Suppose you and a friend are playing a game that involves flipping a fair coin 3 times. Let X = the number of times that the coin shows heads. The probability distribution of X is shown in the table.

The expected number of heads is _____.

The standard deviation of the number of heads is ____. Round to three decimal places.

The equation that represents the relationship between the number of miles to tread thickness will be y = - 0.12x + 9.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

Let 'x' be the number of miles and 'y' be the tread thickness. Then the two points are (15, 7.2) and (35, 4.8). Then the equation is given as,

(y - 7.2) = [(7.2 - 4.8) / (15 - 35)] (x - 15)

y - 7.2 = -0.12(x - 15)

y - 7.2 = - 0.12x + 1.8

y = - 0.12x + 9

The equation that represents the relationship between the number of miles to tread thickness will be y = - 0.12x + 9.

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a. The amplitude is 12m, the midline is 13m, and the period of h (t) is 16 minutes.

a. The amplitude of the height function h(t) is 12 meters (24 meters diameter / 2).

The midline of the height function is 12 meters (24 meters diameter / 2) + 1 meter (height of the platform).

The period of the height function is the time it takes for the Ferris wheel to complete one full cycle, which is 16 minutes.

b. The height function h(t) can be modeled as a sinusoidal function, where h(t) = 12 cos (2πt/16) + 13.

The cosine function models the cyclical change in height as the Ferris wheel turns.

The 2π in the argument of the cosine function represents the full revolution of the Ferris wheel, and the 16 in the argument of the cosine function represents the time it takes for the Ferris wheel to complete one revolution.

The 13 at the end of the equation is the midline of the height function, which represents the average height of the person above the ground.

c. To find the height of a person after 52 minutes, we substitute t = 52 into the height function h(t) = 12 cos (2πt/16) + 13:

h(52) = 12 cos (2π x 52/16) + 13

h(52) = 12 cos (13π) + 13

h(52) = 12(-1) + 13

h(52) = 1 meter

So, a person would be 1 meter above the ground after 52 minutes.

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Using the figure the true trigonometry statements are

A.  (sin A)² + (cos A)² = 1

C. 1/(cos A)² - (tan A)² = 1

D. (sin A)² + (cos A)² + (tan A)²  = 1/(cos A)²

A. (sin A)² + (cos A)² = 1 this is a fundamental trigonometry identity

say angle A = 30

(sin 30)² + (cos 30)² = 1

C. 1/(cos A)² - (tan A)² = 1

1/(cos A)²= 1 + (tan A)²

1/(cos A)²= 1 + (sin A)² / (cos A)²

1/(cos A)²= ((cos A)² + (sin A)²) / (cos A)²

and (cos A)² + (sin A)² = 1, hence

1/(cos A)²= 1/(cos A)² this is true

D. (sin A)² + (cos A)² + (tan A)²  = 1/(cos A)²

recall (sin A)² + (cos A)² = 1

1 + (tan A)²  = 1/(cos A)² same as line 2 in C hence this is true

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Answer:

Step-by-step explanation:

translation:  (x+4, y-6)

original    image

A(5,4)     A'(9,-2)

B(-9,6)    B'(-5,0)

C(-6,2)   C'(-2,-4)

(a) Revolving about the x-axis, the volume of the solid is 3Pi

(b) Revolving about the y-axis, the volume of the solid is 18 Pi

(c) Revolving about the line x=3, the volume of the solid is 0

(d) Revolving about the line x=6, the volume of the solid will be 32/3 Pi

The region bounded by y=x, y=0, and x=3 is a triangle in the first quadrant.

To find the volume of the solid generated by revolving this region about an axis, we can use the disk or washer method.

(a) Revolving about the x-axis:

Each cross-section of the solid perpendicular to the x-axis is a disk with radius x and thickness dx.

The volume of each disk is [tex]\pi x^2 dx[/tex].

The limits of integration are 0 and 3, the x-coordinates of the intersection points of the two curves.

Hence, the volume of the solid is

[tex]V &= \int_0^3 \pi x^2 dx\\\\\&= \left[\frac{\pi}{3}x^3\right]_0^3\\\\\&= \frac{9\pi}{3}\\\\\&= 3\pi.[/tex]

(b) Revolving about the y-axis:

Each cross-section of the solid perpendicular to the y-axis is a washer with outer radius 3 and inner radius x, and thickness dx.

