In the accompanying diagram of parallelogram
ABCD, side AD is extended through D to E and
DB is a diagonal. If EDC = 65 and CBD = 85, find CDB.

The probability that the bridge operator allows less than 18 yachts to pass by in a 3-hour time interval is 0.4733 (approximate). So, Correct option is 0.4733

Given data:

The average number of yachts allowed in 3 hours, λ = 15 yachts

We need to find the probability of allowing less than 18 yachts to pass by in a 3-hour time interval. We know that,

For a Poisson distribution, the probability of x occurrences is given by

P(x) = (λ^x e^(-λ))/x!

Where e = 2.71828... is the base of the natural logarithm.

For x = 0, 1, 2, 3, and so on.

The probability of less than 18 yachts is given by:

P(x<18) = P(x=0) + P(x=1) + P(x=2) + ... + P(x=17)

Using the Poisson distribution formula,

P(x) = (λ^x e^(-λ))/x!= (15^x e^(-15))/x!

Thus, P(x<18) = P(x=0) + P(x=1) + P(x=2) + ... + P(x=17)= Σ P(x)

where x varies from 0 to 17= Σ (15^x e^(-15))/x! where x varies from 0 to 17

By adding all the values in the table below, we get the sum as 0.4732.

Hence, the correct option is .4733.

Learn more about Poisson distribution from:

https://brainly.com/question/9123296

#SPJ11

The area of the window is 305.12 square inches.

given that

jaylon created this stained glass window the upper two coners are quater ciecleseach with a radius of 4 inches.

The window's area is equal to the sum of the areas of a rectangle, two quarter circles, and the smaller square between the two upper corners.

The quantity of space occupied by a flat surface with a specific shape is referred to as the area.

now, find the area of rectangle

A = length x breadth

A = 12 x (26-4)

A = 12 x 22

A = 264 square inches

find the area of the two quarter circle

\( A= 2( \frac{1}{4} (3.14) \times {4}^{2} ) \\ A = 25.12 {in}^{2} \)

Find the area of the smaller square between the two upper corners

A = (12-8) (4)

A = 4 x 4

A = 16 sq.in

now, find the total area

A = 264 + 25.12 + 16

A = 305.12 square inches

Hence, the area of the window is 305.12 square inches.

Learn more about area of rectangle from here:

https://brainly.com/question/25292087

#SPJ4

Answer:

-------------------------

Step-by-step explanation:

the angles 5 and 8 are also congruent to A.

Answer:

Step-by-step explanation:

im not sure

Answer:

the answer will be

K' = -9, 5

L' = 0,5

M' = -8,3

Step-by-step explanation:

the x axis is written first and the y axis is written after that.

hope it helps!!

PLEASE MARK BRAINLIEST !!..

Answer:

K': (9,5)

L': (0,5)

M': (8,3)

Step-by-step explanation:

Tell me if im wrong!

Answer:  The difference is 6.5 inches.

Step-by-step explanation:

The volume of a cone uses the formula V= nr^2 h/3

So the large cone's volume is  V= 3.14 * 1.5^2 *5/ 3

                                              v= 11.775

The volume of the small cone is V= 3.14 * 1^2* 5/3

                                                      V=5.23

Now find the difference.   11.775 - 5.23= 6.54

Round to the nearest tenth is  6.5

The difference between the median high temperature and median low temperature is 22.5°F

The data set has an odd number of values, the median is the middle value when the data is arranged in numerical order.

Hence Median of the data is given by

Median = value at position (n + 1) / 2,

where n is the number of data points.

Here we have

The weather forecast is shown.

High 84°F 90°F 82°F  79°F  83°F  92°F  82°F

Low  56°F 63°F 60°F  52°F  60°F  61°F  53°F  

To find the difference between the median high temperature and the median low temperature, Calculate the median temperatures for both high and low temperatures.

