Use an exponent to write each expression 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9 x 7/9

Answer:

The expected number of boys a family might have is 2.5.

Step-by-step explanation:

Let X denote the number of boys in a family with 5 children.

The probability of a boy is, p = 0.50.

The child can either be a by or a girl independently.

The random variable X follows a binomial distribution with parameters n = 5 and p = 0.50.

The probability mass function is:

[tex]p_{X}(x)={5\choose x}(0.50)^{x}(1-0.50)^{5-x};\ x=0,1,2...5[/tex]

Compute the expected number of boys a family might have as follows:

[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]

x                                      p (x)                                           x · p (x)

0       [tex]p(0)={5\choose 0}(0.50)^{0}(1-0.50)^{5-0}=0.03125[/tex]          [tex]0\times 0.03125=0[/tex]

1        [tex]p(1)={5\choose 1}(0.50)^{1}(1-0.50)^{5-1}=0.15625[/tex]          [tex]1\times 0.15625=0.15625[/tex]

2       [tex]p(2)={5\choose 2}(0.50)^{2}(1-0.50)^{5-2}=0.3125[/tex]           [tex]2\times 0.3125=0.625[/tex]

3       [tex]p(3)={5\choose 3}(0.50)^{3}(1-0.50)^{5-3}=0.3125[/tex]           [tex]3\times 0.3125=0.9375[/tex]

4       [tex]p(4)={5\choose 4}(0.50)^{4}(1-0.50)^{5-4}=0.15625[/tex]         [tex]4\times 0.15625=0.625[/tex]

5       [tex]p(5)={5\choose 5}(0.50)^{5}(1-0.50)^{5-5}=0.03125[/tex]         [tex]5\times 0.03125=0.15625[/tex]

Then,

[tex]E(X)=\sum x\cdot p_{X}(x)[/tex]

         [tex]=0+0.15625+0.625+0.9375+0.625+0.15625\\\\=2.5[/tex]

Thus, the expected number of boys a family might have is 2.5.

Answer:

Step-by-step explanation:

If y= -5 when x= -20  that means x is 4 times y

y=  8.75  when x= 35

Answer:

Our equation is:

[tex]\displaystyle y=-\frac{1}{4}x[/tex]

When x=35, y=-35/4 or -8.75.

Step-by-step explanation:

We know that y varies directly with x.

The standard equation is:

[tex]y=kx[/tex]

We know that y is 5 when x is -20.

So, let’s substitute 5 for y and -20 for x and solve for k, our constant of variation. So:

[tex]5=k(-20)[/tex]

Divide both sides by -20:

[tex]\displaystyle k=-\frac{1}{4}[/tex]

Therefore, our constant of variation is -1/4.

Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{4}x[/tex]

To find y when x=35, let’s substitute 35 for x. So:

[tex]\displaystyle y=-\frac{1}{4}(35)=-\frac{35}{4}=-8.75[/tex]

So, when x=35, y=-8.75.

Answer:

P(t) = 1000e^(0.01155)t

Step-by-step explanation:

Let the population of barangay be expressed according to the exponential formula;

P(t) = P0e^kt

P(t) is the population of the country after t years

P0 is the initial population

t is the time

If barangay has 1000 initially, this means that P0 = 1000

If the population doubles after 60years then;

at t = 60, P(t) = 2P0

Substitute into the formula

2P0 = P0e^k(60)

2 = e^60k

Apply ln to both sides

ln2 = lne^60k

ln2 = 60k

k = ln2/60

k = 0.01155

Substitute k = 0.01155 and P0 into the expression

P(t) = 1000e^(0.01155)t

Hence an exponential model for barangay's population is

P(t) = 1000e^(0.01155)t

Answer:

Slope, [tex]m=\dfrac{1}{5}[/tex]

Step-by-step explanation:

It is given that,

A road rises 20 feet for every 100 feet in horizontal distance.

Rise (vertical distance) = 20 feet

Run (horizontal distance) = 100 feet

Slope of the road is given by the ratio of rise to the run. It can be calculated as :

[tex]m=\dfrac{20}{100}\\\\=\dfrac{1}{5}[/tex]

So, the slope is [tex]\dfrac{1}{5}[/tex].

