Two dice are rolled 100 times. The number of double sixes X is counted. (a) Show that X follows a binomial distribution, that is, X∼Binomial(n,p). Moreover, find n and p. (b) Is it suitable to approximate the distribution of X by Poisson (pn) ? Justify your answer. (c) Find P(X≥3) using X∼Binomial(n,p) and find P(X≥3) using X∼

The median of the data set would be affected as the median points per game decreases. That is option C.

The median of a data set is defined as the value of a data set the is found in the middle of a data after it has been arranged in an ascending order.

The first number line plots points per game;

= 16, 17 ,18 ,19 ,20 ,21 = 18+19 = 37/2 = 18.5

The second number line plots points per game;

= 21, 22, 23, 24 = 22 + 23 = 45/2 = 22.5

The third number line plots points per game:

= 9 points through 35 points

= 22 as the median.

Therefore, the scores of the next two games led to a decrease in the median determined per game point.

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Answer:

the answer would be 4/10 but the simplified version would be 2/5.

Step-by-step explanation:

add up how many bows you have, that will be the denominator. Then, the numerator is the number of purple bows. and if your going to simplify it divide the numerator and denominator by 2.

Answer:

fraction wise(4/10 chance)

percent wise:(40% chance)

Step-by-step explanation:

(There are 2 options) First add all of the bows then see how many purple bows there are. Since there are 4 bows it would be 4/10 or 40%.

Answer:

Estelle paid $104 in total.

Step-by-step explanation:

15% of $80.00 is 12. So add 12 two times to 80 because of 15% sales tax and 15% tip.

The complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

The equation is given as:

3x+9+4x+x=

Represent the blank with y

So, we have:

3x + 9 + 4x + x = y

Evaluate the like terms

8x + 9 = y

For the equation to have no solution the value of y and 8x + 9 must not be equal.

Take for instance

y = 8x + 1

So, we have:

8x + 9 = 8x + 1

Subtract 8x from both sides

9 = 1

The above equation is false because 1 and 9 are not equal

Hence, the complete equation so that the statement is true is 3x+9+4x+x= 8x + 1

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Complete question

Use the drop-down menus to complete each equation so the statement about its solution is true.

No Solutions

3x+9+4x+x=

Answer:

1/8

Step-by-step explanation:

Answer:

1 3/32

Step-by-step explanation:

7/8 + 1/4(3/2 - 5/8)

= 7/8 + 1/4(7/8)

=7/8 + 7/32

=28/32 + 7/32

=35/32

=1 3/32

The good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.

An inferior good occurs when an increase in income causes a fall in demand.

An inferior good has a negative income elasticity of demand. (YED) Inferior goods are characterized by low quality – and are goods with better alternatives.

Suppose that good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.

An inferior good is one whose demand drops when people's incomes rise. When incomes are low or the economy contracts, inferior goods become a more affordable substitute for more expensive goods.

Inferior goods are the opposite of normal goods, whose demand increases even when incomes increase.

Hence, the good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.

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Using inequalities we know that x=68 and x=66 respectively.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

So, solve the inequalities as follows:

x+3>70

x>70-3

x>67

Then, it will be x = 68.

Then,

x+3<70

x<70-3

x<67

Then, it will be s = 66.

Therefore, using inequalities we know that x=68 and x=66 respectively.

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Answer:

remember to give me brainliest :p

one solution

Step-by-step explanation:

:)

Answer:

No solutions

Step-by-step explanation:

6 - 3x = 4 - x - 3 - 2x

6 - 3x = 1 - 3x

6 = 1

No solutions (6 does not equal 1)

Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.

The exponential function for depreciation given in the problem is:

y = 45,529(0.78)^x

This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.

To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:

y > 0

In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.

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here: 4.2727757e+15. Please mark brainliest. Thanks.

The step at which Marcus made his first mistake in solving this equation (2.5b = 5) is at calculating.

An expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities.

In order to determine the correct steps for solving the given expression, we would have to simplify the given mathematical equation by applying the division property of equality as follows:

Dividing both sides by 2.5, we have:

2.5b = 5

2.5b/2.5 = 5/2.5   ⇒ Setting up

b = 5/2.5

b = 2   ⇒  Calculating

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Complete Question:

Marcus tried to solve an equation.

2.5b = 5

2.5b/2.5 = 5/2.5   Setting up

b = 3                      Calculating

​

Where did Marcus make his first mistake?

Setting up

Calculating

The algebraic expression for this problem is given as follows:

2C - D = -2x² + 2x + 11.

