there is a machine with $8$ toys in it that each cost between $25$ cents and $2$ dollars, with each toy being $25$ cents more expensive than the next most expensive one. each time sam presses the big red button on the machine, the machine randomly selects one of the remaining toys and gives sam the option to buy it. if sam has enough money, he will buy the toy, the red button will light up again, and he can repeat the process. if sam has $8$ quarters and a ten dollar bill and the machine only accepts quarters, what is the probability that sam has to get change for the $10$ dollar bill before he can buy his favorite toy- the one that costs $\$1.75$? express your answer as a common fraction.

Answer:2

Step-by-step explanation:

When raising an exponential expression to a power, you need to multiply the exponents. Applying this rule to (y^3)^5, we get (y^3)^5 = y^(3*5) = y^15.

So, (y^3)^5 • y^4 = y^15 • y^4 = y^(15+4) = y^19.

Therefore, the simplified expression is y^19, and the answer is 2.

Answer:

b=A/h

Step-by-step explanation:

In order to solve for b, we need to isolate b. We can do this by dividing both sides by h:

A = bh

A/h=b

b=A/h

Answer:

39.5m

Step by step explanation:

Answer:

1289155 golf balls

Explanation:

The total volume of all the balls equals to the storage unit space volume.

Let the number of total balls in the storage be b.

Conversion:

1 ft³ = 1728 in³

For the ball:

diameter = 1.6 in

radius = diameter/2 = 1.6/2 = 0.8 in

Equation created:

\(\sf \rightarrow volume \ of \ all \ balls = volume \ of \ storage\)

\(\sf \rightarrow b\left(\dfrac{4}{3} \pi r^3\right) = length \times width \times height\)

\(\sf \rightarrow b\left(\dfrac{4}{3} \pi (0.8)^3\right) =20 \times 10 \times 8 \times 1728\)

\(\sf \rightarrow b =\dfrac{20 \times 10 \times 8 \times 1728}{\left(\dfrac{4}{3} \pi (0.8)^3\right)}\)

\(\sf \rightarrow b =1289155\)

The slope of the least squares line, also known as the regression coefficient or beta coefficient (b1), is calculated using the covariance between the two variables (x and y) and the variance of x. The formula for calculating the slope of the least squares line is: False.

b1 = Cov(x, y) / Var(x)

In the given statement, it is mentioned that the covariance of x and y is 26.16, and the standard deviation of x is 32.7. However, the variance of x is needed to calculate the slope of the least squares line, not the standard deviation.

Therefore, without knowing the variance of x, we cannot determine the slope of the least squares line with the given information. The statement "b1 = 0.80" is not correct as it is not supported by the information provided.

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Answer: the square root of 25 is 5

and also it’s an app called Desmos that finds the square root for you !

Answer:

6v-12y+30

Step-by-step explanation:

Hope this helps:)

The variance of a binomial distribution is np(1-p), so probability of success is 0.9798 (rounded to 4 decimal places).

Using the hypergeometric distribution, the probability of selecting exactly 3 rods that meet the specification is:

P(X=3) = (12 choose 3) * (3 choose 3) / (15 choose 6) ≈ 0.2727

To find the standard deviation of X, we use the formula:

σX = sqrt(np(1-p)/N)

where n is the sample size (6), p is the probability of success (12/15), and N is the population size (15).

σX = sqrt(6 * (12/15) * (3/15)) ≈ 0.925

Using the binomial distribution formula with n = 6 and p = 12/15 = 0.8:

P(X = 3) = (6 choose 3) * (0.8)^3 * (0.2)^3 = 0.27648

The variance of a binomial distribution is np(1-p), so:

σX = sqrt(np(1-p)) = sqrt(60.80.2) = 0.9798 (rounded to 4 decimal places)

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If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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Answer:

24÷6+7 is the correct answer

Answer:

a) the coordinates of the gas station are (1, -2)        

b) 1 : 2 ratio, since the gas station is exactly at the middle.

c) the coordinates of the fast food restaurant are (3, -1)

On the attached graph, you will find Mario's house and school, plus the gas station and fast food restaurant.

