You are part of the rescue team in a ship at sea. One of your divers is 250 feet below sea level, and she injured herself. She has only a 7 minute supply of air in her tank, and can only rise towards the surface at a rate of 10 feet per minute. You are sending down a rescue sub. The sub can descend at a rate of 30 feet per minute. At what depth, to the nearest foot, will the two meet?

Answer:

5

Step-by-step explanation:

The slope or gradient of the line

using this formula as our guide line

y = mx +b

where m = slope

x = x– intercept

b = y– intercept

so

y = 5x + 12

the slope will be 5

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The colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

Given is that a colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm.

The logistic model is given as -

y(t) = {c/(1 + a[tex]e^{-bt}[/tex])}

For y(t) = 2000

2000 = {c/(1 + a[tex]e^{-bt}[/tex])}

(2000/c) = 1/(1 + a[tex]e^{-bt}[/tex])

(1 + a[tex]e^{-bt}[/tex]) = (2000/c)

a[tex]e^{-bt}[/tex] = (2000/c) - 1

a[tex]e^{-bt}[/tex] = (2000 - c)/c

[tex]e^{-bt}[/tex] = (2000 - c)/(ac)

(-bt)log{e} = log {(2000 - c)/(ac)}

- bt = log(2000 - c) - log(ac)

- bt = log(2000 - c) - log(a) + log(c)

t = - {log(2000 - c) - log(a) + log(c)}/b

Therefore, the colony will reach a population of 2000 in time -

t = - {log(2000 - c) - log(a) + log(c)}/b.

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By using properties of triangle, it can be calculated that-

The pilot is 2740 miles from her starting position.

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.

Here,

The diagram has been attached

Time = 130 minutes = 2 hrs 10 minutes = [tex]2 + \frac{10}{60}[/tex] hours = [tex]\frac{13}{6}[/tex] hours

Speed = 600 miles per hour

Distance = [tex]\frac{13}{6} \times 600[/tex] = 1300 miles

Now,

Time = 145 minutes = 2 hrs 25 minutes = [tex]2 + \frac{25}{60}[/tex] hours = [tex]\frac{29}{12}[/tex] hours

Distance = [tex]\frac{29}{12}\times 600[/tex] = 1450 miles

Angle = [tex]10^{\circ}[/tex]

[tex]c^2 = 1300^2 + 1450^2 - 2\times 1300\times 1450\times cos(180-10)\\c^2 = 1690000 + 2102500 - (-3712725.2)\\c^2= 7505225.2\\c= \sqrt{7505225.2}\\c = 2740[/tex]

The pilot is 2740 miles from her starting position.

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The integral to express the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units is:

p(s) = 4s

Integral = ∫2s5s ds

= ∫2s5s dx

= [s2/2]2s5s

= (25/2) - (4/2)

= 20/2

= 10

Therefore, the increase in the perimeter of the square when its side length s increases from 2 units to 5 units is 10 units.

To calculate this increase, we used the formula for the perimeter of a square, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two side lengths. We then solved for the integral and multiplied it by 4 to get the increase in the perimeter.

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[tex] \Large{\boxed{\sf Slope = 3}} [/tex]

[tex] \\ [/tex]

The slope of a line passing through two points, also known as its gradient, is calculated using the slope formula.

[tex] \\ [/tex]

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]

Where m is the slope of the line.

[tex] \\ [/tex]

First, let's identify our values:

[tex] \sf (\underbrace{\sf 0}_{x_1} \ , \ \overbrace{\sf 0}^{y_1} ) \ \ and \ \ (\underbrace{\sf 4}_{x_2} \ , \ \overbrace{\sf 12}^{y_2} ) [/tex]

[tex] \\ [/tex]

Now, substitute these values into the formula:

[tex] \sf \rightarrow m = \dfrac{12 - 0}{4 - 0} \\ \\ \sf \rightarrow m = \dfrac{12}{4} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = 3}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Answer:

slope = 3

How to Solve:

The question is asking us to find the slope, given two points.

These points are (0,0) and (4,12).

We will use the slope formula:

[tex]\boldsymbol{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where:

Plug in the data:

[tex]\boldsymbol{m=\dfrac{12-0}{4-0}}[/tex]

[tex]\boldsymbol{m=\dfrac{12}{4}}[/tex]

Simplify the fraction to its lowest terms:

[tex]\boldsymbol{m=3}[/tex]

Therefore, the slope is 3.