The volume of each washer is [tex]\pi(3^2-x^2)dx.[/tex]

The limits of integration are 0 and 3.

Hence, the volume of the solid is

[tex]V &= \int_0^3 \pi(3^2-x^2)dx\\\\\&= \left[\pi(9x-\frac{x^3}{3})\right]_0^3\\\\\&= \pi(27-\frac{27}{3})\\\\\&= 18\pi.[/tex]

(c) Revolving about the line x=3:

Each cross-section of the solid perpendicular to the line x=3 is a washer with outer radius 3-x and inner radius 3-x-|x|, and thickness dx.

The volume of each washer is[tex]\pi((3-x)^2-(3-x-|x|)^2)dx[/tex].

The limits of integration are -3 and 3.

Hence, the volume of the solid is

[tex]V &= \int_{-3}^3 \pi((3-x)^2-(3-x-|x|)^2)dx\\\\\&= \left[8\pi\int_0^3 (3-x-|x|)dx\right]\\\\\&= 8\pi\int_0^3 (3-2x)dx\\\\\&= 8\pi\left[3x-x^2\right]_0^3\\\\\&= 8\pi(9-9)\\\\\&= 0.\\\\[/tex]

(d) Revolving about the line x=6:

Each cross-section of the solid perpendicular to the line x=6 is a washer with outer radius |3-x| and inner radius |x-6|, and thickness dx.

The volume of each washer is[tex]\pi(|3-x|^2-|x-6|^2)dx.[/tex]

The limits of integration are 0 and 3.

Hence, the volume of the solid is

[tex]V &= \int_0^3 \pi(|3-x|^2-|x-6|^2)dx\\\\\&= \left[\frac{32\pi}{3}\right]\\\\\&= \frac{32}{3}\pi.[/tex]

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Answer:

[tex]A)81x^{-12}y^{20}\\\\B)5\\\\C) x^\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]A) (3x^{-3}y^5)^4=(3)^4 \,\cdot\, (x^{-3})^4\,\cdot\,(y^5)^4=81x^{-12}y^{20}\\\\B) 5x^0=5(1)=5\\\\C) \frac{x^{\frac{5}{6} }}{x^{\frac{1}{6} }} =x^{\frac{5}{6} -\frac{1}{6} }=x^{\frac{5-1}{6} }=x^{\frac{4}{6} }=x^\frac{2}{3}[/tex]

If events A and B are independent, then they remain independent when conditioned on event C.

To prove that if events A and B are independent, then they are also independent conditioned on event C, we can use the definition of conditional probability.

Recall that two events A and B are independent if and only if P(A and B) = P(A) * P(B). And the conditional probability of A given B can be calculated as P(A | B) = P(A and B) / P(B).

It follows that P(A and B) = P(A) * P(B) if occurrences A and B are independent. Substituting this into the expression for conditional probability, we get:

[tex]P(A | B) = P(A) * P(B) / P(B) = P(A)[/tex]

Similarly, we can prove that P(B | A) = P(B). This means that the probability of A and B given event C are equal to the probabilities of A and B, respectively, given that A and B are independent. Hence, events A and B are also independent conditioned on event C

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The value of the scale factor of dilation (k) is 5/3 and the value of x is 21

The variable k is the scale factor of dilation of the triangles

This is calculated as

k = Image triangle/Pre-image triangle

Substitute the known values in the above equation, so, we have the following representation

k = 15/9

So, we have

k = 5/3

This is calculated as

x * 5/3 = 35

So, we have

x = 3 * 35/5

Evaluate

x = 21

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Answer:

14.5

Step-by-step explanation:

2.9(5)=14.5

Answer:

14.5p

here,

lets start off by looking at the full scale problem. We already know that each crate can hold 2.9 apples at a time. We also know that we have 5 crates in total.

hence,

we would multiply [tex]5(2.9)=14.5[/tex]  or  [tex]5x2.9=14.5[/tex]

Answer: 6 days

120 miles divided into 30 days is 4 miles per day.

