Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle. y = ex, y = x2 − 1, x = −1, x = 1

Part (c) is the correct option i.e. The total dealer's cost is $16588.36.

What is Percentage ?

Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Given, Cost paid for car's options = 82 % $3,098 = $2540.36

           Cost paid for base price = 85 % $15,480 = $13158.

           Destination charge = $890

∴ The total dealer's cost will be :

 = Cost paid for car's options +  Cost paid for base price +  Destination charge

=  $2540.36 + $13158 + $890

= $16588.36.

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Answer:

Step-by-step explanation:

First Line:

0, 1//7, 2/7, 3/7, 4/7, 5/7, 6/7, 1, 8/7, 9/7, 10/7

Second Line:

-1/3, 0, 1/3, 1/2, 1, 4/3

Third Line:

0, 1/3, 2/3, 1, 4/3, 5/3, 2

Answer: 60 minutes or 1 hour.

Step-by-step explanation:

Since one moderator was typing every 20 minutes while the other moderator was typing every 30 minutes, then the time the other one will find about the insult simply means that we should find the lowest common multiple of 20 and 30. This will be:

20 = 20, 40, 60, 80, 100, ..

30 = 30, 60, 90, 120 .....

Here, we can see that the lowest common multiple is 60. Therefore, the other one will find about the insults in 60 minutes.

Answer:

5

Step-by-step explanation:

23 - 10 = 13

13 - 8 = 5

Answer:

5

Step-by-step explanation:

p = a + b + c

23 = 8 + 10 + c

23 = 18 + c

5 = c

Answer:

at school in my country the maximum number can be from 200 to 45 that can be in one class room

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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To determine if the experimental probability for getting a 6 is close to the theoretical probability, we need to compare the observed frequency of rolling a 6 to the expected probability based on a fair six-sided die.

In the given list of rolls, we have a total of 20 rolls. To calculate the experimental probability of rolling a 6, we count the number of times a 6 appears and divide it by the total number of rolls.

From the list, we can see that a 6 appears 6 times. Therefore, the experimental probability of rolling a 6 is:

Experimental probability = Number of 6's / Total number of rolls = 6/20 = 0.3

Now let's compare this experimental probability to the theoretical probability. In a fair six-sided die, each face has an equal chance of occurring, so the theoretical probability of rolling a 6 is 1/6 ≈ 0.1667.

Comparing the experimental probability of 0.3 to the theoretical probability of 0.1667, we can see that the experimental probability is higher than the theoretical probability for rolling a 6.

Therefore, the statement "the experimental probability for getting a 6 is close to the theoretical probability" is false. The experimental probability is higher than the theoretical probability in this case.

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Answer: BCD

Step-by-step explanation:

A is incorrect since there is no angle Y to exist

Hope this helps

The surface described by the equation \(r^2 + z^2 = 4\)is a right circular cylinder with a radius of 2 units, centered along the z-axis.

The surface whose equation is given is a cylinder with a radius of 2 units and a height of 4 units, centered on the z-axis.
Hi! I'd be happy to help you identify the surface with the given equation. The equation provided is:

\(r^2 + z^2 = 4\)

This equation represents a right circular cylinder with a radius of 2 units, centered along the z-axis. Here's why:

1. Notice that the equation contains r^2 and \(z^2\) terms, which suggests a cylindrical coordinate system.
2. The equation does not contain the θ term, which implies that the surface is symmetric about the z-axis.
3. The equation is in the form \(r^2 + z^2\) = constant, which is the equation of a right circular cylinder in cylindrical coordinates.

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Answer:

Identify the sequence, hten use the formula to find the first term a1=2

Identify the sequence, then use if the formula to find the second term a3=-6

Step-by-step explanation:

The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that the expression is;

- 4n + 6

Now the expression as

A. (-6n) + (6 + 2n)

After adding, we have;

(-6n) + (6 + 2n) = -6n + 6 + 2n

= - 4n + 6

B. (- 10n + 2) + (6n + 4)

After adding we have;

(- 10n + 2) + (6n + 4) = - 10n + 2 + 6n + 4

= - 4n + 6

Hence, The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)

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Answer:

equal

Step-by-step explanation:

Answer:

there are 63 dogs

and 147 sheeps

Answer:

so 3:7 thats means 30 percent of animals are dogs so

0.3 times 210= 63

so there is 63 dogs in the field

Hope This Helps!!!

The mean number of people with the genetic mutation in these groups is 80 as this follows a Binomial Distribution.

It is given that 10% of the population has a genetic mutation. We have a sample of 800 here.

Let X be the random variable that defines the number of people with the mutation in the sample.

Since every person can or can't have the mutation, this is a Binomial distribution.

Here,

n = 800

p = 0.1

According to the formula for a Binomial Distribution,

the mean = np

Therefore, the mean for the above distribution will be

800 X 0.1

= 80.

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Answer: 369

Step-by-step explanation:

This is becuase 18% of 450 is 81, and 18% off means you subract the 81 leaving 369.

