a solenoid 1.30 m long and 2.60 cm in diameter carries a currentof 18.0 a. the magnetic field inside the solenoid is 23.0 mt.find the length of the wire forming the solenoid.

Answer:

the 90th percentile is 9.

The 90th percentile of the distribution is 9.

The 90th percentile of the distribution in the table is 9.

To find the 90th percentile, we need to look at the values of X and their corresponding cumulative percentages (C%). The 90th percentile is the value of X at which 90% of the data falls below.

Looking at the table, we can see that the value of X at the 90th percentile is 9, as it corresponds to a cumulative percentage of 100%. This means that 90% of the data falls below the value of 9.

Therefore, the 90th percentile of the distribution is 9.

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When the triangle's area is 20 cm³ and its height is 4 cm, the rate at which its base is changing is -3 cm/sec.

The answer to the query is:

A triangle's area is growing at a pace of 4 cm²/sec and its height is growing at a rate of 2 cm/sec.

First, distinguishing between area and height.

dA/dt = 4 cm²/sec.

dH/dt = 2 cm/sec

Knowing that the triangle's area can be calculated using,

Area = 1/2xBxH

20 = 1/2xBx4

B = 10 cm

Now, the formula for estimating the rate of change for area is,

dA/dT = 1/2[B.dH/dT + H.dB/dT]

4 = 0.5[10×2 + 4×dB/dT]

dB/dT = -3 cm/sec

As a result, when the triangle's area is 20 and its height is 4 cm, the rate that its base is changing is -3 cm/sec.

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Let x be the total number of questions on the test; then,

Which is equivalent to

Solve for x as shown below

The answer is 20 questions in total on the test

The SSS(Side-Side-Side) Triangle congruency is proven by following rule.

In SSS (Side-Side-Side) condition the two triangles are said to be congruent if the three sides of one triangle are equivalent to the corresponding three sides of the second triangle.

In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes. A triangle is a closed polygon with three line segments that intersect at each of its three angles.

Two shapes are congruent if their sizes and forms are comparable. Additionally, if two shapes are congruent, then their mirror images are likewise congruent.

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The distance from Jim's house to the mall is given as follows:

11.25 miles.

Suppose that we have two points with coordinates given as follows:

\((x_1, y_1)\) and \((x_2, y_2)\)

Then the equation for the distance between these two points is given as follows:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates are given as follows:

Hence the distance is given as follows:

\(D = \sqrt{(17 - 8)^2+(13 - 1)^2}\)

D = 15 units.

Each unit represents 0.75 miles, hence the distance in miles is given as follows:

15 x 0.75 = 11.25 miles.

The problem is given by the image presented at the end of the answer.

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Given that the sheet metal has an average of 7 defects per 19 square feet, we can use the Poisson distribution formula to find the probability of 8 defects in a 34 square foot metal sheet.

The Poisson distribution formula is given by:P(X = x) = (λ^x * e^(-λ))/x!where λ is the average number of defects, x is the number of defects, and e is the base of the natural logarithm. For this problem, λ = (7/19) * 34 = 12.63 and x = 8. Plugging these values into the formula, we get:P(X = 8) = (12.63^8 * e^(-12.63))/8!P(X = 8) = (5428582.85 * 0.000281)/40320P(X = 8) = 0.0373Therefore, the probability that a 34 square foot metal sheet has 8 defects is 0.0373, or 3.73%, rounded to four decimal places.

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Answer:

15.14%

Step-by-step explanation:

The formula for APR is stated thus:

APR=fees+interest/principal/n*365*100

principal is the loan amount of $700

fees is the processing fees on the loan which is $50

interest amount=principal*interest %=$700*8%=$56

n is the number of days of the loan which is a year i.e 365 days

APR=($50+$56)/$700/365*365*100

APR=$106/$700/365*365*100

APR=0.151428571 /365*365*100

APR=0.151428571 *100=15.14%

The annual percentage rate on the loan is 15.14% which represents the actual cost on the loan not just the interest cost of 8% annually

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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The equation given is;\(x = ct^5 - bt^7\)Where \(c = 2.6 m/s^5\) and \(b = 1.1 m/s^7\)(a) Displacement is obtained by finding the difference between the initial and final position of the particle.

