A line with a slope of –12 passes through the points (–3,–6) and (r,–10). What is the value of r?

The percentage by which the radius of the artery reduces is 1.44% of original radius.

According to Poiseuille’s law, we got that  there is relation between radius, length, average pressure  for blood which is flowing in our body and that relation is  is given by

Q = ((P₂-P₁)πr⁴) /(8ηl)

where Q is flow rate

P is the pressure

r is the radius of the artery

η is the viscosity

Now,we have given that Flow rate is reduced by 12%,new flow rate is 88% of normal value.

Also, we have also given that pressure is increased by 22%,so new pressure is 122% of initial value,

therefore Q = ((P₂-P₁) × π × r⁴) /(8ηl)

=>(Q-12Q/100)=[((122 / 100) × P₁-P₁) × π × r₂⁴] / (8ηl)

=>(88 / 100)Q=(22 / 100)×(P₁ × π × r₂⁴)/(8ηl)

=>(88/22)Q=(P₁ × π × r₂⁴)/(8ηl)

=>[[4 × (8ηl)] × Q]/ (P₁ × π)=r₂⁴

=>4r₁ =r₂⁴

=>r₂=√2r₁

or r₂=1.44% of original radius.

Hence, by 1.44% radius of artery would reduce.

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The answer of the given expression as a common fraction in lowest terms is  437/495  .

In the question ,

it is given that ,

the expression is 0.4overline 8 + overline 0.37 ,

that can be written as [tex]0.4\overline{8}[/tex] + [tex]0.\overline{37}[/tex]

On further simplifying the above expression further ,

we get ,

= (48 - 4)/90 + 37/99

= 44/90 + 37/99

taking the LCM of 90 and 99 as 990 and solving further ,

we get ,

= 484/990 + 390/990

= ( 484 + 390 )/990

= 874/990

in lowest form it is = 437/495 .

Therefore , the answer to the expression is  437/495  .

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Answer:

x = 3

and

y = 2

Step-by-step explanation:

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{4 }{7 +3} \implies \cfrac{ 4 }{ 10 } \implies \cfrac{2 }{ 5 }[/tex]

The standard deviation of the sampling w would be 0.06.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

Population proportion

                         [tex]p=\frac{2756}{5500} \\\\\\p=0.501091\\\\p=0.501[/tex]

The mean of the sampling distribution for samples of size n=70 customers = 0.501

The standard deviation of the sampling distribution for samples of size n=70 customers is

                         [tex]=\sqrt{\frac{p* (1-P)}{n}} \\\\=\sqrt{\frac{ 501091(1-0.501091) }{2}}\\\\ = 0.059761 \\\\=0.06[/tex]

Hence, the standard deviation of the sampling w would be 0.06.

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Answer:

Step-by-step explanation:

Planet A has a mass of 8× 10²5 kilograms. Planet B has a mass of 6×10 kilograms. Choose which planet has the larger mass. Then fill in th blank with a number written in standard notation. Planet A has the larger mass. The mass of Planet A is times as large as the mass of Planet B. O Planet B has the larger mass. $0 times as large as the mass of Planet A.

Answer:

10

Step-by-step explanation:

im him trust

A graph to model the proportional relationship between cost and number of songs is shown in the image attached below.

Mathematically, a proportional relationship and the constant of proportionality can be represented or modeled with the following equation or mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for a song as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 10/20

Constant of proportionality (k) = 0.2

Therefore, an equation for any number of song for this karaoke is given by:

y = 0.2x.

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Technically, it would be impossible to truly know without "computing" at all, but once you add 2 and 3, you would be able to know that the sum of all three numbers of positive without accounting for the -2, because 6 is a greater absolute value than -1.

Some examples:
12 + - 4
7 + - 3
18 + -10

All will be positive because those positive numbers (12, 7, 18) are greater than the others (4, 3, 10).

Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.

Unlike, in the case of a Binomial distribution, for a Poisson distribution, the knowledge of number of trials to get the observed number of successes is not required. The Poisson distribution has only one parameter namely “m” the mean number of successes per given unit of time.

The Poisson distribution is often taken as a limiting case of Binomial distribution, under the following conditions.

The number of trails is indefinitely large i.e., n → ∞

The probability of success, “p” is very small i.e., p → 0

np is finite i.e., np = m where p = m/n and q = 1 – m/n and m > 0.

However, it is not defined if “n” is large means how large and “p” is closed to zero means how small? It is left to the readers to assume how large n should be and how small p should be? As mentioned earlier, the Poisson distribution is often described as a limiting case of Binomial distribution.

Based on the results of the study , published by me clearly proves that even when 10 ≤ n ≤50 and p ≤ 0.2, the Poisson distribution can be a good approximation to Binomial distribution.

Hence the answer is Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.

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Answer:

x = 1, p = 32

Step-by-step explanation:

4(4x+4) = 2(x+2x+13)

16x+16 = 6x+26

10x+16=26

10x=10

x=1

4(4(1)+4) = 4(4+4) = 4(8) = 32

Answer: 16

Step-by-step explanation:

u=5

v=3

u² - v²

5² - 3²
——————————

5² = 5 • 5 = 25

3² = 3 • 3 = 9

——————————

25 - 9 = 16

Yes, it is worth the extra drive, going to the further store is cheaper.

