NOENHailey bought a 9 ft piece of ribbon that she will out into 2/3 ft long pieces. How many 2/3 ft pieces con Hailey aut?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

9/(2/3) = 27/2 = 13.5

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Rewrite the following using the GCF and Distributive properly ?63 + 27
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A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. Step 1: m∠m + m∠n + m∠o = 180 degrees (sum of angles of a triangle) Step 2: m∠p − m∠o = 90 degrees (alternate interior angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? 1.) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (corresponding angles) 2.) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) 3.) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) 4.) Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)
Blood potassium level, continued. Judy’s measured potassium level varies according to the Normal distribution with with μ=3.8 and σ=0.2mmol/l. Let’s consider what could happen if we took 4 separate measurements from Judy. What is the blood potassium level L such that the probability is only 0.05 that the average of 4 measurements is less than L? (Hint: This requires a backward Normal calculation.)the book says about 3.64 but i got 3.28

Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value.Minimize

Exam Image

Subject to
x ≤ 3
y ≤ 9
x + y ≥ 9
x ≥ 0
y ≥ 0

Answers

Answer:

Minimum value of function $C=x+10y$ is 63 occurs at point (3,6).

Step-by-step explanation:

To minimize :

$C=x+10y$

Subject to constraints:

$x\leq 3---(1)\ny\leq 9---(2)\nx+y\geq 9----(3)\nx\geq 0\ny\geq 0$

Eq (1) is in blue in figure attached and region satisfying (1) is on left of blue line

Eq (2) is in green in figure attached and region satisfying (2) is below the green line

Considering $x+y\geq 9$ , corresponding coordinates point to draw line are (0,9) and (9,0).

Eq (3) makes line in orange in figure attached and region satisfying (3) is above the orange line

Feasible region is in triangle ABC with common points A(0,9), B(3,9) and C(3,6)

Now calculate the value of function to be minimized at each of these points.

$C=x+10y$

at A(0,9)

$C=0+10(9)\nC=90$

at B(3,9)

$C=3+10(9)\nC=93$

at C(3,6)

$C=3+10(6)\nC=63$

Minimum value of function $C=x+10y$ is 63 occurs at point C (3,6).

Applying the method of corners to the linear programming problem yields a minimum value of 6 at the point (3, 0) for the given objective function and constraints.

The linear programming problem involves minimizing an objective function subject to certain constraints. The constraints are given as follows:

Minimize z = 2x + 3y

Subject to:

x ≤ 3

y ≤ 9

x + y ≥ 9

x ≥ 0

y ≥ 0

To find the minimum value, we employ the method of corners. The feasible region is determined by the intersection of the inequalities. The corner points of this region are where the constraints intersect.

Intersection of x ≤ 3 and y ≥ 0 gives the point (3, 0).

Intersection of y ≤ 9 and x ≥ 0 gives the point (0, 9).

Intersection of x + y ≥ 9 and y ≥ 0 gives the point (9, 0).

Now, evaluate the objective function z = 2x + 3y at each corner point:

z1 = 2(3) + 3(0) = 6

z2 = 2(0) + 3(9) = 27

z3 = 2(9) + 3(0) = 18

The minimum value occurs at point (3, 0) with z_min = 6.

For more such information on: linear programming

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Find the radius and height of a cylindrical soda can with a volume of 256cm^3 that minimize the surface area.B: Compare your answer in part A to a real soda can, which has a volume of 256cm^3, a radius of 2.8 cm, and a height of 10.7 cm, to conclude that real soda cans do not seem to have an optimal design. Then use the fact that real soda cans have a double thickness in their top and bottom surfaces to find the radius and height that minimizes the surface area of a real can (the surface area of the top and bottom are now twice their values in part A.

B: New radius=?

New height=?

Answers

Answer:

A) Radius: 3.44 cm.

Height: 6.88 cm.

B) Radius: 2.73 cm.

Height: 10.92 cm.

Step-by-step explanation:

We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.

a) We can express the volume of the soda can as:

$V=\pi r^2h=256$

This is the constraint.

The function we want to minimize is the surface, and it can be expressed as:

$S=2\pi rh+2\pi r^2$

To solve this, we can express h in function of r:

$V=\pi r^2h=256\n\nh=(256)/(\pi r^2)$

And replace it in the surface equation

$S=2\pi rh+2\pi r^2=2\pi r((256)/(\pi r^2))+2\pi r^2=(512)/(r) +2\pi r^2$

To optimize the function, we derive and equal to zero

$(dS)/(dr)=512*(-1)*r^(-2)+4\pi r=0\n\n(-512)/(r^2)+4\pi r=0\n\nr^3=(512)/(4\pi) \n\nr=\sqrt[3]{(512)/(4\pi) } =\sqrt[3]{40.74 }=3.44$

The radius that minimizes the surface is r=3.44 cm.