The value of 1204.2 + 4.72613 is 1208.92613.

What is meaning of significant figures of a number?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.

Given number is 1204.2 and  4.72613.

If add zeros after the last digit of the decimal number, then the number will remains same.

The rewrite form of 1204.2 is 1204.20000.

Before combining two decimal integers, make sure they both have the same number of digits after the decimal point. If they don't, move a number's right by a number of zeros until they do.

Then, place the decimal points vertically and write one number on top of the other. Bring the decimal point directly below the decimal point and add as you would with full numbers.

The sum of 1204.20000 and 4.72613

1204.20000

    +4.72613

__________

1208.92613

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The solution is once more 1.28 since a combined area of 0.10416 to the right implies that it must also have an area of 0.90 to the left.

Since each normally distributed random variable has a slightly different distribution shape, standardizing the variable to give it a mean of 0 and a standard deviation of 1 is the only method to determine regions using a table. How do we go about doing that? Employ the z-score!

Z = ( x - μ)/σ

If a mean and standard deviation are present for the random variable X,

Then a random variable with a mean of 0 and a standard deviation of 1 is produced by converting X using the z-score!

With that in mind, all that remains is to understand how to find areas under the standard normal curve, which can then be applied to any random variable with a normal distribution.

Since an area of 0.10416 to the right means that it must have an area of 0.90 to the left, the answer is once again 1.28.

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Answer:

She Does NOT

Step-by-step explanation:

3/4 is .75 1 1/3 is 1.33 3/4*2= 1.5 which is more than 1.33

The domain and range of the given function are  {-2, 0, 1, 2, 3} and {-3, 0, 2, 3, 4} respectively

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function can be said as all possible values of x and the range of a function is all possible values of y.

The given function is

f(x) = {(0, -3), (2, 0), (3, 2), (1, 4), (-2, 3)

The domain of the function can be given as;

Domain : {-2, 0, 1, 2, 3}

Range : {-3, 0, 2, 3, 4}

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Answer:

5x+48=130

Step-by-step explanation:

5 is the money she gets each week. X is the number of weeks. X can be found easily but for the sake of this question, It's unknown. so 5x and then add the 48 she's already saved you get 5x+48=130 or 5x+48 is greater than or equal to 130.

Part (A)

Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.

P/Q = R/S

where,

In this case,

Therefore, we go from this

P/Q = R/S

to this

(1.8)/6 = h/60

Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.

--------------

====================================================

Part (B)

Let's cross multiply and solve for h.

(1.8)/6 = h/60

1.8*60 = 6h

108 = 6h

6h = 108

h = 108/6

h = 18

--------------

Answer:

A). [tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

B). 18 meters tall

Step-by-step explanation:

We see TWO right triangles in this problem:

These triangles are proportional so we can make a ratio out of them

the height of the man over the side of the triangle (6m)

and the height of the tower over the length of its triangle (60m)

Set these equal to each other to complete part A

[tex]\frac{1.8}{6} = \frac{height}{60}[/tex]

And by using cross multiplication (which is what you do for ratios), solve for h!

For a quick example of cross multiplication, I've attached a picture.

Now let's do it!

1.8 × 60 = 6 × h

108 = 6h

108/6 = h

h = 18

The height of the cell phone tower is 18 meters.

Thus ,  it  is False. As there is confidence level is not given, then cant calculate the sample size.

The standard deviation in statistics is a measure of how widely spread a set of values can be or how much they can vary. A low standard deviation denotes that values are typically close to the mean of the collection, whereas a high standard deviation indicates that values are dispersed across a greater range.

Here,

The standard error of the sample mean is equal to 2 for samples of size n if all conceivable samples of that size are taken from a population with an infinite mean and standard deviation.

In the above statement confidence level is not given.

Thus ,  it  is False. As there is confidence level is not given, then cant calculate the sample size.

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The height of the cliff in terms of A, B and h are 40 meters.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

A man standing on the deck of a ship.

Let C be the position of man.

And the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively 60° and 30°.

That means, ∠DCH = 60° and  ∠BCD = 30°.

The diagram is given in the attached image.

HD = x And BD = 10 meters.

In right-triangle ΔCDH,

we have,

tan60° = HD / CD

√3 = x / CD

CD = x/√3

In right-triangle  ΔCDB,

we have,

tan30° = BD/CD

CD = 10√3

So, the distance of the ship from the cliff is 10√3 meters.

Comparing, the both values of CD,

 10√3 =  x/√3

x  =  10√3 × √3

x = 10 × 3

x = 30 meters.

Now, the total height of cliff  = BD + DH

= 10 + 30

= 40 meters.

Therefore, the height of the cliff is 40 meters.

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The motion of the object on the graph, can best be represented as an object that d. was at rest and is accelerating uniformly.

The object on the graph is accelerating such that the acceleration is stable and uniform. This is why the speed - time line is a straight and diagonal line to show that the speed is proportional to time.

We know that the object started from rest because at the point where time was 0, the object was not accelerating and so was not moving. As time moves on, the object increases speed, thereby accelerating.

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Option (b) is correct as mean of top five scorers on soccer team is 8 from given bar graph.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

Mean = (Sum of values)/(Total observations)

Using above formula, we get

Calculating mean for given bar graph,

[tex]=\frac{4+6+10+9+11}{5}\\=\frac{40}{5}\\=8[/tex]

So, mean score of five players comes out to be 8.

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Answer:

x=6

Step-by-step explanation:

9-3=6 or 6+3=9

The cotangent of the angle is -√570/30

From the question, we have the following parameters that can be used in our computation:

(√30/7,-√19/7)

This means that

(x, y) = (√30/7,-√19/7)

The cot(θ) is calculated as

cot(θ) = y/x

Substitute the known values in the above equation, so, we have the following representation

cot(θ) = (-√19/7)/(√30/7)

Evaluate

cot(θ) = -√19/√30

Rationalize

cot(θ) = -√570/30

Hence, the value of cot(θ) is -√570/30

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Thus after 12 minutes concentration of drug is 0.045.

The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula [tex]c(t) = 0.05(1-e^{-0.2t} )[/tex]

Drug concentration is amongst the most important determinants of clinical response to a drug.

Drug concentration will be seen to increase in biological samples drawn from the systemic circulation when the amount of drug absorbed exceeds the amount of drug that is distributed into the extravascular tissues and the drug that is metabolized and/or excreted during this period.

Thus after 12 minutes concentration of the drug is = C(5).

Now

C(5) = [tex]0.05(1-e^{-0.2t} )[/tex]

= [tex]0.05(1-e^{-2.4} )[/tex]

= 0.05(1-0.0907)

= 0.05×0.9093

= 0.045

The drug concentration is 0.045.

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Answer:

$4.50

Step-by-step explanation:

Use a proportion:

$6.75 is to 3 bags as x is to 2 bags.

6.75/3 = x/2

3x = 2 × 6.75

x = 4.50

Answer: $4.50

Answer:

  $4.50

Step-by-step explanation:

Given 3 bags of cat food cost $6.75, you want the cost of 2 bags.

Unless there is a volume discount (or surcharge), the price is proportional to the quantity. That means 2 bags will cost 2/3 the amount that 3 bags cost.

  cost of 2 bags = 2/3 · $6.75 = $4.50

Amelia would spend $4.50 on 2 bags of cat food.

Answer:

$44,334.34

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the continuous compounding formula and solve for A:

[tex]\implies A=6000e^{0.05 \times40}[/tex]

[tex]\implies A=6000e^2[/tex]

[tex]\implies A=6000(7.3890560...)[/tex]

[tex]\implies A=44334.33659...[/tex]

Therefore, the balance of the account after 40 years will be $44,334.34 (nearest cent).

Answer:

  20^2 = 400, the 2nd power of 20

Step-by-step explanation:

Given that k=20^20 and 20^k/k^20 = 20^n, you want the largest power of 20 that divides n.

Taking the base-20 logarithm of both equations, we have ...

  [tex]\log_{20}{k}=\log_{20}{20^{20}}\ \Longrightarrow\ \log_{20}{k}=20\\\\\log_{20}{\dfrac{20^k}{k^{20}}}=\log_{20}{20^n}\ \Longrightarrow\ k-20\log_{20}{k}=n[/tex]

Substituting for k and log(k), we get ...

  [tex]20^{20} -20\cdot20=n\\\\20^2(20^{18}-1)=n[/tex]

This shows us the largest power of 20 that is a factor of n is 20².

The common ratio is 1/5. By dividing each word by the term before it, we may find the geometric progression's common difference.

The common ratio in geometric progression is the ratio of any term in the sequence to divided by the first term.

