(a) Plot the following function ona Karnaugh map.(Do not expand to minterm form before plotting.)
F(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
(b) Find the minimum sum of products.
(c) Find the minimum product of sums

Answer:

x=2

Step-by-step explanation:

[tex]f(x)=\frac{x^2-4}{x^2-12x+20}[/tex]

Factor the numerator and denominator:

[tex]f(x)=\frac{(x-2)(x+2)}{(x-2)(x-10)}[/tex]

We can remove (x-2) from the function:

[tex]f(x)=\frac{x+2}{x-10}[/tex]

(x-2) is a removable discontinuity.

The x-value of x-2 is x=2.

Answer:

the answer would be calculations

Step-by-step explanation:

because they have do determine if the check out times differ between the two systems so they need to calculate the difference between the two

Answer:

the width of the rectangle is 24 centimeters and the length is 31 centimeters.

Step-by-step explanation:

We first have to write an equation for this, but let's just recall that the area of a rectangle is equal to the length times the width. A=L×W.

A is the area

L is the length

W is the width.

So, for our equation we can start out by putting that 744= ? times ?.

So, we are given that the length is 7 more than the width. We are going to have to translate that to represent the length.

We need a variable. Let's use the letter "W," the width of the rectangle.

W=W.

The length is 7 more than the width, so it is L=W+7.

Length represents the W+7

Width represents W.

Now, we can complete our equation.

744=W(W+7).

Simplify the expression.

744=[tex]W^{2}[/tex]+7W.

Alright, you may be thinking on how we are going to solve this problem. This equation correlates with quadratic functions.

Let's complete the square.

In a quadratic function, the standard from is y=[tex]ax^{2} +bx+c[/tex].

We need to find the c value.

We can do this by applying a formula. The formula states that c= b/2 and the whole thing squared. In other words, [tex](\frac{b}{2} )^{2}[/tex].

In this case, the b value is 7.

square 7, which is 49 and square 2 which is 4.

Now, the c value is 49/4.

We have now just created a perfect square trinomial.

Not only do we add 49/4 to W squared plus 7W, we also add 49/4 to 744.

744 plus 49/4 is 756/25.

Now, we have [tex]W^{2}+7w+\frac{49}{4} = 756.25[/tex]

Change W squared plus 7w plus 49/4 to a binomial squared.

Just take the square root of the a value, W, and 49/4 for c. the square root of W squared is W. the square root of 49/4 is 7/2.

Those values are to the power of 2.

In other words, [tex](W+\frac{7}{2})^{2} =756.25[/tex]

To isolate for W, take the square root of both sides.The square root of W plus 7/2 squared is just W+7/2. The square root of 756.25 is 27.5

There are two solutions for W because square roots be positive or negative, but we are dealing with positive since negative doesn't make sense with the context of the problem.

We have [tex]W+3.5 or \frac{7}{2}=27.5[/tex]

Isolate for W by subtracting both sides by 3.5 You get to W=24.

Therefore, the width of the rectangle is 24 centimeters.

Alright, we found the width. We now need to find the length. The problem stated that the rectangle was 7 more than the width. So, 24+7=31. Therefore, the length of the rectangle is 31 centimeters.

L=31cm

W=24cm.

I hope this was helpful! I wish you have an amazing day!

Answer: 59.342

Step-by-step explanation:

The chi-square critical values are used to find the confidence interval for σ.

Left critical value = [tex]\chi^2_{\alpha/2, n-1}[/tex] [i.e. chi-square value from chi-square table corresponding to degree of freedom n-1 and significance level of [tex]\alpha/2[/tex]]

To find : left critical value for 95% confidence interval for σ with n = 41.

Significance level : [tex]\alpha=1-0.95=0.05[/tex]

degree of freedom = 41-1=40

Now, the  left critical value for 95% confidence interval for σ with n = 41 is the chi-square value corresponding  to degree of freedom n-1 and [tex]\alpha/2=0.025[/tex]

=59.342  [from chi-square table ]

Answer: 23 cans of soda/4 people.

or (23/4) cans of soda per person.

Step-by-step explanation:

So we have the rate:

46 cans of soda/ 8 people

First, 46 and 8 are multiples of 2, so we can divide both numerator and denominator by 2:

46/2 = 23

8/2 = 4

Then the rate can be:

23 cans of soda/4 people.