The definition for C in this problem is given as follows:

C = x + 3.

We applying the distributive property to multiply by 2 as follows:

2C = 2(x + 3) = 2x + 6.

The definition for D in this problem is given as follows:

D = 2x² - 5.

The subtraction is then obtained as follows:

2C - D = 2x + 6 - (2x² - 5)

2C - D = 2x + 6 - 2x² + 5

2C - D = -2x² + 2x + 11.

Meaning that the second option is correct.

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66 kilogram is equal to 145.50 lbs. To convert kg to lbs, multiply the kg by 2.2046226218.

Kilograms (kg) and pounds (lbs) are two different units of measurement for mass. Kilograms are the primary unit of measurement for mass in the metric system, while pounds are the primary unit of measurement for mass in the imperial system. To convert from kilograms to pounds, you need to multiply the number of kilograms by 2.2046226218. This number is the conversion factor that is used to convert from kg to lbs. For example, if you have 66 kg, you would multiply it by 2.2046226218 to get 145.50 lbs. This means that 66 kg is equal to 145.50 lbs. Converting between kilograms and pounds is a very common calculation that is often used in many different types of applications. Knowing how to quickly convert between these two units of measurement can be very helpful in various situations.

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Answer:

No because one is negative and the other one is positive

Step-by-step explanation:

Answer:

Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.

Step-by-step explanation:

Using the concept of proportional, it is found that the value of x  for the given similar triangles is 2.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Since two triangles ΔACD and ΔABE are similar triangles, then their corresponding sides will be proportional.

Therefore, AC/ AB = AD / AE

By substituting the measures of the sides here;

AC/ AB = AD / AE

(x + 10) / 10 = (15 +3) / 15

15(x + 10) = 180

x + 10 = 12

x = 12 - 10

x = 2

Therefore, the value of x  for the given similar triangles is 2.

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The 97% confidence interval for the proportion of yellow M&Ms in that bag is [0.118, 0.285]. (option c).

Now, let's apply this formula to our scenario. We are given the counts of each color of M&Ms in the sample, so we can compute the sample proportion of yellow M&Ms as:

Sample proportion = number of yellow M&Ms / sample size

= 22 / (22 + 21 + 13 + 17 + 22 + 14)

= 0.229

Next, we need to find the critical value from the standard normal distribution for a 97% confidence level. This can be done using a z-table or a calculator, and we get:

z* = 2.17

Finally, we need to compute the standard error using the formula mentioned earlier. Since we are interested in the proportion of yellow M&Ms, we can set p = 0.20 (the claimed proportion by Mars Inc.) and q = 0.80 (1 - p), and n = 109 (the sample size). Thus,

Standard error = √[(p * q) / n]

= √[(0.20 * 0.80) / 109]

= 0.040

Plugging in the values in the formula for the confidence interval, we get:

Confidence interval = 0.229 ± 2.17 * 0.040

= [0.118, 0.285]

Hence the correct option is (c).

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Complete Question:

Mars Inc. claims that they produce M&Ms with the following distributions:

| Brown = 30% || Orange = 10% | Red = 20%  |Green = 10% |Yellow = 20% | Blue = 10%

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

Brown = 22 | Red = 21| Orange = 13 | Green = 17| Yellow = 22 | Blue = 14

Find the 97% confidence interval for the proportion of yellow M&Ms in that bag.

a) [0.018, 0.235]

b) [0.038, 0.285]

c)  [0.118,0.285]

d) [0.168, 0.173]

e) [0.118,0.085]

f) None of the above

Answer:

39

Step-by-step explanation:

(12−7)×9−6

Subtract 7 from 12 to get 5.

5×9−6

Multiply 5 and 9 to get 45.

45−6

Subtract 6 from 45 to get 39.

The answer is equal to 15

Step-by-step explanation:

Answer:

\(\frac{{5}}{w^{2}}\)

Step-by-step explanation:

We begin with \(\frac{15w^{4}v^{5}}{3w^{6}v^{5}}\).

Firstly, as with simplifying fractions we can simplify the numbers. 15 is divisible by 3, so this becomes \(\frac{5w^{4}v^{5}}{w^{6}v^{5}}\).

To simplify indices (aka exponents or powers), we must subtract the power on the denominator from the matching one on the numerator, and then use that number as the power in the numerator. In this case, 4-6 and 5-5, which becomes -2 and 0.

So now we have \(\frac{5w^{-2}v^{0}}{1}\).

For a negative power, we switch it into the other half (numerator to denominator) and take away the negative sign, leaving \(\frac{5v^{0}}{1w^{2}}\).

