Let D be the region enclosed by the two paraboloids z = 3x2 + + y2 z = 16 – x2 Then the projection of D on the xy-plane is: 2 *-* = 1 = 1 16 = 1 4 16 O This option O This option x None of these 16 4

To determine the number of tokens Frank bought, we need to set up an equation using the given information. Frank spent $2 for every 11 tokens and spent a total of $16 on tokens.

Let t be the total number of tokens Frank bought. We know that for every 11 tokens, he spent $2. So, we can express the relationship between the amount spent and the number of tokens as follows:

(amount spent) = (cost per token set) × (number of token sets)

Since Frank spent $2 for every 11 tokens, the cost per token set is $2, and the number of token sets is t/11. Therefore, the equation can be written as:

$16 = $2 × (t/11)

Alternatively, we can also use the equation:

t = (11/2) x ($16/$2)

Simplifying this expression gives us:

t = 11 x 8

t = 88

This equation can be used to determine t, the number of tokens Frank bought at the arcade.

To learn more about equations, click here:

brainly.com/question/10413253

#SPJ11

The required solutions of the situation of the function are  x = 3/4  or x = -1/4.

A unique connection where each input only produces one output. A common notation for it is "f(x)," where x denotes the input value. as in f(x) = x/2 ("f of x equals x divided by 2") Since there is only one output ("x/2") for each input ("x"), it is a function: • f(2) = 1.

We have,

f(x)=2x-1

g(x)=3/8x

To find the value of x for f(x) = g(x).

f(x) = g(x)

2x-1 = 3/8x

16x² - 8x = 3

16x² - 8x - 3 = 0

16x² - 12x + 4x - 3 = 0

4x(4x - 3) + (4x - 3) = 0

(4x - 3)(4x + 1) = 0

x = 3/4  or x = -1/4

Thus, required solution are  x = 3/4  or x = -1/4.

To know more about Quadratic equation visit:

brainly.com/question/30098550

#SPJ1

Answer:

F=8

Step-by-step explanation:

6f=48

Divide each side by 6

f=8

Substiuite

8x6=48??

Yes

Step-by-step explanation:

Simplifying 6f = 48 Solving 6f = 48 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by '6'. f = 8 Simplifying f = 8

Answer:

Step-by-step explanation:

An identity is an equation which is always true, no matter what values are substituted. 2 x + 3 x = 5 x is an identity because 2 x + 3 x will always equal regardless of the value of . Identities can be written with the sign ≡, so the example could be written as 2 x + 3 x ≡ 5 x .

The generated value X of the Exponential random variable is approximately 2.3817. This means that the Exponential random variable with an average lifetime of 5.8 years and a generated standard uniform value of 0.5647 has a value of approximately 2.3817 years. The answer is 2.3817.

To find the generated value X of the Exponential random variable, we can use the formula X = - (1 / λ) * ln(U), where λ is the rate parameter and U is the given standard uniform value.

To start, we need to calculate the rate parameter λ. The average lifetime of the Exponential distribution is given as 5.8 years, which means that the mean or expectation E(X) is also 5.8 years. We can calculate λ as follows:

E(X) = 1 / λ

5.8 = 1 / λ

λ = 1 / 5.8

Now, we can substitute the values of λ and U into the formula to find the generated value X:

X = - (1 / λ) * ln(U)

X = - (1 / (1/5.8)) * ln(0.5647)

X = - 5.8 * ln(0.5647)

X ≈ 2.3817

Therefore, the generated value X of the Exponential random variable is approximately 2.3817. This means that the Exponential random variable with an average lifetime of 5.8 years and a generated standard uniform value of 0.5647 has a value of approximately 2.3817 years. The answer is 2.3817.

Learn more about Exponential random variable

https://brainly.com/question/31491733

#SPJ11

Answer:

The discount is 6.8536

so her new bill is 78.8164

Step-by-step explanation:

Prove that the equation \(x^5 + 5x + 1 = 0\) has exactly one solution in the interval (-1, 0).

To prove that the equation has exactly one solution in the given interval, we can use the Intermediate Value Theorem. According to this theorem, if a continuous function takes on different signs at two points in an interval, then it must have at least one root (solution) in that interval.

In this case, consider the function f(x) = \(x^5 + 5x + 1\). We can observe that f(-1) = -5 and f(0) = 1. Since f(-1) is negative and f(0) is positive, the function changes sign within the interval (-1, 0). Therefore, by the Intermediate Value Theorem, there must exist at least one root of the equation \(x^5 + 5x + 1 = 0\) in the interval (-1, 0).

