhat like this (Refer to the image attached below) after the rotation of 90°.

Therefore, after the 90° rotation, Block C will resemble this in some ways (see the image below).

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The bottom is moving at a rate of [tex]4\sqrt{3}[/tex] ft/s along the ground when the botton of the ladder is at a distance of 6 ft from the wall.

Here we have been mentioned that a 12 feet ladder is leaning against the wall which is represened by AC in the below given triangle.

We have AB = y = distance of top of the ladder from the wall

BC = x = distance of bottom of the ladder from the wall

AC = z = height of the ladder = 12 ft (given)

The top of the ladder AB is sliding down at a rate of 4 [tex]ft/s[/tex]

∴ [tex]\frac{dy}{dt}[/tex] = - 4 ft/s (negative sign indicates that the top is sliding downwards)

Let the rate at which the bottom of the ladder is sliding be [tex]\frac{dx}{dt}[/tex]

Now in the right angled triangle [tex]ABC[/tex] by using Pythagoras theorem we have,

[tex]AB^{2} + BC^{2} =[/tex][tex]AC^{2}[/tex]

[tex]y^{2} +x^{2} = z^{2}[/tex]    (equation 1)

When x = 6ft and z = 12 ft,

[tex]y^{2} +6^{2} = 12^{2}[/tex]

⇒ [tex]y^{2} = 144 - 36[/tex]

⇒ [tex]y^{2} = 108[/tex]

⇒ y = √108

⇒ y = 6 √3 ft

Differentiating equation 1 with respect to [tex]time[/tex] we get,

[tex]\frac{d}{dt} (y^{2} +x^{2} ) = \frac{d}{dt} (z^{2})[/tex]

⇒ 2y[tex]\frac{dy}{dt}[/tex] + 2x[tex]\frac{dx}{dt}[/tex] = 2z[tex]\frac{dz}{dt}[/tex]

Putting the values of dz/dt = 0 (as the height is constant) , dy/dt = - 4 ft/s , y = 6 √3 ft, x = 6ft and z = 12ft we have,

∴ 2(6√3) (-4) + 2(6)[tex]\frac{dx}{dt}[/tex] = 2(12)(0)

⇒ -48√3 + 12[tex]\frac{dx}{dt}[/tex] = 0

⇒ 12[tex]\frac{dx}{dt}[/tex] = 48√3

⇒ [tex]\frac{dx}{dt} = \frac{48\sqrt{3} }{12}[/tex]

⇒ [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft/s

Hence the rate at which the bottom of the ladder is sliding is [tex]\frac{dx}{dt} = 4\sqrt{3}[/tex] ft\s

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It is determined that 188 students should be sampled to use the confidence interval for a proportion.

π ± z√π(1-π)/n

In which case,

z is indeed the z-score with the p-value of 1+α/2

The error margin is as follows:

M = z√π(1-π)/n

In this case:

Then:

M = z√π(1-π)/n

0.02 = 1.96√0.02(1-0.02)/n

√n = 13.72

n = 188.23

To summarize:

A total of 188 students must be sampled to estimate the proportion of of students who owns a scooter.

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Answer:

31 & 32

Step-by-step explanation:

3 x 32 = 96

2 x 31 = 62

62 + 34 = 96