Write an equation of the line below.

Answer:

D.

Step-by-step explanation:

You could find the 8 terms and then add them up.

Let's do that.

Luckily we have the common ratio which is -5.   Common ratio means it is telling us what we are multiplying over and over to get the next term.

The first term is -11.

The second term is -5(-11)=55.

The third term is -5(55)=-275.

The fourth term is -5(-275)=1375.

The fifth term is -5(1375)=-6875.

The sixth term is -5(-6875)=34375.

The seventh terms is -5(34375)=-171875.

The eighth term is -5(-171875)=859375.

We get add these now. (That is what sum means.)

-11+55+-275+1375+-6875+34375+-171875+859375

=716144 which is choice D.

Now there is also a formula.

If you have a geometric series, where each term of the series is in the form [tex]a_1 \cdot r^{n-1}[/tex], then you can use the following formula to compute it's sum (if it is finite):

[tex]a_1\cdot \frac{1-r^{n}}{1-r}}[/tex]

where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio. n is the number of terms you are adding.

We have all of those. Let's plug them in:

[tex]a_1=-11[/tex], [tex]r=-5[/tex], and [tex]n=8[/tex]

[tex]-11 \cdot \frac{1-(-5)^{8}}{1-(-5)}[/tex]

[tex]-11\cdot \frac{1-(-5)^{8}}{6}[/tex]

[tex]-11 \cdot \frac{1-390625)}{6}[/tex]

[tex]-11 \cdot \frac{-390624}{6}[/tex]

[tex]-11 \cdot -65104[/tex]

[tex]716144[/tex]

Either way you go, you should get the same answer.

Final answer:

The sum of the 8-term geometric series with the given first term and common ratio is calculated using the geometric series sum formula, resulting in a sum of 716,144, Which is option D.

Explanation:

The sum of a geometric series is determined by the formula Sₙ = a(1 - rⁿ)/(1 - r), where Sₙ is the sum of the first N terms, a is the first term, r is the common ratio, and N is the number of terms. Since we have an 8-term geometric series with a first term of -11 and a common ratio of -5, we can calculate the last term (-11 x (-5)⁷) to ensure it is indeed 859,375, confirming the ratio and the number of terms.

The sum can then be calculated as follows: S₈ = -11 x (1 - (-5)⁸) / (1 - (-5)) = -11 x (1 - 390625) / (1 + 5) = -11 x (-390624) / 6 = -11 x -65104 = 716,144, which corresponds to option D.

Answer:

The first two graphs are the exact same but it is the first two.

Step-by-step explanation:

Answer:

In the beginning ,number of inventory in the warehouse =6,000

 Increment in each month in inventory in the warehouse=3000

So, writing the above situation in terms of linear equation

 if,y is the number of inventory after x months

 y=6000 +3000x

Correct graph is attached below

⇒Items in Inventory(Thousands) ----X axis

⇒Number of Months since Opening----Y axis

Check the picture below.

Step-by-step explanation:

We are asked to graph the equation of an ellipse given by [tex]\frac{x^2}{36}+\frac{y^2}{49}=1[/tex].

We know that standard from of an ellipse [tex]\frac{x^2}{a^2}+\frac{y^2}{b^1}=1[/tex], when [tex]a>b[/tex], then the ellipse will be horizontal and when [tex]a<b[/tex], then the ellipse will be vertical.

We can rewrite our given ellipse as: [tex]\frac{x^2}{6^2}+\frac{y^2}{7^2}=1[/tex].

Upon looking at our given ellipse we can see that the horizontal radius is less than vertical radius, so our ellipse will be a vertical ellipse. The center of our ellipse is at origin (0,0).

Upon graphing our ellipse, we will our required graph as:

Answer:

[tex](\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2})[/tex]

Step-by-step explanation:

Unit circle has a radius of 1.