To show that there is exactly one solution, we need to establish that the function does not change sign again within the interval. This can be done by analyzing the behavior of the function and its derivative. By studying the derivative, we can confirm that the function is increasing and crosses the x-axis only once in the given interval, ensuring that there is a single solution.

Therefore, we have proven that the equation \(x^5 + 5x + 1 = 0\) has exactly one solution in the interval (-1, 0).

Learn more about Theorem here:

https://brainly.com/question/30066983

#SPJ11

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

To know more about radius of Deimos:

https://brainly.com/question/14834131

#SPJ11

Answer:

i cannot understand

Step-by-step explanation:

Given:

The given endpoints are ( -2,10) and (-10, -12).

Required:

We need to find the midpoint of te given endpoints.

Explanation:

Consider the formua to find the midpoint.

Consider the points ( -2,10) and (-10, -12).

Final answer:

Answer:

The volume of the solid figure is 625 cubic inches.

Step-by-step explanation:

The volume of a rectangular prism is found by multiplying its length, width, and height.

For the top prism, the volume is:

5 inches x 5 inches x 5 inches = 125 cubic inches

For the bottom prism, the volume is:

20 inches x 5 inches x 5 inches = 500 cubic inches

To find the total volume of the solid figure, we need to add the volumes of the two prisms together:

Total volume = 125 cubic inches + 500 cubic inches = 625 cubic inches

Therefore, the volume of the solid figure is 625 cubic inches.

Regenerate response

Answer:

292 and 2092

Step-by-step explanation:

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

Total : 240 + 600 + 90 = 730

So, cost of painting = 730/25 x 10 = 29.2 x 10 = 292

Total: 292 + 1800 = 2092

The total cost of paint would be 2092 dollars.

The area of the cuboid is the sum of product of the length, breadth of the given prism.

Surface area:

Wall 1: 40 x 3 = 120m^2

Wall2: 40 x 3 = 120m^2

Wall 3: 15 x 3 = 45m^2

Wall 4: 15 x 3 = 45m^2

Ceiling: 15 x 40 = 600m^2

The Total area: 240 + 600 + 90 = 730

So, The cost of painting = 730/25 x 10

= 29.2 x 10

= 292

Total: 292 + 1800 = 2092

Learn more about cuboid;

https://brainly.com/question/15843335

#SPJ2

The equation in cylindrical coordinates for the given surface is z = r² - 6.

To convert the rectangular equation z = x² + y² - 6 into cylindrical coordinates, we substitute x = rcos(θ) and y = rsin(θ), where r is the radial distance and theta is the azimuthal angle.

Substituting these values into the equation, we get:

z = (rcos(θ))² + (rsin(θ))² - 6

z = r²cos²(θ) + r²sin²(θ) - 6

z = r²(cos²(θ) + sin²(θ)) - 6

z = r² - 6

Therefore, the equation in cylindrical coordinates for the given surface is z = r² - 6.

The complete question is:

Find an equation in cylindrical coordinates for the surface represented by the rectangular equation. z=x²+y²-6

To know more about surface:

https://brainly.com/question/31530341

#SPJ4

Answer:

1.14285714

Step-by-step explanation:

Answer:

Step-by-step explanation:

help

If AB=BA, then each eigen vector of A is an eigen vector of B.2 and if AB−BA=2B and λ is an eigen value of AA then λ−2 is also an eigen value of A, the statement is false, and λ-2 is not necessarily an eigenvalue of A.

1. Let's consider the first statement: If AB=BA, then each eigen vector of A is an eigen vector of B.

Proof:

Let v be an eigenvector of matrix A with eigenvalue λ, then Av = λv. We need to show that Bv is an eigenvector of A as well.

Now, since AB = BA, we can multiply both sides by v:

ABv = BAv

Using the eigenvector property, Av = λv, we have:

ABv = B(λv)

Now, since λ is a scalar, we can rewrite it as:

ABv = λ(Bv)

From this equation, we can see that Bv is an eigenvector of A with eigenvalue λ. Therefore, each eigenvector of A is also an eigenvector of B.

2. Let's consider the second statement: If AB−BA=2B and λ is an eigenvalue of A, then λ−2 is also an eigenvalue of A.

Disproof:

Assume v is an eigenvector of A with eigenvalue λ, then Av = λv. We need to check if A(u) = (λ-2)u for some vector u, where u = Bv.

