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The mother will give the child $3 for each dot on the upside of the die. the greater expected value is Mother's Offer

The expected value of father's offer is $10, since the probability of getting heads is 50% and the reward for getting heads is $20.

The expected value of mother's offer is $3, since the probability of getting any number is 1/6 and the reward for getting any number is $3.

Therefore, the mother's offer has a greater expected value than the father's offer.

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The root of a tree is the vertex from which all other vertices can be reached by following edges. The root of a tree is the only vertex that does not have an incoming edge.

In a rooted tree, a vertex is called a leaf if it has no children (i.e., it does not have any edges going out from it). Internal vertices are those that have children and are connected by edges to other vertices in the tree. If a vertex d is the root of a tree, the subgraph with d as its root is defined as the set of vertices that can be reached from d by traversing its edges, as well as the edges connecting them. The root is the only vertex that does not have an incoming edge, and all other vertices can be reached from the root.

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Answer:

The width of the rectangle is 32cm and the length is 37cm.

Step-by-step explanation:

The graph of the polynomial is given below.

The interval of the polynomial is

(-∞, 3) U (-3, -1) U (-1, ∞).

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

f(x) = x³ + 4x² + 3x

The graph of this polynomial is given below.

The interval of the graph are:

(-∞, 3) U (-3, -1) U (-1, ∞)

Thus,

The graph is given below.

The interval of the graph is (-∞, 3) U (-3, -1) U (-1, ∞).

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Answer:

See Attached Images

Step-by-step explanation:

First, draw the lines without < or > signs, just use equals signs:

3x + y = -3

y = -3x - 3 (slope of -3, y-intercept at (0,-3) )

x + 2y = 4

2y = -x + 4

y = -(1/2)x + 4

Now shade the region above and including line (1) and below and including line (2).

Note for similair problems: If you have to multiply or divide by a negative number when solving for y, remember to flip the < or > sign to the other one when determining where to shade on the graph.

The sum of geometric series is 12.34 and the series is converges

According to the question,

Geometric series is  100/81 + 10/9 + 1 + 9/10 + 81/100 + 729/1000 + . . .

The given series looks like to be in geometric progression with constant ratio r

r = 2nd term/1st term = a2/a1

= (10/9) / (100/81)

=> 9/10

We know that if the ‘r’ is less than 1 then it is convergent

Here 9/10 < 1, it is convergent.

Clearly, this is the sum of an infinite geometric series.

Sum of infinite series in GP = a/(1 - r)

Where a is the first term, 9/10 is the common ratio.

Sum of the geometric series = (100/81) / (1 - 9/10)

=> (100 / 81) / ( 1 / 10)

=> 100 / 8.1

=> 12.34

Therefore, the given series is convergent and its sum is 12.34

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Answer:

16

Step-by-step explanation:

2 × | 6 + 2 |

= 2 × | 8 |

= 2 × 8

= 16

Using the Law of Sines, we get an angle of 2.41 degrees and no triangles are produced.

Option (C) is the correct one.

Given, Two sides and an angle are given below.

we have to determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all.

If b = 5, c = 6 and B = 20 degrees in the triangle.

On using the concept of Laws of Sines, we get

sinA/a = sinB/b = sinC/c

sin 20°/5 = sin C/6

0.34/5 = sin C/6

0.007 = sin C/6

sin C = 0.042

C = 2.41

So, the angle C be 2.41 degrees.

which implies that no triangle can be formed or produced with the given data of the triangle.

Hence, No triangles are produced.

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On solving the provided question we can sat that, the geometric series' total is 12.34, and they care convergent.

An infinite series in mathematics known as a geometric series has the formula a + ar + ar2 + ar3 +, where r is referred to as the common ratio. One straightforward illustration is the geometric series with a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, totaling 2 (or 1 if the first term is locked out).

The answer to the query is

The geometric series is made up of the numbers 100/81, 10/9, 1, 9/10, 81/100, 729/1000, and so on.

The provided series appears to be moving forward geometrically with a fixed ratio r.

r = second term, first term, or a2, a1.

[tex]= (10/9) / (100/81)[/tex]

[tex]= > 9/10[/tex]

We are aware that convergence occurs when 'r' is smaller than 1.

In this case, 9/10 1 is convergent.

