If you flip three fair coins, what is the probability that you'll get at least two heads?

So matrix which show equation 4x+2y=4 is  [tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex] .

Given that we have an equation that is 4x+2y=4

So equation is a statement that the values of two mathematical expressions are equal (indicated by the sign =).

So in order to write this equation in matrix form we have to write it into augmented matrix

So augmented matrix is a matrix whose elements are the coefficients of a set of simultaneous linear equations with the constant terms of the equations entered in an added column.

Therefore the matrix will be:

[tex]\left[\begin{array}{ccc}4&2&4\\12&-1&26\end{array}\right][/tex]    .

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Answer: Ok

Step-by-step explanation:

9-0-0

Answer:

16

Step-by-step explanation:

16: 16=4^2 and is even. 16/2=8

30: 30 is even, 30/2=15. However, the square root of 30 is between 5 and 6([tex]\sqrt{25}[/tex]and [tex]\sqrt{36}[/tex]).

81: 81=9^2, but 81 is not even. 81/2=40.5.

99: 99 is not even and doesn't have a square root. The square root of 100 is 10, so the square root of 99 is around 9.9, slightly less than 10.

Answer:

-3/2

Step-by-step explanation:

x < -3/2

Using the normal distribution, it is found that 55.7% of response times are between 4 and 6 minutes.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 4.5, \sigma = 1.2[/tex]

The proportion between 4 and 6 minutes is the p-value of Z when X = 6 subtracted by the p-value of Z when X = 4, hence:

X = 6:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (6 - 4.5)/1.2

Z = 1.25

Z = 1.25 has a p-value of 0.8944.

X = 4:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (4 - 4.5)/1.2

Z = -0.42

Z = -0.42 has a p-value of 0.3372.

0.8944 - 0.3372 = 0.5572 = 55.72%.

Hence:

55.7% of response times are between 4 and 6 minutes.

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The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x

The domain is x >= 0 and the range is c(x) >= 9.99

The given parameters are:

One topping = 9.99

Additional topping = 1.25 each

We have x to represent the number of toppings

This means that

C(x) = One topping + Additional topping  * x

So, we have

C(x) = 9.99 + 1.25x

We have

C(x) = 9.99 + 1.25x

The smallest number of topping is 0

So, the domain is x >= 0

Substitute 0 for x in C(x) = 9.99 + 1.25x

C(0) = 9.99 + 1.25(0)

This gives

C(0) = 9.99

So, the range is c(x) >= 9.99

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Answer:
C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]

Step-by-step explanation:

a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.

We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.

So the equation is C(x) = 9.99 + 1.25x right?

Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!

So the new equation is:

    C(x) = 9.99 +1.25(x - 1)

or, C(x) = 9.99 + 1.25x - 1.25

or, C(x) = 1.25x + 8.74  

b) We need to find the Domain of C(x).

We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.

So we can choose up to 10 different toppings. And we need at least 1 topping.

∴ Domain is 1 ≤ x ≤ 10.

b) We need to find the Range of C(x).

We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.

Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.

    C(10) = 1.25(10) + 8.74

or, C(10) = 12.50 + 8.74

or, C(10) = 21.24

∴ Range of C(x) = [9.99, 21.24]

Answer:

C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]

Answer:

(a) $878.24

(b) $848.30

(c) Amy would pay less for the golf clubs if she gets them directly from the distributor

Step-by-step explanation:

Part (a)

The wholesale price is $499. When the pro shop gets them from the distributor, it has to pay a mark-up of 10%. 10% expressed as decimal is 10/100 = 0.10

10% of 499 = 0.10 x 499 = 49.90

So total cost including markup for the pro shop is 499 + 49.90 = $548.90

We can compute this directly without computing mark-up cost using the formula

Cost = 499(1+0.10) = 499 x 1.1 = 548.90

The pro shop puts a mark up of 60% which in decimal is 60/100 = 0.6 on the above cost

So the price Amy pays = 548.90(1+0.6) = 548.90 (1.6) = $874.28

Part (b)

Wholesale price = $499

If Amy purchases directly from distributor there is a 70% markup on the wholesale price. 70% = 70/100 = 0.7

So the price Amy would have to pay = 499(1+0.7) = 499 x 1.7 = $848.30

Part (c)

Since the cost of purchasing directly from distributor is less than the cost of purchasing from pro shop the answer is

Amy would pay less for the golf clubs if she gets them directly from the distributor

Answer: Domain {-4,-2,2}

Range{4,6}

Step-by-step explanation:

[tex]y(\pi/3)=1 \implies 1=C-2\cos(\pi/3) \\ \\ 1=C-1 \\ \\ C=0 \\ \\ \therefore y=\boxed{-2\cos x}[/tex]

a) The best description of the bias in the survey is A. Nonresponse bias.

b) To remedy this bias, B. The polling organization should try contacting households that do not respond by phone or face-to-face.

Nonresponse bias is the type of bias when survey participants are not interested in the survey or send an empty or unsatisfactory response.

Nonresponse bias means that the sample is filled with those who are not willing or able to respond, making the number of non-respondents surpass the number of respondents.

Thus, a response of 22/1,495 is too significant to be ignored, meaning that the nonresponse bias is much more critical.

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responded.

a) Which of these best describes the bias in the survey?

A. Nonresponse bias

B.  Sampling bias

C. Undercoverage bias

D. Response bias

b) How can the bias be remedied?