The height is then

$h=(256)/(\pi r^2)=(256)/(\pi (3.44)^2)=6.88$

The height that minimizes the surface is h=6.88 cm.

b) The new equation for the real surface is:

$S=2\pi rh+2*(2\pi r^2)=2\pi rh+4\pi r^2$

We derive and equal to zero

$(dS)/(dr)=512*(-1)*r^(-2)+8\pi r=0\n\n(-512)/(r^2)+8\pi r=0\n\nr^3=(512)/(8\pi) \n\nr=\sqrt[3]{(512)/(8\pi)}=\sqrt[3]{20.37}=2.73$

The radius that minimizes the real surface is r=2.73 cm.

The height is then

$h=(256)/(\pi r^2)=(256)/(\pi (2.73)^2)=10.92$

The height that minimizes the real surface is h=10.92 cm.

Final answer:

The minimal surface area for a cylindrical can of 256cm^3 is achieved with radius 3.03 cm and height 8.9 cm under uniform thickness, and radius 3.383 cm and height 7.14 cm with double thickness at top and bottom. Real cans deviate slightly from these dimensions possibly due to practicality.

Explanation:

For a cylinder with given volume, the surface area A, radius r, and height h are related by the formula A = 2πrh + 2πr^2 (if the thickness is uniform) or A = 3πrh + 2πr^2 (if the top and bottom are double thickness). By taking the derivative of A w.r.t r and setting it to zero, we can find the optimal values that minimize A.

For a volume of 256 cm^3, this gives us r = 3.03 cm and h = 8.9 cm with uniform thickness, and r = 3.383 cm and h = 7.14 cm with double thickness at the top and bottom. Comparing these optimal dimensions to a real soda can (r = 2.8 cm, h = 10.7 cm), we see that the real can has similar but not exactly optimal dimensions. This may be due to practical considerations like stability and ease of holding the can.

Learn more about Optimal Dimensions here:

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Solve the equation. Check the solution. 8 - 6x - 5 - 4x = 5 Type an integer or a simplified fraction

Answers

Answer:

x = -0.2

Step-by-step explanation:

In this problem, an equation is given as follows :

8- 6x - 5 - 4x = 5

We need to solve the above equation

Taking like terms together:

-6x-4x=5+5-8

-10x=2

x = -0.2

So, the value of x is -0.2.

What is the initial value of the exponential function shown on the graph? a. 0, b. 1, c. 2, d. 4

Answers

Answer:

Step-by-step explanation:

4 is the initial value of the exponential function shown on the graph.

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An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 50% of the people were aware of the product after 50 days of advertising. The number of people who become aware of the product at time t is:

Answers

Answer:

$P(t)=3,000,000-3,000,000e^(0.0138t)$

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

$P'(t)=K(3,000,000-P(t))$

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

P(0) = 0 and P(50) = 1,500,000

We have and ordinary differential equation of first order that we can write

$P'(t)+KP(t)= 3,000,000K$

The integrating factor is

$e^(Kt)$

Multiplying both sides of the equation by the integrating factor

$e^(Kt)P'(t)+e^(Kt)KP(t)= e^(Kt)3,000,000*K$

Hence

$(e^(Kt)P(t))'=3,000,000Ke^(Kt)$

Integrating both sides

$e^(Kt)P(t)=3,000,000K \int e^(Kt)dt +C$

$e^(Kt)P(t)=3,000,000K((e^(Kt))/(K))+C$

$P(t)=3,000,000+Ce^(-Kt)$

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

$e^(-50K)=(1)/(2)\Rightarrow K=-(log(0.5))/(50)=0.0138$

And the equation that models the number of people (in millions) who become aware of the product by time t is

$P(t)=3,000,000-3,000,000e^(0.0138t)$

Dr. Smith wants to use only students with "normal" IQ in his experiment. He defines "normal" as anyone who scores in the middle 50% of IQ scores. Using this rule, what will be the lowest IQ score that could be included in the study and what would be the highest IQ score that could be included in the study? You know that the population of IQ scores are normally distributed, have µ = 100, and have σ = 15. (1 point)

Answers

Answer:

Lowest IQ: 89.875

Highest IQ: 110.125

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 100, \sigma = 15$ .

He defines "normal" as anyone who scores in the middle 50% of IQ scores. Using this rule, what will be the lowest IQ score that could be included in the study and what would be the highest IQ score that could be included in the study?

The middle 50% is the interval from the 25th percentile to the 75th percentile.

Lowest IQ:

This is the measure in the 25th percentile. That is X when Z has a pvalue of 0.25. So it is $Z = -0.675$