Answer:

A theorem is a statement of

mathematical truth, while a proof is the series of statements that support the theorem's claim

Step-by-step explanation:

In simple words

Answer:

$1,377

Step-by-step explanation:

the way that I did it-

100-25=75

1700x0.75=1275

8%=0.08, just add a 1 to the sales tax whenever you are calculating that.

1275x1.08=1377

therefore it is $1,377

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Answer:

Step-by-step explanation:

vertex form of an equation of the parabola:  

f(x) = a(x - p)² + q

vertex (0, 3)  ⇒  p = 0,  q = 3

so:

   f(x) = a(x - 0)² + 3

    f(x) = ax² + 3

the parabola goes through point (1, -4)  ⇒  x=1,  f(x)=-4

   -4 = a(1)² + 3

   -4 = a + 3

    a = 7

Therefore the equation of the parabola in vertex form:

f(x) = 7x² + 3

Answer:

t_n =a +(n-1)d

t_100 = 2+ (100-1)6

= 2+99× 6

= 2 +594

= 596

Step 3 is incorrect because it states that if all the sides of two figures are proportional then those two figures are similar.

Step 6 is incorrect because it states that if needed, we should reflect A B C D over segment WX. This is incorrect because reflection is not required to prove two figures are similar.

A segment is part of a market that is specifically targeted for a product or service. It is defined by characteristics such as demographics, geography, buying behavior, and interests. Segmentation helps companies to identify their target market and direct their marketing activities accordingly.

We can prove two figures are similar using a sequence of transformations that includes translations, rotations, and dilations, but not reflections. Reflection may be used to help visualize similar figures, but it is not necessary to prove that they are similar.

from the question:

Step 3 is erroneous since it implies that two figures are identical if all of their sides are proportionate. This isn't always the case because two figures can resemble one another without having sides that are proportional. When two figures of the same shape, such as two squares or two circles, proportional sides can only ensure that the two figures are identical.

Step 6 is erroneous because it instructs us to reflect A, B, C, and D over segment WX if necessary. This is false since the similarity between two figures can be established without thought. Using a series of transformations that includes translations, rotations, and dilations but not reflections, we may demonstrate the similarity of the two figures. Reflection may be employed to aid in seeing related figures, but it is not required to establish their similarity.

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The maximum value of 3x + y is 5/3, which is achieved when x = 1/3 and y = 4/3.

We can solve this optimization problem using the simplex method. First, we convert the problem to standard form:

Maximize: 3x + y + 0u + 0v + 0s1 + 0s2

Subject to:

-x + y + u + s1 = 1

2x + y + v + s2 = 4

x, y, u, v, s1, s2 ≥ 0

We then construct the initial simplex tableau:

| 1 -1 1 0 1 0 | 1

| 2 1 0 1 0 4 | 4

| 3 1 0 0 0 0 | 0

The pivot element is the entry in the first row and first column, which is 1. We use row operations to make all other entries in the first column zero. We subtract row 1 from row 2, and subtract 3 times row 1 from row 3:

| 1 -1 1 0 1 0 | 1

| 0 3 -1 1 -1 4 | 3

| 0 4 -3 0 -3 0 | -3

The new pivot element is the entry in the second row and second column, which is 3. We use row operations to make all other entries in the second column zero. We divide row 2 by 3, and subtract 4 times row 2 from row 3:

| 1 0 1/3 -1/3 2/3 4/3 | 5/3

| 0 1 -1/3 1/3 -1/3 4/3 | 1

| 0 0 -1/3 -4/3 -5/3 -16/3 | -5

All entries in the objective row are positive or zero, so we have found the optimal solution. The maximum value of 3x + y is 5/3, which is achieved when x = 1/3 and y = 4/3.

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Answer: No, Kate can't completely cover the shape.

Step-by-step explanation:

S=Area of Square. T=Area of each Triangle. A=Total Area

S=6*6

S=36 in^2

T=1/2 * 6 * 7.5

T=3*7.5

T=22.5 in^2

4T=4*22.5

4T=90 in^2

A=4T+S

A=90+36

A=126 in^2

120<126 ==> No, Kate can't completely cover the shape.

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

to get the equation of any straight line we only need two points off of it, hmmm let's use P and Q here and then let's set the equation in standard form, that is

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{6}}}\implies \cfrac{2}{-3}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{6})\)

\(\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-0)~~ = ~~3\left( -\cfrac{2}{3}(x-6) \right)}\implies 3y=-2(x-6) \\\\\\ 3y=-2x+12 \implies \stackrel{a}{2} x+\stackrel{b}{3} y=12\)

First, we need to convert 253 lb to kilograms. Given that 1 kg is equivalent to 2.205 lb, then:

The dosage Justin should receive is directly proportional to his weight. Given that a dosage of 11 mg corresponds to a weight of 20 kg, then to find the dosage that corresponds to 114.74 kg we can use the next proportion:

Solving for x:

He should receive a dosage of 63.1 mg

Answer:

Formula for volume of cone;

V = πr^2 · h/3

Plug in the values you know:-

65.94 = 3.14r^2 · 7/3

r = 3, -3.