So x=cos(3pi/4)=-sqrt(2)/2 and y=sin(3pi/4)=sqrt(2)/2

So the ordered pair is (-sqrt(2)/2  , sqrt(2)/2)

The terminal point for the unit circle that is determine by the [tex]$\frac{3 \pi}{4} $[/tex]   radians is

[tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]

We know the coordinates of the terminal point will be :

[tex]$x= \cos \left( \frac{3 \pi}{4} \right)$[/tex]    and   [tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]

Therefore,

[tex]$x= \cos \left( \pi - \frac{ \pi}{4} \right)$[/tex]

[tex]$x= - \cos \frac{\pi}{4}$[/tex]

   [tex]$=-\frac{1}{\sqrt 2}$[/tex]

And

[tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]

[tex]$y = \sin \left( \frac{\pi}{2} + \frac{\pi}{4} \right)$[/tex]

   [tex]$=\cos \frac{\pi}{4}$[/tex]

   [tex]$=\frac{1}{\sqrt 2}$[/tex]

Therefore the terminal points are : (x, y) = [tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]

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Answer:

If you want to round to the nearest hundredths, the answer is 1.73 seconds.

Step-by-step explanation:

So we want to solve h(t)=5 for t because this will give us the time,t, that the diver was 5 m above the water.

[tex]-4.9t^2+1.5t+17=5[/tex]

My goal here in solving this equation is to get it into [tex]at^2+bt+c=0[/tex] so I can use the quadratic formula to solve it.

The quadratic formula is [tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

So let's begin that process here:

[tex]-4.9t^2+1.5t+17=5[/tex]

Subtract 5 on both sides:

[tex]-4.9t^2+1.5t+12=0[/tex]

So let's compare the following equations:

[tex]-4.9t^2+1.5t+12=0[/tex]

[tex]at^2+bt+c=0[/tex].

[tex]a=-4.9[/tex]

[tex]b=1.5[/tex]

[tex]c=12[/tex]

Now we are ready to insert in the quadratic formula:

[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]

I know this can look daunting when putting into a calculator.

But this is the process I used on those little calculators back in the day:

Put the thing inside the square root into your calculator first.  I'm talking about the [tex](1.5)^2-4(-4.9)(12)[/tex].

This gives you:  237.45

Let's show what we have so far now:

[tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]

[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{2(-4.9)}[/tex]

I'm going to put the denominator, 2(-4.9), into my calculator now.

[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{-9.8}[/tex]

So this gives us two numbers to compute:

[tex]t=\frac{-1.5 - \sqrt{237.45}}{-9.8} \text{ and } t=\frac{-1.5+\sqrt{237.45}}{-9.8}[/tex]

I'm actually going to type in -1.5-sqrt(237.45) into my calculator, as well as, -1.5+sqrt(237.45).

[tex]t=\frac{-16.90941271}{-9.8} \text{ and } t=\frac{13.90941271}{-9.8}[/tex]

We are going to use the positive number only for our solution.

So we have the answer is whatever that first fraction is approximately:

[tex]t=\frac{-16.90941271}{-9.8}=1.725450277[/tex].

The answer is approximately 1.73 seconds.

Final answer:

To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. Using the given equation h(t) = -4.9t² + 1.5t + 17, we substitute 5 for h(t) and solve the resulting quadratic equation. The solution is t ≈ 1.82 seconds.

Explanation:

To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. We can substitute 5 for h(t) in the given equation and solve for t:

5 = -4.9t² + 1.5t + 17

-4.9t² + 1.5t + 12 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac))/2a

Plugging in the values a = -4.9, b = 1.5, and c = 12, we get:

t = (-1.5 ± √(1.5^2 - 4(-4.9)(12)))/(2(-4.9))

Simplifying further, we find two solutions: t ≈ 1.82 seconds and t ≈ -0.44 seconds. Since time cannot be negative in this context, the diver was 5 m above the water at approximately 1.82 seconds.

Answer:

a. x-intercept = 3 , y-intercept = 9.

