Assume y varies directly as x.

If y = 7 when x = 3, find x when y = 21.

Answer:

166 quarters,  40 dimes

Step-by-step explanation:

x - quarters

y - dimes

      x  +        y =  206

0.25x + 0.10y = 45.50

y = 206 - x

0.25x + 0.10(206 - x) = 45.50

0.25x + 20.6 - 0.10x = 45.50

0.15x = 45.50 - 20.6

0.15 x = 24.9

x = 24.9/ 0.15 = 166 quarters

y =206 - 166 = 40 dimes

Check:

0.25*166+ 0.10*40 = 45.50

45.50 = 45.50

Answer:

Not enough evidence to reject Null hypothesis

Step-by-step explanation:

Solution:-

- A comparative study for bacterial growth in manual and electronic faucets is made.

- It is observed that there is a higher growth in electronic faucets due to slower flow rates, i.e electronic faucets are not thoroughly flushed; hence, giving more resident time for the scaled bacteria to grow.

- It is known that 15% of cultures from older faucets were tested positive for the Legionella bacteria.

- A study at John Hopkins was conducted on a sample n = 20 electronic faucets with the probability of bacteria growing in a faucet is 0.15.

- We will conduct a hypothesis for at-least half proportion of electronic faucets have cultured bacteria.

- State the hypothesis for the proportion of electronic faucets culturing Legionella bacteria:

        Null Hypothesis:  P = 0.15

        Alternate hypothesis: P > 0.15    

- To determine the test statistics for the study conducted at John hopkins. We had a sample size of n = 20, and the probability for a bacteria to grow in a faucet is 0.15.

- Denote random variable, X: The number of electronic faucets culturing Legionella bacteria.

- Since, the probability for a bacteria to grow in a faucet is independent for each new faucet. We will assume the RV " X " to follow binomial distribution with probability of success 0.15:

                      X ~ Bin ( 20 , 0.15 )                  

- We are to determine that at-least half of the sample is subjected to the said bacteria. This is the probability of P ( X ≥ 10 ).

- The pmf for a binomially distributed random variable X is given below:

                     [tex]P ( X = r ) = n_C__r * ( p(success) )^r * ( p (fail) )^(^n^-^r^)[/tex]

Where,

            p ( success ) = 0.15

            p ( fail ) = 1 - p ( success ) = 1 - 0.15 = 0.85

- Use the pmf to determine the required test statistics:

[tex]P ( X \geq 10 ) = 1 - P ( X \leq 9 )\\\\P ( X \geq 10 ) = 1 - [ (0.85)^2^0 + 20*(0.15)*(0.85)^1^9 + 20_C_2 (0.15)^2*(0.85)^1^8 +\\\\ 20_C_3 (0.15)^3*(0.85)^1^7 + 20_C_4 (0.15)^4*(0.85)^1^6 + 20_C_5 (0.15)^5*(0.85)^1^5+\\\\ 20_C_6 (0.15)^6*(0.85)^1^4 + 20_C_7 (0.15)^7*(0.85)^1^3 + 20_C_8 (0.15)^8*(0.85)^1^2 + \\\\ 20_C_9 (0.15)^9*(0.85)^1^1\\\\\\P ( X \geq 10 ) = 1 - [ 0.03875 + 0.13679 + 0.22933 + 0.24282 + 0.18212 + 0.10284 + \\\\ 0.04537 + 0.01601 + 0.00459 + 0.00108 ]\\\\[/tex]

[tex]P ( X \geq 10 ) = 1 - [ 0.997 ] = 0.003[/tex]

- The probability that 10 or more electronic faucets is found to have Legionella bacteria growing is 0.003              

- The test proportion of 10 and more electronic faucets have culturing bacteria is p = 0.003.

- Assuming normality of the population, the Z-statistics would be:

                  [tex]Z-test = \frac{ (p - P) \sqrt{n} }{\sqrt{P*(1 - P )} } \\\\Z-test = \frac{ (0.003 - 0.15) \sqrt{20} }{\sqrt{0.15*(0.85)} } \\\\Z-test = -1.84109[/tex]

- If we were to test the claim to 90% level of confidence:

                  significance level (α) = 1 - CI = 1 - 0.9 = 0.1

- The rejection region Z-critical is defined by a right-tail:

                 [tex]Z-critical \geq Z_\alpha \geq Z_0_._2\\\\Z-critical \geq 1.28[/tex]    

- Compare the test statistics with the rejection criteria defined by the Z-critical:

                Z-test < Z-critical

                -1.84 < 1.28

Conclusion:

There is not enough evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%.

