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Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X [tex]\sim[/tex] N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

[tex]P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})[/tex]

[tex]P(X < 76) = P(Z< \dfrac{3}{12.5})[/tex]

[tex]P(X < 76) = P(Z< 0.24)[/tex]

From the standard normal distribution tables,

[tex]P(X < 76) = 0.5948[/tex]

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

[tex]P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]

[tex]P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})[/tex]

[tex]P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})[/tex]

[tex]P( \overline X < 76) = P(Z< 1.2)[/tex]

From the standard normal distribution tables,

[tex]P(\overline X < 76) = 0.8849[/tex]

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Answer:

The answer is usted

Step-by-step explanation:

And if you want to learn more download duolingo

Answer:

(-0.3, 2.3)

Step-by-step explanation:

(-1.8+1.2)/2 = -0.3

(1.9+2.7)/2 = 2.3

Answer:

Step-by-step explanation:

Let the points be A and B

A ( - 1.8 , 1.9 ) ⇒( x₁ , y₁ )

B ( 1.2 , 2.7 )⇒ ( x₂ , y₂ )

Now, let's find the midpoint:

[tex] \mathsf{ (\frac{x1 + x2}{2} \: , \frac{y1 + y2}{2} )}[/tex]

Plug the values

[tex] \mathsf{ = (\frac{ - 1.8 + 1.2}{2} \: , \frac{1.9 + 2.7}{2} )}[/tex]

Calculate

[tex] \mathsf{ = ( \frac{ - 0.6}{2} \: , \frac{4.6}{2} )}[/tex]

[tex] \mathsf{ = (- 0.3 \:, 2.3)}[/tex]

Hope I helped!

Best regards!

Answer:

i dont know lol

Step-by-step explanation:

Answer:

[tex]W = 5h - 90 \\ 5h = W + 90 \\ h = \frac{W + 90}{5} [/tex]

Answer:

h = w+90/ 5

Step-by-step explanation:

5h-90=w

5h/5= w+90/5

h= w+90/5

[tex]A\cup B=\{q,s,u,w,y,z\}\\(A\cup B)'=\{r,t,v,x\}\\\boxed{(A\cup B)'\cap C=\{v,x\}}[/tex]

Answer:

The angle of elevation is not properly represented

Step-by-step explanation:

Given

The question in the attachment;

Required

Determine the error

See attachment for proper representation of the angle of elevation;

Solving further (From the Attachment)

[tex]Tan22 = \frac{x}{3000}[/tex]

Multiply both sides by 3000

[tex]x = 3000 * tan22[/tex]

[tex]x = 3000 * 0.4040[/tex]

[tex]x = 1212[/tex]

The cliff is about 1212 feet high

Answer:

2 seconds

Step-by-step explanation:

Given the equation:

[tex]f(x) = -x^2 + x + 2[/tex]

Where f(x) represents the height of each ball thrown by machine.

and x represents the time in seconds.

To find:

The number of seconds after which the machine throws the balls hits the ground = ?

Solution:

In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]

(Because when the ball hits the ground, the height becomes 0).

Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]

[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]

[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.

So, the answer is after 2 seconds, the ball hits the ground.

Answer:

V≈113.1

Step-by-step explanation:

V=πr2h

3=π·32·12

3≈113.09734

Answer:

540

Step-by-step explanation:

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99

Answer:

540

Step-by-step explanation:

Hey there!

Well we need to first find all the palindromic numbers,

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99

Add

= 540

Hope this helps :)

Answer:

0.204

Step-by-step explanation:

The formula to use to solve this is the combination formula.

Combination formula =

C(n, r) = nCr = n!/r! (n - r)!

Total number of kittens = 8 boy kittens + 9 girl kittens

= 17 kittens

Step 1

We find the probability of choosing 4 boy kittens out of 8 boy kittens

= 8C4 = 8!/4! × (8 - 4)!

= 8C4 = 8! / 4! × 4!