Step-by-step explanation:

-6x - 2y = -18

Convert to slope-intercept form:

-2y = 6x - 18

y = -3x + 9

So the y-intercept  (when x = 0) is  when y = 9..

Solving for x to find the x-intercept:

0 = -3x + 9

3x = 9

x = 3.

Answer:

Step-by-step explanation:

1.6 pounds

Answer:

She needs 11374 cm to buy

Step-by-step explanation:

* Lets explain how to solve the problem

- The dimensions of the first rectangle is 1809 cm and 2891 cm

- The dimensions of the first rectangle is 738 cm and 249 cm

- Elly wants to put a fence around both

- To find the length of the fence calculate the perimeters of the two

 rectangles

- The perimeter of the rectangle = 2(b + h), where b , h are the

 dimensions of the rectangle

# First rectangle

∵ The dimensions are 1809 cm and 2891 cm

∵ P = 2(b + h)

∴ P = 2(1809 + 2891) = 2(4700) = 9400 cm

# Second rectangle

∵ The dimensions are 738 cm and 249 cm

∵ P = 2(b + h)

∴ P = 2(738 + 249) = 2(987) = 1974 cm

∵ The length of the fence = the sum of the perimeters of the two

  rectangles

∴ The length of the fence = 9400 + 1974 = 11374 cm

* She needs 11374 cm to buy

Answer:

She needs to purchase 11374

The difference i the length of her and her brother's fence is 8442

Step-by-step explanation:

First you need to find the perimeter by adding the lengths and widths all together.

1809+2891+738+249=5687

But you need to times it by 2 because it says Elly has 2 gardens.

5687 x 2=11374.

If you are confused on the second question the answer is down below ( The person who ask this question did have to ask the second question but on my math test this question has 2 parts).

The question is Elly's brother also wants to put up a fence around his garden that is 1034 centimeters by 432 centimeters. What is the difference in the length of fence that each will purchase?

First you have to find the perimeter of Elly's brother garden.

1034+432+1034+432=2932

Last we have to find out what is the difference in the length of fence that each will purchase.

To do that you will have to subtract Elly's perimeter and Elly's brothers perimeter.

11374-2932=8442

So Elly difference in the length of the fence is 8,442.

Answer:

  B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Step-by-step explanation:

You are right, it is easy. Any relation with a repeated first value is not a function.

A has (-3, -1) and (-3, -3), so the value -3 is a repeated first value.

C has (2, 5) and (2, 3), so the value 2 is a repeated first value.

D has (5, 8), (5, 9), and (5, -3), so the value 5 is a repeated first value.

None of A, C, or D is a relation that is a function. The correct choice is B, which has first values 0, 1, 2, 3, 4 -- none of which is repeated.

_____

If you plot points with repeated first values, you find they lie on the same vertical line. If a vertical line passes through 2 or more points in the relation, that relation is not a function. We say, "it doesn't pass the vertical line test."

A relation must pass the vertical line test in order to be a function. This is true of graphs of any kind, not just graphs of discrete points.

Answer:

The correct answer option is B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}.

Step-by-step explanation:

We are to determine whether which of the given relations in the possible answer options is a function.

We know that the x values of a function cannot be repeated. It means that for each output, there must be exactly one input.

Therefore, we will look for the relation where no x value is repeated.

Function ---> {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Answer:

Step 4

Step-by-step explanation:

4^-4 is 1/256

-(1/4^-4) is -256

Answer:

  a.  F(x) = 1.2(2.5)^(x – 1)

Step-by-step explanation:

The sequence is geometric with first term 1.2 and common ratio 3/1.2 = 2.5. The explicit formula for such a sequence is ...

  a[n] = a[1]·r^(n-1)

For a[1] = 1.2 and r = 2.5, and using x as the term number, the formula is ...