24 miles divided by 4 miles is 6 , which means the bear spent 6 days walking along Kissimmee River.

I hope this helped & Good Luck <3 !!

The number of marshmallows and graham crackers will Janna use to make 13 s'mores is 26 and 36, the correct option is 36.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

S'mores Marshmallows Graham Crackers 4 8 12 13

Now,

8/4 = 2 Marshmallows for each S'mores,

12/4 = 3 Graham Crackers for each S'mores.

For, 13 S'mores,

2*13=26

3*13=39

Therefore, by algebra the answer will be 26 and 39.

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The statement true for A, C and E is the second statement r → p ∨ q.

Truth table is a table which describes the truth value of a complex statement regarding to the truth value of single statements.

Given is a truth table.

Consider r → p ∨ q, for the statements A, C and E.

For A, p is true and q is true, then p ∨ q is true. So r is true.

For C, p is true and q is false, then p ∨ q is true. So r is true.

For E, p is false and q is true, then p ∨ q is true. So r is true.

Hence the correct statement is r → p ∨ q.

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Answer:

2/3 x 2/3 as a fraction is 4/9.

Step-by-step explanation:

We are performing simple fractional multiplication to get the answer, i.e., 2 x 2 = 4. The numerator of the fraction is multiplied with the numerator of the other, i.e., 3 x 3 = 9.

Answer:

4/21

Step-by-step explanation:

Just line them up side by side, then multiply 2×2 and 3×7. Hope this helps

The solution is, the line of reflection is y = 1.

When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.

here, we have,

The given figure shows two triangles reflected horizontally.}

We can find the line reflection because it would be an horizontal line half way. Remember that horizontal lines have the form y = k, where k = 1 in this case,

Hence, the line of reflection is y = 1.

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The parametric equation of a line segment joining two points (x1, y1) and (x2, y2) is given by [tex]x = x1 + t(x2 - x1) and y = y1 + t(y2 - y1)[/tex].

The parametric equation of a line segment joining two points (x1, y1) and (x2, y2) is given by [tex]x = x1 + t(x2 - x1) and y = y1 + t(y2 - y1)[/tex]. Here, t is a real variable and its value lies between 0 and 1. This is because when t = 0, the equation gives the coordinates of the first point (x1, y1) and when t = 1, the equation gives the coordinates of the second point (x2, y2). For example, if the two points are (3, 4) and (7, 8), then the parametric equation of the line segment joining them can be obtained as [tex]x = 3 + t(7 - 3) = 3 + 4t and y = 4 + t(8 - 4) = 4 + 4t[/tex]. This equation can be used to easily find the coordinates of any point on the line segment joining the two points.

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The ratio of students to classrooms  is 26:1

A ratio is defined as the comparison of two or more numbers indicating their sizes in relation to each other.

It  shows how many times one number contains another.

For example, if there are 20 oranges and 15 lemons in a bowl of fruit, then the ratio of oranges to lemons is 20 to 15.

From the information given, we have that;

234 students in 9 different classrooms

The ratio of students to classrooms would be;

= 234: 9

Find the least common factor

= 26: 1

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As per compound interest, the account balance at the end of 12 years is approximately $17,217.

Compound interest is an important concept in finance and investing, and it plays a critical role in understanding how your money can grow over time. When you invest money, your initial investment earns interest, and over time, that interest can also earn interest, resulting in exponential growth.

In the context of this question, the investment into a college fund is represented by the equation

=> [tex]A = 12,000e^{0.023*12}[/tex]

where A is the amount of money in the account at the end of the time given. Let's break down the different components of this equation and see how they relate to compound interest.

First, we have the initial investment, which is not explicitly given in the equation, but we can infer that it is 12,000. This is the amount of money that is initially invested into the college fund.

Next, we have the interest rate, which is 0.023.

Finally, we have the amount of time that the money is invested, which is 12 years in this case. The longer the money is invested, the more time there is for compound interest to work its magic and grow the account balance.

Putting all of these components together, we can use the equation

=> [tex]A = 12,000e^{0.023*12}[/tex]

to calculate the amount of money in the college fund at the end of 12 years.

