pls help me . full working out needed

The correct option for this question is c) approximately 68% of the students spent between $200 and $400.


Step 1: Identify the given information. The mean is $300, and the standard deviation is $50. The range is between $200 and $400.

Step 2: Calculate the number of standard deviations between the mean and each boundary. For $200, it's ($200 - $300) / $50 = -2 standard deviations. For $400, it's ($400 - $300) / $50 = 2 standard deviations.

Step 3: Since we don't have information about the shape of the distribution, we will use the Empirical Rule, which states that for a normal distribution, approximately 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

Step 4: In this case, we are looking at 2 standard deviations from the mean (between $200 and $400). According to the Empirical Rule, approximately 95% of the data falls within this range. However, since we don't know the exact shape of the distribution, we can't say for certain that 95% of the students spent between $200 and $400. However, we do know that at least 68% of the students would fall within 1 standard deviation of the mean. Thus, we can conclude that approximately 68% of the students spent between $200 and $400.

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Answer:

True; this \(x\) would indeed be a factor of \(z\).

Step-by-step explanation:

"\(x\) is a factor of \(y\)" means that there is a whole number \(p\) such that \(x\, p = y\).

Likewise, \(y\) is a factor of \(z\) if and only if there is a whole number \(q\) such that \(y\, q = z\).

This \(x\) would be a factor of \(z\) if there is some whole number \(r\) such that \(x\, r = z\).

The first equality \(x\, p = y\) implies that \(y\) may be substituted with \(x\, p\).

Substitute the \(y\) in the second equality \(y\, q = z\) with \((x\, p)\) to obtain:

\((x\, p)\, q = z\).

Rearrange to obtain:

\(x\, (p\, q) = z\).

The product of two whole numbers is still a whole number. Since \(p\) and \(q\) are both whole numbers, \(p\, q\) would also be a whole number.

Thus, if \(r = p\, q\), then \(x\, r = x\, (p\, q) = z\), while \(r\) would be a whole number.

Therefore, this \(x\) would indeed be a factor of \(z\).

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

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The tennis ball has traveled a horizontal distance of 3.717 m, to the nearest tenth of a metre, when it lands on the ground. Hence, the correct option is (A) 3.7.

The given function is h(d) = -0.12d² +0.22d+1.1.

It models the path of a tennis ball hit from a height of 1.1 m above the ground.

Here, d represents the horizontal distance in meters, and h(d) represents the height in meters.

To find how far the tennis ball travelled horizontally when it lands on the ground, we need to find the value of d when h(d) = 0, because the ball will hit the ground when its height is zero.

Substituting h(d) = 0 in the given function, we get:

0 = -0.12d² +0.22d+1.1

Simplifying, we get: 0.12d² - 0.22d - 1.1 = 0

We can solve this quadratic equation using the quadratic formula, which is given by:

-b ± sqrt(b² - 4ac) / 2a, where a, b, and c are the coefficients of the quadratic equation.

Here, a = 0.12, b = -0.22, and c = -1.1.

Substituting the values, we get:

d = [0.22 ± sqrt(0.22² - 4(0.12)(-1.1))] / 2(0.12)

Simplifying,

We get:

d = [0.22 ± sqrt(0.5964 + 0.528)] / 0.24d

= [0.22 ± sqrt(1.1244)] / 0.24d

= [0.22 ± 1.0604] / 0.24

We get two values of d as follows:d = 3.717 m, -1.598 m

Since the ball cannot travel a negative distance, the only possible solution is d = 3.717 m.

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Answer:

There are 101 marbles in each bag with 10 marbles leftover.

Step-by-step explanation:

To find how marbles will go in each bag, divide 1525 by 15.

1525/15 = 101 with a remainder of 10.

There's your answer!

So, Lana gave away 26.32% of he Pokemon cards  to her little brother.

To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.

In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:

(125 / 475) * 100 = 0.2632 * 100 = 26.32%.

