Find the area of the region that is bounded by the line

f(x)=−x−3 and the curve g(x)=−x2−x+6 over the interval [−4,−2]

Answer:

The answer is B

Step-by-step explanation:

I got a 100% on the quiz

Answer:

B - Initially there were 1,000 bacteria; the population will not reach 0

Explanation:

Edg2020

15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:  See the image below.

Answer:

Step-by-step explanation:

5(n+6)+15(n-2)-2(n-2)=0

5*n + 5*6 + 15*n - 15*2  + n*(-2) - 2(-2) = 0

5n  + 30  + 15n - 30 - 2n + 4 = 0

5n + 15n - 2n + 30 - 30 + 4 = 0

Combine like terms

18n + 4 = 0

Subtract 4 from both sides

18n = -4

Divide both sides by 18

n = -4/18

n = -2/9

The simplest form of a fraction is when the numerator (top number) and denominator (bottom number) have no common factors.

A fraction is a mathematical expression that represents a part of a whole, where a numerator is divided by a denominator. To simplify a fraction, we must divide both the numerator and the denominator by the same number until we cannot divide any further. To simplify a fraction, you must divide both the numerator and denominator by their greatest common factor (GCF).

For example, let's simplify the fraction 24/36. The GCF of 24 and 36 is 12. So, dividing both numbers by 12 will give us the simplified fraction 2/3.

24 ÷ 12 = 2

36 ÷ 12 = 3

Therefore, the simplified fraction of 24/36 is 2/3.

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Answer:

16.35

Step-by-step explanation:

Using an inverse normal distribution, we can calculate the z score given the percentile, which can then be used to find our value.

First, we can use an inverse normal distribution calculator to figure out that the z score given the 75th percentile is 0.674.

Next, we know that the z score is (observed value - mean) / standard deviation. We can plug our values in to get

\(\frac{x-15}{2} = z\\\frac{x-15}{2} = 0.674\\x-15 = 0.674 * 2\\x = 0.674 * 2 + 15\\x= 16.348\)

Rounding, we get x = 16.35 as our answer

Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

Given:

The area of a square picture frame is 55 square inches.

To find:

The length of one side of the frame.

Solution:

Let the length of one side of the frame is x inches.

Area of square is

\(Area=a^2\)

where a is side length.

Area of frame is

\(Area=x^2\)

\(55=x^2\)

Taking square root on both sides.

\(\sqrt{55}=x\)

\(x=7.4161985\)

\(x\approx 7\)

\(49<55<64\), so \(7<\sqrt{55}<8\). Since 55 is closer to 49, therefore, \(\sqrt{55}\) is closer to 7.

Therefore, the length of one side of the frame is 7 inches.

Answer:

the approximate volume of the come is 1206 cm³.

Step-by-step explanation:

v = 3.14*12²*8/3 = 1206.37158 cm³

Answer:

Step-by-step explanation:

as you see the top "moves" like

2,4,6,8, and next will be 10

the bottom adds 3 to the previos answer

5,8,11,14,  next will be 15

5th card is 10/15

Answer:

1.4 is the answer i think hope this helped

The integration is as follow

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, \(\int\limits {e^{4x} / 19 - e^{8x}} \, dx\)

= \(\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx\)

let \(e^{4x}\) = z

4\(e^{4x}\) dx = dz

= 1/4 \(\int\limits {dz / \sqrt{19} ^2 -z^2} \,\)

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|(\(e^{4x}\) + √19)/ (\(e^{4x}\) - √19)| + C

Second,

\(\int\limits {33 sec^5 (x)} \, dx\)

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

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d. Expected life in years of the depreciable asset. The acceptable way to express the useful life of a depreciable asset is in terms of the expected life in years.

The useful life refers to the period of time over which the asset is expected to contribute to the revenue-generating activities of a business.

While options a, b, and c may be relevant factors for certain specific assets (such as units produced, hours of productivity, or miles driven), they do not encompass the overall concept of useful life. Useful life is a broader measure that takes into account the anticipated duration of productive use, regardless of specific output or activity metrics.

