Determine whether the series is convergent or divergent by expressing Sn as a telescopic sum (as in example 7). If it is convergent, calculate its sum

Answer:

54.55% probability that only the Asian project is successful

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: At least one of the projects is successful.

Event B: Only the Asian project is successful.

We use P(A) for event A and event B, not related to the P(A) and P(B) given in the exercise.

Probability that at least one of the projects is successful.

Either none are successful, or at least one is. The sum of the probabilities is 1.

The Asian project has a probability of 0.8 of being successfull, which means that it has a probability of 1 - 0.8 = 0.2 of not being successful.

Following the same logic, the event B has a probability of 1 - 0.4 = 0.6 of not being successful. So

[tex]P(A) + 0.2*0.6 = 1[/tex]

[tex]P(A) = 0.88[/tex]

Intersection:

Between at least one being successful and only the Asian project successfull is the Asian succesful(probability 0.8) and the European not successful(probability 1 - 0.4 = 0.6). So

[tex]P(A \cap B) = 0.8*0.6 = 0.48[/tex]

What is the probability that only the Asian project is successful?

[tex]P(B|A) = \frac{0.48}{0.88} = 0.5455[/tex]

54.55% probability that only the Asian project is successful

Answer:

[tex]\Large \boxed{\sf \ \ 28 \ \text{ and } \ 62 \ \ }[/tex]

Step-by-step explanation:

Hello, let's note a and b the two numbers.

We can write that

a = 6 + 2b

ab = 1736

So

[tex](6+2b)b=1736\\\\ \text{***Subtract 1736*** } <=> 2b^2+6b-1736=0\\\\ \text{***Divide by 2 } <=> b^2+3b-868=0 \\ \\ \text{***factorize*** } <=> b^2 +31b-28b-868=0 \\ \\ <=> b(b+31) -28(b+31)=0 \\ \\ <=> (b+31)(b-28) =0 \\ \\ <=> b = 28 \ \ or \ \ b = -31[/tex]

We are looking for positive numbers so the solution is b = 28

and then a = 6 +2*28 = 62

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

5/11, 2/3, 7/8

Step-by-step explanation:

you can just do the numerator divided by the denominator to get a decimal, which can help you rank the fractions easier. hope this helps

Answer:

y = (x + 3)^2 - 6.

Step-by-step explanation:

The vertex formula is Y = a(x - h)^2 + k.

To find the vertex formula, we need to find h and k, by finding the vertex of x^2 + 6x + 3.

h = -b/2a

a = 1, b = 6.

h = -6 / 2 * 1 = -6 / 2 = -3

k = (-3)^2 + 6(-3) + 3 = 9 - 18 + 3 = -9 + 3 = -6

So far, we have Y = a(x - (-3))^2 + -6, so y = a(x + 3)^2 - 6.

In this case, the coefficient of x^2 of the given formula is 1, which means that a will be 1.

The vertex form of x^2 + 6x + 3 is y = (x + 3)^2 - 6.

To check our work...

y = (x + 3)^2 - 6

= x^2 + 3x + 3x + 9 - 6

= x^2 + 6x + 3

Hope this helps!

Answer:

x  =  8   ( 20$ bills)

y  = 5    ( 10 $ bills)

z = 2     ( 5  $  bills)

Step-by-step explanation:

Let call x, y, and z the number of bill of 20, 10, and 5 $ respectively

then according to problem statement, we can write

20*x + 10*y + 5*z = 220         (1)

We also know the total number of bills (15), then

x + y + z = 15     (2)

And that quantity of 20 $ bill is equal to

x = 3 + y     (3)

Now we got a three equation system we have to solve for x, y, and z for which we can use any valid procedure.

As    x = 3 + y    by substitution in equation (2)   and (1)

( 3 + y ) + y + z  = 15       ⇒   3 + 2*y + z = 15  ⇒  2*y + z = 12

20* ( 3 + y ) + 10*y + 5*z  = 220  ⇒ 60 + 20*y + 10*y + 5*z = 220

30*y + 5*z  = 160      (a)

Now we have only 2 equations

2*y + z = 12   ⇒    z = 12 - 2*y

30*y + 5*z  = 160     30*y  + 5* ( 12 - 2*y) = 160

30*y  + 60 - 10*y = 160

20*y = 100

y = 100/20       y = 5      Then by substitution in (a)

30*y + 5*z = 160

30*5  + 5*z = 160

150 + 5*z  = 160    ⇒     5*z = 10     z = 10/5      z = 2

And x

x + y + z = 15

x + 5 + 2 = 15

x = 8

Answer:

x=8 y=5 x=2

Step-by-step explanation:

Answer:

(c) [tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]

(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Step-by-step explanation:

The random variable X follows a Uniform (25, 35).