A. The polling organization should mail the questionnaire to a greater number of households.

B. The polling organization should try contacting households that do not respond by phone or face-to-face.

C. The polling organization should mail the questionnaire to each person in the household.

Answer:

Step-by-step explanation:

-20

When the market price is $20, the number of cars that Denny will be willing to repair is 5 cars.

It should be noted that the total revenue will be:

= price × quantity

= 20 × s

= 20s

where s = number of cars

The marginal revenue will be 20.

The total cost is given as:

= 2s² + 10

The marginal cost will be 4s

We will equate the marginal. This will be:

4s = 20

Divide

s = 20/4

s = 5

Therefore, the number is 5.

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The image of the point (-1,-4) after a rotation of 90 counterclockwise about the origin is (4,-1)

What is coordinate system?

A coordinate system can be defined as the method used to  identifying the location of a point graphically. Most of the coordinate systems use two numbers generally x and y to define a  coordinate and to identify location of any point. The center of graph or system is known as origin and generally pointed as zero (0).

The 2 coordinates is generally written as x and y. There are generally 4 quadrants in 2d coordinate system. These are :

Now in the given question the point is (-1,-4)

i.e. the point lie in 4th quadrant (-x,-y)

If the point is rotated 90 degree counterclockwise then the point becomes (y , -x)

Thus, point (-1,-4) becomes (4,-1)

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The company's profit will start to decline if it only produces one bag.

Given f(x) = 2x⁴ ₋ 4x³ ₊ 7

Differentiate it with respect to x.

therefore, f'x) = 8x³ ₋ 12x²

= 4x²(2x ₋ 3)

For decreasing, f'(x) ≤ 0

⇒ 4x²(2x ₋ 3) ≤ 0

⇒ 2x ₋ 3  ≤  0

⇒ x  ≤ 3/2

Since the number of bags are represented by x.

Hence, x ∈ N

Therefore, x = 1 is only possibility.

Therefore, if the company only produces one bag, its profit begins to decline.

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Your question was incomplete. Please find the missing the content here.

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson's eventual profit function is given as: pi = 2x⁴ ₋ 4x³ ₊ 7 where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson's profit start decreasing?

Answer:

i don't known the question you are asking

The amount that he owes will be $6610.54.

From the information, the base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.

Therefore the amount that will be paid will be:

= ($30.45 × 2) + (15.75 × 415.85 miles)

= $60.90 + $6549.64

= $6610.54

The cost is $6610.54.

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The predicted area of the circle is 49.67 cm²

Given the expression that represents the least regression line as shown below:

log(Area) = 0.490 + 2.004log(time)

Given that the time after the stone is dropped is 4 seconds, the equivalent area is expressed as:

log(Area) = 0.490 + 2.004log(4)

log(Area) = 0.490 + 8.016

log(Area) = 1.6965cm

Area = 10^1.696

Area= 49.67 cm²

Hence the predicted area of the circle is 49.67 cm²

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Answer:

I'm pretty sure the answer is 6.

Step-by-step explanation:

Labeling the rooms A, B, and C makes it easier.

Room A - All BUT 4

Room B - All BUT 4

Room C - All BUT 4

Since you can see each room is all but four, you can split the 4 into 2 into 2 OTHER rooms than the one stated. For example, Room A is all but 4, so 2 go to Room B and the other 2 go to Room C because each room is all BUT 4.

Basically, 2+2+2 = 6

Explanation:

1/4 = 0.25

0.25*360 = 90

90 white beans, 360-90 = 270 black beans

The ratio of white to black is 90:270 which fully simplifies to 1:3 after dividing both parts by the GCF 90.

Answer: 3998 cents, or $39.98

Step-by-step explanation: Hope it helps!

The number of different ways to plan his trip is 240240

The given parameters are

Places, n = 14

Stops, r = 5

From the question, we understand that the places are in specific order

This represents permutation

So, the number of different ways to plan his trip is

Ways = [tex]^nP_r[/tex]

This gives

Ways = [tex]^{14}P_5[/tex]

Apply the permutation formula

Ways = 14!/9!

Evaluate

Ways = 240240

Hence, the number of different ways to plan his trip is  240240

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3 and 17

7 and 13

Step-by-step explanation:

........

The apprοpriate dοmain fοr this situatiοn is t ≥ 0.

In mathematics, a functiοn is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput. It can be thοught οf as a rule οr a machine that takes inputs and prοduces οutputs accοrding tο a specific set οf instructiοns οr οperatiοns.

The dοmain οf a functiοn represents the set οf all pοssible input values fοr which the functiοn is defined. In this case, the functiοn h(t) represents the height οf the rοcket as a functiοn οf time t after launch.

Since time cannοt be negative in this cοntext (we can't have negative secοnds), the apprοpriate dοmain fοr this situatiοn is t ≥ 0, which means the functiοn is defined fοr all nοn-negative values οf t after the rοcket is launched.

Therefοre, the apprοpriate dοmain fοr this situatiοn is t ≥ 0.

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Answer:

Formulas for a rectangular prism:

Volume of Rectangular Prism: V = lwh.

Surface Area of Rectangular Prism: S = 2(lw + lh + wh)

Space Diagonal of Rectangular Prism: (similar to the distance between 2 points) d = √(l2 + w2 + h2)

Answer: 450 miles

Step-by-step explanation: we can put the info we got from the question into an equation. since the car was only rented for a day, the daily rate that was paid was $26. and $0.10 for every mile the car was driven. So we can put into the equation 71 = 26 +0.10m, where m represents miles. Now subtract 26 from both sides and we get 45 = 0.10m. Divide both sides by 0.10 and we get m= 450