The cheaper option saves you $0.09.

Given:

Price or sale = $3.19 a pound

1.) Neighborhood store

Distance = 2.1 miles away

As, the car averages about 19 miles per gallon,

=2.1 miles / (19 miles/gallon)

= 0.1105 gallons of gas < 17 gallons

The gas is about $3.83/gallon, then the cost be

=0.1105 gallons x ($3.83/gallon)

= $0.42

The chicken is sold for $3.59 a pound, and you need 3 pounds, then you would pay:

= 3 pounds x ($3.59/pound)

= $10.77

So, the total is

= $0.42 (gas) + $10.77 (chiken)

= $11.19

2.) Store across town

Distance = 8.5 miles away

The car averages about 19 miles per gallon, then you would need:

=8.5 miles / (19 miles/gallon)

= 0.447 gallons of gas < 17 gallons

The gas is about $3.83/gallon, then the gas would cost:

=0.447 gallons x ($3.83/gallon)

= $1.71

The chicken is sold for $3.19 a pound, and you need 3 pounds, then you would pay:

= 3 pounds x ($3.19/pound)

= $9.57

The total cost

= $1.71 (gas) + $9.57

= $11.28

Thus, $11.19 < $11.28, then it is worth the extra drive.

Hence, cheaper option saves you= $11.28 - $11.19 = $0.09

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The relationship is not proportional because the number of used bottles increases more. Option B

A relationship is said to be proportional when the two variables that are in question are either increasing or decreasing at the same rate. It could also be that one one quantity is increasing and the other is  decreasing.

If we look at the proportionality in the proper sense of it, there appears to be no relationship between the two variables as the number of used bottles is increasing at a much higher rate than the number of bottles that is recycled.

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7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.

Given that,

In a study comparing the perceived effects of two painkillers, 200 randomly chosen persons were given the first one, and 93% reported noticeably lessening of their pain. 96% of the 450 people who received the other painkiller reported feeling noticeably relieved.

We have to estimate the percentage of adults overall who would say they felt their pain was relieved after taking each painkiller. give the estimate's 95% confidence interval.

We know that,

p=(186+432)/(200+450)

p=0.95

We get

L.B= 0.93-0.96+0.96√0.95(1-0.95)(1/200+1/450)

L.B= 0.07

Therefore, 7% percentage of adults overall who would say they felt their pain was relieved after taking each painkiller.

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Answer:

C. 0.625

Step-by-step explanation:

5 divided by 8 is .625

A.

       .625      

8   5.000

   - 48

        20

       - 16

           40

         - 40

             0

B.

or you can multiply by 8 the answers to see if you get 5

A. 0.375 * 8 = 3

B. 0.40 * 8 = 3.2

C. 0.625 * 8 = 5

D. 0.875 * 8 = 8

C.

if you dont have to you could estimate using the first number after the decimal to see if you get 5

A. 0.375

first number after the decimal is 3

3 * 8 = 24 ≈ 2.4 ≈ 3

B. 0.40

first number after the decimal is 4

4 * 8 = 32 ≈ 3.2 ≈ 3

C. 0.625

first number after the decimal is 6

6 * 8 = 48 ≈ 4.8 ≈ 5

D. 0.875 * 8 = 8

Answer: 4in

Step-by-step explanation:

Mr Jones have to drive 270 miles to get to his home

The question is a percentage problem, percentage deals with a fraction hundred and used to solve the problem

From the equation 180 miles represents 40% of the journey

let the total journey be x, hence we say

0.4x = 180

x = 180 / 0.4

x = 450 miles

Then the 60% left is calculated

60% of 450

= 0.6 * 450

= 270 miles

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To view the sketched cubic function and label the zeros using the factors check the attached image and the rewrite the function in general form is

2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] -26x + 30.

Given that :

f(x) = (x + 3)(-x + 5)(2 - 2x)

To find  : zeroes of f(x) , sub f(x) = 0

(x + 3)(-x + 5)(2 - 2x) = 0

          x + 3 = 0

                x = -3

        - x + 5 = 0

                x = 5

        2 - 2x = 0

               x = 1

      The zeroes are -3 , 1 , 5  

Rewrite the function in general form  

     f(x) =  (x + 3)(-x + 5)(2 - 2x)

           = (- [tex]x^{2}[/tex] + 2x + 15 )(2 - 2x)

     f(x) = 2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] - 26x + 30

Therefore,  f(x) = 2[tex]x^{3}[/tex] - 6[tex]x^{2}[/tex] - 26x + 30 is a general form.

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The inequality to represent the situation is 16c + 63r ≤ 640.

What is simple inequality?

Mathematical expressions with simple inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given, total saving = $640

Mya cooks lunch or dinner = $16

restaurant for lunch or dinner = $63

For c meals that Mya cooks = 16c

For r meals, the family eats at a restaurant = 63r

Total cost = 16c + 63r

Based on conditions, 16c + 63r ≤ 640

Hence, the inequality representing the situation is 16c + 63r ≤ 640.