Now 23 is a prime number, so we can not simplify it furthermore

Answer:

Hello some parts of your question is missing below is the missing part

suppose we use a person's dad's height to predict how short or tall the person will be by building a regression model to investigate if a relationship exists between the two variables. Suppose the regression results are as follows:

Least Squares Linear Regression of Height

Predictor

Variables    Coefficient    Std Error T P

Constant    20.2833    8.70520 2.33    0.0223

DadsHt 0.67499 0.12495    5.40    0.0002

R² 0.2673 Mean Square Error (MSE) 23.9235

Adjusted R² 0.2581    Standard Deviation 4.9000

Answer : We expect most of the sampled heights to fall within 9.8 inches of their least squares predicted values.

Step-by-step explanation:

standard deviation is the statistical measurement of the level at which a dataset disperses from its mean value

interpreting the standard deviation in this problem ,

given that the standard deviation is 4.9 inches, it simply means that the dataset heights will be either +4.9 inches or -4.9 inches away from the mean value. this means that most of the sampled Dad/'s height will fall within 9.8 inches of their least squares predicted values

Answer:

Unpredictable

Step-by-step explanation:

Cuz if u look at it it is also random and u cant predict a random thing, so its quite simply unpredictable

Answer:

LL

Step-by-step explanation:

We have two right triangles

The two legs are congruent

We can use the LL congruence theorem

Answer:

D

Step-by-step explanation:

an inverse function is a function that reverses another function for ex. if f(x)=y and g(y)=x.

Answer:

A and C

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

Let the total number of rugs be x

To find the total number of rugs we must first find the total parts which is

3 + 4 = 7

4/7 of the total rugs are 84 Oriental rugs

Which is written as

[tex] \frac{4}{7} x = 84[/tex]

Multiply through by 7

[tex]7 \times \frac{4}{7} x = 84 \times 7[/tex]

Simplify

[tex]4x = 588[/tex]

Divide both sides by 4

[tex] \frac{4x}{4} = \frac{588}{4} \\ \\ \\ \\ x = 147[/tex]

Hope this helps you

Answer:

Step-by-step explanation:

Hello!

This is an example of a pared sample test, the experiment is based on two dependent variables:

X₁: centimeters on a pain scale before hypnosis

X₂: centimeters on a pain scale after hypnosis

Out of these two variables a new variable is determined Xd= X₁-X₂

If the variables have an approximate normal distribution then the variable resulting from their difference will also have an approximate normal distribution.

The claim is that "hypnosis reduced the pain" if so you'd expect the population mean of the difference to be less than zero, symbolically: μd<0

The statistic for this test is a paired sample t test:

[tex]t= \frac{\frac{}{X_d} - Mu_d}{Sd} ~t_{n-1}[/tex]

To calculate the sample mean and variance you have to calculate the difference between the pairs first.

[tex]\frac{}{Xd}[/tex]= ∑Dif/n

[tex]S_d^2= \frac{1}{n-1} [sumDif^2- \frac{(sumDif)^2}{n} ][/tex]

∑Dif= 6.4

∑Dif²= 12.64

[tex]\frac{}{Xd}[/tex]= 6.4/5= 1.28

[tex]S_d^2= \frac{1}{4} [12.64- \frac{(6.4)^2}{5} ]= 1.112[/tex]

Sd= 1.05

[tex]t_{H_0}= \frac{\frac{}{Xd}-Mu_d }{Sd} = \frac{1.28-0}{1.05} = 1.219= 1.22[/tex]

I hope this helps!

Answer:

The tax creates a deadweight loss of $29.64 dollars per day.

Step-by-step explanation:

a) A bag of potato chips generates $0.19 per bag

If 156 bags are not sold each day because of the imposed tax, the deadweight loss is calculated as follows:

156 x $0.19 = $29.64 per day

b) A deadweight loss is the inefficiency cost imposed by the tax because it causes decreases the equilibrium quantity of bags of potato chips sold each day by 156.  By dislocating the equilibrium and the market forces, the tax makes the economy to suffer overall.  This may imply that the rate of the tax was not economically reasonable.  Unless a tax is imposed to discourage an activity or a consumption, the rate should not be so high as to create inefficiencies in the allocation of economic resources.

Answer:

0

Step-by-step explanation:

x ^2/2 + y^2/2 = 0

Then x and y can be 0

0^2/2 + 0^2/2

0/2 +0/2 = 0

0 + 0 = 0

0 = 0

Answer:

The frequency of f(x) is two times the frequency of the parent function.

Step-by-step explanation:

We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.

Then, for the parent function, we get:

[tex]1 = 2\pi f_1[/tex]

or solving for [tex]f_1[/tex]:

[tex]f_1=\frac{1}{2\pi }[/tex]

At the same way, for f(x), we get:

[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]

But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:

[tex]f_2=2f_1[/tex]

It means that the frequency of f(x) is two times the frequency of the parent function.