\(i.e At , the particle is at a distance ofDisplacement = Displacement = = - 1.57 m(b) When t = 1.0 s,\)

the velocity of the particle can be found by taking the derivative of the displacement with respect to time;i.e \(v = \frac{dx}{dt}\)\(x = ct^5 - bt^7\)\(\frac{dx}{dt} = 5ct^4 - 7bt^6\)At \(t = 1.0 s\), \(v = 5*2.6(1.0)^4 - 7*1.

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Answer:

  A, D

Step-by-step explanation:

The independent variable is plotted on the x-axis. It is labeled "number of cans". The dependent variable is plotted on the y-axis. It is labeled "number of tennis balls". Then each ordered pair is ...

  (independent variable, dependent variable) = (cans, balls)

Then the point (2, 6) corresponds to (2 cans, 6 balls).

The applicable descriptive statements are ...

  A.  2 cans contain 6 tennis balls

  D.  There are 6 tennis balls in 2 cans

Answer:

x = 3

Step-by-step explanation:

This is an isosceles triangle.  Two angles (D and F) are equal because the sides opposite them are equal (or vice versa).

Thus, side DE = side EF, or

12x - 8 = 4x + 16

Combining like terms:  8x = 24

Thus, x = 24/8 = 3

x = 3

A graph of the line going through the point (-6, 1) with a slope of -2/3 is shown in the image below.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-6, 1) and a slope of -2/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -2/3(x + 6)  

y = -2x/3 - 4 + 1

y = -2x/3 - 3

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To find the value of x, we can use the formula for the mean (average) of a data set:

Mean = (Sum of all data values) / (Number of data values)

Given that the new mean is 15, we can set up the equation as follows:

(4 + 4 + 8 + 8 + 20 + 20 + 25 + 25 + 32 + 32 + x) / (11) = 15

Now, let's solve the equation to find the value of x:

4 + 4 + 8 + 8 + 20 + 20 + 25 + 25 + 32 + 32 + x = 15 * 11

Simplifying the equation:

188 + x = 165

Subtracting 188 from both sides:

x = 165 - 188

x = -23

Therefore, the value of x is -23.

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Answer:

\( \frac{ - 13}{15} \)

Step-by-step explanation:

\( \frac{ - 11}{15} + \frac{ - 2}{15} = \frac{( - 11 - 2)}{15} = \frac{ - 13}{15} \)

Given:

A number is 74% of 58.

To find:

The number.

Solution:

Let the unknown number be n.

The number n is 74% of 58.

\(n=\dfrac{74}{100}{58}\)

\(n=0.74\times 58\)

\(n=42.92\)

The required equation is \(n=0.74\times 58\) and the solution (unknown number) is \(n=42.92\).

Therefore, the correct option is B.

Answer:

B.6 is the correct answer

Answer:

40 percent

Step-by-step explanation:

covert fraction 4 out of ten is 40 %

Answer:

40%

Step-by-step explanation:

A percentage is basically x/100.

Therefore, if we convert Siobhan's mark into a fraction, we get 4/10. Then, by converting the fraction to fit x/100, we get 40/100 (remember, we must do the same to both the numerator and the denominator, so in this case it's multiply them by 10). Now that we have x, we can fit that into the answer to get 40%.

The remainder when f(x) is divided by (x+5) is -4645.  This result is obtained by applying the Remainder Theorem, which provides a convenient and efficient way to determine the remainder of a polynomial division without actually performing the division process.

Using the Remainder Theorem, we can find the remainder when a polynomial, f(x), is divided by a linear divisor, (x-c).

In this case, f(x) = x^5 - 6x^4 + 2x^3 + 4x – 5 and the divisor is (x+5), so c = -5.

The Remainder Theorem states that if f(x) is divided by (x-c), the remainder is f(c). Therefore, we need to find the value of f(-5) to determine the remainder when f(x) is divided by (x+5).

f(-5) = (-5)^5 - 6(-5)^4 + 2(-5)^3 + 4(-5) - 5
      = -3125 - 6(625) + 2(-125) - 20 - 5
      = -3125 - 3750 - (-250) - 20 - 5
      = -3125 - 3750 + 250 - 20 - 5
      = -4870 + 250 - 25
      = -4645

Hence, the remainder when f(x) is divided by (x+5) is -4645. This result is obtained by applying the Remainder Theorem, which provides a convenient and efficient way to determine the remainder of a polynomial division without actually performing the division process.