This sums up an endless geometric sequence, without a doubt.

Infinite series' sum in GP equals a. (1 - r)

The usual ratio is 9/10, where an is the first word.

The geometric series' sum is equal to (100/81) / (1 - 9/10).

[tex]= > (100 / 81) / ( 1 / 10)\\ = > 100 / 8.1\\ = > 12.34[/tex]

The given series is therefore convergent, and its total is 12.34.

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The derivative of y = 5ˣ + e⁷ is 5ˣ ln 5.

What is derivative?

dy/dx = d(5ˣ + e⁷) / dx

= 5ˣ ln 5 + 0

= 5ˣ ln 5

e⁷ is constant with respect to x , the derivative of e⁷ with respect to x is 0.

Hence, the derivative of y = 5ˣ + e⁷ is 5ˣ ln 5.

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Postage of the total cards is 20(.17w + .44) = 15.60 (word problem)

given, total no of cards = 20

cost of each card = .44

additional cost for each ounce = .17

total cards = 20(.17w + .44) = $15.60

Word Problems:

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For the given height and distance  the answer of the following questions are:

a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.

b. Change in the angle of elevation is equal to 0.144rad/sec.

As given in the question,

Let 'α' be the angle of elevation

'h' be the height of the rocket

'x' be the distance between the camera and the rising rocket.

a. Relation between x , h, and 4000 ft during launching pad is given by Pythagoras theorem:

x² = h² + 4000²

Differentiate with respect to time 't' we get,

2xdx/dt = 2hdh/dt + 0 __(1)

When h = 3000ft

x² = 3000² + 4000²

⇒x = 5000ft

dh/dt = 900ft/s

Substitute all values in (1) we get,

2(5000)dx/dt= 2(3000)(900)

⇒dx/dt = 5,400,000/ 10,000

⇒dx/dt = 540ft/sec.

b. tanα = h/4000 __(2)

when h = 3000ft

tanα = 3/4

⇒α = 0.6435

Differentiate (2) with respect to t we get,

sec²α dα/dt = (1/4000) dh/dt

⇒sec²(0.6435) dα/dt = (1/4000)(900)

⇒dα/dt = (0.225)/ 1.5625

⇒dα/dt = 0.144 rad/ sec.

Therefore, for the given height and distance the answer of the following questions are:

a. Change in distance between the camera to the rocket at that moment is equal to 540ft/sec.

b. Change in the angle of elevation is equal to 0.144rad/sec.

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Answer: In the below pic attached

Answer:

2(x + 1)

Step-by-step explanation:

x is the unknow number.  Add 1 to that and then take that expression (x+1) and multiply it by 2.

Answer: The difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.

Step-by-step explanation:

To find the difference in minutes between 2 hours 35 minutes and 1 3/4 hours, we can first convert 1 3/4 hours to minutes.

There are 60 minutes in 1 hour, so 1 3/4 hours is equal to 1 + 3/4 = 1 3/4 hours = 1.75 hours.

Since there are 60 minutes in 1 hour, 1.75 hours is equal to 1.75 * 60 = 105 minutes.

Then, we can subtract 105 minutes from 2 hours 35 minutes to find the difference in minutes:

2 hours 35 minutes - 105 minutes = 135 minutes - 105 minutes = 30 minutes

So, the difference in minutes between 2 hours 35 minutes and 1 3/4 hours is 30 minutes.

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There are four possible  values of C if there exist distinct complex numbers.

A complex number is an element of a number system that extends the real numbers with a specific element denoted i is called the imaginary unit . the equation every complex number can be expressed as,

             a + bi

where a and b are real numbers.

Let p(z) denote the cubic on the left-hand side; the right-hand side is then c3p(z/c). Write p(z)=z3+Az2+Bz+C so

z3 + Az2 + Bz + C ≡  z3+ cAz2 + c2Bz + c3C

⟹ (c−1)A =  (c2−1)B = (c3−1)C = 0.

Solving this we can find the possible values of C.

A real number can be said as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. continuous means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion.

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Question is incomplete. The complete question is:

Let c be a complex number. Suppose there exist distinct complex numbers r, s, and t such that for every complex number z, we have

    (z−r) (z−s) (z−t) = (z−c r) (z−c s) (z−c t).

Compute the number of distinct possible values of c.