Answer:

B. -3x

Step-by-step explanation:

A term is defined as either a constant or a variable with a coefficient.

-3 is incorrect because there is no constant -3 in the expression.

-3x is correct because there is a -3x in the expression

(x + 4) is incorrect because that is a linear binomial and has yet to be distributed.

-7 is incorrect because it has to be distributed.

Answer:

x > 4

Step-by-step explanation:

Answer:

The cosine of 86º is approximately 0.06976.

Step-by-step explanation:

The third degree Taylor polynomial for the cosine function centered at [tex]a = \frac{\pi}{2}[/tex] is:

[tex]\cos x \approx -\left(x-\frac{\pi}{2} \right)+\frac{1}{6}\cdot \left(x-\frac{\pi}{2} \right)^{3}[/tex]

The value of 86º in radians is:

[tex]86^{\circ} = \frac{86^{\circ}}{180^{\circ}}\times \pi[/tex]

[tex]86^{\circ} = \frac{43}{90}\pi\,rad[/tex]

Then, the cosine of 86º is:

[tex]\cos 86^{\circ} \approx -\left(\frac{43}{90}\pi-\frac{\pi}{2}\right)+\frac{1}{6}\cdot \left(\frac{43}{90}\pi-\frac{\pi}{2}\right)^{3}[/tex]

[tex]\cos 86^{\circ} \approx 0.06976[/tex]

The cosine of 86º is approximately 0.06976.

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = [tex]r_{0}[/tex] + t.v

where

[tex]r_{0}[/tex] is the position vector;

v is the vector;

For point (7,4,5):

[tex]r_{0}[/tex] = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = [tex]x_{0}[/tex] + at

y = [tex]y_{0}[/tex] + bt

z = [tex]z_{0}[/tex] + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

Answer:

It is a geometrical progression

Step-by-step explanation:

Geometric progressions have a constant number that they are multiplied by

To find that number you divide the 2nd term by the 1st term and also the 4th term by the 3rd term. ie,

[tex]\frac{-40}{20} = \frac{-10}{5} \\[/tex]

[tex]-2 = -2[/tex]

since they are both equal it is a G.P

Because they have a constant ratio.

Answer:

Geometric progression.

Step-by-step explanation:

I suppose you mean this equation:

5, -10, 20, -40, ...

For a geometric progression, an n^th term is given by:

[tex]a_{n}[/tex] = [tex]a_{n - 1}[/tex] × r

Where a is the first time, n is the term and r is the common ratio.

The common ratio here is -2 .

For instance to check the forth term;

[tex]a_{4}[/tex] = [tex]5_{4 - 1}[/tex] × -2  = 20 × -2 = -40

Answer:

[tex]\large \boxed{\sf \ \ x = -\dfrac{\sqrt{33}+1}{4} \ \ or \ \ x = \dfrac{\sqrt{33}-1}{4} \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+\dfrac{1}{2}x-2=0\\\\\text{*** complete the square ***}\\\\x^2+\dfrac{1}{2}x-2=(x+\dfrac{1}{4})^2-\dfrac{1^2}{4^2}-2=0\\\\\text{*** simplify ***}\\\\(x+\dfrac{1}{4})^2-\dfrac{1+16*2}{16}=(x+\dfrac{1}{4})^2-\dfrac{33}{16}=0[/tex]

[tex]\text{*** add } \dfrac{33}{16} \text{ to both sides ***}\\\\(x+\dfrac{1}{4})^2=\dfrac{33}{16}\\\\\text{**** take the root ***}\\\\x+\dfrac{1}{4}=\pm \dfrac{\sqrt{33}}{4}\\\\\text{*** subtract } \dfrac{1}{4} \text{ from both sides ***}\\\\x = -\dfrac{1}{4} -\dfrac{\sqrt{33}}{4} \ \ or \ \ x = -\dfrac{1}{4} +\dfrac{\sqrt{33}}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

1,114.6 kPa

Step-by-step explanation:

P(t) = 1300 (0.95)^t

P(3) = 1300 (0.95)^3

P(3) = 1114.6

Answer:

Step-by-step explanation:

∆ BCD ~ ∆ DCA

[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]

Plug the values:

[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]

[tex] \frac{5}{y} = \frac{ y}{11} [/tex]

Apply cross product property

[tex]y \times y = 11 \times 5[/tex]

Calculate the product

[tex] {y}^{2} = 55[/tex]

[tex]y = \sqrt{55} [/tex]

Hope this helps...