= 8C4 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1)

8C4 = 70

Step 2

We find the probability of choosing 7 girl kittens out of 9 girl kittens

9C7 = 9!/7! × (9 - 7)!

= 9C7 = 9! / 7! × 2!

= 9C7 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (7 × 6 × 5 × 4 × 3 × 2 × 1) × (2 × 1)

9C7 = 36

Step 3

Find the probability of Picking 11 kittens out of 17 kittens

17C11 = 17!/11! × (17 - 11)!

= 17C11 = 17! / 11! × 6!

= 17C11 = 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)

17C11 = 12,376

Step 4

The final step

The probability that the director chooses 4 boy kittens and 7 girl kittens

= 8C4 × 9C7/ 17C11

= 70 × 36/12376

= 2520/12376

= 0.2036199095

Approximately to 3 decimal places = 0.204

Therefore, the probability that the director chooses 4 boy kittens and 7 girl kittens is 0.204

hi

it's equal to as X = 1X  

so 1X-0.3X = 0.7X

Answer:

yes

Step-by-step explanation:

as

x - 0.3x = 1×x - 0.3x = (1-0.3)x = 0.7x

Answer:

0.85714285714286 x 100 = 85.7143%.

Step-by-step explanation:

Answer:

C) 3/2x-1/8

Step-by-step explanation:

We can see that it has a generally positive slope, which rules out B and D.

Plugging in a few numbers for x, we can quickly see that 6 is too high of a slope. (If we plug in 6 for x, the y value would be almost 35, not 10).  This rules out A.

While it doesn’t fit perfectly, C is by far the closest.

Answer:

total number(n)=10

divided the total number into two equal parts so

in one group of number =5

ln first phase group of number middle value =44

In second phase group of number middle value=50

then using formula,q1=44 q3=50

inter quartile range =q3_q1

=50-44

=6

therefore interquartile range =6

Answer: The answer is 6

Answer:

2.8

Step-by-step explanation:

Hey there!

Well to find the amount of minutes needed to fill a 46.2 gallon bathtub we’ll divide.

46.2 / 16.5

= 2.8

2.58 minutes

Hope this helps :)

Step-by-step explanation:

Set up f(x).

[tex] \sqrt[3]{11x - 3} = f(x)[/tex]

Replace f(x) with y

[tex] \sqrt[3]{11x - 3} = y[/tex]

Swap x and y

[tex] \sqrt[3]{11y - 3} = x[/tex]

Solve for y

Cube both sides

[tex]11y - 3 = {x}^{3} [/tex]

Add 3 to both sides

[tex]11y = {x}^{3} + 3[/tex]

Divide both sides by 11

[tex]y = \frac{x {}^{3} + 3 }{11} [/tex]

so

[tex]f {}^{ - 1} (x )= \frac{ {x}^{3} + 3}{11} [/tex]

[tex]\begin{cases}\large\bf{\green{ \implies}} \tt \: - \frac{6}{5} \: k \: = \: 12 \\ \\ \large\bf{\green{ \implies}} \tt \: - \frac{6k}{5} \: = \: 12 \\ \\ \large\bf{\green{ \implies}} \tt \: - 6k \: = \: 12 \: \times \: 5 \\ \\ \large\bf{\green{ \implies}} \tt \: - 6k \: = \: 60 \\ \\ \large\bf{\green{ \implies}} \tt \: k \: = \: \cancel\frac{60}{ - 6} \\ \\ \large\bf{\green{ \implies}} \tt \: k \: = \: - 10 \end{cases}[/tex]

Answer:

4.5

Step-by-step explanation:

2/8=x/18

Answer:

4.5 cups

Step-by-step explanation:

first you set up the problem like servings/cups. This would look like 8/2. Then you add the 18 servings and make it a cross multiplication problem. The expression would look like 8/2=18/x. You cross multiply and get 8x=36. Divide by 8 and get x=4.5 cups.