By plugging in the values for the initial investment, interest rate, and time, we can see that the account balance at the end of 12 years is approximately $17,217.

This represents the power of compound interest and how it can turn a modest initial investment into a substantial sum over time.

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Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

Answer:

Step-by-step explanation:

The expression for the team time is:

[tex]11\frac{3}{5} =3\frac{3}{10} +2\frac{4}{5} +2\frac{1}{10} +X\\[/tex]

Where X= Cindy's Time

Isolating X from the equation:

[tex]X=11\frac{3}{5}-(3\frac{3}{10} +2\frac{4}{5}+2\frac{1}{10})\\\\ X=11\frac{3}{5}-(8\frac{1}{5})\\ \\ X=3\frac{2}{5}[/tex]

Cindy's time was [tex]3\frac{2}{5}[/tex] minutes.

Answer:

do you have an image of the question?

The generalization suggested by these results is that as the number of contrasts increases, the multiples decrease.

a. For each of the g numbers of pairwise comparisons in the family (2, 5, and 15), the T, S, and B multiples can be calculated using the following formulas:

[tex]T = t α/2 (g-1)S = t α/2 (g-1) √2/(n-1)B = t α/2 (g-1) √(2/n)[/tex]

Where tα/2 is the t-value associated with the given family confidence coefficient (in this case, 90%) and g is the number of pairwise comparisons.

For g=2, the T, S, and B multiples are 3.078, 2.179, and 2.500 respectively. For g=5, the multiples are 2.571, 1.711, and 2.001 respectively. For g=15, the multiples are 2.228, 1.429, and 1.641 respectively.

The generalization suggested by these results is that as the number of pairwise comparisons increases, the multiples decrease.

b. For each of the g numbers of contrasts in the family (2, 5, and 15), the S and B multiples can be calculated using the following formulas:

[tex]S = t α/2 (g-1) √2/nB = t α/2 (g-1) √(2/n)[/tex]

Where tα/2 is the t-value associated with the given family confidence coefficient (in this case, 90%) and g is the number of contrasts.

For g=2, the S and B multiples are 2.179 and 2.500 respectively. For g=5, the multiples are 1.711 and 2.001 respectively. For g=15, the multiples are 1.429 and 1.641 respectively.

The generalization suggested by these results is that as the number of pairwise comparisons or contrasts increases, the multiples decrease.

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a) The result of the limit as x tends to +7/4 as required is; -∞.

b). The result of the limit as x tends to -7/4 as required is; -21/8.

Since the limit expression which is to be evaluated is; (-21x / 7 -4x).

a). Therefore, when x tends to; +7/4; we have;

= (-21 • 7/4) / ( 7 - (4• 7/4) )

= (-147/4 ) / 0

= -∞

b) When x tends to; -7/4 ; we have that;

= (-21 • -7/4) / ( 7 - (4 • -7/4) )

= ( -147/4 ) / 14

= -21 / 8.

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The mass and volume of two metals is 93.98g, 165.56g and 39.37cm3,81.89cm3.

Suppose that a finite amount of substance is there having its properties as:

mass of substance = m kg

density of substance = d kg/m³

volume of that substance = v m³

Then, they are related as:

[tex]d = \dfrac{m}{v}[/tex]

Given that;

Mass of 100cm3 of metal = 254g

Mass of b volume with 37cm3 and 64cm3 is 100g and 208g.

Now,

m=pv

254=p*100

p=2.54g/cm3

m=2.54v

Part A;

V1 =37cm3

V2=64cm3

m1= 2.54 x 37= 93.98g

m2= 2.54 x 64= 165.56g

Part B:

V1=m1/2.54 = 100/2.54 = 39.37cm3

V2=208/2.54 = 81.89cm3

Therefore, the volumes will be 39.37cm3 and 81.89cm3

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Answer:

b. 2/3

Step-by-step explanation:

8 = 4 x 2
√8 = √4 x √2

√4 = 2

√8 = 2 x √2 = 2√2

18 = 9 x 2

√18 = √9 x √2

√9 = 3

√18  = 3 x √2 =3√2

√(8/18) = 2√2 / 3√2 = 2/3

Answer:

The x-intercept is 27/8, or 3.375.

