If you toss 9 fair coins, in how many ways can you obtain at least two tails?
("At least two" is the complement of "zero or one.")
There are different ways of obtaining at least two tails.
(Type a whole number.)

a)

The total number of possible 3​-card poker hands is 22100

b)

The number of possible black flushes is 2600

c)

The probability of being dealt a black flush is 0.1176

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of cards = 52

Number of cards in hand = 3

Combination formula.

[tex]^nC_r[/tex] = n! / r! (n -r)!

a)

The total number of possible 3​-card poker hands.

= [tex]^{52}C_3[/tex]

= (52 x 51 x 50) / (3 x 2)

= 22100

b.

Number of black cards (spades and clubs) = 13 + 13 = 26

The number of possible black flushes.

= [tex]^{26}C_3[/tex]

= (26 x 25 x 24) / (3 x 2)

= 2600

c.

The probability of being dealt a black flush.

From (a) and (b)

= 2600/22100

= 0.1176

Thus,

The total number of possible 3​-card poker hands = 22100

The number of possible black flushes = 2600

The probability of being dealt a black flush = 0.1176

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The perimeter of the figure after a dilation with a scale factor of 4 is

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]

Thus, scale factor is the ratio of the new measurement to the old measurement.

Given;

The perimeter= 12units

Scale factor=4

Now,

Dilation with the given scale factor;

= 12*1/4

=12/4

=3

Therefore, dilation by the given scale factor will be 3.

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Answer: 3

Step-by-step explanation:

Took the test

The table that represents a linear relationship that is also proportional is; Table 2

A proportional relationship is defined as one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y = 2x is proportional), but usually a linear equation has a proportional component plus some constant number (for example y = 2x + 3).

Table 1:

The proportions are;

-3/2, 0/3, 3/4

They are not equal and so not proportional

Table 2:

The proportions are;

-2/4 and -1/2

They are equal and so are proportional

Table 3:

The proportions are;

0/-2, 1/1 and 2/4

They are not equal and so not proportional.

Table 4:

The proportions are;

-4/0, 0/1 and 4/2

They are not equal and so not proportional.

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Answer:

you are to use patagorious theory

a).The function1 changes at greater rate of 45.

b). At x = 1; the function1 = 45 and function2 = 50.

c).The functions are equal to 90 at x = 2.

A function in the equation form "y = mx + c" represents a straight line in a two-dimensional coordinate system. "y" and "x" are variables representing the coordinates of points on the line, "m" is the slope of the line, and "c" is the y-intercept, which is the point at which the line crosses the y-axis.

The slope "m" represents the rate at which the line rises or falls as x increases. The y-intercept "c" determines the location of the line along the y-axis. This equation is known as the slope-intercept form of a linear equation.

For the function1, when y = 0 and x = 0, we can solve for c and m as follows:

0 = 0m + c

c = 0

when y = 90 and x = 2;

90 = 2m + 0

m = 45

Hence, the function1 with y = 45x changes at a greater rate of 45.

At x = 1:

for function1;

y = 45(1) + 0 = 45

for function2;

y = 40(1) + 10 = 50.

At the point when x = 2:

for function1;

y = 45(2) + 0 = 90

for function2;

y = 40(2) + 10 = 90.

Therefore, the function1 changes at greater rate of 45. At x = 1; the function1 = 45 and function2 = 50. The functions are equal to 90at x = 2.

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Answer:

I know that answer

Step-by-step explanation:

answer is -23

It looks like 1) adjacent angles.

The number 7.787887888 is option (C) not a rational number, it has a pattern which is predictable, but not repeating

The given number is 7.787887888

The rational numbers is a number that can be expressed as the p/q format, where p and q are integers and p will not be equal to zero. So the rational number is the ratio of the two integers.

Here the given number is 7.787887888.

So this is an non terminating number

But here we can see that there is a pattern which is predictable but its not repeating

Therefore, it is not a rational number ,but it has a pattern which is predictable, but not repeating

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Answer:

Step-by-step explanation:

The correct answer is D. m∠6 + m∠7 = 180°.