The percentage of total variation in the dependent variable that is described by the independent variable is expressed by coefficient of determination . So, correct answer is option (a).

The coefficient of determination R² is equal to the square of the correlation coefficient, r² expressed as a percentage, represents the percentage of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line. Coefficient of determination is a statistical measure that examines how differences in one variable can be explained by differences in her second variable. In other words, this coefficient, commonly known as R-squared (or R²), measures how strong the linear relationship between two variables is. This coefficient is commonly known as the R-square (or R²) and is sometimes called the "goodness of fit". This measurement is expressed as a value between 0.0 and 1.0..

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Refer to the photo taken. Please rate :)

The Time taken for David and Amy to be exactly 23 miles apart is 1.014 Hours.

Let [tex]t[/tex] be the time taken to reach 23 miles apart from a single point.

David and Amy start at same point and move towards different directions, making them move at perpendicular to each other.

According to Pythagoras theorem, and distance = Speed x time.

[tex](17t)^2 + (15t)^2 = 23^2[/tex]

[tex]289t^2 + 225t^2 = 529[/tex]

[tex]\therefore 514t^2 = 529[/tex]

[tex]t^2 = \frac{529}{514}[/tex]

[tex]t^2 = 1.029[/tex]

[tex]\therefore t = \sqrt{1.029} = 1.014 \text{ hours}[/tex]

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The answer is 53

It is the process of substituting values of individual respective variables and solving using elementary arithmetic operations.

Given here, the expression as 8 - (m/n) + p² & substituting  the values as m=8 , n=2 , p=7 we get

8- 8/2 + 7² = 8-4+53

                  = 53

Hence, the final answer is equal to 53

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The probabilities, using the Poisson distribution, are given as follows:

11. A shark attack next year: 0.038.

12. More than one shark attack next year: 0.001.

13. At least one shark attack in the next 100 years: 0.982.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Considering that there have been 8 attacks in 200 years, the mean for n years is given as follows:

[tex]\mu = \frac{8n}{200}[/tex]

Hence the probability of one shark attack in the next year(n = 1, mean = 0.04) is given as follows:

[tex]P(X = 1) = \frac{e^{-0.04}(0.04)^{1}}{(1)!} = 0.038[/tex]

The probability of more than one shark attack is obtained as follows:

P(X > 1) = 1 - P(X ≤ 1)

In which:

P(X ≤ 1) = P(X = 0) + P(X = 1).

Then:

Thus:

P(X > 1) = 1 - (0.961 + 0.038) = 0.001.

For 100 years, the mean is of:

100 x 8/200 = 4.

Thus the probability of at least one attack is of:

P(X > 0) = 1 - e^(-4) = 0.982.

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The probability of selecting a student that drink both coffee and tea is

1/10.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

From the algebra of sets, we know n(A∪B) = n(A) + n(B) - n(A∩B).

A university polls 200 students. 80 students drink tea, 140 drink coffee, and 30 drink neither.

Therefore,

200 = 140 = 80 - N(A∩B).

200 = 220 - N(A∩B).

N(A∩B) = 20.

So, out 0f 200 students 20 drink both.

Therefore the probability of students drink both is,

= 20/200.

= 1/10.

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Answer:

(10 * 312) + (10 * 612) + (10 * 812)

Step-by-step explanation:

To find the total amount of shampoo that Christa purchased in ounces, we can use the expression (10 * 312) + (10 * 612) + (10 * 812), which is equivalent to the expression that Christa used. This expression is also equivalent to 3120 + 6120 + 8120, which can be simplified to 3120 + 6120 + 8120 = 3120 + 6150 + 8100 = 9280 + 6150 = 15,430. Therefore, the expression (10 * 312) + (10 * 612) + (10 * 812) is equivalent to 15,430.

The value of c in the interval (-4 , -3) is -√12 such that f'(c) = 0 as

f'(-√12) = 0, so c = -√12.

Given, the function below satisfies Rolle's Theorem on the specified interval.

we have to find the value of c in the interval (-4 , -3) such that

f'(c) = 0.

the function given is,

f(x) = x + 12/x

First we have to find the derivative of the given function f(x).

f(x) = x + 12/x

f'(x) = 1 - 12/x²

Now, equating the derivative with 0 we get

f'(x) = 0

1 - 12/x² = 0

1 = 12/x²

x² = 12

x² - 12 = 0

(x + √12)(x - √12) = 0

x = √12 or x = -√12

we have two values of x be, ±√12.

but only -√12 lie in the interval (-4 , -3).