Answer:

12.4+3√7 is  irrational

Step-by-step explanation:

12.4 is a rational number

3√7 is an irrational number

The sum of a rational number and an irrational number is irrational.

So, 12.4+3√7 is  irrational

Answer:

82.76

Step-by-step explanation:

77 x 7.5%=5.775

5.775 +77

Answer:

64.40$

Step-by-step explanation:

Answer:

3kg = $34.20

34kg= ?

x= (34 x $34.20)/3

x= 1162,80/3

x= $387,60

Answer:

Yes

Step-by-step explanation:

For a triangle to be rights angled.

It should follow Pythagoras theorem.

Pythagoras theorem states that if sides containing right angle is  a and b

then  is given by

hypotenuse =  [tex]\sqrt{a^2+b^2}[/tex]

As hypotenuse is always the greatest side

Out of the given sides 144m,165m,219m

219 can only be hypotenuse

Thus side containing right angle will be 144m and 165m .

Lets plug these value in formula of Pythagoras theorem

[tex]hypotenuse = \sqrt{144^2 + 165^2} \\hypotenuse = \sqrt{20,736 + 27,225} \\hypotenuse = \sqrt{47961} \\hypotenuse = 219\\[/tex]

As we can see that hypotenuse calculated by us is same as given in problem.

Thus the given triangle is right angled.

Answer:

$20 after the applied coupon

Step-by-step explanation:

The required sale price of the shirt after getting  1/3 off is $20.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A $30 shirt is marked, "Get 1/3 off.
The sale price of the shirt,
= 30 - 1 / 3×30
= 30 - 10
= $ 20

Thus, the required sale price of the shirt after getting  1/3 off is $20.

Learn more about percentages here:

brainly.com/question/13450942

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Answer:

B.

Step-by-step explanation:

Yes, because the product of their slopes are -1. Rest explanation in the attached file. Hope it helps :)

Answer:

AB(y = ax + b) contains A(2, 1) and B(3, 4)

=> 2a + b = 1

    3a + b =4

=> a = 3, b= -5 => Slope AB = a = 3

CD (y = cx + d) contains C(-2, -1) and D(1, -2)

=> -2c + d = -1

       c  + d = -2

=> c = -1/3, d = -5/3 => Slope CD = c =-1/3

If AB is perpendicular to CD, then Slope's AB x Slope's CD = -1

Check:

a x c = 3 x (-1/3) = -1

=> AB is perpendicular to CD

=> Option B is correct.

Hope this helps!

:)

Answer:

1/3 cup Serving will provide 120 calories and 4 grams of fibre

Step-by-step explanation: one gram = 7.716 calories

1/2 cup serving provides 180 calories and 6 grams.

One cup serving with you provide 360 calories and 12 grams

So

1/3 cup Serving will provide 360/3 calories and 12/3 grams

1/3 cup Serving will provide 120 calories and 4 grams of fibre

Answer:

B.

Step-by-step explanation:

Data

Center = (2, -16)

A (2, -13)

P (-1, -16)

Equation

(x - h)² + (y - k)² = r² or

(x₁ - h)² + (y₁ - k)² = (x₂ - h)² + (y₂ - k)²

Substitution

(2 - 2)² + (-13 + 16)² = (-1 - 2)² + (-16 + 16)²

The signs in my equation and the one in the options are different but the results are the same

Answer:

(A) Probability that the port handles less than 5 million tons of cargo per week is 0.7291.

(B) Probability that the port handles 3 or more million tons of cargo per week is 0.9664.

(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is 0.2373.

(D) The number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.

Step-by-step explanation:

We are given that the port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge.

The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week with a standard deviation of 0.82 million tons.

Let X = Number of tons of cargo handled per week

SO, X ~ Normal([tex]\mu=4.5,\sigma^{2}=0.82^{2}[/tex])

The z score probability distribution for normal distribution is given by;

                               Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 4.5 million tons

            [tex]\sigma[/tex] = standard deviation = 0.82 million tons

(A) Probability that the port handles less than 5 million tons of cargo per week is given by = P(X < 5 million tons)

        P(X < 5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{5-4.5}{0.82}[/tex] ) = P(Z < 0.61) = 0.7291

The above probability is calculated by looking at the value of x = 0.61 in the z table which has an area of 0.7291.

(B) Probability that the port handles 3 or more million tons of cargo per week is given by = P(X [tex]\geq[/tex] 3 million tons)

        P(X [tex]\geq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\geq[/tex] -1.83) = P(Z [tex]\leq[/tex] 1.83)

                                                                          = 0.9664

The above probability is calculated by looking at the value of x = 1.83 in the z table which has an area of 0.9664.