When a transversal cuts two parallel lines, corresponding angles are equal and alternate interior angles are supplementary. This means that the sum of alternate interior angles is equal to 180°. In this diagram, ∠6 and ∠7 are alternate interior angles, so it is necessarily true that m∠6 + m∠7 = 180°.

The other options are not necessarily true. Option A states that m∠1 = m∠7, but this is only true if the two lines being cut by the transversal are perpendicular. Option B states that m∠3 = m∠6, but this is only true if the two lines being cut by the transversal are parallel. Option C states that m∠5 + m∠8 = 90°, but this is only true if the two lines being cut by the transversal are perpendicular.

The volume of the Cone A will be 4m³.

What is a cone?

A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.

Volume of cone=πr²h where r=radius of base and h=height of cone

Curved surface area=πrL , where L=slant height

Now,

As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³

After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4

and Then volume of A=1*4

=4 m³

hence,

          The volume of the Cone A will be 4m³.

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Answer: it is actually 64m^3

Step-by-step explanation:

i did it and this was the right answer

Answer:

≈29.93 [units].

Step-by-step explanation:

according to the attachment the required perimeter is:

P=2*6+4.25*2+3.1415*3=12+8.5+9.4245=29.9245 [units].

Step-by-step explanation:

for z -> 3 (3z - 2) -> (3×3 - 2) = 7

Answer:

Set up the equation ... 60 + 40X = total charges... where X is the number of hours (6.5)

60 + 40(6.5) = ?

60 + 260 = ?

320 = total charges

The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

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Answer: B

Step-by-step explanation:

Answer:

[tex] \frac {3}{8} + \frac{2}{8} = \frac{5}{8} = 1 \frac{3}{8} [/tex]

[tex] = \frac{5}{ \\ 8} = 1 \frac{3}{8} [/tex]

(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

(b) When q = 1, the expected score is 1, which is the maximum possible score.

(c) The optimal value of p also depends on the value of q in this case.

a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - q^2)

To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2q(1 - q) = 1 - 2p

Solving for p, we get:

p = (1 - 2q + 2q^2) / 2

So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

b) If the meteorologist chooses p = q, then the expected score simplifies to:

Expected score = q(1 - (1 - q)^2) + (1 - q)(1 - q^2)

= q^3 + (1 - 2q)q^2 + (1 - q)

To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:

3q^2 - 4q + 1 = 0

This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.

c) If the payoffs are {1 - (1 - p)^2, 1 - 1.1p^2}, then the expected score of the meteorologist is:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - 1.1q^2)

To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2.2q^2 - 2q + 1 = 2p

Solving for p, we get:

p = (2.2q^2 - 2q + 1) / 2

So, in this scenario, the value of q also affects the ideal value of p.

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14. The mean of  the Zoo-venir Stand sales is of 23.9, representing the quotient between the sum of all the amounts and the number of observations.

15. The range of the Zoo-venir Stand sales is of 30, representing the difference between the highest number and the lowest number.

Considering the key format of the stem-and-leaf plot, the observations are given as follows:

12, 13, 13, 13, 14, 15, 15, 16, 17, 20, 21, 21, 22, 22, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 32, 34, 34, 37, 41, 42.

The mean is given by the sum of all observations divided by the number of observations, hence it's value is of: 23.9.

The range is the difference between the highest observation and the lowest observation, hence it is of:

42 - 12 = 30.

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Answer:

Step-by-step explanation:

m∠2 = 90° - 56° = 34°. So, m∠1 = m∠2 = 34°

here the answers

Answer:

132ft

Step-by-step explanation:

The height of the Great Sphinx can be found by using the relationship between the height of an object, the length of its shadow, and the angle of elevation of the sun.

Let h1 be the height of the Great Sphinx and h2 be the height of the person. We know that the length of their shadows are 220 ft and 20 ft, respectively.

