Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. A) Find the expected number of games that are played when (a) i= 2 and (b) i= 3. B) Find P(X = 4).

Answer:

3.75 minutes

Step-by-step explanation:

For every 2/3 minutes, Aaron's Tire loses 8/9 of a liter of air

Total Volume of Air in the Tyre = 5 liters

Now, we divide the total volume by volume of air lost every stated interval to know how many air loss it will take the Tyre to be empty

[tex]\dfrac{5}{8/9} =\dfrac{5X9}{8} =\dfrac{45}{8}[/tex]

Then, to get when the tire will be completely flat in:

[tex](\frac{2}{3}X\frac{45}{8}) minutes[/tex]=3.75 minutes=3 minutes 45 seconds

The tyre will be empty in 3 minutes 45 seconds

Answer:

Yes.

Step-by-step explanation:

A prime number is a number that is ony divisible by itself and 1.

2 is only divisible by 2(=1) and 1 (=2)

Answer:

YES

Step-by-step explanation:

PRIME NUMBERS A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. ... The number 1 is neither prime nor composite.

Answer:

a. Blank time = 7:12 am

b. Blank Minutes = 30 minutes

Step-by-step explanation:

The individual got downstairs 25 minutes after 6:47am

Hence Blank time = 6:47am + 25 minutes = 7:12 am

To calculate amount of blank minutes he spent reading books

7:42am - 7:12am = 30 minutes

Geometry (like any other branch of math) starts from a set of statements that we assume to be true, which we call axioms.

Then, we declare some rules that allow us to deduce true things from true things. For example, syllogism is one of this rules. So, if we know that [tex]A[/tex] is true, and it is also true that [tex]A\implies B[/tex], then we're allowed to deduce that [tex]B[/tex] is true as well.

So, the purpose of a proof is to show that a certain statement is true.

In its structure, you'll always start from some true facts, and you'll deduce new true facts by using allowed deductive methods.

In Geometry, a proof is used to demonstrate the validity of a statement or theorem. A proof consists of a statement, diagram, given conditions, logical reasoning, and a conclusion. It provides a convincing and rigorous argument.

Purpose of a proof in Geometry

In Geometry, a proof is used to demonstrate the truth or validity of a statement or theorem. It provides a logical and systematic argument, using previously established statements (called axioms or postulates) and mathematical reasoning, to support the conclusion.

The main purpose of a proof is to build a convincing and rigorous argument, ensuring that the result can be trusted and applied in various mathematical contexts.

Structure of a proof in Geometry

A proof in Geometry typically consists of several components:

Answer:

1. Exponential

Step-by-step explanation:

The simplest RC-Circuit, that is, a capacitor and a resistor in a series configuration can be modeled by using Ohm's Law and Kirchhoff's Circuit Laws:

[tex]C \cdot \frac{dV}{dt} + \frac{V}{R} = 0[/tex]

By rearranging the formula, an homogeneous linear first-order differential equation is found:

[tex]\frac{dV}{dt} + \frac{1}{R \cdot C} \cdot V = 0[/tex]

Whose solution has the form of a exponential model:

[tex]V(t) = V_{o} \cdot e^{-\frac{t}{R \cdot C} }[/tex]

Answer:

The person will feel dizzy.

Answer:

Step-by-step explanation:

The person will feel energetic because the heart rate will increase. ... The heart will pump less blood per beat because the blood vessels will have less blood to circulate.

Answer:

26.9 degrees to the nearest tenth.

Step-by-step explanation:

The height  = opposite side and length of the shadow = the adjacent side, so we use the tangent function.

If the angle of elevation  is x degrees, then

tan x = 38/75

x =  26.9 degrees.

Option B: 5 is the value of f(3)

Explanation:

The equation of the piecewise function is given by

[tex]f(x)=\left\{\begin{aligned}-x^{2}, & x<-2 \\3, &-2 \leq x<0 \\x+2, & x \geq 0\end{aligned}\right.[/tex]

We need to find the value of [tex]f(3)[/tex]

The value of the function f can be determined when [tex]x=3[/tex] by identifying in which interval does the value of [tex]x=3[/tex] lie in the piecewise function.

Thus, [tex]x=3[/tex] lies in the interval [tex]x\geq 0[/tex] , the function f is given by

[tex]f(x)=x+2[/tex]

Substituting [tex]x=3[/tex] in the function [tex]f(x)=x+2[/tex], we get,

[tex]f(3)=3+2[/tex]

[tex]f(3)=5[/tex]

Thus, the value of [tex]f(3)[/tex] is 5.