(a)

The probability density function of an Uniform distribution is:

[tex]f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A<X<B} \atop {0;\ Otherwise}} \right.[/tex]

Then the probability density function of the random variable X is:

[tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]

(b)

Compute the value of P (X > 33) as follows:

[tex]P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20[/tex]

Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c)

Compute the mean of X as follows:

[tex]\mu=\frac{A+B}{2}=\frac{25+35}{2}=30[/tex]

Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:

[tex]P(30-2<X<30+2)=P(28<X<32)[/tex]

                                      [tex]=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40[/tex]

Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Complete Question

Which of the following statements are true?

I. The sampling distribution of [tex]\= x[/tex] has standard deviation [tex]\frac{\sigma}{\sqrt{n} }[/tex] even if the population is not normally distributed.

II. The sampling distribution of [tex]\= x[/tex]   is normal if the population has a normal distribution.

III. When  n is large, the sampling distribution of [tex]\= x[/tex]  is approximately normal even if the the population is not normally distributed.

A  I and II

B  I and III

C II and III

D I, II, and III

None of the above gives the complete set of true responses.

Answer:

The correct option is  D

Step-by-step explanation:

Generally the mathematically equation for evaluating the standard deviation of the mean([tex]\= x[/tex]) of samples is  [tex]\frac{\sigma}{\sqrt{n} }[/tex]  hence the the first statement is correct

   Generally the second statement is true, that is the sampling distribution of the mean ([tex]\= x[/tex]) is  normal given that the population distribution is  normal

 Now  according to central limiting theorem given that the sample size is  large the distribution of the mean ([tex]\= x[/tex]) is approximately  normal notwithstanding the distribution of the population

Answer:

25

Step-by-step explanation:

The method that should be used is substitution:

Do this by taking 3x+9y=21 and transforming it to be [tex]y=-\frac{1}{2} x+\frac{7}{3}[/tex]

Once you have this, substitute the value of y that we just found into 3x+9y=21 to find the value of x: [tex]3x+9(-\frac{1}{2} +\frac{7}{3} ) =21[/tex]

Solve for x. You should get 1.5

Once you have this, Plug in 1.5 for the value of x into the y= equation that we found in the beginning: [tex]y=-\frac{1}{2} (1.5)+\frac{7}{3}[/tex]

Solve for y. You should get 1.583 (19/12)

Plug in the values of x and y that we found into the last equation to find its value: 4(1.5+3(1.583))

Answer:

85

Step-by-step explanation:

im new↑∵∴∵∴∞

Answer:

x ≈ 13.8 units

y ≈ 22.0 units

Step-by-step explanation:

We must use trigonometry to address this problem.

First, we know that y is the side opposite to the labelled angle, and x is the side adjacent to the labelled angle. 26 is the length of the hypotenuse.

We use cosine to find x (because cosine = adjacent / hypotenuse) and sine to find y (because sine = opposite / hypotenuse).

cos(58) = x/26

x = 26 * cos(58) ≈ 13.8

sin(58) = y/26

y = 26 * sin(58) ≈ 22.0

Thus, x ≈ 13.8 units and y ≈ 22.0 units.

~ an aesthetics lover

Answer:

(a) -3125, 15625

(b)

[tex]a_n=-5a_{n-1}, \\n\geq 2 \\a_1=1[/tex]

(c)[tex]a_n=(-5)^{n-1}[/tex]

Step-by-step explanation:

The sequence [tex]a_n$ _{n=1}^\infty[/tex] is given as:

[tex]\{1,-5,25,-125,625,\cdots\}[/tex]

(a)The next two terms of the sequence are:

625 X -5 = - 3125

-3125 X -5 =15625

(b)Recurrence Relation

The recurrence relation that generates the sequence is:

[tex]a_n=-5a_{n-1}, \\n\geq 2 \\a_1=1[/tex]

(c)Explicit Formula

The sequence is an alternating geometric sequence where:

Therefore, an explicit formula for the sequence is:

[tex]a_n=1\times (-5)^{n-1}\\a_n=(-5)^{n-1}[/tex]

Answer:

Option D.

Step-by-step explanation:

The given vertices of a polygon are D(-4,5),E(-1,5),F(1,2), and G(-1,-1).

Here, number of vertices is 4.

In heptagon, number of vertices = 7

In hexagon, number of vertices = 6

In octagon, number of vertices = 8

In quadrilateral, number of vertices = 4

Since the given polygon has 4 vertices, therefore it is a quadrilateral.

Hence, option D is correct.

