How many 1/4 cup servings are in an 8-cup box of cereal?

a. 99% confidence level requires 452 subjects.

b.  95% confidence level requires  246 subjects.

c. Decreasing the confidence level decreases the sample size needed

We are to solve for  using the data that is gitten in the question

a. The z value using the 99 percent confidence level is given as (2.576

We have to put the value in the formula

n = (Z * s / E)^2

n = (2.576 * 17.7 / 2)^2

n ≈ 451.24

B For 95 percent, the critical value of Z is given as 1.96

when we out the value in the formula we would have

n =  (1.96 * 17.7 / 2)^2

n ≈ 245.24

C. The decrease in the confidence level leads to a fall in the sample size. From the results, the sample size fell from 452 to 246 when the confidence was reduced from 99 to 95 percent

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In the quadratic equation y = a\(x^{2}\) + c ,the value of x = ± \(\sqrt \frac{y-c}{a}\)

A quadratic equation is any equation containing one term wherein the unknown is squared and no term wherein it's far raised to a higher power.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, in which a and b are the coefficients, x is the variable, and c is the constant term.

To find the value of x

Assuming \(a\neq o\)

First, subtract c from both the sides to get:

\(y-c=ax^{2}\)

then, divide both sides by \(a\) and transpose to get:

\(x^{2} =\frac{y-c}{a}\)

So, \(x\) must be a square root of \(\frac{y-c}{a}\)  and we can deduce:

\(x=\) ± \(\sqrt \frac{y-c}{a}\)

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The measure of the variable 'b' from the line is 11

Collinear points are points that lies on the same straight line. From the given diagram:

XY = YZ  (since Y is the midpoint of XZ)

where:

XY = 2b + 7

YZ = 3b - 4

Substitute the given parameters to have:

2b + 7 = 3b - 4

2b - 3b = -4 - 7

-b = -11

b = 11

Hence the measure of the value of b from the line is 11

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Answer:

Step-by-step explanation:

sum of angles in a triangle=180º

90+60x+30x=180

90+90x=180

90(1+x)=180

1+x=2

x=1

angle A=30º

Answer:

answer is 11 or 5

Step-by-step explanation:

x+y=16 ------ 1

x-y= 6 ------ 2

______

2x = 22

x =22/2 =11

put the value of x on equation 1

x+y =16

11+y =16

y =16-11 =5

Answer:

m<6 = 119

Step-by-step explanation:

m<4 + m<6 = 180 (Linear Pair)

61 + m<6 = 180

=> m<6 = 180 - 61

=> m<6 = 119

The decreasing temperature of the parcel as it travels up the mountain, from 0–m to 1,000–m are;

20 °C, 25 °C, 30 °C

The Dry Adiabatic Lapse Rate is the rate of change in temperature air which is unsaturated as it moves towards or away from a surface.

The given temperature of the parcel at an elevation of 0 meters = 20 °C

The Dry Adiabatic lapse Rate, DAR = (5°C/ 500–m)

The temperature, T, of the parcel at 1000–m is found as follows;

Using the DAR of 5°C/500–m, we have;

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The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

the answer is -40

Step-by-step explanation:

Complete Question:

You want to install a 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the​ walk? Use 3.14 for pi π.

Answer:

75.36 square yard

Step-by-step explanation:

From the question,

The diameter of this circular pool inside is 23 yd.

This means that the radius = Diameter/2 = 23yd/2 = 11.5 yd.

The formula for the area of a circle =

A = πr²

A = π(11.5)²

A =3.14 × 11.5²

A = 415.265 yd²

This is the Area of the inner circle.

We were told in the question also that he wants to install a walk of 1 yard

Hence, the radius of outer circle =

radius of inner circle +length of the walk

11.5yard + 1 yard

= 12.5 yard

A = πr²

A = 3.14 × (12.5)²

A = 490.625yd²

Area of the walk = Area of the Outer circle - Area of the inner circle

= (490.625 - 415.265)yd = 75.36 yd²

Therefore, the area of the walk is 75.36 square yards.

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

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The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

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Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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Answer:

19.64 ft

Step-by-step explanation:

7/25 = 5.5/x

7x = 137.5

x = 19.64

Answer:

27.5 pages read per hour

Step-by-step explanation:

The minimum quantity that the factory must sell in order to obtain benefits is x is 3.

Assuming that the unit price and unit cost are known, in addition to the fixed costs, the following formulas are proposed to determine the minimum quantity number of units that the factory must sell in order to obtain benefits: Input, cost, total cost, benefit, and utility. This example illustrates these formulas.

Unities sold = x =?