Therefore, Option B is the correct answer.

Answer: the computer towers will be worth $10521 after 8 years

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the computer towers after t years.

t represents the number of years.

P represents the initial value of the computer towers.

r represents rate of decay.

From the information given,

P = $30900

r = 12.6% = 12.6/100 = 0.126

Therefore, the function that models the value of the computer towers after (t)years from now is

A = 30900(1 - 0.126)^t

A = 30900(0.874)^t

Therefore, when t = 8 years, then

A = 30900(0.874)^8

A = $10521

Answer:

  64 ft

Step-by-step explanation:

The equation can be factored as ...

  s = -16t(t -4)

This is the equation of a downward-opening parabola with t-intercepts of 0 and 4. The maximum height is at the vertex, halfway between those values, at t=2. At that time, the height is ...

  s = -16(2)(2-4) = 64 . . . . feet

The maximum height is 64 feet and it occurs at 2 seconds.

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables. There are different types of polynomials such as linear, quadratic, cubic, etc.

A quadratic equation is of degree two and it has only two solution.

Given that  s= -16t²+64t

The maximum height is at ds/dt = 0

Hence:

ds/dt = -32t + 64

-32t + 64 = 0

32t = 64

t = 2 seconds

The maximum height is at 2 seconds, hence:

Maximum height = -16(2)² + 64(2) = 64 feet

The maximum height is 64 feet and it occurs at 2 seconds.

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Since [tex]\alpha[/tex] lies in quadrant II and [tex]\beta[/tex] lies in quadrant IV, we expect [tex]\sin\alpha>0[/tex], [tex]\cos\alpha<0[/tex], and [tex]\sin\beta<0[/tex].

Recall the Pythagorean identities,

[tex]\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x[/tex]

It follows that

[tex]\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}[/tex]

[tex]\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}[/tex]

[tex]\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45[/tex]

Recall the angle sum identity for sine:

[tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha[/tex]

So we have

[tex]\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}[/tex]

The value of sin(α+β) is 56/65

Given the following parameters

tan α = -12/5 = opposite/adjacent

Determine the hypotenuse using Pythagoras theorem:

hyp² = 12² + 5²

hyp² = 144 + 25

hyp² = 169

hyp = 13

Determine the value of  sin α and cos α

sin α = opp/hyp

sin α = 12/13

cos α = adj/hyp = -5/13

Similarly if cosβ=3/5 = adj/hyp

opp^2 = 5^2 - 3^2

opp^2 = 16
opp = 4

sin β = opp/hyp = -4/5

Determine the value of sin(α+β)

sin(α+β) = sinαcosβ + cosαsinβ

sin(α+β) = 12/13(3/5) + (-5/13)(-4/5)

sin(α+β) = 56/65

Hence the value of sin(α+β) is 56/65

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Answer:

No

Step-by-step explanation:

I think your full question is attached in this photo

My answer:

No, because the expression does not involve a quotient

When one number dividend is divided by another number divisor, the result obtained is known as Quotient. I dont see the result in his expression

Answer:

[tex]3\frac {6}{25} hrs \ or \ 3 hrs\ 14 mins \ 24 sec[/tex]

Step-by-step explanation:

The question calls requires one to get the product of the given time. Since first debate lasted for :

[tex]1\frac {4}{5} \ hrs[/tex]

-and the second lasted

[tex]1\frac {4}{5} hrs[/tex] times more than the first then the second took then the first step will involve converting the mixed fractions into improper fraction which will be:

[tex]\frac {9}{5}[/tex]

-Now multiplying

[tex]\frac {9}{5}\times\frac{9}{5}\\\\=\frac{81}{25}=3\frac{6}{25}[/tex]hrs

The values of x that make the inequality x > 1/2 true are Choice A (2 1/3) and Choice D (1).

The inequality x > 1/2 means that we are looking for any values of x that are greater than 1/2. Looking at our choices, Choice A (2 1/3) and Choice D (1) are correct since these values are greater than 1/2. Choices B (0), C (-1 1/2) and E (-3/4) are all less than 1/2, so they do not make the inequality true.

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Answer:

Thus he was able to save 4.438 dollars by paying 30 days before due.

