Marilyn moves 1/2 the remaining to the goal every second. if the goal if 50 yards away, how many seconds does it take to travel 49.5 yards? How to do?

Answer:

Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.

Step-by-step explanation:

We can use the Poisson approximation to the binomial distribution when n (the number of trials) is large and p (the probability of success) is small. In this case, n = 100 and p = 0.05, so np = 5, which is not too small. However, we can still use the approximation as long as we adjust for continuity, by adding and subtracting 0.5 from the number of successes we're interested in.

Let X be the number of books with defective bindings out of 100. We want to find the probability that X = 2. Using the Poisson approximation, we have:

λ = np = 5

P(X = 2) ≈ P(1.5 < Y < 2.5), where Y is a Poisson random variable with parameter λ

To find this probability, we can use the cumulative distribution function (CDF) of Y:

P(X = 2) ≈ P(1.5 < Y < 2.5) = F(2.5) - F(1.5), where F(x) is the CDF of Y evaluated at x

The CDF of a Poisson distribution with parameter λ is given by:

F(x) = e^(-λ) * Σ(λ^k / k!, k = 0 to floor(x))

where floor (x) is the greatest integer less than or equal to x. Using this formula, we can calculate:

F(1.5) = e^(-5) * Σ(5^k / k!, k = 0 to 1) ≈ 0.0337

F(2.5) = e^(-5) * Σ(5^k / k!, k = 0 to 2) ≈ 0.1247

Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.

The probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution is  0.0842.

Since the number of books bound, n = 100, is large and the probability of defective bindings, p = 0.05, is small, we can use the Poisson approximation to the binomial distribution.

The mean, µ, of the Poisson distribution is µ = np = 100 x 0.05 = 5.

The probability of 2 defective bindings can be calculated using the Poisson probability formula:

P(X = 2) = (e^-µ) * (µ^x) / x!

= (e^-5) * (5^2) / 2!

= 0.0842 (rounded to four decimal places)

Using the Poisson approximation to the binomial distribution, the likelihood that 2 of the 100 volumes bound by this bindery will have faulty bindings is roughly 0.0842.

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Step-by-step explanation:

(1/6²)⁵ = 1/6¹⁰ = 6^-10

because in the case of exponent of an exponent the exponents are multiplied with each other.

and 1/n = n^-1

(6^-5)² = 6^-10

because as above the exponents are multiplied with each other.

6^-3 / 6⁷ = 6^(-3 - 7) = 6^-10

a^n × a^m = a^(n+m)

a^n / a^m = a^(n-m)

the others are not 6^-10 :

6^-5 × 6² = 6^(-5 + 2) = 6^-3

6⁵×6^-3 / 6^-8 = 6^(5 - 3 - -8) = 6^(5 ‐ 3 + 8) = 6¹⁰

Answer: -32.00

Step-by-step explanation:

Answer:

A) -32.00

Step-by-step explanation:

-32.00 would be more debt than -25

Helping in the name of Jesus.

a) We would expect approximately 0.2325 × 200 = 46.5 vehicles

to fail in their first 2 years. Since we cannot have a fraction of a vehicle

failing, we would expect around 46 or 47 vehicles to fail in their first 2

years.

b) The approximate probability that 50 or more vehicles fail in

the first 2 years is 0.0004.

c) The approximate probability that no more than 10 of the remaining

vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.

a) The average lifespan of the vehicle is 8 years, and it follows an

exponential distribution, which has a probability density function of

[tex]f(x) = (1/θ) \times e^(-x/θ)[/tex],

where θ is the mean of the distribution. Thus, θ = 8.

The probability that a vehicle fails in the first 2 years can be found by

integrating the exponential probability density function from 0 to 2:

P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx

Using a calculator or a table of integrals, we can find this probability to

be approximately 0.2325.

b) The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.

The probability that 50 or more vehicles fail in the first 2 years can be

found using the Poisson distribution with parameter λ = 46.5:

P(X ≥ 50) = 1 - P(X < 50)

Using a Poisson distribution table or a calculator, we can find that P(X <

50) is approximately 0.9996.

Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).

c) Given that 30 vehicles have already failed in under 2 years, we need

to find the probability that no more than 10 of the remaining 170 vehicles

fail in their first 2 years.

The number of vehicles that fail in the first 2 years follows a Poisson

distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525

(rounded to 40).

Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable

with parameter λ = 40.

Using a Poisson distribution table or a calculator, we can find that P(Y ≤

10) is approximately 0.0002.

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To check the normality of the sampling distribution for a one-sample z confidence interval for proportions, the sample size should be large (typically n > 30), and the number of successes and failures in the sample should both be at least 10.

To check for normality of the sampling distribution for a one-sample z confidence interval for proportions, we need to ensure that the following conditions are met:

Large sample size: The sample size should be sufficiently large (typically n > 30). This is because the central limit theorem states that for large enough sample sizes, the sampling distribution of the sample proportion will be approximately normal, regardless of the underlying distribution of the population.

Success-Failure Condition: The number of successes (np) and failures (n(1-p)) in the sample should both be at least 10. This condition ensures that the binomial distribution of the sample proportion is approximately normal.

If these conditions are met, then we can assume that the sampling distribution of the sample proportion is approximately normal, and we can proceed to construct a one-sample z confidence interval for proportions.

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The work done pulling the bucket to the top of the well of depth 76 feet is equals to the 346.56 pounds/ feet.

Work is the product of force and distance, W=F×d. A Riemann Sum is a collection of rectangles used to approximate the area underneath a curve. In this case the "height" of the rectangle will be the force being exerted, and the "width" of the rectangle will be the amount of distance it moved. The work done by the force on the object can be expressed as an integral, [tex]W = \int_{a}^{b}F(x)dx[/tex]

Weigh of bucket = 5 pounds

A rope with negligible weight is used to draw water from a well. The depth of well = 76 feet.

Initially, Water in bucket = 37 pounds

Rate of pulling rope = 1.8 feet per second

Rate of water leaking in bucket = 0.25 pounds per second

Changing rate of leaking from pounds/sec to pounds/ feet : Q = 0.25/1.8 pounds/feet

= 0.139 pounds per feet

Thus, the rate of water leak from bucket hole is 0.12 pounds per feet. Let 'x' be height of bucket in feet from bottom of well. So, the total water leaked from hole = 0.12x

After leakage Remaining water in bucket = (37 - 0.12x )pounds

Also, add the weigh of buket in above expression. The limits of integration varies with depth of well that is 0 to 76 feet. Using Riemann sum method, work done pulling the bucket to the top of the well, [tex]W = \int_{0}^{76} ( 37 - 0.12x + 5 ) dx [/tex]

=>[tex]W = \int_{0}^{76} ( 42 - 0.12x ) dx [/tex]

=> [tex]W = [0 - \frac{0.12x²}{2}]_{0}^{76} \\ [/tex]

=> [tex]W = \frac{0.12×76²}{2} - 0 [/tex]

=> W = 0.12× 38×76 = 346.56 pounds/ feet. Hence required work done is 346.56 pounds/ feet.

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Answer: 112 ft²

Step-by-step explanation:

The area of a triangle can be found with the equation

[tex]A=\frac{1}{2} bh[/tex], where b is the base (bottom line of the triangle) and h is the height (the distance of the line from the peak of the triangle that forms a right angle with the base).

In this problem we are given the base and height: the base is 16 feet, and the height is 14 ft.

Therefore, the area is [tex]\frac{1}{2} *16*14[/tex], which is 112 ft²

The required fraction for the given condition is [tex]\frac{1}{3}[/tex]

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Give shape contain 12 squares out of then four squares are shaded.

so, required fraction can be determine as

[tex]$Fraction=\frac{4}{12}[/tex]

[tex]$Fraction=\frac{1}{3}[/tex]

Thus, required fraction is [tex]\frac{1}{3}[/tex]

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Complete question;

Answer:

3 inches

Step-by-step explanation:

area of a rectangle

12×5

The average speed of a falling object during the first 3 seconds of its fall is h(3)-h(0)/3.