  F(x) = 1.2·2.5^(x-1) . . . . . matches selection A

The formula that could be used for showing the sequence is option A.[tex]F(x) = 1.2(2.5)^{(x - 1)}[/tex]

The sequence should be geometric which means the first term 1.2 and the common ratio is [tex]3\div 1.2[/tex] = 2.5.

Now The explicit formula should be

[tex]a[n] = a[1].r^{(n-1)}[/tex]

Now

Here a[1] = 1.2

and r = 2.5,

So, the formula is

[tex]F(x) = 1.2\times 2.5^{(x-1)[/tex]

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Answer:

A.

Step-by-step explanation:

you add all prices together and then mulitplied by the 15%. that gives you 20.0655 so you subtract that from the total price so 133.77-20.0655 and get 113.7045 or 113.70 which is the final price you pay

Answer:

8 + i

Step-by-step explanation:

What you need to simplify this is the following "definitions" of i to different powers.

[tex]i^1=i[/tex]

[tex]i^2=-1[/tex]

[tex]i^3=i^2*i=-1*i=-i[/tex]

[tex]i^4=1[/tex]

Now we can sub these in for the various powers of i in our expression:

[tex]6(1)+6(-i)-2(-1)+\sqrt{-1*49}[/tex]

Simplifying a bit:

[tex]6-6i+2+\sqrt{i^2*49}[/tex]

Since we know that the square root of i-squared is i, and that the square root of 49 is 7, we can get rid of the radial sign as follows:

6 - 6i + 2 + 7i

And the final answer, in a + bi form, is

8 + i

Answer:

(3 x + 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + 17 x + 6

Factor the quadratic 12 x^2 + 17 x + 6. The coefficient of x^2 is 12 and the constant term is 6. The product of 12 and 6 is 72. The factors of 72 which sum to 17 are 8 and 9. So 12 x^2 + 17 x + 6 = 12 x^2 + 9 x + 8 x + 6 = 3 (3 x + 2) + 4 x (3 x + 2):

3 (3 x + 2) + 4 x (3 x + 2)

Factor 3 x + 2 from 3 (3 x + 2) + 4 x (3 x + 2):

Answer:  (3 x + 2) (4 x + 3)

The quadratic expression 12x^2 + 17x + 6 can be factored completely as (4x +3) * (3x +2).

To factor the quadratic expression 12x^2 + 17x + 6 completely, we need to find two binomial factors that multiply together to give the original quadratic expression.

The factored form will have the following structure: (ax + b)(cx + d), where a, b, c, and d are constants.

To factor 12x^2 + 17x + 6, we can look for two numbers whose product is equal to the product of the leading coefficient (12) and the constant term (6), which is

12 * 6 = 72.

we can split 72 into 8 * 9= 72

Next, we need to find two numbers whose sum is equal to the coefficient of the linear term (17x). In this case, we need two numbers that add up to 17.

so

8+9=17

Now we can write the expression:

12x^2 + 17x + 6

12x^2 + 8x + 9x + 6

Now take common:

4x (3x + 2 ) + 3 (3x +2)

Taking 3x + 2 common we get:

(4x +3) * (3x +2)

Therefore, the quadratic expression 12x^2 + 17x + 6 can be factored completely as (4x +3) * (3x +2).

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Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x=-31+2y&\text{subtract}\ 2y\ \text{from both sides}\\5x+6y=23\end{array}\right\\\\\left\{\begin{array}{ccc}3x-2y=-31&\text{multiply both sides by 3}\\5x+6y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}9x-6y=-93\\5x+6y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad14x=-70\qquad\text{divide both sides by 14}\\.\qquad x=-5\\\\\text{Put it to the second equation:}\\\\5(-5)+6y=23\\-25+6y=23\qquad\text{add 25 to both sides}\\6y=48\qquad\text{divide both sides by 6}\\y=8[/tex]

Answer:

y = 2

Step-by-step explanation:

r tan θ / sec θ = 2

First, simplify tan θ / sec θ:

r (sin θ / cos θ) / (1 / cos θ) = 2

r sin θ = 2

Remember that r cos θ = x and r sin θ = y:

y = 2

Answer:

Answer is A hope that helped

Step-by-step explanation:

Answer:

speed in still water is 15 miles per hour; the speed of the current is 9 miles per hour

Step-by-step explanation:

This is a distance = rate times time problem.

