Question 3:
A 12-sided solid has faces numbered 1 to 12. The table shows the results
of rolling the solid 200 times. Find the experimental probability of
rolling a number greater than 10.
Results
1 2 3 4 5 6 7 8 9 10 11 12 Total
Number
rolled
Frequency
18 14 17 17 23 15 17 16 16 15 15 17 200
32
4
P(for having a number greater than 10)= 200 25

The start point the graph of a function of this form is (h, k)

From the question, we have the following parameters that can be used in our computation:

f(x) = a√(x - h) + k

The domain is given as

x ≥ h

This means that the initial x value is h

From the question, we have the following parameters that can be used in our computation:

f(h) = a√(h - h) + k

Evaluate

f(h) = k

Hence, teh initial point is (h, k)

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Answer:

the answer is d bro

Step-by-step explanation:

yo the answer is d I think if I get this wrong sorry

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Answer:

hi half human half zombie

what you gonna do sir

what you gonna do with the wigle wigle

- rastaman

Answer:

5.5

Step-by-step explanation:

12+6=18

18÷2=9

9-3.5=5.5

Answer: You use the method of pendas and in this case u gonna do first the division, then addition and last substract. first u do 6/2 = 3. Now that u had that answer you sum 3 + 12 = 15 - 3.5 = 11.5

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer:

1,884

Step-by-step explanation:

The formula for solving the area of a right cylinder like this one is:

=2πrh+2πr2

Note:

Pls notify me if my answer is incorrect for the other users that will see this response. Thank you.

-kiniwih426

Answer:162

Step-by-step explanation:

162

If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

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The incircle centered at point P has a radius of 7 units.

Here given that,

PA = 12 units.

PZ = 7 units

The complete question is :

"Point P is the incenter of triangle ABC, PZ = 7 units, and PA = 12 units.

The radius of the incircle centered at point P is ? units."

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Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

To find the percentage by which Sara needs to reduce the price to provide the same value for money as Zak's idea, we need to compare the original price and the new price under Zak's idea.

Let's assume the original price of a box of pet food is P and the original amount of pet food in each box is A.

According to Zak's idea, the company will put 50% more pet food into each box without changing the price. Therefore, the new amount of pet food in each box will be 1.5A.

To calculate the value for money under Zak's idea, we divide the amount of pet food by the price:

Value for money (Zak's idea) = (1.5A) / P

Now, let's consider Sara's idea. She wants to reduce the price but keep the amount of pet food unchanged. Let's assume Sara reduces the price by a percentage represented by x.

Under Sara's idea, the new price of a box of pet food will be P - (x/100)P = P(1 - x/100).

Since Sara wants her idea to provide the same value for money as Zak's idea, we can equate the two value for money expressions:

(1.5A) / P = (A) / (P(1 - x/100))

Cross-multiplying and simplifying the equation:

1.5A * P(1 - x/100) = A * P

1.5(1 - x/100) = 1

Simplifying further:

1 - x/100 = 2/3

-x/100 = -1/3

x/100 = 1/3

x = 100/3

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

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The inequality that shows the minimum number of hours, n, that Gavin should work as a babysitter to earn enough to buy the fish tank is 8 + 9n ≥ 80.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Gavin needs $80 to buy a fish tank a.s.he has saved $8 and plans to work as a babysitter to earn $9 per hour.

Let the number of hours be n. The inequality will be:

8 + 9(n) ≥ 80

8 + 9n ≥ 80

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if the diameter of a tennis ball is 2.6 what is the circumference ​

we have that

the circumference is

C=Pi*D

we have

D=2.6 units

so

C=pi*2.6

C=2.6pi units ------> exact value

the approximate value is

C=3.14*2.6

C=8.16 units -----> approximate value

The value of x in the equation 3/5(4x+1)=3(2-4x)+9 is

Algebraic equation, statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root. Examples are x3 + 1 and (y4x2 + 2xy – y)/(x – 1) = 12.

