How many turns must an ideal solenoid 10 cm long have if it is to generate a magnetic field of 1.5 mT when a current of 1.0 A passes through it?
a) 3.5
b) 1.8
c) 2.2
d) 0.50
e) 2.8

Answer:

680

Step-by-step explanation:

Given that:

All the pupils at a primary school come from one of three villages: Elmswell, Haughley or Woolpit.

\(\frac{1}{4}\) of the pupils come from Elmswell

\(\frac{3}{5}\) of the pupils come from Haughley

102 pupils come from Woolpit.

To find:

Total number of pupils in the school.

Solution:

Let total number of pupils = \(100x\)

So, number of pupils that come from Elmswell = \(\frac{1}{4}\) of 100x

OR

\(\dfrac{1}{4} \times 100x\\\Rightarrow 25x\)

And, number of pupils that come from Haughley= \(\frac{3}{5}\) of 100x

OR

\(\dfrac{3}{5} \times 100x\\\Rightarrow 60x\)

Number of pupils that come from Woolpit = \(100x - 25x - 60x \Rightarrow 15x\)

As per given statement:

\(15x = 102\\\Rightarrow x =6.8\)

Number of pupils from Elmswell = 25x = 25 \(\times\) 6.8 = 170

Number of pupils from Haughley = 60x = 60 \(\times\) 6.8 = 408

Total number of pupils at the school = \(100x \Rightarrow 100 \times 6.8=680\)

With an error of magnitude no more than 6×10^−4, the values of x for which sin x can be replaced by x - x^3/6 are roughly: -0.3728 ≤ x ≤ 0.3728

To find the values of x for which sin x can be replaced by x - x^3/6 with an error of magnitude no greater than 6×10^−4, we need to analyze the Taylor series expansion of sin x around x = 0. The Taylor series for sin x is:

sin x = x - x^3/6 + x^5/120 - x^7/5040 + ...

We are given the approximation sin x ≈ x - x^3/6, which corresponds to the first two non-zero terms of the Taylor series. To find the error bounds, we consider the next term in the series, x^5/120. To have an error no greater than 6×10^−4, we need:

|x^5/120| ≤ 6×10^−4

Now, solve for x:

|x^5| ≤ 72×10^−4
|x| ≤ (72×10^−4)^(1/5)

Calculating the fifth root gives:

|x| ≤ 0.3728

Therefore, the values of x for which sin x can be replaced by x - x^3/6 with an error of magnitude no greater than 6×10^−4 are approximately:

-0.3728 ≤ x ≤ 0.3728

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The money saved by the younger teenager will be $8.3 and the money saved by the older teenager will be $16.7.

Equation modelling is a process of creating a mathematical relation from a mathematical word problem keeping in mind the correct use of operations, variables and constants as per need.

Assume that the older teenager is represented by T[O] and the younger teenager by T[Y].

Assume that the money saved by T[Y] is $x.

Then, the money saved by T[O] will be $2x.

The total money to be saved = $25

Then we can write -

x + 2x = 25

3x = 25

x = 8.33

Money saved by T[Y] = $8.3

Then, the money saved by T[O] = $2x = $16.7

Therefore, the money saved by the younger teenager will be $8.3 and the money saved by the older teenager will be $16.7.

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Answer:

Did I see this quesiton before..?

Step-by-step explanation:

Answer:

m∠RMS = 20°

Step-by-step explanation:

Find ∠RMS and look at the two values it crosses.

∠RMS crosses through 180 and 160.

Find the difference between the two values to get the measure:

180 - 160 = 20°

So, m∠RMS = 20°

(Its also an acute angle.)

Answer:

20

Step-by-step explanation:

The mistake is in using 160 as the answer. It isn't.

The angle is very small well under 90. It is acute.

The horizontal part of the angle is on 180 degrees of the protractor.

Therefore the angle size is 180 - 160 = 20 degrees.

Answer:

42:30

Step-by-step explanation:

10 x 3 = 30

14 x 3 = 42

Answer:

Step-by-step explanation:

Find the diagram attached

The sum of the two adjacent angles is 180 degrees. Hence;

8x-9 + 53 = 180

8x + 44 = 180

Subtract 44 from both sides of the equation

8x + 44 - 44 = 180 - 44

8x = 136

Divide both sides by 8

8x/8 = 136/8

x = 17

Hence the value of x is 17

Answer:

The same thing

Step-by-step explanation:

2/2 = 1 so it would have the same effect

Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

You do -8 - 3 and you get 11

The diagonal measurement as √5625 ft, which is approximately 75 feet, the correct answer is B. 75 ft 0 in.