We have to set up a table with the info we have and then take it from there.

                                                   d      =      r      x      t

downstream (w/ current)

upstream (against current)

We know the distance is 72 miles each way, so filling that in (I am also abbreviating downstream to d.s. and upstream to u.s.)

                  d      =      r      x      t

d.s             72

u.s             72

We also know that the trip with the current took 3 hours, and the trip back took 12.  Filling that in:

                d      =      r      x      t

d.s           72      =             x     3

u.s           72     =              x     12

Now we just need the rate values.  But we don't have anything solid to put in there.  We only know that WITH the current, the rate of the boat is faster; we also know that AGAINST the current, the rate of the boat is slower.  So the rate with the current is whatever the rate in still water is + the rate of the current or r + c.  The rate against the current is whatever the rate is in still water - the rate of the current or r - c.  Those values will fit into the rate column:

           d      =      r      x      t

d.s      72     =   (r + c)     x     3

u.s.     72     =   (r - c)      x     12

Since distance = rate * time, we set that equation up for each part of the trip.  For the first part:

72 = 3(r + c) and

72 = 3r + 3c

For the second part:

72 = 12(r - c) and

72 = 12r - 12c

Since the rate of the boat in still water is going to be the same whether you are being pushed along or being pushed against by the current, I solved the first equation for r:

72 = 3r + 3c and

3r = 72 - 3c so

r = 24 - c

and subbed that in for r in the second equation to solve for the rate of the current:

72 = 12(24 - c) - 12c and

72 = 288 - 12c - 12c

Combining like terms and we have

-216 = -24c so

c = 9

Now we can go back up the rate in terms of current, r = 24 - c, and plug in 9 for c to solve for r:

r = 24 - 9 so

r = 15

The boat's speed in still water is 15 miles per hour, and the speed of the current is 9 miles per hour.

The boat's speed in still water is 15 miles per hour, and the speed of the current is 9 miles per hour, determined by setting up equations based on rate, time, and distance for both downstream and upstream travel.

The question involves determining the speed of a boat in still water and the speed of the current given the times it takes to travel a certain distance downstream and upstream. To solve the problem, we use the concept of rate, time, and distance, where distance equals rate multiplied by time (D = RT). We know the distance (72 miles), the time downstream (3 hours), and the time upstream (12 hours).

Let's define the speed of the boat in still water as 'b' and the speed of the current as 'c'. When the boat travels downstream, it moves with the current, so its effective speed is 'b + c'. Upstream, it moves against the current, so its effective speed is 'b - c'. Using the distances and times given, we can set up two equations:

1) Downstream: 72 = (b + c) * 3

2) Upstream: 72 = (b - c) * 12

By solving these simultaneous equations, we find out:

Adding these two equations gives us 2b = 30, meaning b = 15 miles per hour. By substituting b in any of the above equations, we find c = 9 miles per hour.

Therefore, the boat's speed in still water is 15 miles per hour, and the speed of the current is 9 miles per hour.

Answer:

B. assumption of conclusions without prior experimentation or observation.

Step-by-step explanation:

In scientific investigation is quite important to demonstrate with facts, with observations, with numbers.  All discoveries, new insights, new knowledge found in scientific investigation is based on a very careful finding of facts in a very systematic way of doing that to establish conclusions about the question to be answered and constantly looking for objective evidence.

For instance, one hundred years ago, some physicists found a crucial fact that support one of the predictions that Einstein posted regarding a phenomena described as curved space because of the effect that a massive object exerts around its surrounding space. In fact, that year of 1919, those physicists observed that light traveled around a massive start not in straight line but curving around start's space (a fact), of course, using telescopes, writing observations and quantifying them (a systematic way).

