Which of the following is a true statement?

Answer:

The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

In a random sample of 250 students, we found that 75 work out 4 or more times a week.

This means that [tex]n = 250, \pi = \frac{75}{250} = 0.3[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.2432[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.3568[/tex]

The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).

Answer:

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Independent events:

If two events, A and B are independent, the probability of both events happening is the multiplication of the probabilities of each event happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Probability of getting a head on the coin:

Head or tails, fair coin, so:

[tex]P(A) = \frac{1}{2}[/tex]

Probability of getting the number 2 on the die:

6 numbers, one of which is 2, so:

[tex]P(B) = \frac{1}{6}[/tex]

What is the probability of getting a head on the coin and the number 2 on the die?

[tex]P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die

Answer:

the car travels 10km then 15km 60* north of east

Step-by-step explanation:

Answer:

x = ±i√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Algebra II

Imaginary root i

Step-by-step explanation:

Step 1: Define

Identify

5x² - 2 = -12

Step 2: Solve for x

Answer:

All of them are in the domain.

Step-by-step explanation:

The function is f(x)= (x+1)^2. If you simplify this, you get y=x^2+2x+1=0. This is a quadratic that opens upwards. There are no gaps in the x values and no impossible values. The domain is all real numbers and all the answer choices are real numbers.

Answer:

[tex] \displaystyle \boxed{|2m| }[/tex]

Step-by-step explanation:

we are given that

[tex] \displaystyle 2 \sqrt{ {m}^{2} } [/tex]

since m is greater than or equal to 0 it's a positive number therefore, the square root of m is defined and recall that √x²=|x| thus

[tex] \displaystyle \boxed{2 |m|}[/tex]

remember that,|a|•|x|=|ax| hence,

[tex] \displaystyle \boxed{ |2m|}[/tex]

and we're done!

Answer:

2m

Step-by-step explanation:

Given :-

By question,

→ 2√m²

→ 2 * m

→ 2m

40

Step-by-step explanation:

Each number is followed by a number that is half its value, so the sequence goes like

320, 160, 80, 40, 20, 10.

Answer:

Third one.

BO is not 7.8 cm

Step-by-step explanation:

Answer:

djjdjdjdjdjdjdjdjdidi

$28.62 not including tax.

Answer: 75%

Step-by-step explanation:

answer:2700sec

Step-by-step explanation:

if 60 sec=min

therefore;60×45

Answer:

6.09 is the answer rounded to nearest hundredths.

Step-by-step explanation:

It gives you n=150, p=0.55, and q=1-p.

If p=0.55 and q=1-p, then by substitution property we have q=1-0.55=0.45.

It ask you to evaluate the expression sqrt(npq).

So npq means find the product of 150 and 0.55 and 0.45. So that is 150(0.55)(0.45)=37.125.

The sqrt(npq) means we need to find the square root of that product. So sqrt(37.125)=6.093 approximately .

Answer:

a+3b

Step-by-step explanation:

3a+4b-2a-b

=3a-2a+4b-b

=a+3b

9514 1404 393

Answer:

  p > 3

Step-by-step explanation:

  3p -4 -8p < -19 . . . . . . given

  -5p -4 < - 19 . . . . . . . . collect terms

  -5p < -15 . . . . . . . . . . . add 4

  p > 3 . . . . . . . . . . . . . . divide by -5 (reverses the inequality symbol)

Answer:

Step-by-step explanation:

this is the famous dirt formula,  :P  I made it up   :D

D=rt    ( notice it looks like   Dirt  , kinda,  but it also means it dirt simple )

D= distance

r = rate  ( think speed or how fast)

t = time  ( in what ever units of time you want to use, seconds, minutes, hours )

13:28 - 11:20 = 128 minutes ( b/c the question is asking in MPH convert to hours)   2.4666667 hours

210 miles =  r * 2.46666667

210 / 2.46666667 = r   ( in MPH) ( does anyone else find it odd that they are saying miles in London instead of kilometers? :/ )

85.135 MPH = rate

so no, not even close to 104 MPH  :/  

Answer:

Average speed is 98 mph

Step-by-step explanation:

[tex]\frac{distance (miles)}{time (hours)}[/tex] = speed [tex]\frac{mile}{hours}[/tex]  (miles per hour is a ratio)

The time is 2 hours and 8 minutes.

[tex]\frac{8}{60}[/tex] = .13333 ( 8 minutes / 60 minutes in a hour)

So time is 2.133333 hours .