To find the median, we need to first arrange the temperatures in ascending order  

For the high temperatures, we have:

79°F, 82°F, 82°F, 83°F, 84°F, 90°F, 92°F

Here median = 4th term [ Since the number of terms 7 is an odd number ]

The median of high temparature = 83°F

For the low temperatures, we have:

52°F, 53°F, 56°F, 60°F, 60°F, 61°F, 63°F

Here median = 4th term [ Since the number of terms 7 is an odd number ]

The median of low temparature = 60°F

The difference between the median high temperature and median low temperature is:

83°F - 60.5°F = 22.5°F

Therefore,

The difference between the median high temperature and median low temperature is 22.5°F

Learn more about Median at

https://brainly.com/question/28060453

#SPJ9

Explanation

We are to first find the inverse of the function:

To do so, we will follow the steps below:

Step 1:

Step2: Interchange x with y

Step 3: solve for y

Thus, the inverse of the function is

Part 2

Simplifying further

Also

Simplifying further

The future value of the deposits at the end of 5 years is approximately $6,138.74.

To calculate the future value of the deposits, we can use the formula for compound interest:

FV = P(1 + r/n)^(nt)

Where: FV is the future value

P is the principal amount (initial deposit)

r is the annual interest rate (3% in this case)

n is the number of times interest is compounded per year (quarterly in this case)

t is the number of years

In this case, the principal amount is $1,000, the annual interest rate is 3% (or 0.03), the number of times interest is compounded per year is 4 (quarterly), and the number of years is 5.

Plugging in these values into the formula, we get: FV = $1,000(1 + 0.03/4)^(4*5)

Calculating this, the future value of the deposits at the end of 5 years is approximately $6,138.74.

Learn more about interest rate at

https://brainly.com/question/32122915

#SPJ11

If the continuous distribution is given then The age of people who have retired represents Normal distribution.

a) The age of people who have retired would likely follow a normal distribution, as it tends to have a symmetric bell-shaped curve.

b) The number of red Smarties in boxes of Smarties would have a discrete distribution, as it can only take on certain whole numbers and cannot be fractionally or continuously measured.

c) The shoe sizes of Stouffvillians may exhibit a bimodal distribution, as there might be two distinct peaks indicating two groups with different average shoe sizes.

d) The wait time between calls to Pizza Pizza could potentially follow an exponential distribution, as it is often used to model the time between events in a Poisson process, such as the arrival of phone calls. The distribution would have a long tail, representing longer wait times occurring less frequently.

To learn more about “exponential distribution” refer to the https://brainly.com/question/22692312

#SPJ11

16  is the approximate interquartile range (iqr) of the ages .

What does IQR, or interquartile range, mean?

The spread of the middle half of your data is measured by the interquartile range (IQR). The IQR shows the difference between the lowest and highest readings for that particular week. The spread in the center of the data for that week is roughly represented by the IQR.

                       It is the range for your sample's middle 50%. To evaluate the variability where the majority of your results are located, use the IQR. Larger values suggest a wider dispersion of the central component of your data. The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.

IQR  = Q3 - Q1

       = 20 - 4

       = 16

Learn more about interquartile range IQR

brainly.com/question/26421076

#SPJ4

The expression when rewritten is 3^1/2

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

(3^3/4  * 3^3/8)^4/9

Apply the law of indices

So, we have

(3^9/8)^4/9

Simplify the exponent

3^1/2

Hence, the solution is 3^1/2

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The expression can be rewritten as 3^1/2 = √3

We want to simplify the expression below:

(3^3/4  * 3^3/8)^4/9

Remember that we can add these exponents, so we get:

3/4 + 3/8 = 9/8

Then we can rewrite this as:

(3^9/8)^4/9

Takin the product between the exponents we will get:

(3^9/8)^4/9 = 3^(4/8) = 3^1/2

the solution is 3^1/2

Read more about expressions at:

brainly.com/question/15775046

#SPJ1

Answer

Anita's total number of dolls = 30

Explanation

Let the total number of dolls be x

20% of x = 6

0.2x = 6

Divide both sides by 0.2

(0.2x/0.2) = (6/0.2)

x = 30 dolls

Hope this Helps!!!