Answer:

y=2

Step-by-step explanation:

the image and preimage are 6 units apart so thhe line of reflection is in the middle at 3 units and is a line that is paralel to the x-axis

y=2

Answer:

A

Step-by-step explanation:

I got it right on the assignment 100%

Answer:here’s the answer for this question

Step-by-step explanation:edge2023

Answer:

I would say that for Catherine, the best place to inform her investors about a new stock issue would be a news release on her company website so in that way it is made public, informs the investors and may attract more capital investment in the company as well.Step-by-step explanation:

Answer:

I believe the answer is company website

Step-by-step explanation:

if i'm incorrect i'm sorry

Answer:

The distance should be [tex]3\sqrt{13[/tex]

Step-by-step explanation:

Distance formula

Answer:

D

Step-by-step explanation:

Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

Step-by-step explanation:

Total fabric needed by Sam = 2.75

According to directions on a sewing pattern they say to buy an extra 12.5%

So, extra fabric would be: 12.5% of 2.75

Solving

Now adding 0.343 into 2.75 to get extra fabric quantity:

2.75+0.343

=3.09

Therefore Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

Answer:

C.

Step-by-step explanation:

Add the whole numbers first

then add 1/4 and 3/4 which makes 4 cups then 2/4 =1/2

4 and 1/2 cups

Answer:

A. 60°

General Formulas and Concepts:

Geometry

Step-by-step explanation:

From the picture given, we see that all the side lengths are 12. Therefore, we can conclude that triangle ABC is an equilateral triangle.

Therefore, m∠y must equal 60°.

Answer:

16.86 ft/s

Step-by-step explanation:

Given that,

Angular speed of a carousel, [tex]\omega=14\ rev/min[/tex]

The diameter of the carousel, d = 23 feet

We need to find the speed of the carousel and jump on.

[tex]\omega=14\ rev/min=1.46\ rad/s[/tex]

Radius, r = 11.5 feet

Let v is the velocity. So,

[tex]v=r\omega\\\\=11.5\times 1.46\\\\=16.79\ ft/s[/tex]

Hernce, the correct option is (d) "16.86 ft/s"

Answer:m∠11 = 11x

m∠13 = 10x + 12

Step-by-step explanation:

m∠11 = 11x

m∠13 = 10x + 12

Given:

Fixed cost = $3,450

Variable cost = $12 per basketball

Selling price = $25 per basketball

Number of basketball sold = 300

To find:

Whether Rebotar did break even.

Solution:

According to the question,

Cost of 1 basketball = $12

Cost of 300 basketball = $12×300

We know that,

Total cost = Fixed cost + Variable cost

[tex]TC=3450+12(300)[/tex]

[tex]TC=3450+3600[/tex]

[tex]TC=7050[/tex]

So, the total cost is $7050.

Now,

Selling price of a basketball = $25

Selling price of 300 basketball = $25×300

Total revenue is

[tex]TR=25\times 300[/tex]

[tex]TR=7500[/tex]

So, total revenue is $7500.

At break even situation the profit is zero. In other words, the total revenue is equal to total cost.

Since, [tex]TC\neq TR[/tex], therefore, Rebotar did not break even.

Answer:4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3 (6)-9 (1)=9

18-9=9

i think that is the answer

Answer:

It travels 530 more miles on the first trip than the second trip and travels 469 more miles on the first trip than the third trip.

Step-by-step explanation:

Take 872-342=530 so then that's your answer to the first part of the question, now do the same thing just plug in the different numbers: 872-403=469

Answer:

Step-by-step explanation:

- 2 ≤ x ≤ 1

x ∈ [ - 2 , 1 ]

Answer:

How we will solve:

- 2 ≤ x ≤ 1

x ∈ [ - 2 , 1 ]

Answer:

Step-by-step explanation:

Using the sample size formula

n= (zs/e)²

z is the z score at 99% = 2.58

s is the standard deviation = 250

e is the sample mean = 50

Substitute

n = (2.58×250/50)²

n = (2.58×5)²

n = (12.9)²

n=166.41

hence the sample size is 166.41

Answer:

3rd option.) 1/8a^12

Step-by-step explanation:

(2a⁴)^-3

=1/(2a⁴)³

=1/8a^12

Answer: The next one is 3. 7/2v^2

Step-by-step explanation: In case you needed help with that

Answer:

A C E F

Step-by-step explanation:

Answer:

A, C, E, and F.