(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is given by = P(3 million tons < X < 4 million tons)

     P(3 million tons < X < 4 million tons) = P(X < 4) - P(X [tex]\leq[/tex] 3)

      P(X < 4) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{4-4.5}{0.82}[/tex] ) = P(Z < -0.61) = 1 - P(Z [tex]\leq[/tex] 0.61)

                                                = 1 - 0.7291 = 0.2709

      P(X [tex]\leq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\leq[/tex] -1.83) = 1 - P(Z < 1.83)

                                                 = 1 - 0.9664 = 0.0336

The above probability is calculated by looking at the value of x = 0.61 and x = 1.83 in the z table which has an area of 0.7291 and 0.9664 respectively.

Therefore, P(3 < X < 4) = 0.2709 - 0.0336 = 0.2373

(D) Now, it is given that 85% of the time the port can handle the weekly cargo volume without extending operating hours, that means;

           P(X > x) = 0.85     {where x is the required no. of tons of cargo}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85

           P(Z > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85

In the z table, the critical value of x which represents top 85% area is given as -1.036, that is;

                      [tex]\frac{x-4.5}{0.82} = -1.036[/tex]  

                    [tex]{x-4.5} = -1.036\times 0.82[/tex]

                     x  =  4.5 - 0.85 = 3.65 million tons

Hence, the number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.

Answer:

The other endpoint of the​ segment is [tex](-18,-7)[/tex].

Step-by-step explanation:

The midpoint of the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the following formula:

                                          [tex](x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]

where [tex](x_m,y_m)[/tex] = coordinates of the midpoint.

We know that the midpoint is (-15, 2) and an endpoint is (-12, 11). Substituting the information we have gives:

                                         [tex](-15,2)=(\frac{x_1-12}{2}, \frac{y_1+11}{2} )[/tex]

To find [tex]x_1[/tex] we need to solve this equation:

[tex]-15=\frac{x_1-12}{2} \\\\\frac{x_1-12}{2}=-15\\\\\frac{2\left(x_1-12\right)}{2}=2\left(-15\right)\\\\x_1-12=-30\\\\x_1-12+12=-30+12\\\\x_1=-18[/tex]

and to find [tex]y_1[/tex] we need to solve this equation:

[tex]2= \frac{y_1+11}{2} \\\\\frac{y_1+11}{2}=2\\\\\frac{2\left(y_1+11\right)}{2}=2\cdot \:2\\\\y_1+11=4\\\\y_1=-7[/tex]

The other endpoint of the​ segment is [tex](x_1,y_1)=(-18,-7)[/tex].

Answer:

I think it's true. hope this helps!!

Answer:

a. [tex]f^-^1(x)=\frac{x}{4} +3[/tex]

b. [tex]f(-9)=-48[/tex]

c. [tex]f^-^1(-9)=\frac{3}{4}[/tex]

Step-by-step explanation:

In a, the -1 means inverse of f(x). To find the inverse, you rewrite the equation in terms of x and y. You replace the x with y and y with x. Then you solve for y.

[tex]f^-^1(x)=4x-12[/tex]

[tex]y=4x-12[/tex]

[tex]x=4y-12[/tex]

[tex]x+12=4y[/tex]

[tex]\frac{x}{4} +3=y[/tex]

[tex]f^-^1(x)=\frac{x}{4} +3[/tex]

In b, all you have to do is plug in -9 into f(x).

[tex]f(9)=4(9)-12[/tex]

[tex]f(9)=-48[/tex]

In c, you plug in -9 into inverse function f.

[tex]f^-^1(-9)=\frac{3}{4}[/tex]

Answer:

1650

Step-by-step explanation:

The shape is a pyramid on top of a prism.

Volume of a pyramid is V = ⅓ Ah, where A is the area of the base and h is the height of the pyramid.

Volume of a prism is V = Ah, where A is the area of the base and h is the height of the prism.

The base of both shapes is a right triangle.  The area is:

A = ½ bh

A = ½ (22) (10)

A = 110

The height of the prism is 6.  The height of the pyramid is 33 − 6 = 27.  The total volume is:

V = (110) (6) + ⅓ (110) (27)

V = 1650

Answer:

  see below

Step-by-step explanation:

A percentage change is computed as follows:

  percent change = ((new value) -(original value))/(original value) × 100%

For your first one, this looks like ...

  percent change = ($25 -$75)/$75 × 100% = (-50/75) × 100% = -0.667×100%

  percent change = -66.7%

__

When there are a lot of similar calculations to do, I like to use a spreadsheet. See below for the other percentage changes (rightmost column).