Step-by-step explanation:

given that Mr. Davis borrowed $600 for 60 days at 9% annual interest.

Thus interest payable for 60 days = [tex]\frac{600*60*9}{365*100} \\=8.876[/tex]

Because he paid fully after 30 days his interest would have been only for 60 days

or half of interest for 60 days

So savings of interest = 50% of 8.876

=4.438 dollars

Thus he was able to save 4.438 dollars by paying 30 days before due.

Answer:

1215

Step-by-step explanation:

Using the Binomial theorem

With coefficients obtained from Pascal's triangle for n = 6, that is

1  6  15  20  15  6  1

and the term 3x decreasing from [tex](3x)^{6}[/tex] to [tex](3x)^{0}[/tex]

and the term - y increasing from ([tex](-y)^{0}[/tex] to [tex](- y)^{6}[/tex]

Thus

[tex](3x-y)^{6}[/tex]

= 1 × [tex](3x)^{6}[/tex] [tex](-y)^{0}[/tex] + 6 × [tex](3x)^{5}[/tex] [tex](-y)^{1}[/tex] + 15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex] + .........

The term required is

15 × [tex](3x)^{4}[/tex] [tex](-y)^{2}[/tex]

= 15 × 81[tex]x^{4}[/tex] y²

with coefficient 15 × 81 = 1215

that is 1215[tex]x^{4}[/tex]y²

Answer:

25 and 21 hours respectively

Step-by-step explanation:

Let the number of hours worked by each welder be x and y respectively.

They worked a total of 46 hours. This means :

x + y = 46 hours.......(I)

Now, given their hourly charges, since we have the total amount of money realized, we can make an equation out of it. This means:

34x + 39y = 1669........(ii)

We then solve both simultaneously. From I, x = 46 -y

We can substitute this into ii

34(46 -y) + 39y = 1669

1564 -34y + 39y = 1669

5y = 1669 - 1564

5y = 105

y = 105/5 = 21

x = 46 - y

x = 46 - 21 = 25 hours

The numbers of hours worked by the welders are 25 and 21 respectively

Final answer:

To determine the hours worked by each welder, we set up two equations based on their hourly rates and solve them. A system of equations is used to find that each welder worked 23 hours, each earning $782, summing to the total earnings of $1669.

Explanation:

To solve the problem of how many hours each welder worked, we need to set up two equations based on the given information. Let's designate x as the number of hours the first welder worked, and y as the number of hours the second welder worked. The first welder's rate is $34 per hour, and the second welder's rate is $39 per hour. We know that x + y = 46 because together they worked a total of 46 hours. We also have the total earnings equation, which is 34x + 39y = $1669.

We can now solve these equations using substitution or elimination. For instance, if we solve the first equation for x, we get x = 46 - y. Substituting this into the second equation gives us 34(46 - y) + 39y = $1669. After distributing and combining like terms, we can find the value for y, and then substitute back to find x.

After solving, we would find that the first welder worked 23 hours and the second welder worked 23 hours as well. Each welder earned $782, which adds up to the total earnings of $1669.

Answer:

Step-by-step explanation:

Use the given equation, and use your understanding of quadratic functions to reason about the solution.

  R = xp

  R = (1500 -100p)p . . . . . substitute the given expression for x

This is q quadratic function in p. It has zeros where p=0 and p=15. (These are the values that make the factors be zero.) We know this function has a maximum (because we're told to find it, and because p^2 has a negative coefficient). That maximum is the vertex of the parabola, which is located on the line of symmetry, halfway between the zeros.

The maximum revenue is obtained when p = (0+15)/2 = 7.5. That value of revenue is R = (1500 -100·7.5)(7.5) = 5625.

The price $7.50 will yield the maximum revenue, $5625.

To find the price that will bring in the maximum revenue, substitute the given equation for x into the revenue equation. Use calculus to find the value of p that yields the maximum revenue. Substitute the value of p into the revenue equation to find the maximum revenue.

To find the price that will bring in the maximum revenue, we need to determine the value of p that maximizes the revenue function R = xp. We can substitute the expression for x into the revenue function to get R = (1500 - 100p)p. To find the p that yields the maximum revenue, we can use calculus by finding the critical points of the revenue function. Taking the derivative and setting it equal to zero, we can solve for p. After finding the value of p, we can substitute it back into the revenue function to find the maximum revenue.