Expressing the useful life in years provides a common standard for comparison and allows for consistency in depreciation calculations and financial reporting. It is a practical and widely accepted approach to estimating the lifespan of a depreciable asset.

It is worth noting that the estimated useful life in years may vary depending on the nature of the asset and industry practices. It is typically determined based on factors such as technological advancements, physical wear and tear, economic obsolescence, and the intended purpose of the asset.

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A. non-contact

B. poles

C. protons

D. attraction

HopeItHelps you

Answer:

c?

Step-by-step explanation:

It's the closest number to 51.

1245/24

In the derivation of Average Variable Cost (AVC), to find its minimum, you need the minimum-slope ray out of the origin to the TVC (Total Variable Cost).

Average Variable Cost (AVC) is calculated by dividing Total Variable Cost (TVC) by the quantity of output. The TVC represents the variable costs incurred in producing a certain level of output.

The minimum point of the AVC curve occurs where the slope of the TVC curve is at its minimum. The minimum-slope ray out of the origin represents the tangent line to the TVC curve at the origin, and this tangent line intersects the TVC curve at its minimum point. The AVC curve takes its minimum value at this point.

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Answer:

The answer is D

Step-by-step explanation:

Answer:

$30

Step-by-step explanation:

Use the formula:

Interest = Principal(rate)(time)

I = Prt

P = 300

r = 5%, change to a decimal by dividing by 100. 5/100 = .05

t = 2

Plugin in the numbers and multiply

I = 300(.05)(2)

I = 30

The length of segment AB is 9 units.

A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within. The Euclidean distance between two ends of a line segment determines its length.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Consider the triangle ACD,

The length of AD is 16 units and the length of BC is 9 units.

From the figure, we get that the B is the midpoint of AC therefore:

AB = BC = 9 units

The length of the segments AB is 9 units.

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Answer:

a = 4

b = 10

Step-by-step explanation:

Price of an apple $1.25

Price of a banana $0.5 0

The two equations:

10 = 1.25a + 0.5b

a + b = 14

solve for one variable

b = 14 - a

10 = 1.25a + 0.5(14-a)

10 = 1.25a+ 7 - 0.5a

10 = 0.75a + 7

0.75a = 3

a = 4

Then solve for the second

b = 14 - 4

b = 10

Answer:

\(Range=14\)

\(\sigma^2 =32.4\)

\(\sigma = 5 .7\)

The standard deviation will remain unchanged.

Step-by-step explanation:

Given

\(Data: 136, 129, 141, 139, 138, 127\)

Solving (a): The range

This is calculated as:

\(Range = Highest - Least\)

Where:

\(Highest = 141; Least = 127\)

So:

\(Range=141-127\)

\(Range=14\)

Solving (b): The variance

First, we calculate the mean

\(\bar x = \frac{1}{n} \sum x\)

\(\bar x = \frac{1}{6} (136+ 129+ 141+ 139+ 138+ 127)\)

\(\bar x = \frac{1}{6} *810\)

\(\bar x = 135\)

The variance is calculated as:

\(\sigma^2 =\frac{1}{n-1}\sum(x - \bar x)^2\)

So, we have:

\(\sigma^2 =\frac{1}{6-1}*[(136 - 135)^2 +(129 - 135)^2 +(141 - 135)^2 +(139 - 135)^2 +(138 - 135)^2 +(127 - 135)^2]\)

\(\sigma^2 =\frac{1}{5}*[162]\)

\(\sigma^2 =32.4\)

Solving (c): The standard deviation

This is calculated as:

\(\sigma = \sqrt {\sigma^2 }\)

\(\sigma = \sqrt {32.4}\)

\(\sigma = 5 .7\) --- approximately

Solving (d): With the stated condition, the standard deviation will remain unchanged.