Divide the distance 210 by the time 2.13333 and get the speed.

Its 98.437..

Round to 98 miles per hour.

Answer:

1 /2

Step-by-step explanation:

Given :

Bag 1 : Red (R) ; Blue (B) ; White (W)

Bag 2 : Red (R) ; Pink (P) ; Yellow (Y) ; Green (G)

Total number of possible outcomes :

3C1 * 4C1 = 3 * 4 = 12 outcomes

Sample space (S) ;

_______ R ______ B _______ W

R_____ RR _____ RB ______ RW

P_____ PR _____ PB ______ PW

Y _____YR_____ YB ______ YW

G _____GR ____ GB ______ GW

To win price of baked goods ; Atleast one red ball must be drawn :

Probability of winning ; P(winning) = required outcome / Total possible outcomes

Required outcome = {RR, RB, RW, PR, YR, GR} = 6

Total possible outcomes = S = 12

P(winning) = 6/12 = 1/2

Answer:

so the measure of both angle is 24°

Step-by-step explanation:

original angle = 48°

so since its bisected the both angles are equal and let the angles be x

so,

x + x = 48°

2x = 48°

x = 48°/2

so, x = 24°

Answer:

The zeroes of f(x) = (x-7)(x+8) are 7 and -8.

Step-by-step explanation:

You have to figure out what makes each of the equal to zero.

Step 1 : Make the 2 equations both equal 0.

x-7 = 0

x+8 = 0

Step 2: Solve for x

x-7 = 0

x=7

x+8 = 0

x=-8

So 7 and -8 are both zeroes of this function.

Answer:

Length = 14 m, Width = 7 m

Step-by-step explanation:

Let the length is l and width is b.

Width, b = l-7

Area of the rectangle, A = 98 m²

We know that, the area of a rectangle is as follow :

[tex]A=lb[/tex]

So,

[tex]98=l(l-7)\\\\98=l^2-7l\\\\l^2-7l-98=0\\\\l^2+7l-14l-98=0\\\\l(l+7)-14(l+7)=0\\\\l=14,-7[/tex]

Length can't be negative. So,

Width, b = 14-7 = 7 m

So, the dimensions of the rectangle are 14 m and 7 m respectively.

9514 1404 393

Answer:

  no

Step-by-step explanation:

For lines to be parallel, any obtuse angle where a transversal crosses must be supplementary to any acute angle at that transversal. Here the sum of the obtuse and acute angles is 105° +65° = 170°, so it is not possible for this geometry to include parallel lines.

Answer:

D

Step-by-step explanation:

Use the midpoint formula to find the midpoint of the line segment.

Answer:

Step-by-step explanation:

a) 52 is divisible by 4 and 5 - 2 = 3

b) 63 is divisible by 9 and 3*2 = 6 -> ten digit

c) 50 is divisible by 10 and 5 + 0 = 5

d) 72 is divisible by 6 and 7*2 = 14

Answer:

2√14 prob I'm not 100% sure

Answer:

a. $10  

b. 10.46  

c. 10.46  

d. 0.096

Step-by-step explanation:

Let us take a nominal square of area 25 cm².

So, in this question, we can say that:-

a. The length of one of its sides will be less than 5 cm.

b. Its perimeter will be less than 20 cm.

Hope it helps :)

Step-by-step explanation:

area= 25cm squared

length of one side = 5cm as 5*5 =25

perimeter= 5*4= 20cm

But since the area is less than 25cm squared

we can say that the length of one side is less than 5cm and we can also say that the length of the perimeter is less than 20cm.

Hope this helps.

Answer:

In general gf(x) is not equal to fg(x)

Some pairs of functions cannot be composed. Some pairs of functions can be composed only  for certain values of x.

Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.

Step-by-step explanation:

g(x) = 3x + 6 - 8, f(x) = √x.

The domain of a composed function is either the same as the domain of the first function, or  else lies inside it

The range of a composed function is either the same as the range of the second function, or else lies inside it.

Or vice versa

Now only positive numbers, or zero, have real square roots. So g is defined only for numbers

greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or

equal to zero. You can work out that

f(x) ≥ 0 only when x ≥3/2

.

Answer:

Step-by-step explanation:

Even function has following property:

It is easy to show this works with the second choice only. All the others don't work:

This is not correct as x - 1 ≠ -x - 1 so as their squares, so g(x) ≠ g(-x)

The last two choices are not even similarly.

Answer:

B. g(x) = 2x2 + 1

Correct on edge