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Answer: angle w = 154 degrees

v = 45 degrees

Step-by-step explanation:

Let w represent the measure of angle W.

Let v represent the measure of angle V.

The measure of angle W is 19 degrees more than three times the measure of angle V. This is expressed as

w = 3v + 19

if the sum of the measures of the two angles is 199 degree, it means that v + 3v + 19 = 199

4v = 199 - 19

4v = 80

v = 180/4 = 45

w = 3v + 19 = (3 × 45) + 19

w = 154

Answer:

The answer to your question is below

Step-by-step explanation:

Data

                            x² + 3x + 5

Factor

- Solve using the formula

                     x = -b ±[tex]\sqrt{b^{2} -4 ac} / 2a[/tex]

- Substitution

                     x = -3 ± [tex]\sqrt{3^{2} - 4(1)(5)} /2[/tex]

- Simplification

                     x = -3 ± [tex]\sqrt{9 - 20} / 2[/tex]

                     x = -3 ± [tex]\sqrt{-11} / 2[/tex]

- Result

       x₁ = -3+[tex]\sqrt{11} i / 2[/tex]                    x₂ = - 3 - [tex]\sqrt{11} i[/tex] / 2

The table represents an exponential function, and the function formula is: [tex]\[ y = 3 \cdot 2^x \][/tex]

To determine whether the table represents a linear or an exponential function, we need to examine the rate of change in the `y` values as `x` increases.

For a linear function, the rate of change (the difference between one `y` value and the next) is constant.

For an exponential function, the rate of change is multiplicative – the `y` value is multiplied by a constant factor as `x` increases by a regular increment.

Looking at the provided table:

- When `x` increases by 1 (from 0 to 1, from 1 to 2, etc.), the `y` values are:

 - At `x=0`, `y=3`

 - At `x=1`, `y=6`

 - At `x=2`, `y=12`

 - At `x=3`, `y=24`

 - At `x=4`, `y=48`

 - At `x=5`, `y=96`

 - At `x=6`, `y=192`

 - At `x=7`, `y=384`

Each time `x` increases by 1, `y` is doubled. This is a characteristic of an exponential function.

The pattern suggests that `y` is being multiplied by 2 as `x` increases by 1. Therefore, we can express the function as:

[tex]\[ y = ab^x \][/tex]

where `a` is the initial value of `y` when `x` is 0 (which is 3 in this case), and `b` is the factor by which `y` is multiplied each time `x` increases by 1 (which is 2 in this case).

So the exponential function that fits the table is:

[tex]\[ y = 3 \cdot 2^x \][/tex]

Thus the table represents an exponential function, and the function formula is:

[tex]\[ y = 3 \cdot 2^x \][/tex]

Answer:

log 2 ( 128 ) = x So C.

Step-by-step explanation:

The second matrix [tex]\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex] represents the triangle dilated by a scale factor of 3.

Step-by-step explanation:

Step 1:

To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.

The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.

Step 2:

If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get

[tex]\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right][/tex]

The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.

Step 3:

The matrix that represents the triangle after dilation is given by

[tex]3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex]

This is the second option.

Answer:

Step-by-step explanation:

You can use the cosine rule to solve this problem:

cos(∠KLJ) = (KL² + JL² - KJ²)/(2*JL*KL) = 21463/21960 = 0.97737

∠KLJ = cos⁻¹(0.97737) = 12.2°

Answer:

Step-by-step explanation:

We would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes

JL² = JK² + KL² - 2(JK × KL)CosK

122² = 39² + 90² - 2(39 × 90)CosK

14884 = 1521 + 8100 - 2(3510)CosK

14884 = 9621 - 7020CosK

7020CosK = 9621 - 14884

7020CosK = - 5263

CosK = - 5263/7020

CosK = - 0.7497

K = Cos^- 1(- 0.7497)

K = 138.6° to the nearest tenth

The possible length of the third side of a triangle with sides of 27 m and 11 m, as per the Triangle Inequality Theorem, ranges between 16 m and 38 m.

In mathematics, the possible length of the third side of a triangle, given the other two sides, is determined using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute value of the difference between those two sides.

Given side lengths of 27 m and 11 m, the possible length of the third side (let's call it 's') is between 27 m - 11 m and 27 m + 11 m.

Therefore, s > 16 m and s < 38 m. So, any value between 16 m and 38 m could be the length of the third side of the triangle.