Answer:

d

Step-by-step explanation:

Answer: a) additive inverse (addition)

              b) multiplicative inverse (division)

Step-by-step explanation:

Step 2: 6 is being added to both sides

Step 4: (3/4) is being divided from both sides

It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:

Step 2: Addition Property of Equality

Step 4: Division Property of Equality

Answer:

-y^2

Step-by-step explanation:

x(x-2y)-(y-x)^2=

Distribute

x^2 -2xy -(y-x)^2=

Foil

x^2 -2xy -(y^2 -2xy+x^2)=

Distribute the minus sign

x^2 -2xy -y^2 +2xy-x^2=

Combine like terms

-y^2

Answer:

A=3797 dollars

Step-by-step explanation:

A=P(1+r)^t  t=time period, r is the rate, P is the principal

A=2000(1+0.06)^11

A=3797 dollars

Answer:

1.8 dishes per minute (Sarah)

1.67 dishes per minute (Sunil)

Step-by-step explanation:

We can find the rate by dividing the number of dishes by the number of minutes:

18/10 = 1.8 dishes per minute

30/18 = 1.67 dishes per minute

My explanation is attached below.

Answer:

True

Step-by-step explanation:

because i'm the best

Hey there! :)

Answer:

A = 10 units².

Step-by-step explanation:

To solve this, we need to find the distance between the two points to derive the side-lengths of the square. Use the distance formula:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Plug in points into the formula to find the distance:

[tex]d = \sqrt{(3 - 2)^2 + (4-1)^2}[/tex]

Simplify:

[tex]d = \sqrt{(1)^2 + (3)^2}[/tex]

[tex]d = \sqrt{(1) + (9)}[/tex]

[tex]d = \sqrt{10}[/tex]

Find the area of the square using the formula A = s² where s = √10:

A = (√10)²

A = 10 units².

Answer:

10

Step-by-step explanation:

We use the distance formula to find the distance between the two points, which is the side length of the square.. Therefore, the area of the square is 10.

Answer:

Of the 500 parents surveyed 275 would be expected to spank their​ children.

Step-by-step explanation:

Let the random variable X represent the number of parents who spank their children.

It is provided that, from previous studies, p = 55​% of parents spank their children.

A random sample of n = 500 adults were selected.

The event whether a parent spank their children is independent of other parents.

The random variable X thus follows a Binomial distribution with parameters n = 500 and p = 0.55.

The expected value of a Binomial random variable is:

[tex]E(X)=np[/tex]

         [tex]=500\times 0.55\\=275[/tex]

Thus, of the 500 parents surveyed 275 would be expected to spank their​ children.

From the 500 parents surveyed, the number of parents that will be expected to spank their​ children is 275 parents.

Number of parents surveyed = 500

Percentage of parents that spank their children = 55%

Therefore, from the 500 parents surveyed, the number of parents that will be expected to spank their​ children  will be:

= 55% × 500

= 0.55 × 500

= 275

Therefore, the number of parents will be 275 parents.

Read related link on:

https://brainly.com/question/18582313

Answer:

m<2 = 73

Step-by-step explanation:

Since <1 and <2 are complementary (which means that they equal 90), all you have to do is subtract 17 from 90 to find your answer:

90 - 17 = 73

thus, m<2 = 73

Answer:

73

Step-by-step explanation:

Answer:

c=21

Step-by-step explanation:

[tex]3(c-5)=48\\3c-15=48\\3c=48+15\\3c=63\\c=63/3\\c=21[/tex]

Hope this helps,

plx give brainliest

Answer:

c=21

Step-by-step explanation:

3(c−5)=48

Divide both sides by 3.

c-5=48/3

Divide 48 by 3 to get 16.

c−5=16

Add 5 to both sides.

c=16+5

Add 16 and 5 to get 21.

c=21

Answer:

The probability that a piece of pottery will be finished within 95 minutes is 0.0823.

Step-by-step explanation:

We are given that the time of wheel throwing and the time of firing are normally distributed variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively.