If Hilda has $210 worth of $10 and $12 stock shares and the number of $10 shares is 5 more than twice the number of $12 shares, then the number of $10 shares and $12 shares she has is equal to 15 and 5 respectively.

The number of $10 shares and $12 shares can be calculated by forming linear equations.

Consider the number of $10 shares to be x and the number of $12 shares to be y.

x = 2y + 5

10x + 12y = 210

Putting the value x = 2y + 5 in the second equation,

10x + 12y = 210

10 (2y + 5) + 12y = 210

20y + 50 + 12y = 210

32y + 50 = 210

32y = 210 - 50

32y = 160

y = 160 ÷ 32

y = 5

Putting y = 5 in the first equation,

x = 2y + 5

x = 2(5) + 5

x = 10 + 5

x = 15

Hence the number of $10 and $12 shares she has is calculated to be 15 and 5 respectively.

To learn more about linear equations, click here:

https://brainly.com/question/12788590

#SPJ4

Answer:

jjjokiioololll.hgyuhhkopohjo

Answer:

2,112 \(ft^{3}\)

Step-by-step explanation:

Volume of the cube

(12)(12)(12) = 1728

Volume of the pyramid

1/3(12x12x8) = 384

1728 + 384 = 2112

Step 1

Given; The length of one side of a right triangle is shown in this diagram.

What could be the lengths of the two remaining sides of the triangle?

Step 2

Euclidean geometry, For a right-angled triangle, the sum of the square of the two shorter sides of a right triangle is equal to the third side, which is the longest; in symbols,

From the image; Using the Pythagoras theorem we have that

Thus the answer is;

Write the highlighted digit's place and value.

3. 567; ones place                4. 6,327; thousandth place

5. 9,325; hundredth place    6. 8,281; tenth place

Write each number in standard form.

7. 5,000 + 500 + 3; 5,503     8. 2,000 + 300 + 20 + 9; 2,329

9. 4,000 + 600 + 8; 4,608     9. 9,000 + 300 + 70 + 2; 9,372

11. 1,221

We know Sierra has the same numbers in the thousandth and ones place, so keep does numbers: 1,?2?

It also has two more hundreds and 3 fewer ones place: Take the original number; 1,024 (Make sure you keep the numbers) into a equation; (1024+200)-3. First Add as it's in the ( ), then subtract, 1,221

I hope I've helped!

Answer:

#3. ones place. #4. thousands place.#5. hundreds place. #6. tens place. #7. 5,503. #8. 2,329. #9. 4,608. #10. 9,372.

Step-by-step explanation:

#11.sierras seat number 1,221

Answer:

x=-5/2

Step-by-step explanation:

Hi there!

We are given the following equation:

\(6^{x+3} = \sqrt{6}\)

We want to find the value of x

This is an exponential equation. In order to find the value of x, we need to make sure that both sides of the equation are at the same bases before we solve the equation

On the left side, we have 6 (the base) raised to the power of x+3

On the right, we have √6

Here's a trick to make this problem easier: the square root of a number is equal to that number, raised to the power of 1/2. In other words, √a is equal to \(a^\frac{1}{2}\)

Therefore, √6 is equal to \(6^\frac{1}{2}\)

Rewriting the equation then:

\(6^{x+3}=6^\frac{1}{2}\)

Both sides have the same base (6)

Now we can solve the equation for x. Simply take what the exponents are, and then set them equal to each other.

This means:

x + 3 = 1/2

Subtract 3 from both sides

x+3=1/2

  -3   -3
___________

x = -5/2

Hope this helps!

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

Learn more about volume of cone here: brainly.com/question/16419032

#SPJ11

There are two questions in the picture, but I'll answer them both. Before you go any further, you should be familiar with the process of substitution. Substitution allows you to replace a variable with a known numeric value. I didn't complete the tables entirely, but hopefully the way I explained it will help you finish the problems.

1. y = 1.5x

if x = 1, then y = 1.5(1) = 1.5

if x = 2, then y = 1.5(2) = 3

if x = 3, then y = 1.5(3) = 4.5

See how we simply replace the x with the value of x? To find another solution, simply find a point that is on the line. For example, we could find x = 10.

y = 1.5(10) = 15

Therefore, another solution on the line is (10, 15).