Einstein's theory (in this case, the famous General Relativity Theory) must be supported, at least in part, with the discovery of an important fact, and not because he assumed that it was 'true' without prior experimentation or observation but because some others experimental physicists took a 'secret' from Nature (objective evidence) and gave a crucial fact about what Einstein had predicted some years before.

But it is not a definitive fact, a definitive list, there will be some more facts to look for in order to support that theory (constantly looking) and, why not, some other scientist or scientists could find another one, make a new experiment, test another hypothesis or model that contradicts the whole theory or some part of it.

Final answer:

To maximize profit, the hotel management should determine the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized. By analyzing different rate increases and subtracting the cost of servicing fewer rooms, the management can identify the rate that will generate the highest profit. For example, by increasing the rate to $42 per room, the hotel could maximize profit at $1940.

Explanation:

To determine the price at which the hotel management should charge per room to maximize profit, the management needs to consider the relationship between the price, the number of rented rooms, and the cost to service each room.

First, let's establish the initial conditions:

60 rooms are rented at a rate of $40 per room.

Each rented room costs $8 per day to service.

Next, management determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. To maximize profit, the management should find the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized.

Here is the step-by-step calculation:

Calculate the initial revenue: $40/room * 60 rooms = $2400

Calculate the initial cost: $8/room * 60 rooms = $480

Calculate the initial profit: $2400 - $480 = $1920

Calculate the new revenue: ($40 + $2)/room * (60 - 5) rooms = $2280

Calculate the new cost: $8/room * (60 - 5) rooms = $440

Calculate the new profit: $2280 - $440 = $1840

Repeat steps 4-6 for different rate increases until the profit is maximized.

Based on this analysis, the management should charge a rate that allows them to profit the most, such as $42/room, which would result in a profit of $1940.

Management should charge $44 per room to maximize profit.

To determine the optimal room rate to maximize profit, we'll utilize concepts from algebra and profit modeling. Let's define the variables:

The revenue, R, can be calculated as:

R = (40 + 2x)(60 - 5x)

The cost, C, of servicing the rooms can be calculated as:

C = 8(60 - 5x)

The profit, P, is given by:

P = R - C

Substituting the revenue and cost formulas:

P = (40 + 2x)(60 - 5x) - 8(60 - 5x)

Let's expand and simplify this equation:

P = (40 + 2x)(60 - 5x) - 8(60 - 5x)

[tex]P = 2400 - 200x + 120x - 10x^2 - 480 + 40x[/tex]

[tex]P = -10x^2 - 40x + 1920[/tex]

To find the value of x that maximizes the profit, we need to find the vertex of the quadratic function. The vertex form of a parabola given by [tex]ax^2 + bx + c[/tex] is at:

[tex]x = \frac{-b}{2a}[/tex]

Substituting a = -10 and b = -40:

[tex]x = -\frac{-40}{2 \times -10} = 40/20 = 2[/tex]

Thus, the management should increase the rate by 2 increments of $2, or $4. Therefore, the optimal room charge is:

$40 + $4 = $44

Answer:

0.034

Step-by-step explanation:

Data:

Let the standard deviation be : [tex]\sigma = 2[/tex]

The mean be: [tex]\mu = 6[/tex]

Therefore, P (x>4) which is  the probability that a person will wait for more than 4 minutes is given by:

[tex]z = \frac{X- \mu }{\sigma }[/tex]

 = [tex]\frac{4-6}{2} \\= -1[/tex]

Therefore,

P(x > 4)  = P (z > -1)

             = P (z < -1)

From the z-tables, we find 0.034

To find the probability that a person will wait for more than 4 minutes, calculate the z-score and use a standard normal distribution table or calculator. The probability is approximately 0.8413 or 84.13%.