The diagonal measurement of the rectangular slab on grade can be found using the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the length and width of the slab.

To calculate the diagonal measurement, we can apply the Pythagorean theorem:

Diagonal² = Length² + Width²

Substituting the given values, we have:

Diagonal² = (60 ft 0 in.)² + (45 ft 0 in.)²

Calculating this expression, we find:

Diagonal² = 3600 ft² + 2025 ft²

Diagonal² = 5625 ft²

Taking the square root of both sides, we obtain:

Diagonal = √5625 ft

Diagonal ≈ 75 ft

Therefore, the diagonal measurement of the rectangular slab on grade is approximately 75 feet.

To find the diagonal measurement of the rectangular slab on grade, we can use the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (length and width).

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The Excel function used when calculating the t critical value is the T.INV function.

The TINV function returns the inverse of the Student's t-distribution, which is a probability distribution that is commonly used in hypothesis testing when the sample size is small and the population standard deviation is unknown. The TINV function requires two arguments: the probability value (alpha) and the degrees of freedom.

The degrees of freedom depend on the sample size and the number of parameters estimated in the model. The TINV function returns the value of the t statistic that corresponds to a given probability and degrees of freedom. This t critical value is compared to the calculated t statistic to determine if the null hypothesis should be rejected or not.

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The computed values are:

u + v = (-3, -2)

v + u = (-3, -2)

5u = (10, -15)

2u + 3v = (-11, -3)

2u + 4w = (0, 2, 0)

u - v + 2w = (5, 0, 0)

|v + w| = 7.95

Vector addition is the operation of adding two vectors together to obtain a new vector. It is performed by adding the corresponding components of the vectors. For example, if we have two vectors u = \((u_1, u_2, u_3)\) and v = \((v_1, v_2, v_3)\), their sum u + v is given by \((u_1 + v_1, u_2 + v_2, u_3 + v_3)\).

Scalar multiplication is the operation of multiplying a vector by a scalar (a real number). It is performed by multiplying each component of the vector by the scalar. For example, if we have a vector u = \((u_1, u_2, u_3)\) and a scalar k, their product k * u is given by \((k * u_1, k * u_2, k * u_3\)).

Both vector addition and scalar multiplication are fundamental operations in linear algebra and are used to manipulate and combine vectors in various applications.

To compute the given expressions, we perform vector addition and scalar multiplication as follows:

u + v =

\(= (2, -3) + (-5, 1) \\= (2 - 5, -3 + 1) \\= (-3, -2)\)

v + u =

\(=(-5, 1) + (2, -3) \\= (-5 + 2, 1 - 3) \\= (-3, -2)\)

5u =

\(= 5 * (2, -3) \\= (5 * 2, 5 * -3)\\ = (10, -15)\)

2u + 3v =

\(=2 * (2, -3) + 3 * (-5, 1) \\= (4, -6) + (-15, 3)\\ = (4 - 15, -6 + 3) \\= (-11, -3)\)

2u + 4w =

\(= 2 * (2, -3) + 4 * (-1, 2, 3/2) \\= (4, -6) + (-4, 8, 6)\\ = (4 - 4, -6 + 8, -6 + 6)\\ = (0, 2, 0)\)

u - v + 2w =

\(= (2, -3) - (-5, 1) + 2 * (-1, 2, 3/2) \\= (2, -3) + (5, -1) + (-2, 4, 3) \\= (2 + 5 - 2, -3 - 1 + 4, 0 - 3 + 3) \\= (5, 0, 0)\)

|v + w| =

\(= |(-5, 1) + (-1, 2, 3/2)| \\= |(-5 - 1, 1 + 2, 0 + 3/2)| \\= |(-6, 3, 3/2)| \\= \sqrt{((-6)^2 + 3^2 + (3/2)^2)} \\= \sqrt{(36 + 9 + 9/4)} \\= \sqrt{(63.25)} \\= 7.95\)

Therefore, the computed values are:

u + v = (-3, -2)

v + u = (-3, -2)

5u = (10, -15)

2u + 3v = (-11, -3)

2u + 4w = (0, 2, 0)

u - v + 2w = (5, 0, 0)

|v + w| = 7.95

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As per given utility function, Tane will accept any job as long as the job comes with a certain payment of at least $40,000 (approx.).

Tane's utility function, \(U(W)=W^{0.5}\), indicates that he has a concave utility function, implying diminishing marginal utility of wealth. This means that Tane values each additional dollar of wealth less as his wealth increases.

