calculate the electric field induced both inside and outside the solenoid of the preceding problem if i = i0 sin ωt.

Answer: z = 1.6

Step-by-step explanation:

1.8 = 3z -3

3z = 4.8

z = 4.8/3 = 1.6

The number of bread rolls that Rita will need will be 60.

To determine the minimum number of bread rolls that Rita will need, we will first determine how many packets of cheese slices and boxes of burgers she needs to buy to have the same number.

20 * 3 = 60

12 * 5 = 60

So, she needs 3 packs of cheese slices and 5 packs of burgers. So, the minimum amount of bread rolls that she will need to contain both the cheese slices and burgers will be 60.

Complete Question:

Rita is going to make some cheeseburgers for a party. She buys some packets of cheese slices and some boxes of burgers. There are 20 cheese slices in each packet. There are 12 burgers in each box. Rita buys exactly the same number of cheese slices and burgers. (a) How many packets of cheese slices and how many boxes of burgers does she buy? (b) Rita wants to put one cheese slice and one burger into each bread roll. She wants to use all the cheese slices and all the burgers. How many bread rolls does Rita need?

Learn more about multiples here:

https://brainly.com/question/26856218

#SPJ1

Answer:

Given that `x^2 : (20 - 3x) = 1:2`, we can solve for possible values of x as follows:

First, we can cross-multiply to obtain the equation `x^2 * 2 = (20 - 3x) * 1`.

Expanding the right-hand side, we get `2x^2 = 20 - 3x`.

Bringing all the terms to one side, we obtain `2x^2 + 3x - 20 = 0`.

This is a quadratic equation, which can be solved using the quadratic formula: `x = (-b ± sqrt(b^2 - 4ac)) / 2a`.

Plugging in the values `a = 2`, `b = 3`, and `c = -20`, we get:

```

x = (-3 ± sqrt(3^2 - 4*2*(-20))) / 4

x = (-3 ± sqrt(169)) / 4

```

Therefore, the possible values of x are `x = (-3 + 13) / 4 = 2` and `x = (-3 - 13) / 4 = -4`.

So, the possible values of x are 2 and -4.

Step-by-step explanation:

Answer:

w less-than-or-equal-to 3.6

The arrow points left.

There is a closed circle at 3.6.

Step-by-step explanation:

8.2w ≤ 29.52

Divide both sides by 8.2

w ≤ 3.6

Answer:

w less-than-or-equal-to 3.6

The arrow points left.

There is a closed circle at 3.6.

Using the sum or difference formula for sine and cosine, we can simplify the expression Sin(6π/7)cos(29π/42) - cos(6π/7)sin(29π/42) to the exact value of -1/2.

To simplify the given expression, we can use the sum or difference formula for sine and cosine, which states:

sin(A - B) = sinAcosB - cosAsinB.

In this case, we have Sin(6π/7)cos(29π/42) - cos(6π/7)sin(29π/42). Comparing this with the sum or difference formula, we can identify A = 6π/7 and B = 29π/42.

Applying the formula, we have:

sin(A - B) = sin(6π/7 - 29π/42) = sin((12π - 29π)/(14*3)) = sin((-17π)/(14*3)).

Now, we can simplify further using the periodicity of sine. Since sin(-θ) = -sinθ, we have:

sin((-17π)/(14*3)) = -sin((17π)/(14*3)).

Next, using the sum or difference formula in reverse, we can rewrite -sin((17π)/(14*3)) as -sin(17π/42) = -1/2.

Therefore, Sin(6π/7)cos(29π/42) - cos(6π/7)sin(29π/42) simplifies to the exact value of -1/2.

Learn more about cosine here:

https://brainly.com/question/29114352

#SPJ11

Step-by-step explanation:

A semicircle  has  1/2 circumference of the full circle = 1/2 pi d

so the entire perimeter will be   1/2 ( pi)(30) + 10 + 10 + 20 = 87.1 cm

The height of the cone is approximately 8.63 feet.

To find the height of the cone, we can use the formula for the volume of a cone, which is given by V = (1/3) * π * r^2 * h, where V is the volume, π is the mathematical constant pi (approximately 3.14159), r is the radius, and h is the height of the cone.

In this case, we are given the diameter of the cone, which is 17 feet. The radius is half the diameter, so the radius would be 17/2 = 8.5 feet.

The volume of the cone is given as 190.07 cubic feet. Substituting these values into the volume formula, we can solve for the height:

190.07 = (1/3) * 3.14159 * (8.5^2) * h

Simplifying the equation further:

190.07 = 3.14159 * 72.25 * h

190.07 = 227.1846275 * h

h ≈ 0.836583

So, the height of the cone is approximately 0.836583 feet, which is approximately 8.63 feet when rounded to two decimal places.