The model of the motion of the body is given by, and the function of the motion of the body is given by h(t) = 300 - 16t².

The speed of object after 3 seconds is given by . The falling speed of object during the first 3 seconds of falling is calculated as follows, v = dh(t)/dt = -32t.

So now the average speed of the movement is calculated as follows,

v = h(3)-h(0)/3.

Option d is therefore the correct option.

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Complete question - the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?

A.) h(3) – h(0)

B.) h(3/3)-h(0/3)

C.) h(3)/3

D.) (h(3)-h(0))/3

Answer:

a = 127° , b = 12° , c = 115°

Step-by-step explanation:

a and 53° are same- side interior angles and sum to 180° , that is

a + 53° = 180° ( subtract 53° from both sides )

a = 127°

c and 115° are alternate angles and are congruent , then

c = 115°

53° , b and c lie on a straight line and sum to 180°

53° + b + c = 180°

53° + b + 115° = 180°

b + 168° = 180° ( subtract 168° from both sides )

b = 12°

then a = 127° , b = 12° , c = 115°

Answer:

a = 127; b = 12; c = 115

Step-by-step explanation:

c =115

b = 180 - 115 - 53

b = 12

a = b + c

a = 12 + 115

a = 127

The 43rd term of the sequence is 149.

Arithmetic progression is a sequence of numbers in which the difference between any two consecutive numbers is a constant value. The constant value is called a common difference.

We can see that the common difference between consecutive terms in the sequence is 4. So, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the term number we want to find.

To find the 43rd term, we plug in the values:

a1 = -19, d = 4, n = 43

an = -19 + (43 - 1)4

an = -19 + 42(4)

an = -19 + 168

an = 149

Therefore, the 43rd term of the sequence is 149.

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In the proportion, Mr.Balewa needs  9 cups to makes 12 dozen cookies.

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here  

He uses 4 1/2 cups of flour to make six dozen cookies then to makes 12 dozen cookies the x cups of flour .

Now using proportion,

= (4 1/2) / 6 = x / 12

= (9/2) / 6 = x/12

x = (9*12)/(2*6) = 9

= 9 cups.

Hence Mr. Balewa needs  9 cups to makes 12 dozen cookies.

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Answer: To find how many free throw shots Shawn makes out of 300 shots, we can first find how many he makes out of 100 shots, and then multiply by 3 to get the number of shots he makes out of 300.

If he makes 15 1/5 shots out of 100, we can convert this to a decimal by dividing 15 by 100 and adding 1/5, which is the same as adding 0.2. This gives:

15/100 + 1/5 = 0.15 + 0.2 = 0.35

So, on average, Shawn makes 35% of the free throw shots he attempts.

To find how many shots he makes out of 300, we can multiply this percentage by 300:

0.35 x 300 = 105

Therefore, Shawn makes about 105 free throw shots out of 300 shots.

Step-by-step explanation:

Answer:

x^4 - mx^2 + n^2 = 0

Step-by-step explanation:

We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:

(x^2)(y^2) = n^2

Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:

x^2(m - x^2) = n^2

Expanding the left side of the equation, we get:

mx^2 - x^4 = n^2

Multiplying both sides by 16, we get:

16mx^2 - 16x^4 = 16n^2

Adding 32xy to both sides, we get:

16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy

Substituting n for xy, we get:

16mx^2 + 32n - 16x^4 = 16n^2 + 32n

Rearranging the equation, we get:

16mx^2 - 16x^4 - 16n^2 = 0

Dividing both sides by -16, we get:

x^4 - mx^2 + n^2 = 0

Answer:

(4x+4y)²

Step-by-step explanation:

Given x²+y² = m ,xy=n.

Now 16m+32n = 16(m+2n)

= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]

(4x+4y)².

Answer:

the last 3 are true

Step-by-step explanation:

hope this helps

To succeed in an i-Ready mastery check, it is essential to review the materials covered in the lessons thoroughly, actively engage in the learning process, and ask questions if anything is unclear.

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i-Ready is an online adaptive learning platform that offers personalized learning experiences for students in reading and mathematics.

Mastery checks play a crucial role in ensuring that students fully understand the concepts being taught before progressing to more advanced topics.