Let X = time of wheel throwing

So, X ~ Normal([tex]\mu_x=40 \text{ min}, \sigma^{2}_x = 2^{2} \text{ min}[/tex])

where, [tex]\mu_x[/tex] = mean time of wheel throwing

            [tex]\sigma_x[/tex] = standard deviation of wheel throwing

Similarly, let Y = time of firing

So, Y ~ Normal([tex]\mu_y=60 \text{ min}, \sigma^{2}_y = 3^{2} \text{ min}[/tex])

where, [tex]\mu_y[/tex] = mean time of firing

            [tex]\sigma_y[/tex] = standard deviation of firing

Now, let P = a random variable that involves both the steps of throwing and firing of wheel

SO, P = X + Y

Mean of P, E(P) = E(X) + E(Y)

                   [tex]\mu_p=\mu_x+\mu_y[/tex]

                        = 40 + 60 = 100 minutes

Variance of P, V(P) = V(X + Y)

                               = V(X) + V(Y) - Cov(X,Y)

                               = [tex]2^{2} +3^{2}-0[/tex]  

{Here Cov(X,Y) = 0 because the time of wheel throwing and time of firing are independent random variables}

SO, V(P) = 4 + 9 = 13

which means Standard deviation(P), [tex]\sigma_p[/tex] = [tex]\sqrt{13}[/tex]

Hence, P ~ Normal([tex]\mu_p=100, \sigma_p^{2} = (\sqrt{13})^{2}[/tex])

The z-score probability distribution of the normal distribution is given by;

                           Z  =  [tex]\frac{P- \mu_p}{\sigma_p}[/tex]  ~ N(0,1)

where, [tex]\mu_p[/tex] = mean time in making pottery = 100 minutes

           [tex]\sigma_p[/tex] = standard deviation = [tex]\sqrt{13}[/tex] minutes

Now, the probability that a piece of pottery will be finished within 95 minutes is given by = P(P [tex]\leq[/tex] 95 min)

     P(P [tex]\leq[/tex] 95 min) = P( [tex]\frac{P- \mu_p}{\sigma_p}[/tex] [tex]\leq[/tex] [tex]\frac{95-100}{\sqrt{13} }[/tex] ) = P(Z [tex]\leq[/tex] -1.39) = 1 - P(Z < 1.39)

                                                            = 1 - 0.9177 = 0.0823

The above probability is calculated by looking at the value of x = 1.39 in the z table which has an area of 0.9177.                                        

Answer:

5x^2+5x-1

Step-by-step explanation:

-2x^2+9x-3+7x^2-4x+2=5x^2+5x-1

━━━━━━━☆☆━━━━━━━

▹ Answer

2,013 cartons

▹ Step-by-Step Explanation

72,468 ÷ 36 = 2,013 cartons

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

72,468 eggs divided by 36 eggs per carton=2,013 cartons

Step-by-step explanation:

Answer: 11/12

Step-by-step explanation:

First find the LCM of 4 and 3(12).  Then make the denominator of both fractions 12(3/12 and 8/12).  Then add the fractions to get that they ate 11/2 of the lasagna.

Hope it helps <3

Answer:

8.5 inches

Step-by-step explanation:

First let's find the time t when the depth of the snow is 7 inches.

To do this, we just need to use the value of D = 7 then find the value of t:

[tex]7 = 1.5t + 4[/tex]

[tex]1.5t = 3[/tex]

[tex]t = 2\ hours[/tex]

We want to find the depth of snow one hour from now, so we just need to use the value of t = 3 to calculate D:

[tex]D = 1.5*3 + 4[/tex]

[tex]D = 4.5 + 4 = 8.5\ inches[/tex]

The depth of snow one hour from now will be 8.5 inches.

The depth of the snow one hour from now is 8.5 inches.

Let D represent the depth of snow in inches at time t. It is given by the relationship:

D=1.5t + 4

Since  the depth of the snow is 7 inches now, hence, the time now is:

7 = 1.5t + 4

1.5t = 3

t = 2 hours

One hour from now, the time would be t = 2 + 1 = 3 hours. Hence the depth at this time is:

D = 1.5(3) + 4 = 8.5 inches

Therefore the depth of the snow one hour from now is 8.5 inches.

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Answer:

Here you go!! :)

Step-by-step explanation:

Given that the sides of the quadrilateral are 3.3

The measure of one angle is 116°

We need to determine the value of x.

Value of x:

Since, the given quadrilateral is a rhombus because it has all four sides equal.

We know the property that the opposite sides of the rhombus are equal.

The measure of the opposite angle is 116°

x = measure of opposite angle

x = 116°

Then, the value of x is 116°

Therefore, the value of x is 116°

Answer:

In the diagram, the measurement of x is 87°

Step-by-step explanation:

In this diagram, this shape is a quadrilateral. This quadrilateral in this picture is known as rhombus. In a rhombus, the consecutive angles are supplementary meaning they have a sum of 180°. Consecutive means the angles are beside each other. So, we will subtract 93 from 180 to find the value of x.

180 - 93 = 87

The measurement of x is 87°

Answer:

the answer is integers if helpful please give 5 star

Answer:

(+16) - (+2) = 14

Step-by-step explanation:

Hope this helped you!

Answer:

14

Step-by-step explanation:

(+16) - (+2) =

= 16 - 2

= 14