Lana gave away 26.32% of her Pokemon cards to her little brother.

Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:

Percentage given away

= (Cards given away / Total cards) * 100

= (125 / 475) * 100

= 26.32%.

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Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Ans .: The dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

To minimize the cost of the container, we need to find the dimensions that will use the least amount of material. Let's call the length of one side of the square base "x" and the height of the container "h".

The volume of the container is given as 2000 cm^3, so we can write:

V = x^2h = 2000

We need to find the dimensions that will minimize the cost, which is determined by the amount of material used. We know that it costs twice as much per square centimeter to make the top and bottom as it does the sides.

Let's call the cost per square centimeter of the sides "c", so the cost per square centimeter of the top and bottom is "2c". The total cost of the container can then be expressed as:

Cost = 2c(x^2) + 4(2c)(xh)

The first term represents the cost of the top and bottom, which is twice as much as the cost of the sides. The second term represents the cost of the four sides.

To minimize the cost, we can take the derivative of the cost function with respect to "x" and set it equal to zero:

dCost/dx = 4cx + 8ch = 0

Solving for "h", we get:

h = -0.5x

Substituting this into the volume equation, we get:

x^2(-0.5x) = 2000

Simplifying, we get:

x^3 = -4000

Taking the cube root of both sides, we get:

x = -16.7

Since we can't have a negative length, we take the absolute value of x and get:

x = 16.7 cm

Substituting this into the equation for "h", we get:

h = -0.5(16.7) = -8.35

Again, we can't have a negative height, so we take the absolute value of "h" and get:

h = 8.35 cm

Therefore, the dimensions of the container that will minimize the cost are a base with sides of length 16.7 cm and a height of 8.35 cm.

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Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Step-by-step explanation:

(gof)(x) is basically g(f(x))

= 4 × (3x - 1)² + 9

= 4 × (9x² - 6x + 1) + 9

= 36x² - 24x + 4 + 9

= 36x² - 24x + 13

The constant of proportionality of the equation is 29.4

If the amount of money an accountant makes, m, is directly proportional to the time taken, this is expressed as:

m = kh

where;

k is the variation constant

Given that the amount of money an accountant makes, m, for working h hours is represented by the equation m = 29.4h, the variation constant is calculated as:

29.4h = kh

k = 29.4

Hence the constant of proportionality of the equation is 29.4

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After evaluating the integral ∫[3 f(x) dx -4], we find that the value is 9.

To evaluate the integral, we need to split it into two parts based on the given function, f(x).

First, we integrate f(x) over the interval [-4, 0], where f(x) is equal to 3:

∫[3 dx] from -4 to 0 = [3x] from -4 to 0 = 3(0) - 3(-4) = 12

Next, we integrate f(x) over the interval (0, 3], where f(x) is equal to 4 - x^2:

∫[(4 - x^2) dx] from 0 to 3 = [(4x - (x^3/3))] from 0 to 3 = (4(3) - (3^3/3)) - (4(0) - (0^3/3)) = (12 - 9) - (0 - 0) = 3

Now, we subtract the value obtained from integrating the first part from the second part:

3 - 12 = -9

Therefore, the value of the integral is -9. However, since the integral is evaluated within the limits of [-4, 0] and (0, 3], we need to consider the absolute value of the result:

| -9 | = 9

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The annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense=  $400, Accumulated Depreciation = $400

The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

1. Straight-Line Depreciation:

The straight-line depreciation method allocates an equal amount of depreciation expense each year over the useful life of the equipment. In this case, the annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense         $400

  Accumulated Depreciation    $400

2. Units-of-Production Depreciation:

The units-of-production method bases depreciation on the actual units produced. The depreciation per unit is calculated as ($4,800 - $800) / 2,000 = $2 per unit. The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

3. Double-Declining-Balance Depreciation:

The double-declining-balance method accelerates depreciation in the early years of the asset's life. The depreciation rate is twice the straight-line rate. The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

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Answer for #3: Yes, Ms. Bartlett is correct.