So, the value of c be -√12.

Hence, the value of c be -√12.

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The correct equation is t = 5 seconds.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Let me mention first that there is an error in the statement that the gravitational pull of the Earth is 16 ft/s^2. It is in fact 32 ft/s^2, and the actual equation uses half of the acceleration multiplied by the square of the variable time, so it gives as final expression :

y(t) = -16t² + 0t + 400

and we want to find the value/s for "t" that make this equation equal zero (when it reaches the ground and the object just touches the ground. This makes the equation we want to solve:

0 = -16t² + 0t + 400

16t² + 0t - 400 = 0

which solving for "t" becomes:

16t² - 400 = 0

16t² = 400

t² = 25

t = √25

t = ± 5

So we adopt the positive answer (positive time) since the negative value has no physical meaning for this problem.

That is: t = 5 seconds

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Using the Normal Distribution , the probability of landing in the circle on ground 10 times or less is 85.32 % , the correct option is (d) None of these   .

The term Normal Distribution is defined as a continuous probability distribution where the values lie in a symmetrical fashion mostly situated around mean .

it is given that ,probability(p) of landing marble on ground is 25% = 0.25

game is played for 30 rounds (n) = 30 ; q = 1 - 0.25 = 0.75 .

we know the mean (μ) = n×p = 30 × 0.25 = 7.5  ;

the standard deviation is (σ) = √n×p×q = √30×0.25×0.75  

= √5.625 = 2.38

By using Normal Distribution , X follows N(μ,σ²)

that is X follows N(7.5 , 2.38²) ;

we have to find P[X<10] = P[ (x-μ)/σ < (10 - 7.5)/2.38]

= P[ z < 2.5/2.38] = P[ z < 1.05 ] = 0.85314094 = 85.32 %

Therefore , the required probability is 85.32 %  .

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Answer:GIVE A BETTER DETAILED QUESTION sorry for caps

Step-by-step explanation:

The area of a rhombus is --336[tex]in^{2}[/tex]

A rhombus is a type of parallelogram where all the sides are equal in length. opposite sides of a rhombus are parallel to each other and opposite angles are equal.

The diagonals of a rhombus bisect each other at the right angle.

let, another diagonal of a rhombus is -b in

another diagonal of a rhombus, b = [tex]\sqrt{4x^{2} -a^{2} }[/tex]

                  = [tex]\sqrt{4*25^{2} - 14^{2} }[/tex]

                  =[tex]\sqrt{4*625 - 196}[/tex]

                  =[tex]\sqrt{2500 - 196}[/tex]

                 = [tex]\sqrt{2304}[/tex]

                 = 48 in

Area of the rhombus (A) = [tex]\frac{a * b }{2}[/tex]

                                       = [tex]\frac{14 * 48 }{2}[/tex] [tex]in^{2}[/tex]

                                       = 7 * 48 [tex]in^{2}[/tex]

                                      = 336 [tex]in^{2}[/tex]

The area of a rhombus is --336[tex]in^{2}[/tex]

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The lengths of the sides of the quadrilateral are:

WX = 7 units

XY = 11 units

YZ = 7 units

WZ = 11 units

A quadrilateral is any polygon that has four sides and four interior angles.

Part A: The quadrilateral WXYZ has the following vertices,

W(-4, 5)

X(3, 5)

Y(3, -6)

Z(-4, -6)

Each of these vertices of quadrilateral WXYZ have been plotted in the graph that is attached below (see attachment).

Part B: To find the length of each of the sides of the quadrilateral, count the number of square boxes between two points on the graph, given that a square is equal to 1 unit.

Length of WX = 7 boxes = 7 units

Length of XY = 11 boxes = 11 units

Length of YZ = 7 boxes = 7 units

Length of WZ = 11 boxes = 11 units

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Answer:

.5648

Step-by-step explanation:

i am good at math :)

Answer:

= 56 + 0.048

= 56.048

Step-by-step explanation:

560 tenths + 48 thousandths

= 560 × 0.1 + 48 × 0.001

= 56 + 0.048

= 56.048

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