A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate. Suppose it is known that heart rate (in beats per minute) is normally distributed with an average of 70 bpm for adults. A random sample of 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption, with a standard deviation of 7 bpm. In order to test belief at the 10% significance level, determine P-value for the test.

Answer:

  -5/7

Step-by-step explanation:

The slope of a line is given by

m = (y2-y1)/(x2-x1)

   = ( -1 -4)/(5 - -2)

   = (-1-4)/(5+2)

   -5/7

Slope formula: y2-y1/x2-x1

= -1-4/5-(-2)

= -5/7

Best of Luck!

Answer:

x and y can have many values

Step-by-step explanation:

-24x - 12y = -16

Then: 24x + 12y = 16

We know: 6x + 3y = 4

X and Y can have a lot of valoues.

6x + 3y = 4

3 ( 2x + y) = 4

2x + y= 4/3

2x+y= 1.333...

Answer:

x ≤ [tex]\frac{9}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{4}[/tex](12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side

3x + 2 ≤ - 2x + 11 ( add 2x to both sides )

5x + 2 ≤ 11 ( subtract 2 from both sides )

5x ≤ 9 ( divide both sides by 5 )

x ≤ [tex]\frac{9}{5}[/tex]

-¼(12x+8) ≤ -2x+11

4X-¼(12x+8) ≤-2x+11

= -12x + 8 ≤ -2x + 11

-12x + 2x ≤ 11 - 8

= -10x/10 ≤ 3/-10

Answer:

The variance is  [tex]\sigma ^2 =25[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  21

     The sum of squares is [tex]SS = 500[/tex]

Generally the variance is mathematically represented as

           [tex]\sigma ^2 = \frac{SS}{n- 1}[/tex]

substituting values

          [tex]\sigma ^2 = \frac{ 500}{21- 1}[/tex]

          [tex]\sigma ^2 =25[/tex]

Answer:

The steps 1-7 have been explained

Step-by-step explanation:

The steps are;

1) We will verify that the population standard deviations are known and that the population is normally distributed which means the sample size must be a minimum of 30.

2) We will state the null and alternative hypothesis

3) We will determine the critical values from the relevant tables

4) From the critical values gotten, we will determine it's corresponding region where it can be rejected.

5)We will calculate the value of the test statistic from the formula;

z = [(x1' - x2') - (μ1 - μ2)]/√[((σ1)²/n1) + ((σ2)²/n2)]

6) If the value of the test statistic gotten from step 5 above falls in the region of rejection noted in step 4,then we will reject the null hypothesis

7) After rejection of the null hypothesis, we will now give a decision/conclusion on the claim.

Answer:

12/27

Step-by-step explanation:

Count all letters and all vowels then divide vowels by letters

The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.

The probability of any event suppose A, in an experiment is given as:

P(A) = n/S,

where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.

In the question, we are given an experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden".

We are asked to find the probability that the selected letter is a vowel.

Let the event of selecting a vowel from the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden" be A.

We can calculate the probability of event A by the formula:

P(A) = n/S,

where P(A) is the probability of event A, n is the number of favorable outcomes to event A in the experiment, and S is the total number of outcomes in the experiment.

The number of outcomes favorable to event A (n) = 12 (Number of vowels in the phrase)

The total number of outcomes in the experiment (S) = 27 (Number of letters in the phrase).

Now, we can find the probability of event A as:

P(A) = 12/27 = 4/9

∴ The probability that a vowel is randomly selected in the experiment of selecting a letter from the phrase "Sean wants to eat at Olive Garden", is 4/9.

Learn more about the probability of an event at

https://brainly.com/question/7965468

#SPJ2

Answer: 0.98

Step-by-step explanation:

given data:

probability they won a game = 58% = 0.58

since outcome of games are independent, and percentage would remain same as 2014.

probablility that Dodgers wins atleast 1 of their next 7 games

= 1 - p

= 1 - ( 0.58 )^ 7

= 1 - 0.02208

= 0.98

probabikotun that Dodgers would win one of their next seven games is 0.98

Answer:

She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Step-by-step explanation:

We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.

And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.

As we know that the margin of error is given by the following formula;

The margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm

         n = sample size of components

         [tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%

         [tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%

Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

                  0.1 mm        =  [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]

                    [tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]

                    [tex]\sqrt{n}[/tex] = 59.22

                     n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.

Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Answer:

[tex]f(a) = 2a + 8[/tex]

[tex]f(x + h) = 2x + 2h + 8[/tex]

[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x + 8[/tex]

Required

[tex]f(a)[/tex]

[tex]f(x + h)[/tex]

[tex]\frac{f(x + h) - f(x)}{h}[/tex]

Solving for f(a)

Substitute a for x in the given parameter

[tex]f(x) = 2x + 8[/tex] becomes

[tex]f(a) = 2a + 8[/tex]

Solving for f(x+h)

Substitute x + h for x in the given parameter

[tex]f(x + h) = 2(x + h) + 8[/tex]

Open Bracket

[tex]f(x + h) = 2x + 2h + 8[/tex]

Solving for [tex]\frac{f(x + h) - f(x)}{h}[/tex]

Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)

[tex]\frac{f(x + h) - f(x)}{h}[/tex] becomes

[tex]\frac{2x + 2h + 8 - (2x + 8)}{h}[/tex]

Open Bracket

[tex]\frac{2x + 2h + 8 - 2x - 8}{h}[/tex]

Collect Like Terms

[tex]\frac{2x - 2x+ 2h + 8 - 8}{h}[/tex]

Evaluate the numerator

[tex]\frac{2h}{h}[/tex]

[tex]2[/tex]

Hence;

[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]

Answer:

300 miles

Step-by-step explanation:

Let us consider the miles they travelled is 'm'

Mileage for Primo= 21 + (m × 0.20) = 21+0.2m

Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m

Question says The mileage is equal when Ultimo's charge is 4× Primo

Thus,

4 × (21+0.2m) = 24+ m

84 + 0.8m = 24 + m

60 = 0.2m

m = 300

Answer:  5.22 seconds

Step-by-step explanation:

t represents time and y represents the height.

Since we want to know when the ball hits the ground, find t when y = 0

Ball 1 starts at a height of 109 --> h = 109

0 = -16t² + 109

16t² = 109

   [tex]t^2=\dfrac{109}{16}\\[/tex]

   [tex]t=\sqrt{\dfrac{109}{16}}[/tex]

   [tex]t=\dfrac{\sqrt{109}}{2}[/tex]

   t = 5.22

=> H = 109

=> 0 = -16t² + 109

=> 16t² = 109

=> t² = 109/16

=> t = 109/2

=> t = 5.22 sec

Therefore, 5.22 second is the answer.

Answer:

Step-by-step explanation:

Volume of a pyramid is given by

[tex]V = \frac{1}{3} \times area \: of \: base \: \: \times height[/tex]

height = 15cm

From the question the pyramid is a square pyramid which means it's base is a square

Area of a square = l²

where l is the length of one side

l = 9cm

Area of square = 9² = 81cm²

So the volume of the pyramid is

[tex]V = \frac{1}{3} \times 81 \times 15[/tex]

[tex]V = 27 \times 15[/tex]

We have the final answer as

V = 405 cm³

Therefore the volume of the pyramid is

Hope this helps you

Answer:

2

Step-by-step explanation:

Pythagoras. c² = a² + b²

since both "side angles" are equal (45 degrees), we know it is an isosceles triangle, that means also the other side = x.

and so,

8 = x² + x² = 2x²

4 = x²

x = 2

Answer:

x = 2

Step-by-step explanation:

sin(45)/x = sin(90)/[tex]\sqrt{8}[/tex]

[tex]\sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}[/tex]

x = [tex]\sqrt{8}[/tex] [tex]\sin \left(45^{\circ \:}\right)[/tex]

[tex]x = \sqrt{8} \frac{\sqrt{2}}{2}[/tex]

x = [tex]\frac{\sqrt{16} }{2}[/tex]

x = 4/2

x = 2

Answer:

2342560 combos

Step-by-step explanation:

so its 1 letter*1number*1 letter*1 letter*1 letter, or 22x10x22x22x22 which should equate to 2342560 possible ID codes, hope this helps :)

Step-by-step explanation:

Substitute the values of a and b into [a-b]2

= [-5-(-2)]2

= [-5+2]2

= [-3]2

= -6

Answer:

Amount = Rs. 30250 when Rate = 10%

Amount = Rs. 31360 when Rate = 12%

Step-by-step explanation:

Given

[tex]Principal, P = Rs.\ 25,000[/tex]

[tex]Time, t = 2\ years[/tex]

[tex]Rate; R_1 = 10\%[/tex]

[tex]Rate; R_2 = 12\%[/tex]

Number of times (n) = Annually

[tex]n = 1[/tex]

Required

Determine the Amount for both Rates

Amount (A) is calculated by:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

When Rate = 10%, we have:

Substitute 25,000 for P; 2 for t; 1 for n and 10% for r

[tex]A = 25000 * (1 + \frac{10\%}{1})^{1 * 2}[/tex]

[tex]A = 25000 * (1 + \frac{10\%}{1})^{2}[/tex]

[tex]A = 25000 * (1 + 10\%)^{2}[/tex]

Convert 10% to decimal

[tex]A = 25000 * (1 + 0.10)^{2}[/tex]

[tex]A = 25000 * (1.10)^{2}[/tex]

[tex]A = 25000 * 1.21[/tex]

[tex]A = 30250[/tex]

Hence;

Amount = Rs. 30250 when Rate = 10%

When Rate = 12%, we have:

Substitute 25,000 for P; 2 for t; 1 for n and 10% for r

[tex]A = 25000 * (1 + \frac{12\%}{1})^{1 * 2}[/tex]

[tex]A = 25000 * (1 + \frac{12\%}{1})^{2}[/tex]

[tex]A = 25000 * (1 + 12\%)^{2}[/tex]

Convert 12% to decimal

[tex]A = 25000 * (1 + 0.12)^{2}[/tex]

[tex]A = 25000 * (1.12)^{2}[/tex]

[tex]A = 25000 * 1.2544[/tex]

[tex]A = 31360[/tex]

Hence;

Amount = Rs. 31360 when Rate = 12%

Answer:

[tex]\large \boxed{\mathrm{B. \ \ \{-10, -6, 10\} }}[/tex]

Step-by-step explanation:

The domain is the x values.