Using the given equation, AB - BA = 2B, we can rearrange it as AB = BA + 2B, and then multiply both sides by v:

ABv = BAv + 2Bv

Using the eigenvector property Av = λv, we get:

ABv = B(λv) + 2Bv

Since λ and 2 are scalars, we can rewrite this as:

ABv = (λ+2)(Bv)

Now, let u = Bv, then:

ABv = (λ+2)u

However, we are looking for an eigenvalue λ-2, but we have found λ+2 instead. This contradicts the given statement. Therefore, the statement is false, and λ-2 is not necessarily an eigenvalue of A.

To know more about eigen vector refer here:

https://brainly.com/question/13050052

#SPJ11

Answer:

SACAN MÃ QR VÀ NHẬN CÂU TRẢ LỜI

VUI LÒNG ĐƯA TÔI Ở BRAINLIEST

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf x = 16.3}\)

Step-by-step explanation:

Firstly we've to find the hypotenuse of the first triangle:

In the first triangle, for the angle 45:

Adjacent = 10

Hypotenuse = ?

Using cos for it.

Cos 45 = adjacent / hypotenuse

0.707 = 10 / hyp

hyp = 10 / 0.707

hyp = 14.14

The hypotenuse of the first triangle is actually the base (or opposite) of the triangle.

Also, hypotenuse = x and angle is 60 degrees.

So, we will use the sin ratio.

sin 60 = opposite / hypotenuse

0.866 = 14.14 / x

x = 14.14 / 0.866

x = 16.3

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

160 people in total

Step-by-step explanation:

The table shows the starting and ending elevations of a hiking trail. Point on Trail Elevation Starting Point 180 ft below sea level Ending Point 260 ft above sea level How much greater is the elevation of the ending point than the starting point for the trail

a) The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price

b) The  down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.

Given,

The purchase price for the studio apartment = $200,000

The down payment they paid = $60,000

a) We have to find the percentage of down payment to purchase price.

Here,

Percentage = (down payment x 100) / purchase price

= (60,000 x 100) / 200,000

= 60/2

= 30

That is,

The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price.

b) We have to find the percentage to purchase price if the down payment is $90,000

Here,

Percentage = (down payment x 100) / purchase price

= (90,000 x 100) / 200,000

= 90/2

= 45

That is,

The  down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.

Learn more about percentage of down payment here;

https://brainly.com/question/26831770

#SPJ1

Based on the poll of the opinion of food by students at a high school, one problem with the study is that B. Nonresponse.

In the question that was asked about how acceptable the food was, the total number of people who responded were:

= 54 + 103 + 15

= 172 responses

This means that the number of people who didn't respond were:
= 200 - 172

= 28 students

This is a problem of nonresponse as 28 students opted not to respond to the question which can affect research conclusions.

Find out more on nonresponse at https://brainly.com/question/14655125

#SPJ1

Answer:97 °

Step-by-step explanation:

83° & b° are a supplementary angle, meaning that they equal 180°. So:

83 + b = 180

b = 97°

Answer:

(a-b) {a raise2+b raise 2 - ab}

Step-by-step explanation:

Answer:

\((a-b)(a^2+ab+b^2)\)

Step-by-step explanation:

\(a^3-b^3=(a-b)(a^2+ab+b^2)\)

The z-score of apple price of $7.99/lb is 0.66

Probability is a measure of the possibility of an event occurring.

The likelihood could range from 0 to 1, where 0 indicates an impossibility and 1 indicates a certainty.

Every event in a sample space has an overall probability of one.

The probability that the apple price is less than or equal to $7.99 / lb can be calculated using the normal distribution method

                                   P(x ≤ 5.99)

The standard form of the given random sample can be found using the formula,

                               Z = (X - μ) / σ

where Z is the standard score

          X is the random sample

          μ is the mean

          σ is the standard deviation.

For x =7.99,

                  Z = (7.99 - 5.99) / 2.99

                      = 2 / 2.99

                  Z  = 0.66

Therefore, by standardizing the random sample, we get

              P(x ≤ 5.99) = P( z ≤ 0.66)

By using the z-table, we get the value of z

            P(z ≤ 0.66) = 0.7454

To know more about probability please visit:

brainly.com/question/16722133

#SPJ4

\(6 \frac{2}{3} = \frac{2}{18} = 9\)

\(3 \times \frac{1}{2} = \frac{1}{6} = 6\)

6×9=54

Answer:

p = -13

Step-by-step explanation: