Answer:

The probability that she wins exactly once before she loses her initial capital is 0.243.

Step-by-step explanation:

The gambler commences with $30, i.e. she played 3 games.

Let X = number of games won by the gambler.

The probability of winning a game is, p = 0.10.

The random variable X follows a Binomial distribution, with probability mass function:

Compute the probability of exactly one winning as follows:

Thus, the probability that she wins exactly once before she loses her initial capital is 0.243.

Malik’s recipe for 4 servings of a certain dish requires 1/{1}/{2} cups of pasta. According to this recipe, what is the number of cups of pasta that Malik will use the next time he prepares this dish?

Answer:

The answer to the question is

cups

Step-by-step explanation:

According to the recipe number of cups of recipe of past required = cups

A recipe is a predefined steps and directions required to make an item mostly especially something to eat.

Recipe in medicine or Latin means to "take" hence, a doctor usually writes on a prescription with a recipe, Latin for take and abbreviated as Rx or similar symbol.

In the original question, the number of cups of pasta that Malik will use the next time he prepares this dish is cups

A balloon is rising vertically above a level, straight road at a constant rate of 2 ft divided by sec. Just when the balloon is 84 ft above the ground, a bicycle moving at a constant rate of 12 ft divided by sec passes under it. How fast is the distance s (t )between the bicycle and balloon increasing 6 seconds later? A coordinate plane has a horizontal x-axis and a vertical y-axis. The angle between the axes is marked with a small square. The location of a balloon on the vertical axis is labeled y(t). An arrow pointing upward lies on the y-axis just below the point y(t). The location of a bicycle on the horizontal axis is labeled x(t). An arrow pointing to the right lies on the x-axis to the right of the point x(t). A segment falling from left to right begins at the balloon and ends at the bicycle and is labeled s(t).

Answer:

Step-by-step explanation:

At time t seconds after the bike passed, the distance z between the balloon and the bike is

z^2 = (84+2t)^2 + (12t)^2

So, at t=6,

z^2 = (84+2*6)^2 + (12*6)^2 = 14400

So, z = 120

2z dz/dt = 2(84+2t)*2 + 2(12t)*12

At time t=6,

240 dz/dt = 2(84+2*6)*2 + 2(12*6)*12 = 2112

dz/dt = 2112/240 = 44/5 ft/s

A coffee shop sells a ceramic refill mug for $8.95. Each refill cost $1.50. Last month rose spent $26.95 on a mug and refills. How many refills did she buy?

Answer:

12 refills

Step-by-step explanation:

$26.95-$8.98=$18 left after buying a refill mug

18/1.5=12 the refills she can buy

Neil has 3 partially full cans of white paint. They contain 1/3 of a gallon and 1/5 and 1/2 of a gallon of paint. About how much paint does Neil have left?

Answer:

1¹/₃₀

Step-by-step explanation:

The 3 gallons were partially full

They contain 1/3 of a gallon and 1/5 and 1/2 of a gallon of paint.

the first is 1/3 of the gallon

the second is 1/5 of galloon

the third is 1/2 of gallon adding them together

1/3 +1/5 +1/2 = (10+6+15)/30 = 31/30 = 1¹/₃₀

Of the 46 cities seven have a lake and 20 want to have a river running through them what fraction of these 46 cities have a lake or river running through them

Answer: The fraction of these 46 cities that have a lake or river running through them is 7/46.

Step-by-step explanation:

Hi, to solve this problem we have to analyze the information given:

- Number of cities: 46
- Cities that have a lake: 7
- Cities that want to have a river: 20

The cities that have a lake or river running through them are 7 (the 20 that only want it don´t count).

So, we have to divide the number of cities that have a lake or river running through them (7) by the total number of cities (46).

Mathematically speaking:

7/46

The fraction of these 46 cities that have a lake or river running through them is 7/46.

A particle moves along the parabola y equals x squared in the first quadrant in such a way that its x-coordinate (measured in meters) increases at a steady 10 StartFraction m Over sec EndFraction . How fast is the angle of inclination theta of the line joining the particle to the origin changing when x equals 1 m question mark

Answer:

(dθ/dt) = 1 rad / s = 57.3° /s

Step-by-step explanation:

- A particle moves along curve with function:

y = x^2

- The rate of change of x-coordinate is given by dx/dt = 10 m/s

Find:

How fast is the angle of inclination theta of the line joining the particle to the origin changing when x equals 1 m

Solution:

- The gradient of the line from origin to particle at position ( x , y ) is given by:

tan ( θ ) = y / x

Where, θ is the angle between x-axis and line from origin

x & y are coordinate of the point on given graph.

- To develop a rate of change expression we will derivate the above expression by time t:

d / dt (tan ( θ )) = d/dt (y / x )

(dθ/dt) / cos^2(θ) = (dy/dt) / (dx/dt)

(dθ/dt) = cos^2(θ) * (dy/dt) / (dx/dt)

- The rate of change of angle (dθ/dt) is given by above expression.

- We will apply the following chain rule to evaluate (dy/dt):

(dy/dt) = (dy/dx) * (dx/dt)

(dy/dt) = 2x * (10)

(dy/dt) = 20*x

@ x = 1, (dy/dt) = 20 m/s

@ x = 1, y = (1)^2 = 1

tan (θ) = 1

θ = 45°

- Now use the derived rate of change of angle expression we get:

(dθ/dt) = cos^2(45) * 20 / 10

(dθ/dt) = 0.5 * 20 / 10

(dθ/dt) = 1 rad / s = 57.3° /s

A pediatrician wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities: r = correlation between X and Y= 0.84 x = mean of the values of X = 5.69 y = mean of the values of Y = 6.26 S_x = standard deviation of the values of X = 3.23 s_y = standard deviation of the values of Y = 2.04 The slope of the least-squares line is: A) 0.53.B) 0.64. C) 0.84. D) 2.04.

Answer:

Answer is option a ) 0.53

Step-by-step explanation:

slope =

Given that a pediatrician wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable.

He finds the following quantities:

r = correlation between X and Y= 0.84

x = mean of the values of X = 5.69

y = mean of the values of Y = 6.26

S_x = standard deviation of the values of X = 3.23

s_y = standard deviation of the values of Y = 2.04

Using the formula for slope given above substitute to get

round off to 0.53

Answer is option a ) 0.53

Meghan also wants to walk to get some exercise, rather than going to the gym. She decides to walk along arc AB. How far will she walk? Round to 3 decimal places.

Answer:

π*AB

Step-by-step explanation:

I m not quite sure about your question because it is lack of details.

However, as my per understanding, Meghan decides to walk along arc AB it means she walks an interval equal to the circumference of the circle AB.

So, apply the formula in caculating the circumference of the circle, we have:

π*d = π*AB

So, she walk a π*AB distance.

Edward bikes the same route to and from school each day. After 28 school says, he bikes a total distance of 389.2 miles. How many miles does he bike each day

Answer:

13.9

Step-by-step explanation:

Bradley has 64 1-inch cubic blocks.He uses all the blocks to build a rectangular prism that is 2 inches high and 2 inches wide.How long is the rectangular prism?

Answer:

The rectangular prism is 16 inches long.

Step-by-step explanation:

Given:

Bradley has 64 1-inch cubic blocks.He uses all the blocks to build a rectangular prism that is 2 inches high and 2 inches wide.

Now, to find the length of rectangular prism.

Volume of rectangular prism = 64 cubic inches.

Height of rectangular prism = 2 inches.

Width of rectangular prism = 2 inches.

Now, to get the length we put formula:

Dividing both sides by 4 we get:

Therefore, the rectangular prism is 16 inches long.

How many different ways can the letters of "referred" be arranged? The number of different ways that the letters of"referred" can be arranged is__________.

Answer:

560 ways

Step-by-step explanation:

Given is a word

referred

We have to find the number of different ways that the letters of"referred" can be arranged

Let us analyse the given word

It contains totally 8 letters

r is repeated 3 times

e is repeated 3 times

f one time and d one time

Using the permutations rule for repeated objects we get

The number of different ways that the letters of"referred" can be arranged

=

560 ways

A random sample of 200 lightbulbs has a mean life of 600 hours and a standard deviation of 53 hours.(a) A histogram of the data indicates the sample data follow a bell-shaped distribution. According to theEmpirical Rule, 99.7% of lightbulbs have lifetimes between _____ and _____ hours.(b) Assuming the data are bell shaped, determine the percentage of lightbulbs that will have a life between494 and 706 hours.(c) Assuming the data are bell shaped, what percentage of lightbulbs will last between 547 and 706 hours?(d) If the company that manufactures the lightbulbs guarantees to replace any bulb that does not last at least 441 hours, what percentage of lightbulbs can the firm expect to have to replace, according to the Empirical Rule?

Given Information:

The average bulb life = μ = 600 hours

standard deviation = σ = 53 hours

Sample follows Bell-Shaped Distribution or Normal Distribution

Step-by-step explanation:

According to the Empirical Rule, 99.7% of the lightbulbs have lifetimes between μ - 3σ and μ + 3σ

600 - 3(53) and 600 + 3(53)

441 and 759 hours

(b) assuming the data are bell shaped, determine the percentage of lightbulbs that will have a life between 494 and 706 hours.

494 = 600 - 106 = 600 - 2(53) = μ - 2σ

706 = 600 + 106 = 600 + 2(53) = μ + 2σ

Therefore, according to the Empirical Rule, 95% of the lightbulbs have lifetimes between μ - 2σ and μ + 2σ

(c) Assuming the data are bell shaped, what percentage of lightbulbs will last between 547 and 706 hours?

547 = 600 - 53 = 600 - 1(53) = μ - σ

653 = 600 + 53 = 600 + 1(53) = μ + σ

Therefore, according to the Empirical Rule, 68% of the lightbulbs have lifetimes between μ - σ and μ + σ

(d) If the company that manufactures the lightbulbs guarantees to replace any bulb that does not last at least 441 hours, what percentage of lightbulbs can the firm expect to have to replace, according to the Empirical Rule?

441 = 600 - 159 = 600 - 3(53) = μ - 3σ

99.7% of the lightbulbs have lifetimes between μ - 3σ and μ + 3σ

100 - 99.7 = 0.3/2 = 0.15 %

According to the Empirical rule, 0.15% lightbulbs will last less than 441 hours.

Martha makes an investment of $500 in an account that pays 6% interest compounded monthly. Write an equation you could use to determine the interest she earns in t years

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited.

t represents the number of years.

From the information given,

P = $500

r = 6% = 6/100 = 0.06

n = 12 because it was compounded 12 times in a year.

An equation that could be used to determine the interest she earns in t years is

A = 500(1+0.06/12)^12 × t

A = 500(1+0.005)^12t

A = 500(1.005)^12t

100 POINTS!!!! The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. However, their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. What is the area of the region of the yard that they want to cover with new grass?

The area of whole backyard:

a = 3x - 5

b = 4x - 10

a · b = (3x - 5) · (4x - 10) = 3x · 4x + 3x · (-10) - 5 · 4x - 5 · (-10) =

= 12x² - 30x - 20x + 50 = 12x² - 50x + 50

The area of swimming pool with patio:

a = x + 8

b = x - 2

a · b = (x + 8) · (x - 2) = x · x + x · (-2) + 8 · x + 8 · (-2) =

= x² - 2x + 8x - 16 = x² + 6x - 16

Then the area of the region they want ot cover with new grass is:

12x² - 50x + 50 - (x² + 6x - 16) = 12x² - 50x + 50 - x² - 6x + 16 =

= 11x² - 56x + 66

Answer:

11x² - 56x + 6 is your answer

Step-by-step explanation:

The price of gold is often reported per ounce at the end of 2005 this price was 513 at the end of 2015 it was 1060 by what percentage did the price per ounce of gold increase

Answer:

206.63 %

Step-by-step explanation:

Hello, I can help you with this.

you can easily solve this by using a rule of three

Step one

define the data to use

year:2005

price:513

this is our initial value, the 100 percent (100%)

513⇔100%

then, in 2015 the price was 1060

year:2015

price:1060

%=x( the unknown number)

Step two

do the relation

so, the percentage that the price per ounce of gold increase was 206.63%

I really hope it helps, Have a great day.

You $5,000 in a simple interest bearing account. If the annual interest rate is 3.5% , what will your account balance be in 10 years if you do not make any additional deposits

Answer:

Therefore my account balance will be in 10 year=$6,750

Step-by-step explanation:

Simple interest: Simple interest is calculated on the same principal each year.

I= simple interest.

r = rate of interest per annum.

t= time

Compound interest: The principal is not same each year. The principal will change from the second year.

The principal of 2nd year = Principal+ interest of 1st year.

The principal of 3rd year = Principal of 2nd year+ interest of 2nd year.

and so on

The Amount

Here P= $5,000

r=3.5%

and t=10 years

=$1750

Therefore my account balance will be in 10 year=$(5,000+1750)=$6,750.

Determine what type of observational study is described. Explain. Researchers wanted to determine whether there was an association between city driving and stomach ulcers. They selected a sample of 900 young adults and followed them for a twenty-year period. At the start of the study none of the participants was suffering from a stomach ulcer. Each person kept track of the number of hours per week they spent driving in city traffic. At the end of the study each participant underwent tests to determine whether they were suffering from a stomach ulcer. The researchers analyzed the results to determine whether there was an association between city driving and stomach ulcers.

Answer: Structured Observation

Step-by-step explanation:

The observation is so named because, the problem has be defined and the behavioural pattern has to be measured, and the method of observation is also known to the participant who weekly turn in their statistics.

Last season 2 running backs on the Steelers football team rushed for a combined total of 1550 yards. One rushed 4 times as many as the others how many yard were rushed by each player.