Answer:

16

Step-by-step explanation:

i would try but not 100% sure

Answer:

0.9 or 90%

Step-by-step explanation:

The probability of shot is 47%

The probability of no shot is 100 -47 = 53%

The dot plot is made from the 10 repeated shots which recorded 25 scores.

The number of dots on the fifth tick is 9 of 10 shots

therefore; 9/10 = 0.9, which 90 in percentage.    

The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts [tex]\dfrac{12}{25}[/tex] or 0.48.

Given information:

A basketball player claims to make 47% of her shots from the field.

It s required to simulate the player taking sets of 10 shots, assuming that her claim is true. Twenty-five repetitions of the simulation were performed.

The dot plot shows the simulated number of makes in each set of 10 shots.

The dots in the 5 shot mark is 9, that in 6 shot mark is 2 and that in 7 shot mark is 1.

So, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated as,

[tex]P(x\geq5)=\dfrac{9+2+1}{30}\\=\dfrac{12}{25}[/tex]

Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts [tex]\dfrac{12}{25}[/tex] or 0.48.

For more details, refer to the link:

https://brainly.com/question/11740746

Answer:

The value of x is 4

Step-by-step explanation:

In a right triangle, if a segment is drawn from the right angle ⊥ to the hypotenuse like the given figure, then

∵ The length of one side of the right triangle = (x + 2)

∵ The length of the hypotenuse = x + 5

∴ (x + 2)² = x (x + 5)

∵ (x + 2)² = (x + 2)(x + 2)

∴ (x + 2)(x + 2) = x(x + 5)

→ Simplify the two sides

∵ (x)(x) + (x)(2) + (2)(x) + (2)(2) = (x)(x) + (x)(5)

∴ x² + 2x + 2x + 4 = x² + 5x

→ Add the like terms in the left side

∴ x² + 4x + 4 = x² + 5x

→ Subtract x² from both sides

∵ x² - x² + 4x + 4 = x² - x² + 5x

∴ 4x + 4 = 5x

→ Subtract 4x from both sides

∴ 4x - 4x + 4 = 5x - 4x

∴ 4 = x

∴ The value of x is 4

Answer:

0.11711612445;

0.99376780489;

2.4494897

Step-by-step explanation:

Given that :

Arrival rate = 6 per hour

Mean Arrival during 90 minute period :

60 min = 6

90 min = (6 * 90) / 60 = 9

λ = 9

Using poisson :

P(x =x) = (e^-λ * λ^x) / x!

1) Exactly 7

P( x = 7) = (e^-9 * 9^7) / 7!

= 590.26526724266 / 5040

= 0.11711612445

Atleast 3:

P(x ≥ 3)

P(x ≥ 3) = 1 - P(x < 3)

P(x < 3) = p(x =0) + p(x = 1) + p(x = 2)

P(x = 0) = (e^-9 * 9^0) / 0! = 0.0001234098

P(x = 1) = (e^-9 * 9^1) / 1! = 0.00111068824

P(x = 2) = e^-9 * 9^2) / 2! = 0.00499809707

1 - P(x < 3) =

1 - (0.0001234098 + 0.00111068824 + 0.00499809707)

1 - 0.00623219511

= 0.99376780489

B.) mean and standard deviation of the number of patients arriving at the hospital accident and emergency department in an hour?

Mean = arrival per hour = λ = 6

Standard deviation = √λ = √6

Standard deviation = 2.4494897

The probability that, during any 90-minute period, the number of patients  arriving at the hospital accident and emergency department is exactly 7 is 0.11711612445 and the probability for at least 3 is 0.99376780489. The mean is 6 and the standard deviation is 2.4494897.