Answer:

The 95% confidence interval is  [tex]0.3795 < p < 0.4405[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 1000[/tex]

      The  number of approved loan is  k =  410

Generally the sample proportion is mathematically represented as

       [tex]\r p = \frac{k}{n}[/tex]

substituting values

      [tex]\r p = \frac{410}{1000}[/tex]

       [tex]\r p = 0.41[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

       [tex]\alpha = 100 - 95[/tex]

        [tex]\alpha = 5\%[/tex]

       [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is  

         [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }[/tex]

substituting values

        [tex]E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }[/tex]

        [tex]E = 0.03048[/tex]

The 95% confidence interval for p is mathematically represented  as

     [tex]\r p - E < p < \r p + E[/tex]

substituting values

     [tex]0.41 - 0.03048 < p < 0.41 + 0.03048[/tex]

    [tex]0.3795 < p < 0.4405[/tex]

Hey there!

If our central angle is 77, our arc on the outside that it intercepts is going to be 77/360 of the total circumference of the arc. This is because a full circle angle is 360 degrees, so if our central angle was 360, we would just find the circumference of the circle as the arc would be the entire circle.

In our case, we will just find the circumference and then multiply it by 77/360 to find our arc length as we are just looking for a fraction of our total circle.

Circumference is 2πr, so we have 2π(6)≈37.68

Now we multiply this by 77/360.

37.68×77/360≈ 8.06

So now, if you have a radius r and a central angle x, you can use the formula x/360 ×2πr to find the arc length.

Have a wonderful day! :D

Answer:

Option (2)

Step-by-step explanation:

1). If two lines have the same slope, lines are defined as parallel.

m₁ = m₂

2). If the multiplication of the slopes of two lines is (-1), lines will be perpendicular.

m₁ × m₂ = (-1)

Line 1 : It passes through two points (-2, 10) and (1, 1).

Slope of the line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                              = [tex]\frac{1+2}{10-1}[/tex]

                              = [tex]\frac{3}{9}[/tex]

                         m₁ = [tex]\frac{1}{3}[/tex]

Line 2 : It passes through two points (-2, 8) and (2, -4).

Slope of the line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                               = [tex]\frac{8+4}{-2-2}[/tex]

                               = [tex]-\frac{12}{4}[/tex]

                         m₂ = -3

Since, m₁ × m₂ = [tex]\frac{1}{3}\times (-3)[/tex]

                        = (-1)

Therefore, given lines are perpendicular to each other.

Option (2) is the correct option.

Answer:

(a = 1/7 (b = .2 (c = 3/9

Step-by-step explanation:

1/7 = .14

1/4 = .25

3/9 = .33

a & b are lower than 1/4 and c is higher

Answer:- 10[tex]m^{2}[/tex] + 3m -9

Step-by-step explanation: Given ;  

  A= -3 -m

  B= 3m -5[tex]m^{2}[/tex]

 2B + 3A

        solution

     2B + 3A

substitute A and B in the formula

    2(3m - 5[tex]m^{2}[/tex]) + 3(-3 -m)

    6m - 10[tex]m^{2}[/tex] - 9 - 3m   group like terms

    - 10[tex]m^{2}[/tex] + (6m -3m) -9

     - 10[tex]m^{2}[/tex] + 3m -9

Answer:

4). 27V

Step-by-step explanation:

Let the edge of the cube A be x

Volume of Cube A= V

Volume= x*x*x= x³

so V = x³

Edge of cube B = 3 times edge of cube A

Edge of cube B = 3x

Volume of cube B =( 3x)³

volume of cube B = 27x³

But x³= V

So volume of cube B = 27v

Answer: Hi!

We can simplify this by combining like terms:

-12w + 7w - 3 - 6

-12w + 7w = -5w

-3 - 6 = -9

Out equation now looks like this:

-5w - 9

There's nothing left to simplify, so we're done!

Hope this helps!

Answer:

$91

Step-by-step explanation:

If a jacket is on sale for 35% off, that means that the price of the jacket is [tex]100-35=65[/tex]% of its original price.

We can find 65% of 140 by making 65% into a decimal - 0.65, then multiply it by 140.