To find the probability that a person will wait for more than 4 minutes, we need to calculate the z-score for the value 4 using the given mean and standard deviation. The z-score formula is z = (x - mean) / standard deviation. Plugging in the values, we get z = (4 - 6) / 2 = -1. Now, we can use a standard normal distribution table or a calculator to find the probability associated with this z-score.

Using a standard normal distribution table, the probability of a z-score less than -1 is approximately 0.1587.

Therefore, the probability of a person waiting for more than 4 minutes is approximately

1 - 0.1587 = 0.8413 or 84.13%.

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Answer:

Step 1: Finding r using the formula ln 2/h

[tex]1.\ r=\frac{ln\ 2}{h}\\ r=\frac{ln\ 2}{140}\\r=0.00495[/tex]

Step 2: Substitute the values in given formula

[tex]2.\ m_t=m_0e^{-rt}\\200=300e^{-0.00495t}[/tex]

Step 3: Divide both sides by 300

[tex]\frac{2}{3} =e^{-0.00495t}[/tex]

Step 4:  Take the natural logarithm on both sides

[tex]ln\ \frac{2}{3} =ln\ e^{0.00495t}[/tex]

Step 5: Simplify

[tex]-0.405 = -0.00495t[/tex]

Step 6: Divide both sides by 0.00495

[tex]\frac{-0.405}{-0.00495} =t[/tex]

Step 7: Simplify

[tex]t=81.8\ days[/tex]

Answer:

No, it is not a linear function. It is an exponential function.

Step-by-step explanation:

You have a secret that you tell to one person.

Every hour, each of the people that know the secret tells one person.

Let N be the people who know the secret.

Let t be the number of hours since you told the first person.

Now, when only you know the secret, means 1 person.

N(0) = 1

Next hour, there are now 2 people that know the secret.  

N(1) = 2

After the next hour, these 2 people will tell 2 more people, so people doubled to 4.

N(2) = 4

One hour later it will be N(3) = 8

We can see the pattern as following.

[tex]N(t)=2^{t}[/tex]

Therefore, the function is exponential not linear.

Answer:

  21,550

Step-by-step explanation:

An increase of 5% means the population is multiplied by 100% +5% = 1.05. This occurs each year for 12 years, so the multiplier is ...

  1.05¹² ≈ 1.7958563

When the initial population is multiplied by this factor, it becomes ...

  12,000×1.7958563 ≈ 21,550

Answer: 21550

Step-by-step explanation:

Answer:

a) 103, b) No

Step-by-step explanation:

a) We need to multiply the probability by the amount of the sample to get:

200 × 51.6% = 103.2, rounded down to 103

b) As we have selected the people randomly, we have no control over the type of people we are given - this is theoretical and the estimate is not definite - all of the sample could have murdered by firearm or even none (even though it is highly unlikely).

Answer:16

Step-by-step explanation:

Answer:

The height of the pyramid is 16 feet.

Step-by-step explanation:

A right pyramid with a square base has a base edge length of 24 feet.

The slant height is 20 feet.

We take the half of base here that is 12.

Let the height be h, applying Pythagoras theorem.

[tex]h^{2} =20^{2} -12^{2}[/tex]

Solving for h;

[tex]h^{2} =400-144[/tex]

=> [tex]h^{2} =400-144[/tex]

=> [tex]h^{2} =256[/tex]

=> [tex]h=\sqrt{256}[/tex]

h = 16

Therefore, The height of the pyramid is 16 feet.

Answer:

1) 51

2) 0.8

3) cosecant

Step-by-step explanation:

Question 1

The image for this scenario is attached below. Note that base of the television tower forms the side adjacent to the angle and the length of the tower forms the side opposite to the angle. The two angles marked in image are equal because of the property of Alternate Interior Angles.