Answer: the number of yards rushed by one player is 310 while the number of yards rushed by the second player 1240

Step-by-step explanation:

Let x represent the number of yards rushed by one player.

Let y represent the number of yards rushed by the second(faster) player.

Last season 2 running backs on the Steelers football team rushed for a combined total of 1550 yards. This means that

x + y = 1550 - - - - - -- - -- - - - - - 1

One rushed 4 times as many as the other. This means that

y = 4x

Substituting y = 4x into equation 1, it becomes

x + 4x = 1550

5x = 1550

x = 1550/5

x = 310

y = 4x = 4 × 310

y = 1240

Analyze relationships. Write >,<, >_,<_, in the blank to express the given relationship. H is at most 56 K is no greater then 9 B is no more then -5 W is no less than 0

Answer:

Step-by-step explanation:

We are given the following relationship the question.

We have to fill the appropriate signs.

H is at most 56

H cannot be greater than 56. Thus, it can be written as:

K is no greater then 9

Again K cannot be greater tan 9. Thus, it can be written as:

B is no more then -5

B cannot be greater than -5. It's value is less than or equal to -5. Thus, it can be written as:

W is no less than 0

W is not less than zero. Its value is greater than or equal to zero.

The National Center for Education Statistics reported that of college students work to pay for tuition and living expenses. Assume that a sample of college students was used in the study. A. Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. B. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses. C. What happens to the margin of error as the confidence is increased from 95% to 99%?

Answer:

A) = 0.0235

B) = (0.4095, 0.5305)

C) = With increase in confidence from 95% to 99%, also comes with increase in the margin of error and width of the confidence interval.

Step-by-step explanation:

Step 1:

size of random sample (n) = 450

Percentage of student working to pay tuition = 47%

Proportion of student working to pay tuition (P) = 0.47

Estimating the Standard error, /

substituting the data in the above equation and solving will give 0.0235

Step 2:

For a 95% confidence, the confidence coefficient is 1 - ∝ = 0.95 ∴ ∝ = 0.05.

Using standard normal area table, ∝/2 = 0.05/2 = 0.025

Z (∝/2) = Z (0.025) = 1.96

95% confidence interval

P±Z(∝/2) *

= 0.47±1.96(0.025)

= 0.47±0.0461

= (0.4239, 0.5161)

Step 3:

For a 99% confidence, the confidence coefficient is 1 - ∝ = 0.99 ∴ ∝ = 0.01

Using standard normal area table, ∝/2 = 0.01/2 = 0.005

Z (∝/2) = Z (0.005) = 2.576

99% confidence interval

P±Z(∝/2) *

= 0.47±2.576(0.0235)

= 0.47±0.0605

= (0.4095, 0.5305)

Step 4:

Observe that it is on the increase.

1. at 95%, confidence intervals are (0.4239, 0.5161)

2. at 99%, confidence intervals are (0.4095, 0.5305)

Coal can be used to generate hydrogen gas (a potential fuel) by the following endothermic reaction:C(s)+H2O(g) ------------->CO(g) + H2(g)If this reaction mixture is at equilibrium, predict whether each of the following will result in the formation of additional hydrogen gas, the formation of less hydrogen gas, or have no effect on the quantity of hydrogen gas:______.A. adding more C to the reaction mixtureB. adding more H2O to the reaction mixtureC. raising the temperature of the reaction mixtureD. increasing the volume of the reaction mixtureE. adding a catalyst to the reaction mixtureF. adding an inert gas to the reaction mixture
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Based on this analysis, a large portion of product cost relates to direct material. Managers should determine whether the direct labor can be automated with machines. A few other ways management can reduce costs is to reduce the number of setups and the cost per setup because producing in small lots increase the setup and shipping costs. True or false?
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Malik’s recipe for 4 servings of a certain dish requires 1/{1}/{2} cups of pasta. According to this recipe, what is the number of cups of pasta that Malik will use the next time he prepares this dish?
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b.peptide
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A balloon is rising vertically above a level, straight road at a constant rate of 2 ft divided by sec. Just when the balloon is 84 ft above the ground, a bicycle moving at a constant rate of 12 ft divided by sec passes under it. How fast is the distance s (t )between the bicycle and balloon increasing 6 seconds later? A coordinate plane has a horizontal x-axis and a vertical y-axis. The angle between the axes is marked with a small square. The location of a balloon on the vertical axis is labeled y(t). An arrow pointing upward lies on the y-axis just below the point y(t). The location of a bicycle on the horizontal axis is labeled x(t). An arrow pointing to the right lies on the x-axis to the right of the point x(t). A segment falling from left to right begins at the balloon and ends at the bicycle and is labeled s(t).
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