Visit here to learn more about volume :

brainly.com/question/28058531

#SPJ11

The equation that models the relationship between the amount of work done (w), the mass of the object (m), and the distance the object is lifted (d) is shown below:

work done  = k * m * d

Work done is described as product of the force and the distance over which the force is applied.

In the equation we wrote above,

k=  constant of proportionality that relates the three variables.

m= mass

d = distance

According to the equation, the amount of work is inversely correlated with the object's mass and its distance.

Learn more about work done at:

https://brainly.com/question/25573309

#SPJ1

The volume of a pyramid with the slant height given is 10 m².

We have,
To find the volume of a pyramid with the slant height given.

Volume = (1/3) x Base Area x Slant Height

Now,

Base area.

= 2²

= 4 m²

And,

Slant height = 5 m

Now,

Volume

= (1/3) x Base Area x Slant Height

= 1/2 x 4 x 5

= 10 m²

Thus,
The volume of a pyramid with the slant height given is 10 m².

Learn more about Prism here:

https://brainly.com/question/12649592

#SPJ1

The polynomial that represents the area of the rectangle is:
[tex]A = 2x^4 + x^3 - 15x^2 + 8x + 24[/tex].

To find the polynomial that represents the area of the rectangle, we need to multiply the polynomials representing the length and width.
Length (L): [tex]2x^3 - 5x^2 + 8[/tex]
Width (W): x + 3
Now, let's multiply these polynomials:
Area (A) [tex]= L \times W = (2x^3 - 5x^2 + 8)(x + 3)[/tex]
To multiply, we'll use the distributive property and multiply each term in the first polynomial by each term in the second polynomial:
[tex]A = (2x^3 \times  x) + (2x^3 \times  3) + (-5x^2 \times x) + (-5x^2 \times  3) + (8 \times  x) + (8 \times  3)[/tex]
Now, let's perform the multiplications:
[tex]A = 2x^4 + 6x^3 - 5x^3 - 15x^2 + 8x + 24[/tex]
Next, we'll combine like terms:
[tex]A = 2x^4 + (6x^3 - 5x^3) - 15x^2 + 8x + 24[/tex]
[tex]A = 2x^4 + x^3 - 15x^2 + 8x + 24[/tex].

For similar question on polynomial.

https://brainly.com/question/29267684

#SPJ11

Answer:

The slope of the line passing through the points (-3, 7) and (2, 3) is -4/5.

Step-by-step explanation:

To find the slope of the line passing through the points (-3, 7) and (2, 3), we can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-3, 7) and (x2, y2) = (2, 3).

So, substituting these values into the formula, we get:

slope = (3 - 7) / (2 - (-3))

slope = -4 / 5

Therefore, the slope of the line passing through the points (-3, 7) and (2, 3) is -4/5.

In calculating a one-sample chi-square test with 3 degrees of freedom, the variable has 4 categories.

Step-by-step explanation:
1. The degrees of freedom (df) in a one-sample chi-square test are calculated as df = k - 1, where k is the number of categories.
2. Given that there are 3 degrees of freedom, we can solve for k: 3 = k - 1.
3. Add 1 to both sides of the equation: 3 + 1 = k.
4. Therefore, k = 4, meaning there are 4 categories in the variable.

To know more about chi-square test refer here :

https://brainly.com/question/14082240#

#SPJ11

The quadratic function in this problem is defined as follows:

f(x) = x² - 18x + 86.

The coefficients are given as follows:

a = 1, b = -18 and c = 86.

Hence the axis of symmetry, representing the x-coordinate of the vertex, is given as follows:

x = -b/2a

x = 18/2

x = 9.

The coefficient a is positive, hence the function has a minimum value, which is given as follows:

f(9) = 9² - 18(9) + 86

f(9) = 5.

More can be learned about quadratic functions at https://brainly.com/question/31895757

#SPJ1

Answer:

211.42 in squared

Step-by-step explanation:

L x W x H
L = 3.1
W = 12.4
H = 5.5
First you multiply the length and the width. 3.1 x 12.4 which equals 38.44. Then you multiply the answer with the height which is 5.5, therefore equals 211.42 inches squared

Hope this helps, have a lovely day <3

The length of the shortest banner is 25 meters.

The shortest banner joining the tops of the two buildings is a right triangle with legs of 24 meters and 7 meters.