Step-by-step explanation:

0 = -8/3x + 9

-8/3x = -9

-9 * -3/8 = 27/8

x = 27/8

The cosine of the angle S is 4/5

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

The triangle

On the triangle and with the use of law of cosines, we have

cos(S) = Adjacent/Hypotenuse

This means that

cos(S) = 8/10

Simplify

cos(S) = 4/5

Hence, the solution is 4/5

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A box plot is a special type of diagram that shows the quartiles in a box and the line extending from the lowest to the highest value.

What is Box plot?

Box plots, also known as box-and-whisker plots or box-whisker plots, provide a clear pictorial representation of the distribution of the data. They also demonstrate how remote the extreme numbers are from the majority of the data. Five values are used to create a box plot: the minimum value, the first quartile, the median, the third quartile, and the maximum value. These numbers are used to gauge how closely other data points adhere to them. Use a horizontal or vertical number line along with a rectangular box to create a box plot. The axis' ends are identified by the smallest and greatest data values. The first quartile designates one end of the box, while the third quartile designates the opposite end.

The box plot distribution will demonstrate how skewed, tightly packed, and symmetrical the data are.

In the box and whisker plot:

The box's upper and lower quartiles serve as its ends, allowing it to cross the interquartile range. The vertical line inside the box denotes the median, and the two lines outside the box serve as its whiskers, extending to the highest and lowest observations.

Hence, A box plot is a special type of diagram that shows the quartiles in a box and the line extending from the lowest to the highest value.

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Answer:

2

Step-by-step explanation:

ab - 10. this means 10 is less than the product of a and b

The statement that is true about the total cost of the carpet and installation is: The total cost of the carpet and installation is $633.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To determine the total cost of the carpet and installation, we first need to calculate the area of Wendy's bedroom floor, which is:

Area = Length x Width

Area = 15 ft x 12 ft

Area = 180 square feet

We can then convert the area to square yards by dividing by 9:

Area in square yards = 180 sq ft / 9

Area in square yards = 20 sq yd

The cost of the carpet is $27.50 per square yard, so the cost of the carpet alone is:

Carpet cost = 20 sq yd x $27.50/sq yd

Carpet cost = $550

The installation cost is $4.15 per square yard, so the cost of the installation alone is:

Installation cost = 20 sq yd x $4.15/sq yd

Installation cost = $83

To find the total cost, we need to add the cost of the carpet and the installation

Total cost = Carpet cost + Installation cost

Total cost = $550 + $83

Total cost = $633

Therefore, the statement that is true about the total cost of the carpet and installation is: The total cost of the carpet and installation is $633.

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The probability of drawing the ace of spades is 1/52 for the first card and 1/51 for the second card. P(B|As) ≈ 0.1176.

The likelihood of drawing the trump card on the primary draw is for sure 1/52. Be that as it may, when the principal card is drawn, there are presently 51 cards remaining, and only one of them is the trump card. In this way, the likelihood of drawing the trump card on the subsequent draw, considering that the principal card isn't the trump card, is 1/51.

With regards to the issue, the occasion As is characterized as the trump card being picked, whether or not it is the first or second card. Since the issue determines that the two cards are drawn without substitution, there are two cases to consider: either the trump card is drawn first, with likelihood 1/52, or it is drawn second, considering that the principal card isn't the trump card, with likelihood (51/52)*(1/51) = 1/52. Accordingly, the likelihood of occasion Similar to the amount of these two probabilities, which is 1/52 + 1/52 = 1/26.

Utilizing Bayes' recipe, we have:

P(B|As) = P(As|B) * P(B)/P(As)

We previously determined P(As) to be 1/26. To ascertain P(As|B), note that in the event that the two cards are aces, the trump card should be one of them, so P(As|B) = 1. At last, to compute P(B), note that there are (4 nCr 2) = 6 methods for picking two aces out of the four in the deck, and there are (52 nCr 2) = 1326 methods for picking two cards out of the deck without substitution, so P(B) = 6/1326 = 1/221.

Subbing these qualities into Bayes' recipe, we get:

P(B|As) = 1 * (1/221)/(1/26) = 26/221 ≈ 0.1176

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