Answer:

3 (7 a - 5) (a - 2)

Step-by-step explanation:

Factor the following:

21 a^2 - 57 a + 30

Factor 3 out of 21 a^2 - 57 a + 30:

3 (7 a^2 - 19 a + 10)

Factor the quadratic 7 a^2 - 19 a + 10. The coefficient of a^2 is 7 and the constant term is 10. The product of 7 and 10 is 70. The factors of 70 which sum to -19 are -5 and -14. So 7 a^2 - 19 a + 10 = 7 a^2 - 14 a - 5 a + 10 = a (7 a - 5) - 2 (7 a - 5):

3 a (7 a - 5) - 2 (7 a - 5)

Factor 7 a - 5 from a (7 a - 5) - 2 (7 a - 5):

Answer: 3 (7 a - 5) (a - 2)

Answer:

4; 7

Step-by-step explanation:

Small box = 25 and Large box = 50

small box = x and large box = x+3

25x+50(x+3)=450

25x+50x+150=450

75x=300

x=4

Large box = 4+3 = 7

Therefore, 4; 7

I hope this helped and have a good rest of your day!

Answer:

2 isnt the domain

Step-by-step explanation:

Answer:

[tex] (17-14) -1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=1.222[/tex]

[tex] (17-14) +1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=4.778[/tex]

So then we can conclude at 90% of confidence that the difference in the two means is between 1.222 and 4.778 beats per minute

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar X_1 = 17[/tex] sample mean for the first sample

[tex] \bar X_2 = 14[/tex] sample mean for the second sample

[tex]\sigma =4.2[/tex] represent the population deviation

[tex] n_1= n_2 =30[/tex] represent the sample size ofr each case

We can construct the confidence interval for the difference of means with the following formula:

[tex] (\bar X_1 -\bar X_2) \pm z_{\alpha/2} \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}}[/tex]

And the confidence for this case is 90% or 0.9 so then the significance level is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2 =0.05[/tex] the critical value for this case is:

[tex] z_{\alpha/2}=1.64[/tex]

And replacing we got:

[tex] (17-14) -1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=1.222[/tex]

[tex] (17-14) +1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=4.778[/tex]

So then we can conclude at 90% of confidence that the difference in the two means is between 1.222 and 4.778 beats per minute

Answer:

  x = -4

Step-by-step explanation:

The equation of a vertical line in standard form is ...

  x = constant

In order for this line to go through the point with x-coordinate -4, the constant must be -4:

  x = -4

Answer:

c) A matched-pairs t-interval for a population mean difference

Step-by-step explanation:

Matched-Pairs t-Test. A matched-pairs t-test is used to test whether there is a significant mean difference between two sets of paired data.

A matched pair t test is used for comparison between means of two sets of paired data.

Thus, Option C: A matched-pairs t-interval for a population mean difference. is correct choice.

The selected sample of people will have to give pretest and then training and then post-test and the difference in the scores is recorded.

The researches want to identify the resultant difference so as to identify the effectiveness of the program.

For such type of cases, we use matched pair t test.

A matched pair t test is used to see if there is significant difference between means of two sets of paired data.

By paired data, we mean the data in both set which is paired.

Since the person is same who gives pre and post  test after training, thus the data is paired.

Also since the difference is to be analyzed to check the significance of the reading program, thus matched pair t test is perfect fit here.

Thus, option C: A matched pairs t-interval for a population mean difference is correct option.

Learn more about t-tests here:

https://brainly.com/question/1189751

The right answer is No solution.

Look at the attached picture

Hope it will help you

Answer:

4 ft

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

9 = 1/2 (4.5)h

9 =2.25 h

Divide each side by 2.25

9/2.25 = 2.25h/2.25

4 =h

Answer:

Hieght=4

hope it helps u...

Step-by-step explanation:

Answer: on edge i got D,   sq rt 13-sq rt 11

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

edge

Answer:

not sure

Step-by-step explanation:

can someone explain?  

Answer:D

Step-by-step explanation:

It’s a permutation

Answer:

The large pizza has the lower cost per square inch, so it is the better buy.

Step-by-step explanation:

A pizza has the format of a circle.

The area of a circle with radius r is given by the following equation:

[tex]A = \pi r^{2}[/tex]

A large pizza with an 18 inch diameter for $20

The radius is half the diameter, so [tex]r = 9[/tex].

In square inches, the area is:

[tex]A = \pi*9^{2} = 81\pi = 254.47[/tex]

254.47 square inches cost $20. So the price per square inch is 20/254.47 = 0.0786.

Medium pizza with a 14 inch diameter for $14:

Radius is 7. So

[tex]A = \pi*7^{2} = 49\pi = 153.938[/tex]

153.938 square inches cost $14. So the price per square inch is 14/153.938 = 0.0909.

The large pizza has the lower cost per square inch, so it is the better buy.