We can remove the \(v^{0}\) in the numerator as it just multiplies the numerator by one, and remove the 1 in the denominator for the same reason.

This leaves us with \(\frac{5}{w^{2}}\).

**This content involves division with indices, which you may wish to revise. Let me know if you have any questions. I'm always happy to help!

Answer:

Associative Property

Step-by-step explanation:Because it includes grouping of three numbers and the parentheses group around two different numbers

The equation of this circle in standard form is: D. (x - 4)² + (y - 1)² = 25.

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided above, we have the following equation of a circle:

x² - 8x + y² - 2y - 8 = 0

x² - 8x + y² - 2y = 8

x² - 8x + (-8/2)² + y² - 2y + (-2/2)² = 8 + (-8/2)² + (-2/2)²

x² - 8x + 16 + y² - 2y + 1 = 8 + 16 + 1

(x - 4)² + (y - 1)² = 25

(x - 4)² + (y - 1)² = 25

Therefore, the center (h, k) is (4, 1) and the radius is equal to 5 units.

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Answer:

Angle 1- 36

Angle 2- 90

Angle 3- 54

Angle 4- 36
Angle 5- 90

Angle 6- 54

Angle 7- 128

Angle 8- 54

Angle 9- 128

Angle 10- 54

Angle 11- 36

Angle 12- 144

Angle 13- 36
Angle 14- 144

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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The lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

The mid-range or mid-extreme is the arithmetic mean of the highest and minimum values of the data set and is used in statistics as a measure of a sample's central tendency.

The difference between the greatest and minimum values, which is a measure of statistical dispersion, is strongly related to the mid-range.

The two measurements are complementary in that one can determine the sample's maximum and minimum values by knowing the range and the midpoint.

Therefore, the lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

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Explanation:

* Demonstrate that the related angles are the same.

* Demonstrate that different interior angles are equivalent.

* Demonstrate the adjacent interior angles are supplementary.

* Demonstrate the adjacent external angles are not mutually exclusive.

* Show that the lines in a plane are perpendicular to the same axis.

<1 and <8 are the same because they are alternate exterior angles that means that they are

Opposite sides of the transversal.

And that they are on the exterior side of the parallel lines.

Now because of that they have the same measures no matter what so would

<2 and <7

<3 and <6

<4 and <5

The function shows that the cost of hotdogs is 1.75 and the cost of hamburger is 1.5.

Let hotdogs = h

Let hamburger = x

The expression will be:

h + x = 3.25

h + 7x = 12.25

Subtract the functions

6x = 9

x = 1.5

Therefore, hot dogs will be:

= 3.25 - 1.5

= 1.75

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At a concession stand, one hot dog and one hamburger cost $3.25; one hot dog and seven hamburger cost $12.25. Find the cost of one hotdog and the cost of one hamburger.

Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

Answer:

\(17 \le t \le 28\)

Step-by-step explanation:

Given

\(t = 22\frac{1}{2}\) --- average time

\(\triangle t = 5\frac{1}{2}\) --- the variation

Required

The inequality to represent the scenario

To do this, we simply add and subtract the variation from the average time.

i.e.

\(t \± \triangle t\)

So, the inequality is:

\(22\frac{1}{2} - 5\frac{1}{2} \le t \le 22\frac{1}{2} + 5\frac{1}{2}\)

Solve:

\(17 \le t \le 28\)

Answer:

D.

Step-by-step explanation:

the dot is right in between zero and one, which makes it 0.50

Answer:

D. 0.50

Between 0 and 1 is 0.50 or 0.5 or \(\frac{1}{2}\)

In hypothesis testing, a Type 1 error occurs when we reject a null hypothesis that's actually true. In other words, we conclude that there's a significant effect or difference when there is not one. The probability of making a Type 1 error is denoted by the symbol alpha( α).

A Type 2 error, on the other hand, occurs when we fail to reject a null hypothesis that's actually false. In other words, we conclude that there's no significant effect or difference when there actually is one. The probability of making a Type 2 error is denoted by the symbol beta( β).

In general, Type 1 errors are considered more serious than Type 2 errors because they lead to false positive results and can have negative consequences, similar as making incorrect opinions or wasting coffers. still, the inflexibility of the consequences depends on the specific situation.

The chances of Type 1 and Type 2 errors are related to the significance position( α) and the power( 1- β) of the hypothesis test, independently. The significance position( α) is the probability of making a Type 1 error and is generally set at 0.05 or 0.01. .

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