D = {-1, 0, 4}

y = 4(-1) - 6 = -4 - 6 = -10

y = 4(0) - 6 = 0 - 6 = -6

y = 4(4) - 6 = 16 - 6 = 10

The range is the y values.

R = {-10, -6, 10}

Answer:

9.63 - 2.25 = 18j

j = 0.41

Step-by-step explanation:

first you set the equation equal to 18 since you want to find out what each bottle of juice  costs.

= 18j

if the total cost was 9.63 you need to subtract 2.25 form it to find out how much the 18-pack of juice bottles was. so you set 9.63 - 2.25 equal to  18j

9.63 - 2.25 = 18j

7.38 = 18j

0.41 = j

Check your work:

9.63 - 2.25 = 18(0.41)

7.38 = 7.38                    true!

hope this helps! if you have any questions, let me know!

Answer:

Use the student t distribution

Step-by-step explanation:

Here is the formula

t = (x - u) ÷(s/√N)

From the information we have in the question:

n = 150

s = 550

x = 3400

u = mean = 2400

= 3400 - 2400÷ 500/√150

= 1000/44.9

= 22.27

At 0.05 significance level, df = 149 so t tabulated will be 1.65.

Answer:

345

Step-by-step explanation:

20*3 = 60 there's 60 minutes in one hour

115*3 = 345

Answer:

I need points plsss

Step-by-step explanation:

Correct question is;

The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consumption to be 74 gallons with a standard deviation of 16 gallons.

a. What is the value of the population mean? What is the best estimate of this value?

b. Explain why we need to use the t distribution. What assumption do you need to make?

c. For a 90 percent confidence interval, what is the value of t?

d. Develop the 90 percent confidence interval for the population mean.

e. Would it be reasonable to conclude that the population mean is 68 gallons?

Answer:

A) Best estimate = 74 gallons

B) because the population standard deviation is unknown. The assumption we will make is that the population follows the normal distribution.

C) t = 1.725

D) 90% confidence interval for the population mean is (67.9772, 80.0228) gallons

E) Yes

Step-by-step explanation:

We are given;

Sample mean; x' = 74

Sample population; n = 21

Yearly Standard deviation; s = 16

A) We are not given the population mean.

So the closest estimate to the population mean would be the sample mean which is 74.

B) We are not given the population standard deviation and as such we can't use normal distribution. So what is used when population standard deviation is not known is called t - distribution table. The assumption we will make is that the population follows the normal distribution.

C) At confidence interval of 90% and DF = n - 1 = 21 - 1 = 20

From t-tables, the t = 1.725

D) Formula for the confidence interval is;

x' ± t(s/√n) = 74 ± 1.725(16/√21) = 74 ± 6.0228 = 67.9772 or 80.0228

Thus 90% confidence interval for the population mean is (67.9772, 80.0228) gallons

E) 68 gallons lies within the range of the confidence interval, thus we can say that "Yes, it is reasonable"

4x+2=6(-2x-5)

<=>4x+2=-12x-30

<=>16x+32=0

<=>x=-2

Answer:

A. 30

Step-by-step explanation:

The interquartile range for a box and whiskers plot, is the value from the right side of the box minus the value of the left side of the box.

In this case at the far right side of the box it is at 130, at the far left side of the box it is at 100.

130-100=30

Answer:

[tex]\huge\boxed{IQR = 30}[/tex]

Step-by-step explanation:

Q1 = 130 (Left hand edge of the box)

Q3 = 100 (Right Hand edge of the box)

Interquartile Range = Q3-Q1

IQR = 130-100

IQR = 30

Answer:

Step-by-step explanation:

59°

Answer:

Step-by-step explanation:

87°32' = 86°92'

(86°92')/2 = 43°46'

B = 13/(16cos(43°46')) = 1.125

Answer:

Step-by-step explanation:

Answer:

3480

Step-by-step explanation:

It always help if you make clear how the state assesses taxes. Usually it is done the way I will do it, but it is no guarantee.

First 3000 = 3000 * 2/100 = 60.00

The next 2000 (excess over 3000) = 2000 * 3/100 = 60

The next 12000 (excess over 5000) = 12000 * 5/100 = 600

The next step would be excess over 12000 = 48000 * 5.75/100 = 2760

That's the way most taxes for federal taxes and state taxes work. What you have to know is this: does the question use the term excess anywhere? Or do your notes.  If you are accustomed to the word then this is the way the question is done.

So the total taxes = 60 + 60 + 600 + 2760 = 3480

Answer:

q =  5000/x  + 6

Step-by-step explanation:

D´= dq/dx  =  - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K   in this equation x is the price per unit and q demanded quantity and K integration constant

If when  1006 units are demanded when the rice is 5 then

x = 5     and   q = 1006

1006  =  5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q =  5000/x  + 6