Step-by-step explanation:

2x - 3 - (x + 1) = x - 4

2x - 3 - x - 1 = x - 4

x - 4 = x - 4

A quadratic expression x² + 6x + 5 into the form  a(x - h)² + k is (x + 3)² - 4    

The correct answer is an option (c)

Here the quadratic expression is: x² + 6x + 5

We need to write this quadratic expression into the form a(x - h)² + k

Comparing above expression with ax² + bx + c we get,

a = 1, b = 6 and c = 5

We use completing the square method to write above expression into  a(x - h)² + k form.

We add and subtract (b/2)² from above expression.

(b/2)² = (6/2)²

         = 3²

         = 9

So, the expression becomes:

x² + 6x + 5

= x² + 6x + 9 + 5 - 9

= (x + 3)² - 4               ........((x + 3)² = x² + 6x + 9)

This expression is in the form a(x - h)² + k with a = 1, h = -3 and k = -4

Therefore, the required expression is:  (x + 3)² - 4    

The correct answer is an option (c)

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The complete question is:

Complete the square to transform the expression x² + 6x + 5 into the form  a(x - h)² + k

a). (x + 6)² + 4

b) (x + 6)² - 4

c) (x + 3)² - 4

d) (x + 3)² + 4

The angle of an inscribed angle in a circle can be determined by measuring of interrupted arc Equals 1/2 * measure of inscribed angle

You must apply the method below to determine the size of an inscribed angle in a circle:

Measure of interrupted arc Equals 1/2 * measure of inscribed angle

Alternatively stated, the measure of an inscribed angle is equivalent to half the measure of the arc that it intercepts. How to apply the following formula:

Make a circle with the letter O in the middle.

In the centre of the circle, draw two chords—lines that link two points on the circle. Identify the junction as A.

From spot A to the circle's nucleus, O, draw a line.

Determine the intercepted arc, or the area of the circle that falls between the two chords and includes point A.

Ascertain the intercepted trajectory.

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Answer:

Im pretty sure its 1

Step-by-step explanation:

If you meant 4^3*4^-3, then yeah, its 1

Solution:

The equation of the plane is 2x + 3y - z - 7 = 0.

Explanation:

To find the equation of a plane through a point and parallel to a plane, we need to know the point and the normal vector of the plane. The normal vector is the vector perpendicular to the plane, and it is the coefficient of the x, y, and z terms in the equation of the plane.

Here are the steps to find the equation of the plane:

1. Find the normal vector of the plane. If the equation of the plane is given in the form Ax + By + Cz + D = 0, then the normal vector is (A, B, C).
2. Find the point through which the plane passes. If the point is given as (x1, y1, z1), then we can use this point in the equation of the plane.
3. Plug in the normal vector and the point into the equation of the plane. The equation of the plane will be in the form (A)(x - x1) + (B)(y - y1) + (C)(z - z1) = 0.
4. Simplify the equation to get the final equation of the plane.

For example, if the normal vector of the plane is (2, 3, -1) and the point through which the plane passes is (1, 2, 3), then the equation of the plane will be:

(2)(x - 1) + (3)(y - 2) + (-1)(z - 3) = 0

Simplifying the equation gives:

2x + 3y - z - 7 = 0

So the equation of the plane is 2x + 3y - z - 7 = 0.

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To find the equation of a plane through a point and parallel to a given plane find a normal vector and a point on the given plane then find the equation of the that plane. Using both point and normal vector, find the equation of the new plane.

1. Find the normal vector of the given plane. This can be done by taking the cross product of two non-parallel vectors that lie on the plane.
2. Find a point on the given plane.
3. Using the point and the normal vector, find the equation of the given plane using the general equation of a plane.
4. Then, using the point and the normal vector, find the equation of the new plane which is parallel to the given plane using the same general equation of a plane.