[tex]140\cdot0.65=91[/tex]

Hope this helped!

Answer:

$91.00

Step-by-step explanation:

The jacket is on sale for 35%. Usually, you pay for 100% of the jacket's price. Since it is on sale, we can subtract 35% from 100%.

100%-35%=65%

With the sale, you only pay for 65% of the price.

Now, we can multiply 65% and 140.

65% * 140

Convert 65% to a decimal. Divide 65 by 100 or move the decimal place 2 spots to the left.

65/100=0.65

65.0 --> 6.5 --> 0.65

0.65 * 140

Multiply

91

$91

The sale price for the sports jacket is $91.00

Answer:

a)0.519

b)requirements for constructing a confidence interval about p are satisfied.

c)0.488, and 0.550

d)yes this is because there is no possibility

that the true proportion is not captured in the confidence interval.

e)

0.450, 0.512

Step-by-step explanation:

a)The point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without can be calculated as

521 of that adult that indicated that televisions are a luxury they could do without/1003 adults surveyed,

p = 521/1003

= 0.519.

b)

np(1-p)=1003×(0.519)×(1-0.519)

=250.39≥10 and the sample size is less than 5% of the population

therefore, requirements for constructing a confidence interval about p are satisfied.

c) we were given 95% confidence,

Then α=(1-0.95)

= 0.05

From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96

confidence interval can the be calculated using the formula below

- p ± Z*√ p (1 – p)/n

=0.519 ± 1.96√0.519×(1 – 0.519)/(1003)

= 0.519 ± 1.96×0.0158

0.519 ± 0.031

= 0.488, and 0.550

d) yes this is because there is no possibility

that the true proportion is not captured in the confidence interval.

e)the sample size can be calculated as

P=x/n

=(1003-521)/1003

=0.481

But we're given 95% confidence interval

Then

α=(1-0.95)=

0.05

From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96

Then convidence interval=

- p ± Z*√ p (1 – p)/n

=0.481 ± 1.96√0.481×(1 – 0.481)/(1003)

0.450, 0.512

Answer:

The correct answer is:

c. Joe will go running, biking and hunting

Step-by-step explanation:

Parallel construction or parallelism or parallel structure is a style used in writing a sentence, where there is a balance in phrases or clauses within one or more sentences by them having the same grammatical structure. parallelism adds elegance, clarity and symmetry to sentences. It essentially has to so with a repetition of a chosen grammatical form within a sentence.

In our example:

a.  Jim likes to hunt, bike, and throwing darts. (not parallel)

    Jim likes to hunt, bike, and throw darts (parallel)

The verbs, hunt, bike and throw must be in the same form (present continuous) to be parallel

b. Mimie has to study, drive her sister to the store, and enjoy herself in the garden. (not parallel).

The sentence in option b is not parallel because the other actions apart from "study" have a place where they took place; drive her sister to the store, enjoy herself in the garden, however, "study" doesn't have a place where the action occurs.

c. Jane will throw a ball, then she will mow the lawn. (not parallel)

the sentence is not parallel because there is an inconsistency in the pattern of the construct. a parallel version is:

Jane will first throw a ball, then she will mow the lawn, or

jane will throw a ball and mow the lawn.

d. Joe will go running, biking, and hunting. (parallel)

all the verbs are in the present continuous form.

[tex]|\Omega|=5\cdot4=20[/tex]

a)

[tex]|A|=3\cdot2+2\cdot1=8\\\\P(A)=\dfrac{8}{20}=\dfrac{2}{5}[/tex]

b)

[tex]|A|=3\cdot2+2\cdot3=12\\\\P(A)=\dfrac{12}{20}=\dfrac{3}{5}[/tex]

c)

[tex]|A|=3\cdot2=6\\\\P(A)=\dfrac{6}{20}=\dfrac{3}{10}[/tex]

d)

[tex]|A|=2\cdot1=2\\\\P(A)=\dfrac{2}{20}=\dfrac{1}{10}[/tex]