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hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.

Odd number integers = 2k + 1, where k is integer

Even number integer = 2k

Odd integer + even integer

 = 2k + 1 + 2k

= 4k + 1

 = 2(2k) + 1

Let 2k = t, where t is integer

  = 2t + 1

 = Odd integer by definition

If number is 2t + 1 where t belongs to integer, then it is odd integer.

Hence proved.

The question is incomplete. The complete question is :

Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd

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An inequality that can be used to find t the amount of money in dollars is

c)t ≤ 350, t is less than or equal to 350. So, correct option is c.

In science, a disparity or an inequality is a connection which makes a non-equivalent examination between two numbers or other numerical expressions. It is utilized generally normal to look at two numbers on the number line by their size. There are a few unique documentations used to address various types of disparities:

The documentation a < b implies that an is not as much as b.

The documentation a > b implies that an is more noteworthy than b.

Regardless, an isn't equivalent to b. These relations are known as severe inequalities, implying that an is completely not exactly or rigorously more prominent than b. Identicalness is barred.

We have Alex total amount =$600 and amount which he want on his account after spending is $250.

So,t+250 ≤600

=>t≤ 600-250

=>t≤ 350.

Hence, option c is correct.

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(Complete question) is:

Alexandra has $600 in her checking account. She wants to spend part of this money on a computer. She wants to have at least $250 left in her checking account after buying the computer. The inequality shown can be used to find t, the amount of money in dollars that Alexandra can spend on the computer.

Which inequality represents all possible values of t?

a)t ≥ 350,

t is greater than or equal to 350

b)t ≤ 850,

t is less than or equal to 850

c)t ≤ 350,

t is less than or equal to 350

d)t ≥850,

t is greater than or equal to 850

Answer:

square root 75

Step-by-step explanation:

The 20 questions test answers may a student mark 8192 ways.

What is the combinations?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Since there are 20 questions, and each question can be answered in if 7 questions mark correctly and 13 incorrectly then:

7 questions can be answered correctly.

13 questions can be answered incorrectly.

The 2 questions can be answered in

2 × 2 ways.

The 3 questions can be answered in 2×2×2 ways and so on.

So we have:

1 × 1 × 1 × 1 × 1 × 1 × 1 × 2¹³

= 8192

Hence, the 20 questions test answers may a student mark 8192 ways.

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The total number of tickets they bought was 3.

What is a math riddle?

To solve a math riddle, children must translate a few sentences from a real-life scenario into the correct combination of mathematical equations. Children can decipher any code, including math riddles, using logic, creative problem-solving, and common sense.

Total 3 tickets-

Grandfather-Also Father of His son

Father-Also son of his father.

Son.

So Two fathers and two sons.

Hence, a total of 3 tickets were bought.

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Groups not counted as unemployed in the official unemployment statistics are the underemployed and discouraged workers.

A discouraged worker is someone who can work and is qualified for employment but is not already working and has not looked for work in the past four weeks. Discouraged workers typically have given up looking for work because they have discovered no relevant employment possibilities or have not been successful in getting a job after applying.

Discouragement among employees has a wide range and complex root causes. Because they lack the skills to deal with technological change at work, workers occasionally leave the workforce. During the Great Recession, the manufacturing industry let go of senior workers who were unable to operate the modern computer numeric control (CNC) equipment, which was used to cut wood and other hard materials.

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p < 0.05, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.

Given,

The test statistics formula for finding the z-score is,

z = (X - μ)/(σ/√n)

Where,

X = sample mean

μ = population mean

σ = population standard deviation

n = sample size

This z-score is used to determine the p-value. The null hypothesis is not rejected if p > α, and it is rejected if p < α.

Here,

The population mean μ = 4.00

The sample size n = 196

The sample mean X = 4.14

The standard deviation σ = 0.83

The significance level α = 0.05

So, the hypothesis is:

The null hypothesis: H0: μ = 4

The alternative hypothesis: Ha: μ ≠ 4

Thus, the test statistic value is,

z = (X - μ)/(σ/√n)

= (4.14 - 4)/(0.83/√196)

= 2.36

So, for z = 2.36, the p-value is 0.009137

Therefore,

The provided significance level of 0.05 is not met by the p-value of (0.009137). Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.

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The margin of error does not take into account the bias caused by nonresponse.

What is nonresponse bias?

The phenomenon known as participation bias, also known as non-response bias, occurs when a disproportionate number of participants have certain characteristics that have an impact on the results of surveys, polls, and other types of research.

Nonresponse bias happens when a portion of the sample's respondents fail to respond. The main distinction in this instance is that the error arises from a lack of respondents rather than the collection of false data.

Usually, the number of responses is used to calculate the margin of error. You can treat a sample from a finite population as infinite if the sampling fraction is small, but if the sampling fraction is high (say, more than 10% of the population size), you must make a finite population correction.

So, the non-response bias is not taken into account by the margin of error.

Longer commuters might take less time to complete a survey.

This would result in our estimate from the sample being lower than the actual mean travel time to work.

Hence, the margin of error does not take into account the bias caused by nonresponse.

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