Considering the job offer with a base salary of $30,000 and a potential $70,000 bonus with a 0.5 probability, we can calculate the expected value of this salary scheme. The expected value is calculated as the sum of each possible outcome multiplied by its respective probability:

Expected Value = (0.5 * $30,000) + (0.5 * $100,000) = $65,000

Since the expected value is less than $80,000 (approx.), which is the minimum certain payment Tane would accept, Tane would not accept the job offer with the probabilistic salary scheme.

However, Tane's utility function indicates that he values certainty in income. As long as the job comes with a certain payment of at least $40,000 (approx.), Tane would prefer to accept the job because the certain payment guarantees a minimum level of income, providing him with a higher level of certainty and potentially higher utility compared to the probabilistic salary scheme. Therefore, Tane will accept any job as long as the job comes with a certain payment of at least $40,000 (approx.).

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Hi!

The y-intercept is the place where the line crosses the y-axis.

-------------------------------------------------------------------------------------------------------------

All points directly above and to the right of the origin are positive, and all the points directly below and to the left of the origin are negative.

Therefore, if the graph of a line crosses above the origin, the y-intercept is POSITIVE.

Answer:

14 cm

Step-by-step explanation:

Given that:

Base, b of triangle = 5 cm

Height, H of triangle = 24 cm

Base of parallelogram, a = 30 cm

Area of triangle = 0.5 * bH

Area of parallelogram = a * h

Where, h = height of parallelogram

Area of parallelogram is 5 times the area of triangle ;

5 * 0.5 * 7 * 24 = 30 * h

420 = 30* h

h = 420 / 30

h = 14 cm

a. The sample proportion is 0.02.

b. Using the one-proportion z-test is appropriate.

c. Yes, we can use the one-proportion z-test to perform the specified hypothesis test.

a. To determine the sample proportion, we divide the number of successes (x) by the sample size (n). In this case, x = 4 and n = 200. Therefore, the sample proportion is calculated as 4/200 = 0.02.

b. In order to decide whether to use the one-proportion z-test, we need to verify if the conditions for its application are met.

The one-proportion z-test is appropriate when the sampling distribution of the sample proportion can be approximated by a normal distribution, which occurs when both np and n(1-p) are greater than or equal to 10.

Here, np = 200 * 0.01 = 2 and n(1-p) = 200 * (1-0.01) = 198. Since both np and n(1-p) are greater than 10, we can conclude that the conditions for the one-proportion z-test are met.

c. Given that the conditions for the one-proportion z-test are satisfied, we can proceed with performing the hypothesis test.

In this case, the null hypothesis (H0) is that the population proportion (p) is equal to 0.01, and the alternative hypothesis (Ha) is that p is greater than 0.01.

We can use the one-proportion z-test to test this hypothesis by calculating the test statistic, which is given by (sample proportion - hypothesized proportion) / standard error.

The standard error is computed as the square root of (hypothesized proportion * (1 - hypothesized proportion) / sample size).

Once the test statistic is calculated, we can compare it to the critical value corresponding to the chosen significance level (a=0.05) to make a decision.

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Answer:

365/1,000 or .365

Step-by-step explanation:

HTH :)

Three hundred sixty five thousand in standard form is 365000.

The standard form of numbers is when we have to write the number in digits according to it's place and face value.

Word form of numbers is that when we have to write numbers given in numerical form to words by determining place and face value.

According to the given question we have to write  three thousand sixty five thousand in standard form.

We know thousand has three zeroes.Suppose we have to write one thousand in standard form which is 1000.

Given we have to write three hundred sixty five thousand in standard form which is 365000.

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The number of problems that were on the text was 240 problems.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total number of problems that were on the text, y represent the time to be spent, hence:

y = x/8

Also:

y - 6 = x/10

x/8 - 6 = x/10

x = 240

The number of problems that were on the text was 240 problems.

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The areas of the two cross-sections would be proportional to k².

If a new cross-section was created in each solid, both at the same height using a scale factor k, the areas of the two cross sections would be proportional to k².

The reason for this is that when a scale factor is applied to a two-dimensional figure, the area of the resulting figure increases by a factor of k². This is because the linear dimensions of the figure (length and width) are multiplied by k, and since the area is calculated by multiplying length and width, the area of the figure is multiplied by k².

Therefore, if the two cross sections are created at the same height and are scaled by the same factor k, their areas will be proportional to k². For example, if k=2, the area of each cross-section will be four times the original area; if k=3, the area of each cross-section will be nine times the original area, and so on.

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Answer:

Joy will need to use 9 cups of strawberries for 6 cups of blueberries.

Step-by-step explanation:

Given,

Cups of blueberries used for 3 cups of strawberry = 2

Ratio of cups of blueberry to strawberry = 2:3

Joy wants to use 6 cups of blueberries.

Let,

x be the cups of strawberry for 6 cups of blueberries.

