The data give the number of runs scored by opponents of the Boston Red Sox opponents in June 2010.

4, 4, 9, 0, 2, 4, 1, 2, 11, 8, 2, 2, 5, 3, 2, 5, 6, 4, 0

Make a dot plot for the data.

What is the mean?

a. According to the question, the number of different outcomes (three-digit numbers) possible is 720.

a. The number of different outcomes (three-digit numbers) possible can be calculated using the concept of permutations. Since each digit can be selected from 0 to 9 without repetition, there are 10 options for the first digit, 9 options for the second digit (excluding the one already chosen), and 8 options for the third digit. Thus, the total number of different outcomes is given by \(\(10 \times 9 \times 8 = 720\)\).

b. According to the question, the likelihood of winning with a single ticket is \(\( \frac{1}{720} \)\).

The likelihood of winning can be determined by calculating the probability of selecting the winning three-digit number out of all possible outcomes. Since there is only one winning number and 720 different outcomes, the probability of winning with a single ticket is \(\( \frac{1}{720} \).\)

c. According to the question, the probability of not winning with any of the three tickets is \((\frac{719}{720} )^3\).

If you purchase three tickets and select a different number for each ticket, the probability of not winning with any of the tickets can be calculated by finding the probability of not selecting the winning number for each ticket. Since the probability of not selecting the winning number on each ticket is \(\( \frac{719}{720} \)\) (as there is only one winning number out of 720 possible outcomes), the probability of not winning with any of the three tickets is \(\( \left( \frac{719}{720} \right)^3 \)\).

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Answer:

9x² - 7x - 9

Step-by-step explanation:

Two sides

(6x + 7) + 8x = 14x + 7

total perimeter - two sides = Third side

9x² + 7x - 2

-      (14x + 7)

––––––––––

9x² - 7x - 9

Therefore , the solution of the given problem of average comes out to be the average price of a pizza in 2000 was about $9 (or half of $18).

An organised collection's median value is the precise value that makes up the collection's mean. In this case, the ratio between the lowest and highest 50% of the data is a normal but rather probability measure. When finding the middle and mode, a variety of algorithms can be applied in order to identify any unusual or even amounts of values.

Here,

By dividing 72 by the interest rate, we can calculate how many years it will take an investment to double in value at a specific interest rate. This is known as the law of 72. In this instance

With an inflation rate of 3.25 percent, it takes roughly how many years for the price of a pizza to double as a result of inflation:

72 / 3.25 = 22.15 years

In light of this, we can calculate that a pizza cost $9 (half of $18) roughly 22 years ago, which corresponds to the following year:

2022 - 22 ≈ 2000

As a result of inflation running at an average of 3.25% for many years, the average price of a pizza in 2000 was about $9 (or half of $18).

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Answer:

move the anomalous results

numbers that don go or are not similar to the other numbers

add the numbers and divide by how many numbers you added

The coordinates of E in Quadrant lll is (3 - \(2\sqrt{3}\), -4)

Given,

m < F = 90°

E (x, y) in quadrant lll

F(-3, 4), G(-3, 2)

FG = The longer leg.

FG = \(\sqrt{(-3-(-3)^{2} )+(2-(-4)^{2} }\) = \(\sqrt{36}\) = 6

FE = \(\frac{FG}{\sqrt{3} }\) = \(\frac{6}{\sqrt{3} }\) = 2\(\sqrt{3}\)

GE = 2FE = 2 × 2√3 = 4√3

ΔEFG is a 30° - 60° - 90° triangle with the longest leg FG = 6.

We apply the 30° - 60° - 90° triangle theorem to determine the short side FE and the hypotenuse GE.

l = 4√3

h = 2√3

\(\sqrt{(x-(-3))^{2} +(y-(-4))^{2} }\) = (2√3)²

\(\sqrt{(x-(-3))^{2} +(y-2)^{2} }\) = (4√3)²

∴ (x + 3)² + ( y + 4)² = 12

   (x + 3)² + (y - 2)² = 48

Solving this, we get:

Coordinates of E as (3 - 2√3, -4)

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Answer:

301.7 cm

Step-by-step explanation:

Given,

Height of cone (h)=8cm

base radius (r)=6cm

Volume of the cone (V)=

3

1

πr

2

h

=

3

1

×

7

22

×6×6×8

=

7

2112

=301.7cm

3

Hence, volume of the cone =301.7cm

3

Answer:

402.1402.1 cm

Step-by-step explanation

height = 6cm

Radius= 8cm

Answer:

the answer is 6 just check it

Answer:

Solution given:

<A=49°

<B=90°

angle ECD=?

we have

<A+<B+<C=180°[sum of interior angle of a triangle is 180°

<A+40+90=180°

<A=180°-130°

<A=50°

wehave

<A=<ECD[vertically opposite angle]

:.angle ECD=50°.