So,

Adjacent side = 120 feet

Opposite side = 150 feet

Tangent of an angle is defined as:

[tex]tan(\theta)=\frac{Opposite}{Adjacent}[/tex]

Using the values, we get:

[tex]tan(\theta)=\frac{150}{120}\\\\ tan(\theta)=1.25\\\\ \theta = tan^{-1}(1.25)\\\\ \theta=51.34[/tex]

Rounded to the nearest degree, the angle of depression would be 51 degrees.

Question 2)

We have to find the cosine of angle Z. cos is defined as:

[tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex]

The side adjacent to angle Z is 24 and the hypotenuse is 30. So cos(Z) would be:

[tex]cos(Z)=\frac{24}{30}\\\\cos(Z)=0.8[/tex]

Therefore, value of cos(Z) for given triangle would be 0.8

Question 3

The opposite of sine ratio is known as cosecant which is abbreviated as csc

Since it is the opposite of sine ratio, it would be calculated as:

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

sine of angle is the ratio of opposite and hypotenuse, so csc would be ratio of hypotenuse to opposite side i.e.

[tex]csc(\theta)=\frac{hypotenuse}{opposite}[/tex]

Answer:

Step-by-step explanation:

QUESTION 1

Bottom leg of right triangle= 120 ft

Height= 150 ft

Angle of depression at the top of the tower = x

tan x= adjacent/opposite leg= 150/120= 1.25

tan x= 1.25

x ≈ 51.35°= 51°

QUESTION 2

Cos Z= adjacent side/hypotenuse

Cos Z= 24/30= 4/5

Z= 41.4°

QUESTION 3

Opposite of sine

The cosecant is the reciprocal of the sine

Cosecant Function:

 csc(θ) =  Hypotenuse/Opposite

Answer:

C. (15/2,9/2)

Step-by-step explanation:

To find the midpoint of two points

midpoint = (x1+x2)/2 , (y1+y2)/2

               = (17+-2)/2, (1+8)/2

               = 15/2, 9/2

Answer:

The correct option is C.

Step-by-step explanation:

The given points are (17,1) and (−2,8).

We need to find the midpoint of given points.

Formula for midpoint :

[tex]Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

The midpoint of the segment between the points (17,1) and (−2,8) is

[tex]Midpoint=(\frac{17+(-2)}{2},\frac{1+8}{2})[/tex]

[tex]Midpoint=(\frac{15}{2},\frac{9}{2})[/tex]

The midpoint of the segment between the points (17,1) and (−2,8) is [tex](\frac{15}{2},\frac{9}{2})[/tex]

Therefore the correct option is C.

Answer:

  Yes

Step-by-step explanation:

One way to tell is to look at the remainder from division by x-1, which is the value of f(1).

  1³ -1² +1 -1 = 0

so (x -1) is a factor of f(x).

  f(x) = (x -1)(x^2 +1) = h(x)(x^2 +1)

Answer:

  10a.  439

  10b.  1253

  11a.  linear

  11b.  $37.23

Step-by-step explanation:

10. Put the numbers in the equation and do the arithmetic. For logarithms, a scientific or graphing calculator will be required. The first attachment shows the result for 2 years = 24 months.

  920log(3) ≈ 439 . . . after 4 months

  920log(23) ≈ 1253 . . . after 2 years

___

11. Your experience with taxis tells you the fare is usually based on time and distance and some fixed charge. That is, it is roughly linearly related to distance. Plotting these data points will tell you the same thing: a linear model is suitable.

A graphing calculator or spreadsheet (or any of several web sites) can help you calculate the regression model. The second attachment shows my result:

  fare ≈ $2.10 + 3.513×miles

So, for 10 miles, the expected fare is ...

  $2.10 + 3.513×10 = $37.23

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Comment on these problems

It is useful to learn to use your calculator's various functions. That can save you a lot of effort and angst.

Answer:

  81.7 mpg

Step-by-step explanation:

"miles per gallon" means the number of miles is divided by the number of gallons.

  (425 mi)/(5.2 gal) = (425/5.2) mi/gal ≈ 81.7 mpg