The equation of the plane through a point and parallel to a given plane is given by Ax + By + Cz = D, where A, B, C, and D are calculated using the point and the normal vector.

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The probability that 100 randomly selected college students will spend less than $10.00 on average for dinner is approximately 0.9525 or 95.25%.

We can utilize as far as possible hypothesis to inexact the conveyance of test implies for an enormous example size of 100. The example mean is regularly dispersed with a mean of the populace mean ($9.50) and a standard deviation of the populace standard deviation partitioned by the square base of the example size ($3/sqrt(100) = 0.3).

To find the likelihood that 100 arbitrarily chosen understudies will spend under $10.00 on normal for supper, we really want to find the z-score related with the worth $10.00 utilizing the recipe:

z = (x - mu)/(sigma/sqrt(n))

Subbing the given qualities, we get:

z = (10 - 9.5)/(0.3) = 1.67

Utilizing a standard typical dissemination table or number cruncher, we can find that the likelihood of a z-score under 1.67 is roughly 0.9525.

Accordingly, the likelihood that 100 haphazardly chosen understudies will spend under $10.00 on normal for supper is roughly 0.9525 or 95.25%.

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The answer to the all parts given below.

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

For 5 cuts number of pieces will be 11 pieces.

General formula:

Tn= 2n+1

For 153 rope pieces number of rope cutting

2n+1=153

2n= 152

n= 76

For 11 cuttings rope pieces will be

2(11)+1

= 23

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The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Answer:

$23.18

Step-by-step explanation:

You have to subtract $562.84 and $238.32 and you get $324.52 then you have to divide $324.52 and 14 to get $23.18

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Answer:

a. 8, 13 b. 375, -1875

Step-by-step explanation:

a. -1(+2), 1(+3), 4(+4), 8(+5), 13

b. -3(-5), 15(-5), -75(-5), 375(-5), -1875

Answer:

1

Step-by-step explanation:

Factors of 14.

1, 2, 7, 14

Factors of 55.

1, 5, 11, 55

The GCF is the greatest factor they both have in common. In this case it’s 1.

Best of Luck!

Hello.

To find the Greatest Common Factor of two numbers, you have to break it down by finding its prime factors, then multiply the greatest number both numbers have in common.

The Factors of 14 are: 14, 7, and 1.

The Factors of 55 are: 55, 11, and 1.

The greatest number both numbers have in common are 1.

1 x 1 = 1

Therefore, the Greatest Common Factor of 14 and 55 is 1.

In order to provide you with the Taylor series and its first five coefficients, I need to know the function or expression for which you want the series expansion.

The Taylor series expansion is a way to represent a function as an infinite sum of terms, where each term is calculated using the function's derivatives at a specific point. Without the specific function or expression, it is not possible to determine the Taylor series or its coefficients. Once you provide the function, I will be able to assist you in finding the first five coefficients of its Taylor series.

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Answer:

the answer is the one below 43 5/7  

Step-by-step explanation:

349/8 =43.625

43x7 =301 and 301+5=306  

306/7=43.7142857143

43.625 or 43.7142857143

the smaller number allways trys to take down the bigger one so its this one no underline though \(\leq\)

Given:

What is 8/9 of 3/8?

So, we will multiply 8/9 by 3/8

So, the answer will be 1/3

A variable without a clear operational definition can greatly impact the accuracy and reliability of statistics performed on it. To ensure accurate and meaningful results, it is important to have clear, well-defined variables in any research study.

The lack of a clear definition can lead to inconsistencies in data collection, making it difficult to accurately interpret and analyze the results.

Step 1: When a variable has no clear operational definition, researchers may measure or interpret it in different ways, leading to inconsistencies in data collection.

Step 2: These inconsistencies can affect the reliability and validity of the collected data, which in turn impacts the accuracy of the statistical analysis performed.

Step 3: As a result, the findings from such analyses may not accurately represent the true relationships or patterns within the sample or the population, leading to incorrect conclusions.

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