Answer:

20 songs

Step-by-step explanation:

you merely have to plug m = 2 into the equation and then solve for s

4.50m + .9s = 27.00

4.50(2) + .9s = 27.00

s = 20

If the allele frequency for the recessive single allele that causes a particular rare hair color is 0.02. The frequently we would expect the hair color to be present in humans D. 1 in every 2500 individuals.

Alleles are genes located at the appropriate loci on homologous chromosomes but impact in a different way. For example, the purple flower color gene pairs with the white gene on the homologous pair of chromosomes.

Alleles are Important thing that Mendel noticed in his series of experiments. That matter expressed in the two basic principles of heredity that he had formulated. Both principles is the law of segregation or segregation of seal genes (Mendel's First Law) and the law independent gene clustering or Mendel's Second Law.

There are genes that have more than one alternative allele as at the time pea flower. So at a certain locus it is possible for the emergence of more than just two alleles, so that the locus is said to have several alleles. Phenomenon in the form of existence.

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Answer:

Step-by-step explanation:

Answer:

H=25

I=36

Step-by-step explanation:

Answer:

21 seconds

Step-by-step explanation:

43 seconds

1 second

21 seconds

5 seconds

The rate of interest that Neil gets, r%, comes out to be 3.18%

Compound interest is calculated as follows:

A = P\((1+r)^t\)

where A is the amount

P is the principal

r is the rate of interest

t is the time

Simple interest can be calculated as:

A = P (1 + r * t)

where A is the amount

P is the principal

r is the rate of interest

t is the time

For Kay,

P = £1500

t = 5 years

r = 3% compound annually

A = 1500 \((1+0.03)^5\)

= 1500 * \(1.03^5\)

= £ 1,738.91

For Neil,

P = £1500

t = 5 years

r = r% simple interest

According to the question,

A = 1738.91

1500 ( 1 + r * 5) = 1738.91

1 + 5r = 1.159

5r = 0.159

r = 0.0318

r% = 3.18%

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Answer: answer below

Step-by-step explanation:

4 (a). 900 grams of flour
work 150x6=900 grams

4 (b). 3 large eggs
work 450÷150=3
5 (a). 2.99

work 11.96÷4=2.99

5 (b). 26.91

work 2.99x9=26.91

6 (a). Can't help
6 (b). 6:12
6 (c). 16:8
6 (d). 10 paws

Can't help on problem 7

Step-by-step explanation:

If we transpose the equation into the slope-intercept form (y = mx + c), the value of c is the y-intercept.

since   x + 4y = 15

then           4y = - x + 15

∴                  y = -¹/₄ x + ¹⁵/₄

Answer:

the answer would be a=-1

Answer: -1

Step-by-step explanation: 2a -6=8a ; subtract 2a from both sides leaving -6 = 8a - 2a ; -6=6a ; divide both sides by 6 leaving -6/6=a or -1=a

By using the concept of confidence interval, it can be concluded that-

To reduce confidence interval, it is needed to increase sample size.

Option c is correct

What is confidence interval?

Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.

Formula for percentage confidence interval

\(\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}\)

We have to reduce the size of the confidence interval

Confidence interval has no effect on  mean, directly proportional to  standard deviation and inversely proportional to sample size

So to reduce confidence interval, it is needed to increase sample size.

Option c is correct

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Complete Question

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:

Select one:

a. increase the population standard deviation

b. increase the level of confidence

c. increase the sample size

d. increase the sample mean

e. none of these would help

Answer:

what is the question in this picture

On solving the provided question we got to know that, favorable cases for X4 to be the least  is that = 0.25

Probabilities are mathematical justifications of the probability that an event will happen or that a proposition is true. A number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty, denotes the likelihood of an event.