The hypotenuse of this triangle is the length of the banner, and can be found using the Pythagorean Theorem:

[tex]a^2 + b^2 = c^2\\24^2 + 7^2 = c^2\\576 + 49 = c^2\\625 = c^2[/tex]

c = 25 meters

Therefore, the length of the shortest banner is 25 meters.

Read more about length here:

https://brainly.com/question/28108430
#SPJ1

The probability that less than 7.1% of the individuals in this sample hold multiple jobs is 15.06%

To calculate the probability that less than 7.1% of the individuals in a sample of 352 employed adults hold multiple jobs, we use the binomial distribution formula:

P(X ≤ k) = ∑ (from i = 0 to k) [C(n, i) * p^i * (1-p)^(n-i)]

Where:

P(X ≤ k) is the cumulative probability of observing up to k successes,

n is the total number of trials (sample size),

p is the probability of success (less than 7.1% in this case),

C(n, i) is the binomial coefficient, calculated as n! / (i! * (n-i)!),

k is the number of successes we want to find the cumulative probability for.

In this case, we want to find the probability of less than 7.1% of individuals holding multiple jobs, so k would be 6 (since we are counting from 0 to 6).

Using a binomial calculator or statistical software, we can calculate the probability as follows:

P(X ≤ 6) = ∑ (from i = 0 to 6) [C(352, i) * (0.071)^i * (1-0.071)^(352-i)]

The sum of these terms gives us the probability that less than 7.1% of individuals hold multiple jobs in the sample.

After performing the calculation, we find that the probability is approximately 0.1506 (rounded to four decimal places).

Therefore, there is a 15.06% chance that less than 7.1% of the individuals in the sample of 352 employed adults hold multiple jobs.

Learn more about probability at https://brainly.com/question/15333069

#SPJ11

The constant that needs to be added to complete the square is 121/4.

To complete the square for the quadratic equation x² - 11x - 14 = 0, we need to add the square of half of the coefficient of x, which is (-11/2)² = 121/4. So we add 121/4 to both sides of the equation, which gives us:

x² - 11x - 14 + 121/4 = 121/4

We can simplify the left side by combining like terms:

(x - 11/2)² = 121/4 + 14

(x - 11/2)² = 169/4

Taking the square root of both sides, we get:

x - 11/2 = ±13/2

Solving for x, we get:

x = 11/2 ± 13/2

x = 12 or x = -1

Therefore, the constant that needs to be added to complete the square is 121/4.

Visit here to learn more about constant brainly.com/question/14279790

#SPJ11

Using the linearized theory, we can obtain the lift and drag coefficients for the symmetrical diamond shaped airfoil.

In order to compute the lift and drag coefficients for the symmetrical diamond shaped airfoil shown in the figure, we need to use the linearized theory. The linearized theory is a mathematical approach that is used to solve the aerodynamic equations for small disturbances in the flow field. This theory assumes that the flow is steady, incompressible, and irrotational. It also assumes that the airfoil is small enough that it does not significantly affect the flow.
To compute the lift and drag coefficients, we need to first calculate the pressure distribution over the airfoil. We can do this by solving the potential flow equations using the boundary conditions at the airfoil surface. Once we have the pressure distribution, we can use it to calculate the lift and drag forces using the lift and drag coefficients.
The lift coefficient is defined as the ratio of the lift force to the dynamic pressure and the planform area of the airfoil. The dynamic pressure is given by 0.5 * rho * V^2, where rho is the density of the air and V is the velocity of the flow. The drag coefficient is defined as the ratio of the drag force to the dynamic pressure and the planform area of the airfoil.
These coefficients will depend on the geometry of the airfoil, the angle of attack, and the Reynolds number of the flow. By varying these parameters, we can analyze the performance of the airfoil and optimize it for specific applications.

To know more about coefficients visit:

https://brainly.com/question/1594145

#SPJ11

Answer: slope = -4/5

Step-by-step explanation:

slope = gradient = (change in y) / (change in x)

slope = (9 - 5) / (2 - 7) = 4/(-5) = -4/5

The segments AB and CD for this problem are neither parallel nor perpendicular.

To classify the segments, we must look at the relation between the slope of each segment, which is calculated as the change in y divided by the change in x.

The slope of segment AB is given as follows:

m = (5 - (-1))/(6 - 3) = 6/3 = 2.

The slope of segment CD is given as follows:

m = (7 - (-5))/(-4 - 2) = -12/6 = -2.

As the slopes are different, and their product is different of -1, segments AB and CD for this problem are neither parallel nor perpendicular.