Answer:

A = 540 m²

Step-by-step explanation:

consider the shape split into 3 rectangles

the length is divided into 3 congruent sections

single dash = 30 m ÷ 3 = 10 m

the width is divided into 3 congruent sections

double dash = 27 m ÷ 3 = 9 m

then area (A) is the total of the 3 rectangular areas

A of left rectangle = 10 × 9 = 90 m²

A of middle rectangle = 10 × (9 + 9) = 10 × 18 = 180 m²

A of right rectangle = 10 × 27 = 270 m²

total area = 90 + 180 + 270 = 540 m²

Answer:

-8

Step-by-step explanation:

-8+3=-5

To find the length of the curve given by r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4, we need to use the formula for arc length:

L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

In this case, we have:

dx/dt = -7 sin(7t)
dy/dt = 7 cos(7t)
dz/dt = -7 sin(t) / cos(t)

So,

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 sin^2(7t) + 49 cos^2(7t) + 49 sin^2(t) / cos^2(t)
= 49 [sin^2(7t) + cos^2(7t) + sin^2(t) / cos^2(t)]
= 49 [1 + sin^2(t) / cos^2(t)]

Now, using the identity sin^2(t) + cos^2(t) = 1, we can rewrite this as:

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 cos^2(t)

Therefore, the length of the curve is:

L = ∫[0,π/4] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
= ∫[0,π/4] 7 cos(t) dt
= 7 [sin(t)]|[0,π/4]
= 7 sin(π/4) - 7 sin(0)
= 7 (√2/2)
= 7√2/2

So the length of the curve is 7√2/2.

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The marginal cost of producing one more unit of the product when x = 100 is $150 per unit. To find the instantaneous rate of change (or the marginal cost) of c with respect to x when x = 100, we need to calculate the derivative of the cost function c(x) with respect to x and evaluate it at x = 100.

Let's assume that we have the cost function c(x) = 0.5x^2 + 50x + 1000, where x is the number of units produced. To find the derivative of this function, we need to use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to our cost function, we get:

c'(x) = d/dx (0.5x^2 + 50x + 1000)
     = 1x^(2-1) + 50x^(1-1) + 0
     = x + 50

Now, we can evaluate this derivative at x = 100 to find the marginal cost:

c'(100) = 100 + 50
       = 150

Therefore, the marginal cost of producing one more unit of the product when x = 100 is $150 per unit. This means that if the company produces one more unit of the product, it will cost them $150 more than the cost of producing the previous unit. The significance of the marginal cost will be explained in a future chapter, but for now, it is important to understand that it is a crucial concept in economics and business decision-making.

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Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

Answer:

1.6

Step-by-step explanation:

first break it up into parts so it’s easier

0.3+0.5 = 0.8

0.8+0.8= 1.6

The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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Answer:

The length and width of another rectangular field with same perimeter but a larger area is 80 m by 70 m

Step-by-step explanation:

The perimeter of the existing field is

2(l + b)

= 2(90 + 60) = 2(150) = 300 yards

So we want another field having the same perimeter but a larger area

The area we have here is 90 * 60 = 5,400 square yards

If we had 80 by 70

Perimeter will still be 2(70 + 80) = 150

But the area will be 80 * 70 = 5,600 square yards

We can say that the probability which is more than 192 of the confidence intervals cover the true proportions i.e, P(X > 192) is 0.9452.

Given: Confidence interval = 95%

We need to find the probability that more than 192 of the confidence intervals cover the true proportions.

P(X > 192) = ?

We know that the sample proportion follows the Normal distribution as n is large.

According to the Central Limit Theorem, the sample proportion follows the Normal distribution with mean and standard deviation as shown below:

μp = pσp = √((pq/n))

Here, p and q are population proportions and p + q = 1.

We do not know the population proportion, p or q, but we can assume that p = q = 0.5 in case we do not have any prior knowledge of p and q.

Now, we standardize the Normal distribution using z-score:

Z = (X - μp) / σp

Z = (X - np) / √((npq/n))

Here, X is the number of confidence intervals that cover the true proportions.

The sample proportion is computed as:

p = X / n

Here, n is the number of samples (towns).

Now, the z-score can be written as:

Z = (X - np) / √((npq/n)) > Z

= (192 - 200 × 0.5) / √((200 × 0.5 × 0.5/200))

= -1.6

P(Z > -1.6) = 0.9452 [from z-table]

Therefore, the probability that more than 192 of the confidence intervals cover the true proportions is P(X > 192)

= 1 - P(X ≤ 192) > 1 - P(Z ≤ -1.6) > 1 - 0.0548

= 0.9452

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