Unitary selling price = \(S.(2x-2)\)

Unit cost is \(\frac{S}{(x+4)}\)

Fixed costs = \(\frac{S}{160}\)

Assumption: I(x) = p*x= x*

\((2x-2)\)

Total cost: C(x)=\(x*(x+4)+160\)

U(x) = \(x*(2x-2)-x*(x+4)+160\)

U(x) = \(2x^{2} -2x-x(4)+160\)

U(x)= \(x^{2} -6x+160\)

derived from and equal to zero:

U'(x)= \(2x-6=0\)

x = 3​.

Therefore, the minimum quantity that the factory must sell in order to obtain benefits is x is 3.

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Based on their given probabilities, e would expect the color blue or green to be spun approximately 75 times in this experiment.

To find the expected number of times the color blue or green will be spun, we first need to add their probabilities:

0.25 + 0.125 = 0.375

This means that, on average, we would expect to see blue or green spun 0.375 times for every spin. To find the expected number of times this will happen over 200 spins, we can multiply the probability by the number of spins:

0.375 x 200 = 75

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Answer:

The cost for 1 chair is $2.75 and the cost for 1 table is $8.75.

Step-by-step explanation:

Use the elimination method of linear equations to find your answer.

Our equations for this problem are:

3c+5t=52 and 9c+7t=86

Multiply the entire first equation by -3.

-3(3c+5t=52)

Simplify the equation from above:

-9c-15t=-156

Stack the two equations on top of each other and add/subtract:

-9c-15t=-156

9c+7t=86

You should be left with -8t=-70. Simplify this to find the value of t:

t=8.75

Plug the value of t into any of the original equations and solve for c.

3c+5(8.75)=52

Simplify the equation above:

3c+43.75=52

Subtract 43.75 from both sides of the equation:

3c=8.25

Divide both sides by 3 to get your c value:

c=2.75

Answer:

The answer is 9(7x – 1).

Step-by-step explanation:

63x – 9

3 × 3 × 7 × x – 3 × 3

9(7x – 1)

Thus, The answer is 9(7x – 1).

-TheUnknownScientist 72

Answer:

12/6 but if you simplify it's 2

Step-by-step explanation:

4+8 = 12

6-3 = 3

2 x 3 = 6

12/6 = 2

The value of h such that the matrix is the augmented matrix of a consistent linear system is 2

For the given matrix to be the augmented matrix of a consistent linear system, we need to check whether the matrix is in row echelon form or not. If the matrix is in row echelon form and the last row is not all zeros, then the linear system is consistent.

We can use elementary row operations to transform the matrix into row echelon form.

\(\left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right]\)

R2 <- R2 - 3R1

\(\left[\begin{array}{ccc}1&h&4\\0&6-3h&-4\end{array}\right]\)

The matrix is in row echelon form. Now, we need to check whether the last row is all zeros or not.

If 6-3h = 0, then the last row will be all zeros, which implies that the linear system is inconsistent.

If 6-3h ≠ 0, then the last row will not be all zeros, which implies that the linear system is consistent.

Therefore, we need to solve the equation 6-3h = 0 to determine the value of h that makes the linear system consistent.

6-3h = 0

3h = 6

h = 2

So, the value of h that makes the matrix the augmented matrix of a consistent linear system is h = 2.

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The arc length of the curve on the given interval is 31.241.

Parametric Equations

Interval: −1 ≤ t ≤ 3

dx/dt = d/dx(6t + 5)

dx/dt = 6

And, dy/dt = d/dt(7 − 5t )

dy/dt = -5

The arc length of curve is estimated as;

L = ∫√(dx/dt)² + (dy/dt)²).dt

L = ∫√(36 + 25t)     Interval: [−1 ≤ t ≤ 3]

L = √61  x  (3 + 1)

L = 31.241

Thus, the arc length of the curve on the given interval is 31.241.

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Answer:

d

Step-by-step explanation:

As you can tell by the graphs the relative minimum is -14 since that is where the curve ends and -3 is the maximum due to the top curve being at -3

Answer:

d)  relative minimum = −14, relative maximum = −3

Step-by-step explanation:

The relative minimum and maximum values are the minimum and maximum y-values of the points in the domain of the function.

From inspection of the given graph, the minimum y-value in the interval [1, 5] is -14 and the maximum y-value in the interval [1, 5] is -3.

Therefore:

the answer is 10

3 to 6 and 7 to 10

it adds three both times

Answer:

0.55 seconds and 10.89 seconds

Step-by-step explanation:

h = 183t − 16t²

95 = 183t − 16t²

16t² − 183t + 95 = 0

Solve with quadratic formula:

t = [ -(-183) ± √((-183)² − 4(16)(95)) ] / 2(16)

t = (183 ± √27409) / 32

t = (183 ± √27409) / 32

t ≈ 0.55 or 10.89

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

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