Given :

Patients arrive at a hospital accident and emergency department at random follow a  Poisson distribution at a rate of 6 per hour.

Accprding to the poisson distribution:

[tex]\rm P(x=x)=\dfrac{(e^{-\lambda} \times \lambda^x )}{x!}[/tex]

a) The probability that, during any 90-minute period, the number of patients  arriving at the hospital accident and emergency department is:

First, determine the value of [tex]\lambda[/tex]:

[tex]\lambda = \dfrac{6\times 90}{60} = 9[/tex]

(i) At (x = 7) the probability is given by:

[tex]\rm P(x=7)=\dfrac{(e^{-9} \times 9^7 )}{7!}[/tex]

Simplify the above expression.

P(x = 7) = 0.11711612445

(ii) At (x [tex]\geq[/tex] 3) the probability is given by:

[tex]\rm P(x\geq 3)=1-P(x<3)[/tex]

[tex]\rm P(x\geq 3)=1-P(x=2)-P(x=1)-P(x=0)[/tex]

[tex]\rm P(x=2)=\dfrac{(e^{-9} \times 9^2 )}{2!}=0.00499809707[/tex]

[tex]\rm P(x=1)=\dfrac{(e^{-9} \times 9^1 )}{1!}= 0.00111068824[/tex]

[tex]\rm P(x=0)=\dfrac{(e^{-9} \times 9^0 )}{0!}= 0.0001234098[/tex]

So, the probability at (x [tex]\geq[/tex] 3) is given by:

[tex]\rm P(x\geq 3)=1-0.0001234098 - 0.00111068824 - 0.00499809707[/tex]

[tex]\rm P(x\geq 3)=1 - 0.00623219511[/tex]

[tex]\rm P(x\geq 3)= 0.99376780489[/tex]

b) The mean and standard deviation of the number of patients arriving at the  hospital accident and emergency department in an hour are given by:

[tex]\rm Mean = \lambda = 6\\\\[/tex]

[tex]\rm Standard\; Deviation=\sqrt{\lambda }= \sqrt{6} = 2.4494897[/tex]

For more information, refer to the link given below:

https://brainly.com/question/17716064

Answer:

$1.85

Step-by-step explanation:

12 gallons = $22.18

1 gallon = $22.18 ÷ 12

1 gallon = $1.85

Answer:

-6

Step-by-step explanation:

Answer:

Colour ---- Probability

Blue ----- 0.2

Red ------- 0.4

Yellow ------ 0.4

Step-by-step explanation:

Given

Colour ---- Probability

Blue ----- 0.2

Red -------

Yellow ------

Required

Complete the table

In probability, all probabilities add up to 1.

i.e.

[tex]P(Blue) + P(Red) + P(Yellow) = 1[/tex]

Substitute 0.2 for P(Blue)

[tex]0.2 + P(Red) + P(Yellow) = 1[/tex]

[tex]P(Red) + P(Yellow) = 1 - 0.2[/tex]

[tex]P(Red) + P(Yellow) = 0.8[/tex]

From the question, we understand that the frequency of yellow and red balls are the same.

Hence:

[tex]P(Red) = P(Yellow)[/tex]

[tex]P(Red) + P(Yellow) = 0.8[/tex] becomes

[tex]P(Red) + P(Red) = 0.8[/tex]

[tex]2P(Red) = 0.8[/tex]

Make P(Red) the subject

[tex]P(Red) = 0.4[/tex]

Recall that:

[tex]P(Red) = P(Yellow)[/tex]

Hence,

[tex]P(Yellow) = 0.4[/tex]

So, the complete table is:

Colour ---- Probability

Blue ----- 0.2

Red ------- 0.4

Yellow ------ 0.4

Answer:

-5/3

Step-by-step explanation:

10-15=-5

6-3=3

Answer:

-5/3

Step-by-step explanation:

m=y2-y1/x2-x1

10-15-(-5)

6-3=3

-5/3

hope this helped :3

sorry if it is wrong