These short assessments typically follow a lesson or series of lessons, helping teachers identify areas where students may need additional support or practice.

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Answer:

[tex]6.45ft^{2}[/tex]

Step-by-step explanation:

The probability that it is yellow is 1/4.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: A bag with 8 marbles has 2 yellow marbles, 3 red marbles, and 3 blue marbles. A marble is chosen from the bag at random.

We have to find the probability that it is yellow.

the probability that it is yellow:

= 2/8

= 1/4

Hence, the probability that it is yellow is 1/4.

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Since the total amount of kids who participated in the survey is 150, 100% of the pie is equal to 150 kids.

We know that 46% of the 150 kids like video games so the number of kids that like video games is 0.46 * 150 = 69.

Similarly, 14 + 16 = 30% of 150 kids like reading and art so the number of kids that like reading and art is 0.3 * 150 = 45.

Your second question is quite hard to understand. But you know that 120 kids like video games and those kids make up 40% of the total so mathematically you can say,

40% * number of total students = 120

number of total students = 120/40% = 300

Since the mid 1950s, both men and women in the U.S. have experienced an increase in the proportion of the population never married. The correct answer is "increase".

This trend has been attributed to various factors such as the rise of individualism, changing gender roles, economic factors, and the decline of traditional social norms. In 1960, only 9% of women and 6% of men aged 25-34 had never been married, while in 2020, these numbers increased to 33% for women and 23% for men.

Therefore, it is evident that the proportion of the U.S. population never married has increased steadily over the past few decades

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The appropriate statistical test for whether the mean rating of guilts are greater for unattractive defendants than for attractive is:

B. 1 tailed t-test.

At the null hypothesis, it is tested if the mean rating of guilt will not be higher for unattractive defendants than for attractive defendants, that is:

H0  : uU <=uA

At the alternative hypothesis, it is tested if the rating is greater, that is:

H1 : uU> uA

We are comparing the means, hence a t-test is used. We are testing if one is greater than other(not different), hence a 1-tailed test is used, and option B is correct.

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Answer:

25

Step-by-step explanation:

Formula 1/2(B1+B2)H

1/2(10)5

1/2 x 10=5

5 x 5 =25

Answer: a ≤ 2

Step-by-step explanation:

How to write an inequality statement:

Step 1: Write the two values being compared in the problem.

Step 2: Determine whether the first value is larger or smaller than the second value.

Step 3: Express the inequality with the right symbols:

≤ = less than or equal to

≥ = greater than or equal to

Therefore, the answer would be a≤2.

Hope this helped!

Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.

We have, a disk with radius of 15 cm.

Maximum error = 0.25

We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)

here, r = 15 cm , dr = 0.25

Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)

=> dA = 2πr dr

Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25

=> dA = 7.50 × π = 23.55

So, absoulte error in area = 22.55

Original value of area = π(15)² = 706.5 cm²

Now, relative error % = (∆A/A)×100

= (22.55/706.5)×100

= 0.031917 × 100

= 3.1917 ~ 3.192 %

Hence, required value is 3.192%.

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Complete question:

the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.

The measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.

An exterior angle is an angle that forms a linear pair with an interior angle of a polygon. It is formed by extending one of the sides of the polygon. In other words, it is the angle formed between a side of a polygon and the extension of an adjacent side.

Based on the problem description, we can see that the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA. Therefore, we need to find the measure of the exterior angle at vertex A.

We know that the sum of the measures of the angles in a triangle is 180 degrees. So, we can find the measure of angle BAC by subtracting the measures of angles BCA and ABC from 180 degrees:

angle BAC = 180 - angle BCA - angle ABC

We can find the measure of angle ABC by subtracting the measure of angle A from 180 degrees:

angle ABC = 180 - angle A

Similarly, we can find the measure of angle BCA by subtracting the measure of angle C from 180 degrees:

angle BCA = 180 - angle C

Substituting these expressions into the equation for angle BAC, we get:

angle BAC = 180 - (180 - angle A) - (180 - angle C)

         = angle A + angle C

Therefore, the measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.

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