The Formula to calculate the common ratio in geometric progression, a, ar, ar2, ar3, ar4, ar5… is,

Common ratio = ar/ a = ar2/ ar = ……. = an/ an-1

As stated in the definition, we can compute the common difference of a geometric progression by dividing any term by its preceding term.

Given, the geometric sequence is 625, 125, 25, 5, 1,....

We have to find the common ratio of the given geometric sequence.

In geometric sequence, a, b, c, d, … the common ratio r is given by

r = b/a = c/b = d/c.

So, r = 125/625 = 25/125 = 5/25 = 1/5;

r = 1/5

Therefore, the common ratio is r = 1/5.

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Answer:

B. 25/125

Step-by-step explanation:

By definition, perpendicular strains are strains intersecting at a proper attitude. The letters T and L are examples of perpendicular strains. By definition, parallel strains are strains at the equal aircraft that in no way intersect.

The letters N and Z include pairs of parallel linetwo non-vertical strains which are withinside the equal aircraft has the equal slope, then they may be stated to be parallel. Two parallel strains might not ever intersect. If non-vertical strains withinside the equal aircraft intersect at a proper attitude then they may be stated to be perpendicular.

We can decide from their equations whether or not strains are parallel with the aid of using evaluating their slopes. If the slopes are the equal and the y-intercepts are different, the strains are parallel. If the slopes are different, the strains aren't parallel. Unlike parallel strains, perpendicular strains do intersect.

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The data Customers on file who visited the store during coupon promo is 32% .

a) We use Z-test for testing hypothesis in this case because it is single proportion.

b) The P-value is 0.0017.

c) As P value < α = 0.05 , So we reject the null hypothesis.

d) Yes, Lotions and Potions continue to offer this promotion in order to increase visits because null hypothesis is rejected that alternative hypothesis is true which gives the same results.

The Null and Alternative hypothesis related to 20 percent off coupon does not increase the number of customers or increase the number of customers.

Sample size ,n = 4,500

Significance level, 0.05

a) We use z-test, because this is single proportion hypothesis test.

Below are the null and alternative Hypothesis,

Null Hypothesis, H₀ : p = 0.3

Alternative Hypothesis, Hₐ : p > 0.3

b) Test statistic,

z = (p-cap - p)/sqrt(p×(1-p)/n)

z = (0.32 - 0.3)/sqrt(0.3× (1-0.3)/4500)

z = 2.93

Using the Z-table, the P value at significance level 0.05 and z = 2.93 is 0.0017

As we see P-value < α = 0.05, so, reject the null hypothesis.

Yes, Lotions and Potions should continue to offer this promotion in order to increase visits.

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The graph of the linear equation, y + 1 = 1/3(x - 3), is given in the attachment below.

A linear equation is an equation of the form "y = mx + b," where x and y are variables, and m is the slope and b is the y-intercept.

To graph a linear equation, of y + 1 = 1/3(x - 3), you can use the following steps:

Rewrite the equation in slope-intercept form to determine its slope (m) and the y-intercept (b).

y + 1 = 1/3(x - 3)

y + 1 = 1/3x - 1

y = 1/3x - 1 - 1

y = 1/3x - 2

The slope (m) of the line would be 1/3, which is the rise over the run of the line.

The y-intercept (b) of the line would be -2, which means the line will intercept the y-axis at -2.

The graph of y + 1 = 1/3(x - 3) is shown in the image below.

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Answer:

Step-by-step explanation:

To find the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0, we can use the following steps:

Rewrite the equation of the circle in standard form: (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius.

In this case, the equation of the circle is already in standard form, so we can skip this step.

Find the slope of the line 3x + 5y + 7 = 0. The slope is -3/5.

Find the slope of the tangent to the circle. The slope of the tangent will be equal to the slope of the line, which is -3/5.

Substitute the slope of the tangent and the coordinates of a point on the circle into the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the circle and m is the slope.

In this case, we can substitute the coordinates of the center of the circle (which is (0, 0)) and the slope of the tangent (-3/5) into the point-slope form to get:

y - 0 = (-3/5)(x - 0)

Simplify to get the equation of the tangent: y = -3/5x.

Therefore, the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0 is y = -3/5x.

Answer:

6/1.5

Step-by-step explanation:

You said equally, so you need to make sure that each person gets an even share. To do this, you can do people/things. Hence why the answer is 6/1.5!