Good luck on your assignment..

When the wavelength of a diffraction grating is decreased,  the distance between lines decreases.

The diffraction grating is used to carry out interference experiments. It consists of a  number of small lines that are constructed to be close to each other and produce an interference pattern.

The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.

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Answer:

The plus 5 is a vertical translation. It would move g(x) up 5 units at all points. So just take g(x) and move the curve up 5 units.

Looks like the equation is

[tex]y(t)+9\displaystyle\int_0^te^{9(t-v)}y(v)\,\mathrm dv=\sin(3t)[/tex]

Differentiating both sides yields the linear ODE,

[tex]y'(t)+9e^{9(t-t)}y(t)=3\cos(3t)[/tex]

or

[tex]y'(t)+9y(t)=3\cos(3t)[/tex]

Multiply both sides by the integrating factor [tex]e^{9t}[/tex]:

[tex]e^{9t}y'(t)+9e^{9t}y(t)=3e^{9t}\cos(3t)[/tex]

[tex]\left(e^{9t}y(t)\right)'=3e^{9t}\cos(3t)[/tex]

Integrate both sides, then solve for [tex]y(t)[/tex]:

[tex]e^{9t}y(t)=\dfrac1{10}e^{9t}(\sin(3t)+3\cos(3t))+C[/tex]

[tex]y(t)=\dfrac{\sin(3t)+3\cos(3t)}{10}+Ce^{-9t}[/tex]

The given answer choices all seem to be missing C, so I suspect you left out an initial condition. But we can find one; let [tex]t=0[/tex], then the integral vanishes and we're left with [tex]y(0)=0[/tex]. So

[tex]0=\dfrac{0+3}{10}+C\implies C=-\dfrac3{10}[/tex]

So the particular solution is

[tex]y(t)=\dfrac{\sin(3t)+3\cos(3t)-3e^{-9t}}{10}[/tex]

Answer:

B. 0.478

Step-by-step explanation:

The diameter of the pin is 0.478 inches as per specification.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators.

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

The hole diameter is specified as 0.500 inches with a tolerance of 0.010 inches.

The maximum pun diameter must be 0.002 inches smaller than the minimum hole diameter.

Diameter: d = 0.500 inch

Tolerance: t = 0.010 inch

Replacing the values:

⇒ dmax = 0.500  - 0.010 - 0.002 - 0.010

Apply the subtraction operation,

⇒ dmax = 0.478 inch

Hence, the diameter of the pin is 0.478 inches as per specification.

Learn more about Arithmetic operations here:

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Answer:

x ≤ 40

Step-by-step explanation:

x/-8 ≥−5

Multiply each side by -8, remembering to flip the inequality

x/-8 *-8 ≤−5 *-8

x ≤ 40

Answer:

x ≥ 40

Step-by-step explanation:

[tex]\frac{x}{-8} \geq -5[/tex]

x ≥ -5 * -8

x ≥ 40

Check

40 / -8 ≥ -5

Answer:

You would basically expand all the equations!

1. 7(4z+8b) is equal to 28z+56b.

2. 8(2x+3^2) is equal to 16x+72

3. 4(r+r+r+r) is equal to 4r+4r+4r+4r

4. 9(3+8x) is equal to 27+72x

5. 4^2(3+6f) is equal to 48+96t

6. (t+t+t)/4 is equal to t/4+t/4+t/4

7. 2(4s^3+2) is equal to 8s^3+4

8. 30(3x+4) is equal to 90x+120

9. 6(5a+9b) is equal to 30a+54b

10. 9(3x+5^4) is equal to 27x+5625

11. 7(c+c+c) is equal to 7c+7c+7c

12. 9(2+7f) is equal to 18+63f

13. 7^5(4g-8d) is equal to 67228g-134456d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Try to use the distance formula to determine whether the sides are congruent. So take every pair of consecutive vertices and apply the distance formula. So you will have which, in any, sides are congruent.

Use the slope formula to determine which sides are parallel or perpendicular or neither of those. If the slopes are equal the sides are parallel, if the product of the slopes is - 1 the sides are perpendicular. In any other case the sides are neither parallel nor perpendicular.

With that and the definitions of the shapes you will be able to classify shapes.

To write a full example would be very long .

An easy one might be this as an example:

Given the  points (0,0), (2,0), (2,2) and (0,2), classify the shape.

When you apply the distance formula: you will find 2 for all the sides, so they are all congruent.

When you apply the slope formula you will find two pair of parallel sides, and the sides that intersects are perpendicular.

Therefore... the classification of the shape is a square.