Since the sun is at the same elevation for both objects, we can set up the following proportion:

h1/220 = h2/20

Cross multiplying, we get:

h1 = (h2 * 220) / 20

Plugging in h2 = 6 ft, we get:

h1 = (6 * 220) / 20 = 132 ft

So, the height of the Great Sphinx is approximately 132 ft.

Thus, the correct answer is 132 ft, which is not in the options provided, but it is a reasonable estimate of the height of the Great Sphinx.

(1) The cost of the phone call was less than $4.16

(2) The cost of the phone call was greater than $3.35

While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.

The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes

According to the above the cost for n minutes, where n>3, is 75 + (n−3)∗20=20n+15

cents. W need to find whether n>15. The cost for 15 minutes is 20n+15=20∗15+15=315

, so we need to find whether the cost is greater than 315 cents.

(1) The cost of the phone call was less than $4.16. Not sufficient.

(2) The cost of the phone call was greater than $3.35. Sufficient.

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Answer:

[tex]a \sqrt[5]{b} [/tex]

Step-by-step explanation:

solution Given:

[tex] \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } [/tex]

since i indices rule if the power is same it can be multiplied or divided.

[tex] \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } [/tex]

since power is added of like terms in multiplication

[tex] \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } [/tex]

again simplifying

[tex] \sqrt[5]{ {a}^{5} b} [/tex]

by using indices formula

[tex] \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } [/tex]

we get

[tex]a \sqrt[5]{b} [/tex]

Answer:

[tex]a \sqrt[5]{b}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex](a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}[/tex]

As the exponents are the same,

[tex]\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](a^3b^2a^2b^{-1})^{\frac{1}{5}}[/tex]

Collect like terms:

[tex](a^3a^2b^2b^{-1})^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex](a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}[/tex]

Simplify the exponents:

[tex](a^5b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:[/tex]

[tex](a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}[/tex]

Simplify:

[tex]a^1 \cdot b^{\frac{1}{5}}[/tex]

[tex]a \cdot b^{\frac{1}{5}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]a \sqrt[5]{b}[/tex]

The length of the dotted line would be 7.922 ft.

What is the diameter of the circle?

The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.

In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:

d = 2r

In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get

q = 17.708 - 4.893 - 4.893

By solving this, we get

q = 7.922

Hence, the length of the dotted line would be 7.922 ft.

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The correct options are sample more families, sample families having children who are not in seventh grade.

Sample families that do not have children. Sample families living in every third house in neighborhood.

To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:

Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.

Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.

Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.

Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of

sampling bias.

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Answer:a

Step-by-step explanation:

Using the distributive property of matrix multiplication A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

We have given that Ax = 0, where A is an m × n matrix and x is an n-dimensional vector in Rn.

To show that A(cu) = 0 for any scalar c, we can use the distributive property of matrix multiplication, which states that A(B + C) = AB + AC for any matrices A, B, and C of appropriate dimensions.

Let us substitute cu for x in the equation Ax = 0, then we get:

A(cu) = A(c × u)

Using the distributive property, we can write:

A(c × u) = c × A(u)

Since u satisfies the equation Ax = 0, we have:

A(u) = 0

Substituting this into the above equation, we get:

c × A(u) = c × 0 = 0

Therefore, we have shown that A(cu) = 0, which implies that cu also satisfies the equation Ax = 0 for any scalar c.

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Answer:

So, Darmal needs to work more than 8.96 hours to earn more than $128.

Step-by-step explanation:

The situation represented by the inequality 14.25x > 128 is B. Darmal earns $14.25 per hour at his job. How many hours does he need to work to earn more than $128?

The inequality states that the product of 14.25 and x (representing the number of hours worked) is greater than 128. Solving for x, we can find the number of hours Darmal needs to work to earn more than $128:

14.25x > 128

x > 128 / 14.25

x > 8.96

So, Darmal needs to work more than 8.96 hours to earn more than $128.

The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is x⁴-13x²+36

Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36

= x²(x²-9)-4(x²-9)

= (x²-9)(x²-4)

= (x²-3²)(x²-2²)

By using the identity a²-b²=(a+b)(a-b)

So, (x+3)(x-3)(x+2)(x-2)

Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).

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