Answer:

7 hours 30 minutes and 0 Seconds

Step-by-step explanation:

Answer:

The water level drop in temperature per hour is 40 °C per hour

Unit rate

   Hours between 10 P.M. and 7:36 A.M = 9 hours 36 minutes

= 9.6 hours

   The total decrease in temperature = 6/25

The unit rate of decrease in temperature per hour = Hours between 10 P.M. and 7:36 A.M ÷ Total drop in temperature

= 9.6 ÷ 6/25

= 9.6 × 25/6

= 240/6

= 40 °C per hour

Therefore, the water level drop in temperature per hour is 40 °C.

The angle B in the triangle is 67.5 degrees.

The sum of angles in a triangle is 180 degrees. A triangle is a polygon that three sides.

Therefore, let's find the angle B in the triangle as follows:

Hence, let's find x

2x + 3x + 3x  = 180

8x = 180

divide both sides of the equation by 8

x = 180 / 8

x = 22.5

Therefore,

angle B = 3(22.5)

angle B = 67.5 degrees.

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Answer:

Personally its a negative real‼️‼️

Answer:

Yes, if the area is all you are asked to calculate.

Step-by-step explanation:

The values of the variables in the equation will be:

1. a = -78

2. m = 209

3. p = -16

4. n = 1/5

5. r = 1/2

6. k = = -3/2

7. a = -13.5

8. p = 2

-6 = a/13

Cross multiply

a = 13 × -6

a = -78

m/11 =19

Cross multiply

m = 19 × 11

m = 209

p -1 = -17

p = -17 + 1

p = -16

3= 3/5n

5n = 3/3

5n = 1

Divide

n = 1/5

31/10= r+ 2⅗

r = 31/10 - 2 3/5

r = 31/10 - 13/5

r = 5/10

r = 1/2

-6/5 =⅘k

Divide

k = -6/5 × 5/4

k = -3/2

-12/5 = 1+a

a = -12.5 - 1

a = -13.5

p+ ½ = 5/2

p = 5/2 - 1/2

p = 2

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Answer:

because 4 + (negative 7) is an equivalent expression, the answer is -3.

Step-by-step explanation:

4 + (-7) = -3

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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The most accurate estimated sum of 181 and 204 is 380

The given numbers are 181 and 204

The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.

To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation

Round 181 to the nearest tens = 180

Round 204 to the nearest tens = 200

Then the sum of compatible numbers will be

180 + 200 = 380

Therefore, the most accurate estimation is 380

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Answer:

2

Step-by-step explanation:

m is the slope = rise/run

take any 2 easi points on the line, for example (0,0) and (1,2)

to get from (0,0) to  (1,2) you had to rise 2 and go run 1 so the slope is

m=2/1=2

Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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The rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station is 313.05 mi/h .

Given :

a plane flying horizontally at an altitude of 2 mi and a speed of 420 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 3 mi away from the station .

Here ,

h = 2

d = 3

we know that ,

x = \(\sqrt{d^2 - h^2}\)

= \(\sqrt{3^2 - 2^2}\)

= \(\sqrt{9 -4}\)

= \(\sqrt{5}\)

d = \(\sqrt{5}\) * 420 / 3

= \(\sqrt{5}\) * 140

= 313.05 mi/h

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Answer:

x = b-a/2

Step-by-step explanation:

2x + a = b

2x = b-a

x = b-a/2

Answer:

The correct answer is -21 degrees.

Step-by-step explanation:

We know that the original temperature was -12 degrees.  If the temperature drops another 9 degrees, this means that it is getting colder or the temperature is getting lower; this lets us know that we should subtract 9 from the original temperature.  This is modeled below:

-12 - 9

Now, we simply have to perform the subtraction to get:

-21 degrees

Hope this helps!

Answer:

Vertical angles are always congruent.

Step-by-step explanation:

Vertical angles are formed when two straight lines intersect each other, thereby forming two pairs of opposite angles, which are called vertical angles. Thus, a pair of these vertical angles formed are congruent to each other. So therefore, if two angles are said to be vertical angles, it follows that they are congruent to each other.

Using the diagram attached below, we can see two straight lines intersecting each other to form two pairs of vertical angles:

<a and <b,

<c and <d.

Thus, <a is congruent to <b, and <c is congruent to <d.

Therefore, the standby that is true about vertical angles is that:

Vertical angles are always congruent.