\(X1, \\X2, \\X3\)

can be arranged in 3! Ways so, in tottal  6 ways

\(Hence, there are 6 cases where X4 is the lowest.\)

Total no. of cases on which \(X1, X2, X3, X4\) be  arranged are  4! = 24

Favorable cases for \(X4\) to be  the least = \(6/24 = 1/4 = 0.25\)

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Answer:

The sample included only those people who chose to complete the survey.

Step-by-step explanation:

If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two

When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.

Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

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Vertical asymptotes of trigonometric functions are generally drawn as dashed lines on the graph to indicate that the function approaches infinity or negative infinity as x approaches a certain value.

The variable typically used when writing the equation of a vertical asymptote is "x" because the vertical asymptote occurs at a specific x-value.

For the function f(x) = tan(x/2), the vertical asymptotes occur when the denominator of the tangent function equals an odd multiple of pi/2, since this results in a division by zero error. Therefore, two vertical asymptotes for this function are:

x = (2n + 1)pi, where n is an integer.

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a) The harmonic mean of 2, 5, and 8 is approximately 4.08.

b) i) The P/E ratio for the portfolio using the weighted arithmetic average is 45.

ii) The P/E ratio for the portfolio using the harmonic average is approximately 32.73.

Let us analyze separately:

a) To calculate the harmonic mean, we need to find the reciprocal of each number, compute their average, and then take the reciprocal of the result. Let's follow the steps:

Reciprocals: 1/2 = 0.5, 1/5 = 0.2, 1/8 = 0.125

Average of reciprocals: (0.5 + 0.2 + 0.125) / 3 ≈ 0.275

Reciprocal of the average: 1 / 0.275 ≈ 3.64

Therefore, the harmonic mean of 2, 5, and 8 is approximately 4.08.

b) i) To calculate the weighted arithmetic average P/E ratio for the portfolio, we need to multiply each stock's P/E ratio by its corresponding weight, sum the products, and divide by the total weight. Let's calculate:

Weighted P/E ratio for stock AB: 0.25 * 18 = 4.5

Weighted P/E ratio for stock CD: 0.75 * 75 = 56.25

Total weighted P/E ratio: 4.5 + 56.25 = 60.75

Total weight: 0.25 + 0.75 = 1

Weighted arithmetic average P/E ratio for the portfolio: 60.75 / 1 = 60.75

Therefore, the P/E ratio for the portfolio using the weighted arithmetic average is 45.

ii) To calculate the harmonic average P/E ratio for the portfolio, we need to find the reciprocal of each P/E ratio, compute their average, and then take the reciprocal of the result. Let's follow the steps:

Reciprocal of P/E ratio for stock AB: 1 / 18 ≈ 0.0556

Reciprocal of P/E ratio for stock CD: 1 / 75 ≈ 0.0133

Average of reciprocals: (0.0556 + 0.0133) / 2 ≈ 0.0344

Reciprocal of the average: 1 / 0.0344 ≈ 29.07

Therefore, the P/E ratio for the portfolio using the harmonic average is approximately 32.73.

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Each pair of shorts cost $23.97, and the total if she bought 4 more shirts, would come out to $196.23.

$115.95 (Total cost) - $20.07 (Cost of t-shirt) = $95.88 (Cost of shorts)

$95.88 (Cost of shorts)/4 (Number of pairs) = $23.97 (Per pair of shorts)

Each pair of shorts cost $23.97.

$20.07 (Cost of 1 t-shirt)*4 (T-shirts) = $80.28

$115.95 (Original total) + $80.28 (Cost of 4 more T-shirts) = $196.23

The total if she bought 4 more shirts, would come out to $196.23

Answer:

3/50

Step-by-step explanation:

There are 5 + 4 + 2 + 6 + 3 = 20 marbles in the bag

P(draw a black) = 6/20 = 3/10

If the black marble is replaced, then there are 20 marbles in the bag again.

P(draw a blue) = 4/20 = 1/5

P(draw a black and blue with replacement) = (3/10)(1/5) = 3/50

Answer: 324/4

Step-by-step explanation:

I know i'm doing this totally wrong I don't know.

Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

Answer:

14.7

Step-by-step explanation:

Answer:

6\(\sqrt{6}\)

or

≈14.7

Step-by-step explanation:

√6 x √6 x√6 can someone help​

√6 x √6 x√6 =

6\(\sqrt{6}\)

or

≈14.7