More can be learned about parallel or perpendicular segments at https://brainly.com/question/13657035

#SPJ1

The measure of the angle U of the circle is m∠U = 28°

Given data ,

In the triangle ΔSRU , the measure of angle is calculated as ∠SRU,

180° - 110° = 70°

70°/2 = 35°

∠SRU = 35° + 90° = 125°

Central Angle = 2 x Angle in other segment

Then angle U from the triangle is determined using this formula,

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

So,

The measure of ∠U = 180° - ∠SRU - ∠S

The measure of ∠U = 180° - 125° - 27°

The measure of ∠U = 28°

Hence , the angle of circle is ∠U = 28°

To learn more about central angle click :

https://brainly.com/question/11877137

#SPJ1

Abi has 13/21 ounces of candy now

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

2/7 of an ounce of chocolate and 1/3 of a ounce of skittles

The amount of candy she has now is

Total = 2/7 + 1/3

Take the like terms and evaluate

So, we have

Total = (6 + 7)/21

Evaluate

Total = 13/21

Hence, she has 13/21 ounces of candy now

Read more about proportions at

https://brainly.com/question/12024093

#SPJ1

Answer: x would equal 5.8

Explanation:  √3²+5²= 5.8

The odds for the event happening = 34:5  

The odds against the event happening = 5:34.

The probability of the given event is 34/39. To find the odds for and against the event happening, follow these steps:

Step 1: Calculate the odds for the event happening.
The odds for an event happening is given by the ratio of the probability of the event happening to the probability of the event not happening. In this case, the probability of the event happening is 34/39.

Step 2: Calculate the probability of the event not happening.
The probability of the event not happening is given by 1 minus the probability of the event happening, which is 1 - (34/39) = 5/39.

Step 3: Calculate the odds for the event happening.
The odds for the event happening is the ratio of the probability of the event happening to the probability of the event not happening, which is (34/39) : (5/39). Since both terms have the same denominator, you can simplify the ratio to 34:5.

Step 4: Calculate the odds against the event happening.
The odds against the event happening is the inverse of the odds for the event happening, which is 5:34.

In conclusion, the odds for the event happening are 34:5, and the odds against the event happening are 5:34.

To learn more about probability visit : https://brainly.com/question/13604758

#SPJ11

The annual interest rate is 6.5%, and the bank compounds the interest annually. The balance of the account will grow exponentially over time.

The given function y = 1.065(4) represents the growth of capital in a bank account, where the initial balance is 4 and the growth rate is 6.5% per year. To calculate the annual interest rate, we can use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, the final amount after one year is 4 * 1.065 = 4.26. Substituting the values in the formula, we get 4.26 = 4(1 + r/1)^(1), which simplifies to 1 + r = 1.065. Solving for r, we get r = 0.065 or 6.5%.

The bank compounds the interest annually, which means that the interest is added to the account balance at the end of each year. As the balance grows, the interest earned in the subsequent years will be higher. This results in exponential growth of the account balance over time. After n years, the account balance will be B = P(1 + r)^n, where P is the initial balance, r is the annual interest rate, and n is the number of years.

For example, after 5 years, the account balance will be B = 4(1 + 0.065)^5 = 5.39. After 10 years, the account balance will be B = 4(1 + 0.065)^10 = 7.27. As we can see, the account balance grows significantly over time due to the effect of compounding interest.

Learn more about interest rate here

https://brainly.com/question/25720319

#SPJ11

The given subsets are subspaces of P4 as

A subspace of P4 must contain the zero polynomial, but the subset of polynomials of degree three does not include the zero polynomial, so it is not a subspace.

The subset of polynomials satisfying p(5)=0 is a subspace because it contains the zero polynomial and is closed under addition and scalar multiplication.

The subset of polynomials of the form p(x)=x^3+c is a subspace because it contains the zero polynomial, is closed under addition, and is closed under scalar multiplication.

The subset of polynomials of the form p(x)=ax^3+bx is a subspace because it contains the zero polynomial, is closed under addition, and is closed under scalar multiplication.

The subset of polynomials satisfying p(5)>0 is not a subspace because it is not closed under scalar multiplication.

For more questions like Polynomial click the link below:

https://brainly.com/question/11536910

#SPJ11

We know that the population proportion of instructors who are satisfied with their careers is 0.73, according to the national educational association.

The mean of the sampling distribution of the sample proportion is equal to the population proportion, which is 0.73 in this case. The standard deviation of the sampling distribution is calculated as:
σ = sqrt(p*(1-p)/n) = sqrt(0.73*(1-0.73)/900) = 0.024
Now, we want to find the probability that 650 or fewer instructors were satisfied with their careers. We need to calculate the z-score associated with this value:
z = (650 - 0.73*900) / sqrt(900*0.73*(1-0.73)) = -5.43
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of -5.43 or lower is very close to 0. Therefore, the probability that 650 or fewer instructors were satisfied with their careers is essentially 0.
In conclusion, it is highly unlikely that only 650 or fewer instructors out of a sample of 900 would be satisfied with their careers, given the national educational association's estimate of a 73% satisfaction rate among all instructors.

According to the National Educational Association, it is estimated that 73% of all instructors are satisfied with their careers. You want to find the probability that 650 or fewer instructors were satisfied with their careers in a random sample of 900 instructors.
To solve this, we will use the following steps:
1. Calculate the mean and standard deviation of the sample distribution of the proportion of satisfied instructors.
2. Convert the number of instructors (650) to a proportion (p) by dividing by the sample size (900).
3. Use the z-score formula to calculate the z-score for the given proportion.
4. Use the z-score to find the probability.
Step 1: Mean (μ) and standard deviation (σ) of the sample distribution:
μ = P * Q = 0.73 * 0.27 = 0.1971
σ = sqrt(P * Q / n) = sqrt(0.1971 / 900) = 0.0147
Step 2: Convert the number of instructors (650) to a proportion (p):
p = 650 / 900 = 0.7222
Step 3: Calculate the z-score using the formula:
z = (p - μ) / σ = (0.7222 - 0.73) / 0.0147 = -0.5306
Step 4: Use the z-score to find the probability:
The probability of having 650 or fewer satisfied instructors is the area to the left of z = -0.5306. Using a z-table or calculator, we find that this probability is approximately 0.2981.
So, in a random sample of 900 instructors, the probability that 650 or fewer instructors were satisfied with their careers is approximately 0.2981.

Visit here to learn more about National Educational Association:

brainly.com/question/536594

#SPJ11

The expression 4^-2 is equivalent to 1/16. The negative exponent indicates that we should take the reciprocal of the base (4) and raise it to the positive exponent (2), resulting in a simplified fraction, 1/16.

The expression 4^-2 represents a mathematical operation involving exponents. To understand this expression, let's break down the terms:

1. The base is 4.
2. The exponent is -2.

In general, an expression in the form of a^(-b) is equivalent to 1/(a^b). This means that a negative exponent indicates the reciprocal of the base raised to the positive exponent.

Now, applying this rule to 4^-2, we can rewrite it as 1/(4^2). To simplify further, calculate 4^2, which is 4*4 = 16. So, the expression 4^-2 is equivalent to 1/16.

In summary, the expression 4^-2 is equivalent to 1/16. The negative exponent indicates that we should take the reciprocal of the base (4) and raise it to the positive exponent (2), resulting in a simplified fraction, 1/16.

To learn more about exponent click here

brainly.com/question/5497425

#SPJ11

Answer:

∠ A = 79° , ∠ B = 112°

Step-by-step explanation:

ABCD is a cyclic quadrilateral.

the opposite angles sum to 180° , then

∠ A = 180° - 101° = 79°

∠ B = 180° - 68° = 112°

Answer:

We will draw a straight line passing through these three points. The line represents the graph of the linear function y = -2/3x + 4/3.

Step-by-step explanation:

To graph the linear function whose equation is y - 2 = -2/3(x + 1), we can follow these steps:

Step 1: Solve the equation for y

y - 2 = -2/3(x + 1)

y = -2/3(x + 1) + 2

y = -2/3x - 2/3 + 2

y = -2/3x + 4/3

Therefore, the equation of the linear function in slope-intercept form is y = -2/3x + 4/3.

Step 2: Find the y-intercept

The y-intercept is the value of y when x = 0. Substituting x = 0 in the equation, we get:

y = -2/3(0) + 4/3

y = 4/3

Therefore, the y-intercept is (0, 4/3).

Step 3: Find the x-intercept

The x-intercept is the value of x when y = 0. Substituting y = 0 in the equation, we get:

0 = -2/3x + 4/3

2/3x = 4/3

x = 2

Therefore, the x-intercept is (2, 0).

Step 4: Find another point

We can find another point on the line by choosing any value of x and then solving for y. For example, let x = 3:

y = -2/3(3) + 4/3

y = -2 + 4/3

y = -2/3

Therefore, another point on the line is (3, -2/3).

Step 5: Plot the points and draw the line

Plot the three points we found: (0, 4/3), (2, 0), and (3, -2/3).

Then, draw a straight line passing through these three points. The line represents the graph of the linear function y = -2/3x + 4/3.

To know more about straight line refer here

https://brainly.com/question/29223887#

#SPJ11