2. y = 1.25x

if x = 1, then y = 1.25(1) = 1.25

if x = 3, then y = 1.25(3) = 3.75

You can use a similiar process as problem #1 to finish.

Answer:

n = 14

Step-by-step explanation:

(n + 6)4 = 5

1. multiply by 4

n + 6 = 20

2. substract 6

n = 14

The required value of n is 14 in the given sum.

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

We have been given that the sum of a number, n, and 6 is divided by 4 the result is equal to 5.

According to the given question, we can write the algebraic form would be as:

⇒ (n + 6)/4 = 5

Apply the cross-multiplication operation,

⇒ (n + 6) = 5 × 4

Apply the multiplication operation,

⇒ (n + 6) = 20

⇒ n = 20 - 6

Apply the subtraction operation,

⇒ n = 14

Therefore, the required value of n is 14.

To learn more about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

Answer:

$46.272

Step-by-step explanation:

We are given with information that , we have to find two consecutive positive integers , sum of whose squares is 365 .

\({\pmb{\bf Assumption \: :-}}\) Let's assume that the first number is x , and as the other no. is it's consecutive so , the second no. is (x+1)

Now , According to the question ;

\({: \implies \quad \sf x^{2}+x^{2}+1^{2}+ 2\cdot x \cdot 1 = 365\quad \{\because (a+b)^{2}=a^{2}+b^{2}+2ab\}}\)

Can be further written as ;

\({: \implies \quad \sf 2{x^{2}}+2x -364=0}\)

\({: \implies \quad \sf 2(x^{2}+x-182)=0}\)

As , \(\sf 2 \neq 0\) . So ;

\({: \implies \quad \sf x^{2}+x-182=0}\)

Using splitting the middle term ;

\({: \implies \quad \sf x^{2} +14x-13x-182=0}\)

\({: \implies \quad \sf x(x+14)-13(x+14)=0}\)

\({: \implies \quad \sf (x+14)(x-13)=0}\)

When (x+14) = 0 , then x = - 14 , which is rejected as it's not +ve

When (x-13) = 0 , then x = 13 , which is +ve

Now ,

Hence , The required numbers are 13 and 14 respectively .

The value of x in the given logarithmic function is: x = 3.379

There are different properties of Logarithm such as:

Product property

Quotient property

Power property

Change of base property

From properties of logarithm, we know that:

If logₐ m = x

Then: m = aˣ

Thus:

log₅230 = x gives us:

5ˣ = 230

x In 5 = In 230

x = 3.379

Read more about Properties of Logarithm at: https://brainly.com/question/12049968

#SPJ1

Answer:

15.059352

Step-by-step explanation:

3.372*4.466= 15.059352

The corresponding standard deviation of this estimate is 3.27.

Given a simple random sample of n = 50, the prevalence of a trait is 76.8%.

We are to calculate the expected number of individuals that are expected to exhibit this trait and the corresponding standard deviation of this estimate.

Expected number of individuals: For a simple random sample, the expected number of individuals who exhibit the trait is given by:

Expected value of trait = prevalence × sample size

= 76.8/100 × 50

= 38.4 individuals

Therefore, the expected number of individuals that are expected to exhibit this characteristic is 38.4.

Corresponding standard deviation of the estimate:

Since the prevalence of the trait is given, we can treat it as a known probability and use the binomial distribution to calculate the standard deviation.

The formula for standard deviation for the binomial distribution is:

Standard deviation = sqrt[n × p × (1 - p)]

where p = prevalence and n = sample size.

Substituting the values in the formula, we get:

Standard deviation = sqrt[50 × 0.768 × (1 - 0.768)]

= sqrt[50 × 0.768 × 0.232]

= 3.27 (approx)

Therefore, the corresponding standard deviation of this estimate is 3.27.  

Learn more about standard deviation -

brainly.com/question/475676

#SPJ11