Ratio of cups of blueberries to strawberries = 6:x

Using proportion;

Ratio of cups of blueberry to strawberry :: Ratio of cups of blueberries to strawberries

Product of extreme = Product of mean

Dividing both sides by 2

The intervals of increase/decrease for the function f(x) cannot be determined without additional information.

To determine the intervals of increase/decrease for a function, we need to analyze the behavior of its derivative. The derivative of a function gives us information about its slope and whether it is increasing or decreasing.

However, in this question, only the function f(x) is given, and no information about its derivative is provided. Without the derivative, we cannot determine the intervals of increase/decrease for the function.

To find the intervals of increase/decrease, we would need to calculate the derivative of f(x) and analyze its sign changes. A positive derivative indicates the function is increasing, while a negative derivative indicates the function is decreasing. The points where the derivative changes sign represent the boundaries between the intervals.

Without the derivative or any additional information about the behavior of the function, it is not possible to determine the intervals of increase/decrease for f(x).

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The statement that is true for the two equations Equation A: 3(2x-5)=6x-15 and Equation B: 2+3x=3x-4 is that "Equation

A has an infinite number of solutions and Equation B has no solution".Explanation:To find the solution for the two equations, we will solve for each equation separately. Solution of equation A: 3(2x - 5) = 6x - 15 ⇒ 6x - 15 = 6x - 15 ⇒ 6x - 6x = -15 + 15 ⇒ 0 = 0

This is a true equation, which means that it is an identity. The equation can be written as 0 = 0. Any value that is inserted in this equation will result in a true statement. Hence the equation A has an infinite number of solutions. Solution of equation B: 2 + 3x = 3x - 4 ⇒ 2 + 4 = 3x - 3x - 4 ⇒ 6 = -4This is a false equation. It means that there is no value that can be inserted into the equation to make it a true statement. Therefore, the equation B has no solution. Hence the statement that is true for the two equations Equation A: 3(2x-5)=6x-15 and Equation B: 2+3x=3x-4 is that "Equation A has an infinite number of solutions and Equation B has no solution".

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer:

In the picture above

Step-by-step explanation:

I solved all questions except no.7 ; I don't know how can be solved.

I hope that its a clear solution. Goodluck

Answer:

w = -4

Step-by-step explanation:

→Distribute the 3 to (-w + 6):

14 + 3(-w + 6) = -11w

14 -3w + 18 = -11w

→Add like terms:

-3w + 32 = -11w

→Add 11w to both sides:

8w + 32 = 0

→Subtract 32 from both sides:

8w = -32

→Divide both sides by 8

w = -4

Answer:

w= -4

work:

14-3w+18=-11w

32-3w=-11

-3w+11w=-32

8w=-32 divide by 8 then you will get your answer

w=-4

We can say with 95% confidence that the true proportion of checking account customers who also have savings accounts in the population lies between 0.25 and 0.35.

a. To find the sample proportion of checking account customers who also have savings accounts, we need to divide the number of customers who have both types of accounts by the total number of checking account customers in the sample. Let's say the bank selected 500 checking account customers and found that 150 of them also had savings accounts. Then, the sample proportion would be:

150/500 = 0.3

So, 30% of the checking account customers in the sample also had savings accounts.

b. To find the standard error of the sample proportion, we use the formula:

SE = sqrt(p*(1-p)/n)

where p is the sample proportion (0.3 in this case), and n is the sample size (500). Plugging in the numbers, we get:

SE = sqrt(0.3*(1-0.3)/500) = 0.025

So, the standard error is 0.025.

c. To find a 95% confidence interval for the population proportion of checking account customers who also have savings accounts, we use the formula:

CI = p ± z*(SE)

where z is the z-score corresponding to a 95% confidence level (which is 1.96), and SE is the standard error we calculated in part b. Plugging in the numbers, we get:

CI = 0.3 ± 1.96*(0.025) = (0.25, 0.35)

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The following expression shows the main expression after the negative exponents have been eliminated: A. m⁷n³n/m.

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as bⁿ.

By applying the property of exponents based on the law of indices for the division of powers, we have the following:

b⁻ⁿ = 1/bⁿ

In this context, the exponent n⁻¹ in the given algebraic expression would be rewritten based on the law of indices for the division of powers as follows;

n⁻¹ = 1/n

Substituting the given parameters into the given algebraic expression, we have the following;

(m⁷n³)/mn⁻¹ = (m⁷n³)/m × n

(m⁷n³)/m × n = (m⁷n³n)/m

(m⁷n³)/mn⁻¹ = m⁷n³n/m

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Answer:

Step-by-step explanation:

its A