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The percentage of tires that will last at least 75000 miles will be 0.1271

Mean = 70000

Standard deviation = 4400

The standard deviation represents the average degree of variability in your dataset. It reveals the average deviation of each statistic from the mean. In general, values with a significant standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near the mean.

The proportion of tires that will last at least 75000 miles is:

P(X>75000) = 1 - P(X<75000)

= 1 - P(X - Mean/Std. deviation)<75000-70000/4400)

= 1 - P(Z<1.1364)

= 1 - 0.8708

= 0.1271

Therefore 0.1271 of the tires will last at least 75000 miles

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The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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Answer: (12x−5)(2x−1)

Step-by-step explanation: Hope this help :D

Answer:

24(x^2)-22x+5

=24(x^2)-(12+10)x+5

=24(x^2)-12x-10x+5

=12x(2x-1)-5(2x-1)

=(2x-1)(12x-5)

Answer:

Step-by-step explanation:

Answer:

A. 1,800≤250+2i .

Step-by-step explanation:

The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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To evaluate the Riemann sum for the function f(x) = x^2 over the interval [1, 3] with three subintervals using left endpoints. Answer : In this case, the Riemann sum of 84/27 represents the sum of the areas of the three rectangles, approximating the area under the curve of f(x) within the interval [1, 3] using left endpoints.

we follow these steps:

1. Divide the interval [1, 3] into three equal subintervals. Each subinterval has a width of (3 - 1) / 3 = 2/3.

2. Choose the left endpoint of each subinterval as the sample point. The left endpoints for the three subintervals are 1, 1 + 2/3, and 1 + 4/3.

3. Evaluate the function f(x) = x^2 at each left endpoint. The corresponding values are 1^2 = 1, (1 + 2/3)^2 = 25/9, and (1 + 4/3)^2 = 16/9.

4. Multiply each function value by the width of the subinterval. The products are (2/3) * 1, (2/3) * (25/9), and (2/3) * (16/9).

5. Sum up the products to obtain the Riemann sum:

(2/3) * 1 + (2/3) * (25/9) + (2/3) * (16/9) = 2/3 + 50/27 + 32/27 = 84/27.

The Riemann sum for f(x) = x^2, with three subintervals using left endpoints, is 84/27.

Now, let's understand what the Riemann sum represents with the help of a diagram:

Consider a graph of the function f(x) = x^2 over the interval [1, 3]. The Riemann sum represents an approximation of the area under the curve of f(x) within this interval.

By dividing the interval into subintervals and using left endpoints, we are constructing rectangles with heights determined by the function values at the left endpoints. The width of each rectangle is the width of the subinterval. The Riemann sum is then the sum of the areas of these rectangles.

In this case, the Riemann sum of 84/27 represents the sum of the areas of the three rectangles, approximating the area under the curve of f(x) within the interval [1, 3] using left endpoints.

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Answer:

y = 2.2x - 11

Step-by-step explanation:

Slope: 2.2

y-intercept: 0 - (2.2)(5) = - 11

Answer:

y = 2x - 3

Step-by-step explanation:

We want to write the equation as y = ax + b, where a is the slope and b is the y-intercept.

#2

Reflexive sides

#3

Already given in question

#4

Given in the question

#5

By bisector definition

#6

Third angle therom

#7

Angle-Side-Angle

Done

Step-by-step explanation:

Missing reasons:

Answer:

\(x=4\)

Step-by-step explanation:

start by squaring both sides:

\((\sqrt{-8+3x} )^2=(2)^2\)

squaring a square root cancels it out:

\(-8+3x = 4\)

solve for x by first adding 8 to both sides:

\(3x=12\)

then divide both sides by 3:

\(x=4\\\)

Jean sold 102 candles, and Victoria sold half as many, which is (1/2)(102) = 51 candles.

Let's assume the number of candles Jean sold is "x". According to the given information, Victoria sold half as many candles as Jean, so the number of candles she sold is (1/2)x.

We know that together they sold 153 candles, so we can set up the equation:

x + (1/2)x = 153

To simplify the equation, we can multiply both sides by 2 to eliminate the fraction:

2x + x = 306

Combining like terms, we have:

3x = 306

To isolate x, we divide both sides of the equation by 3:

x = 306 / 3

x = 102

Therefore, Jean sold 102 candles, and Victoria sold half as many, which is (1/2)(102) = 51 candles.

In summary:

Jean sold 102 candles, and Victoria sold 51 candles.

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