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Answer:

x^3-6x^2+18x-10

Step-by-step explanation:

(f-g) (x) =f(x) - g(x) =

x^3-2x^2+12x-6-(4x^2 - 6x+4)=

x^3-2x^2+12x-6-4x^2+6x-4=

x^3-6x^2+18x-10

Answer:

Solution given:

f(x)=x3−2x2+12x−6

g(x)=4x2−6x+4

now

(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4

=x³-6x²+18x-10

Asuming the added image is part of the complete question...

Answer:

C) rectangle C

Step-by-step explanation:

Observing the image we can see that when the rectangle C is reflected across the x-axis and then moved up 2 units, it will land exactly where the rectangle E is.

I hope you find this information useful and interesting! Good luck!

Answer:

C) Triangle C.

Step-by-step explanation:

The triangle C satisfies all the conditions described in the statement.

Answer:

  ACDBA, $900

Step-by-step explanation:

The cheapest route will be the one with the lowest cost. Of the routes listed, the cost $900 is the lowest, so route ACDBA is the cheapest.

_____

The "Brute Force Method" requires you compute the costs of the possible routes and pick the lowest. The answer choices have done that for you.

The cost of ACDBA is AC +CD +DB +BA = 240 +230 +210 +220 = 900, as shown in the answer selections.

The three routes listed, and their reverses (which are the same cost), are the only possible routes starting and ending at A.

Answer:

A candy costs $6.75 and a bag of popcorn costs $7.25

Step-by-step explanation:

Let the cost of one 1 candy=$x

Let the cost of one bag of popcorn=$y

Now, Total Cost Per Item=Number of Item Bought X Price Per Unit Item.

If Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars.

4x+10y=99.50

Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars.

3x+5y=56.50

Solving the two equations simultaneously

4x+10y=99.50    (I)

3x+5y=56.50     (II)

Multiply Equation (I) by 3 and Equation (II) by 4 to eliminate x

12x+30y=298.5

12x+20y=226

Subtracting

10y=72.5

y=$7.25

Now, from (II)

3x+5y=56.50

3x+5(7.25)=56.50

3x+36.25=56.50

3x=20.25

x=20.25/3=$6.75

Therefore a candy costs $6.75 and a bag of popcorn costs $7.25

Answer:

candy costs - $6.75

a bag of popcorn costs - $7.25

Step-by-step explanation:

Answer:

There is no significant improvement in the scores because of inserting easy questions at 1% significance level

Step-by-step explanation:

given that Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students.

Set up hypotheses as

[tex]H_0: \bar x= 100\\H_a: \bar x >100[/tex]

(right tailed test at 1% level)

Mean difference = 104-100  =4

Std error of mean = [tex]\frac{\sigma}{\sqrt{n} } \\=3[/tex]

Since population std deviation is known and also sample size >30 we can use z statistic

Z statistic= mean diff/std error = 1.333

p value = 0.091266

since p >0.01, we accept null hypothesis.

There is no significant improvement in the scores because of inserting easy questions at 1% significance level

Final answer:

Using a one-tailed test with α = .01 and the provided test scores' information, the calculated z-value was 1.33, which did not surpass the critical value of 2.33. Therefore, it was concluded that there is insufficient evidence to support that inserting easy questions improves performance on the mathematics achievement test.

Explanation:

To determine if inserting easy questions into a standardized mathematics achievement test improves student performance, we conduct a hypothesis test using the given information: the test has a normal distribution of scores with mean µ = 100 and standard deviation σ = 18. A sample of n = 36 students took the modified test, scoring an average of M = 104. We use a one-tailed test with α = .01.

Step 1: Formulate the Hypotheses

Null Hypothesis (H0): µ = 100; the modifications do not affect test scores.

Alternative Hypothesis (H1): µ > 100; the modifications improve test scores.

Step 2: Calculate the Test Statistic

Use the formula for the z-score: z = (M - µ) / (σ/√n)

Substituting values: z = (104 - 100) / (18/√36) = 4 / 3 = 1.33

Step 3: Determine the Critical Value

For α = .01 in a one-tailed test, the critical z-value is approximately 2.33.

Step 4: Make a Decision

Since the calculated z-value of 1.33 is less than the critical value of 2.33, we do not reject the null hypothesis. Therefore, there is not sufficient evidence at the .01 level of significance to conclude that inserting easy questions improves student performance on the math achievement test.