3/5(4x+1)=3(2-4x)+9

multiply through by 5

3( 4x+1) = 15(2-4x) + 45

12x +3 = 30-20x +45

collect like terms

12x+20x.= 30+45-3

32x = 72

x = 72/32

x = 2 8/32

x = 2 1/4

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Answer:

Difference in area of the last square and the initial square = 440 cm²

Step-by-step explanation:

Length of the side of a square = 1 cm

Area of the square = (side)² = 1 cm²

Addition of side length every minute = 2 cm

After x minutes length of each side of the square = (1 + 2x) cm

If x = 10 minutes

Length of each side of the square = [1 + 2(10)]

                                                         = 21 cm

Area of the square after 10 minutes = (21)²

                                                            = 441 cm²

Therefore, difference in area of the last square and area of the initial square

= 441 - 1

= 440 cm²

Answer:

\(volume = 502.4ft^3\)

Step-by-step explanation:

\(volume = \pi r^2 h = 3.14 \times 4^2 \times 10 = 502.4ft^3\)

Answer:

Option D.   \(g(x)=5(0.8)^{x}+2\)

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

-x + 20

Step-by-step explanation:

13-x+3+4

13 - x + 3 - 3 = 4 + 3

13 - x = 7

= -x + 7 + 13

= -x + 20

Answer:

  (a) -2.3°/min

  (b) -2.9°/min

Step-by-step explanation:

The average rate of change is the ratio of the difference in R values to the difference in the corresponding t values.

(a) m = (157.6 -226.6)/(30 -0) = -69/30 = -2.3 . . . degrees per minute

__

(b) m = (61.6 -119.6)/(70 -50) = -58/20 = -2.9 . . . degrees per minute

The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is 27/8 square inches or 3 3/8 square inches

From the question, we are to determine the area of the cross-section of the cone

To determine the area of the cross-section of the cone, we will determine the radius of the cross-section.

Let the radius of the cross-section be x and radius of the base of the be r.

The height of the cone is 8 inches and the height of the cone formed from the cross-section is 3 inches

By similar triangle theorem, we can write that

8/r = 3/x

x = (3r)/8

From the given information,

The area of the base is 24 square inches

Thus,

πr² = 24

Therefore, r² = 24/π

The area of the cross-section will be

A = πx²

But, x = (3r)/8

Thus,

A = π [(3r)/8]²

A = π × 3²/8² × r²

A = π × 9/64 × 24/π

A = 27/8 square inches

Hence, the area is 27/8 square inches or 3 3/8 square inches

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Answer:

The pairs are:

\(\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}\) =>  \(\frac{p^2}{9q^2}\)

\(\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}\) => \(6pq^3\)

\(\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}\) => \(6p^2q^2\)

\(\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}\) => \(\frac{q}{3}\)

Step-by-step explanation:

We are going to solve the questions one by one and then write the quotients with every question.

In order to calculate the division, the terms are multiplied then exponents are added or subtracted between numerator and denominator to get the simplest form of answer.

First Expression:

\(\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}\)

When two fractions have to be divided the second fraction is reversed i.e. numerator becomes denominator and vice versa.

\(= \frac{4p^3q}{6p^2q^2} * \frac{2p^2q^2}{12pq^3}\\=\frac{p^5q^3}{9p^3q^5}\\=\frac{p^2}{9q^2}\)

Second Expression:

\(\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}\)

Removing the division symbol

\(=\frac{10p^3q^3}{2p^2q} * \frac{6pq^2}{5pq}\\=\frac{6p^4q^5}{p^3q^2}\\=6pq^3\)

Third Expression:

\(\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}\)

Removing the division symbol

\(=\frac{14p^2q^3}{2pq} * \frac{6p^3q^2}{7p^2q^2}\\= \frac{6p^5q^5}{p^3q^3}\\= 6p^2q^2\)

Fourth Expression:

\(\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}\)

Removing the division symbol

\(=\frac{16pq^3}{24p^2q^3} * \frac{p^3q^3}{2p^2q^2}\\=\frac{p^4q^6}{3p^4q^5}\\=\frac{q}{3}\)

Hence,

The pairs are:

\(\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}\) =>  \(\frac{p^2}{9q^2}\)

\(\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}\) => \(6pq^3\)

\(\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}\) => \(6p^2q^2\)

\(\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}\) => \(\frac{q}{3}\)

Answer:

I did the math there is no answer

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

Answer:

Thus at this rate, Mike would be able to finish reading the 219 novel in 10 days. Mike is right.

Step-by-step explanation:

Total number of pages of the novel = 219.

1st night, he reads 10 pages.

2nd night, he reads 13 pages.

3rd night, he reads 16 pages.

4th night he reads 19 pages.

5th night, he reads 22 pages.

6th night, he reads 25 pages.

7th night, he reads 28 pages.

8th night, he reads 31 pages.

9th night, he reads 34 pages.

10th night, he reads 37 pages.

Total number of pages read after 10 nights = 235

Thus at this rate, Mike would be able to finish reading the 219 novel in 10 days. Mike is right.

Answer:

First one is b second one is a thrid is c

Step-by-step explanation: