A student researcher compares the heights of American students and non-American students from the student body of a certain college in order to estimate the difference in their mean heights. A random sample of 12 American students had a mean height of 68.4 inches with a standard deviation of 1.64 inches. A random sample of 17 non-American students had a mean height of 64.9 inches with a standard deviation of 1.75 inches. Determine the 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students. Assume that the population variances are equal and that the two populations are normally distributed. Find the point estimate that should be used in constructing the confidence interval.

Answer:

a) x^2-3x-4(you also can express it as (x+1)(x-4))

b)The length is 8 cm, the width is 3 cm

Step-by-step explanation:

a) The length is x+1

The width is (x+1-5)= x-4

The area is the product of the length and the width

(x+1)(x-4)= x^2-3x-4

b) The formula for counting the area is x^2-3x-4

It is equal to 24

S0 x^2-3x-4=24

x^2-3x-28=0

a=1 b=-3 c=-28

D= b^2-4ac= 3^2-4*(-28)= 9+112= 121

sqrtD= 11

x1= (-b-sqrtD)/2a=(3-11)/2=-4  The length is -4+1=-3<0, but the length must be positive, this root isn't suitable.

x2= (-b+sqrtD)/2a=(3+11)/2=7 The length is 7+1=8 (it is suitable)

8-5=3 - The width

Answer:

5,20,80,320

Step-by-step explanation:

a1 = 5

an = 4 an-1

Let n = 2

a2 = 4 * a1 = 4*5 = 20

Let n = 3

a3 = 4 * a2 = 4*20 = 80

Let n = 4

a4 = 4 * a3 = 4*80 = 320

Answer:

x=30.5

Step-by-step explanation:

Using midsegment 's theorea:

[tex]2=\dfrac{RG}{RS} =\dfrac{RH}{RQ} =\dfrac{GH}{SQ} \\\\4x-65=2x-4\\\\2x=61\\\\x=\dfrac{61}{2} \\\\x=30.5\\[/tex]

Answer:

no,  

(

1

,

0

)

is not an ordered pair of the function  

f

(

x

)

=

1

+

x

.

Step-by-step explanation:

Ordered pairs are usually written in the form  

(

x

,

y

)

by tradition.

so usingthe function,

f

(

x

)

=

1

+

x

we can rewrite it as,

y

=

1

+

x

any pair of x and y that satisfy this equation are solutions to the equation.

so subbing in  

(

1

,

0

)

,

0

=

1

+

(

1

)

0

=

2

which is not true so the point does not make the function true.

It might be easier to see graphically,

graph{1+x [-10, 10, -5, 5]}

any combination of x and y on this line make the equation true and as such are an ordered pair of the function.

Answer:

Step-by-step explanation:

From the graph, we can write that

The equatuon of line passes through (0,4) and

(-8,0) points.

So

[tex] \sf \: slope \: \: m = \frac{4 - 0}{0 - ( - 8)} = \frac{4}{8} = \frac{1}{2} \\ \therefore \green{\sf \: m = \frac{1}{2} }[/tex]

Intercept of Y-axis c = 4

So equation is :

[tex] \bf \: y = mx + c \\ \bf = > y = \frac{1}{2} x + 4 \\ \bf = > 2y = x + 4 \\ \bf= > \orange{ \boxed{ \bf \: x - 2y + 4 = 0}}[/tex]

Step-by-step explanation:

i) [tex]\overline{AB} = \sqrt{(x_A - x_B)^2 + (y_A - y_B)^2}[/tex]

[tex]\:\:\:\:\:\:\:=\sqrt{(2)^2 + (12)^2} = 12.3[/tex]

ii) [tex]m = \dfrac{y_A - y_B}{x_A - x_B} = \dfrac{-12}{2} = -6[/tex]

iii) [tex](\overline{x},\:\overline{y}) = \left(\dfrac{x_A + x_B}{2},\:\dfrac{y_A + y_B}{2}\right)[/tex]

[tex]\:\:\:\:\:\:\:=(3,\:-2)[/tex]

Answer:

167.64 cm

Step-by-step explanation:

I dont kno how to work it out

Answer:

2 * 10^3 = 2000.

Step-by-step explanation:

3.8/1.9 * 10^5/10^2

= 2 * 10^3

Answer:

1/3

Step-by-step explanation:

.444444444(repeating)- .111111111111(repeating)

.44444444......

-.11111111........

--------------------

.33333333........

Let x = .3333333.....

10x = 3.3333333.....

Subtract the first equation from the second

10x = 3.33333.....

-x =     .33333.....

--------------------------

9x = 3

x = 3/9

x = 1/3

---------------------------

Answer:

D.

Step-by-step explanation:

Try A:

x = -6, f(x) = -1:-

f(-6) =   -5/3(-6) + 9

= 10 + 9 = 19   NOT A.

Try B:

f(-3) = -5/3(-3) - 9

= 5 - 9 = -4  NOT B

Try C:

9(0) + 5/3 = 5/4   NOT C

Try D:

f(3) = 5 + 9 = 14

f(0) = 9, f(-6) = -1 and f(-3) = 4

Answer:

i dont no the ans

Step-by-step explanation:

Explanation:

Normally, y = cos(x) has a period of 2pi. This means that every 2pi horizontal units, the graph repeats itself. However, we can see that the period here is pi units instead.

One way to see this is to start at (0,1). This is a local max point. Move to its neighboring local max at (pi,1). We have moved pi units along the x axis and the cycle is finished, after which point the cycle repeats itself.

Since T = pi is the period, we then can say B = 2pi/T = 2pi/pi = 2

This is then plugged into y = A*cos(B(x-C))+D where

A = 1

C = 0

D = 0

That leads us to y = cos(2x)

Since the period is often connected to time values, it might help to think of this wave's oscillations occurring twice as often compared to y = cos(x). So that might help see why we replace the x with 2x.

Answer:

False

Step-by-step explanation:

Answer:

Step-by-step explanation:

Confidence Level - "P" values  

90% 1.645

Confidence Interval - "P" values  

(0.7119 , 0.8481 )  

Answer:

Step-by-step explanation:

(2 carts)/(12 bags) = (⅙ cart)/bag

Answer:

is y=x^2 a proportional relationship?

[tex]{ \sf{yes. \: constant \: of \: proportionality = 1}}[/tex]

is y=2+x a proportional relationship?

[tex]{ \sf{no. \: unless \: y \: is \: proportinal \: to \: (2 + x)}}[/tex]

is y=2/x a proportional relationship?

[tex]{ \sf{yes. \: where \: proportianality \: constant \: is \: 2}}[/tex]

is y=2x a proportional relationship?

[tex]{ \sf{yeah. \: constant \: is \: 2}}[/tex]

Answer:

N = 1000

Step-by-step explanation:

The population growth of species per capita of any geographical can be computed by using the formula:

[tex]\dfrac{dN}{dT}=rN (1 - \dfrac{N}{K})[/tex]

here;

N = population chance

T = time taken

K = carrying capacity

r = the constant exponential growth rate

From the given equation, we can posit that the value of r will be the greatest at the time the value of dN is highest:

As such, when the population chance = 1000

[tex]\dfrac{dN}{dT}=0.17 * 1000 (1 - \dfrac{1000}{10000})[/tex]

[tex]\dfrac{dN}{dT}=0.17 * 1000 (0.9)[/tex]

[tex]\dfrac{dN}{dT}= 153[/tex]

At N = 5000;

[tex]\dfrac{dN}{dT}= 85[/tex]

At N= 8000;

[tex]\dfrac{dN}{dT}= 34[/tex]

At N = 10000

[tex]\dfrac{dN}{dT}= 0[/tex]

Answer: TRUE

Step-by-step explanation: THE COMPOUD STATE MEN DETERMEND BY HE GRAPH IS THE SOLUTION AS SAID BY YOU IT IS TRUE BECAUSE THE READINGS ON THE GRAPH SHOW ITS TRUE

Answer:

Let x = the number of ounces of Solution A

Let y = the number of ounces of Solution B

x + y = 180        y = 180 - x

.60x + .85y = .75(180)

.60x + .85y = 135      Multiply both sides of the equation by 100 to remove the decimal points.

60x + 85y = 13500

60x + 85(180 - x) = 13500

60x + 15300 - 85x = 13500

-25x = -1800

x = 72ounces

y = 180 - 72

y = 108 ounces          

Step-by-step explanation:

Wyzant (ask an expert) solution on their website.

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==>   sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0   or   sin(2x) = 0   or   2 cos(2x) + 1 = 0

sin(5x) = 0   or   sin(2x) = 0   or   cos(2x) = -1/2

sin(5x) = 0   ==>   5x = arcsin(0) + 2nπ   or   5x = arcsin(0) + π + 2nπ

… … … … …   ==>   5x = 2nπ   or   5x = (2n + 1)π

… … … … …   ==>   x = 2nπ/5   or   x = (2n + 1)π/5

sin(2x) = 0   ==>   2x = arcsin(0) + 2nπ   or   2x = arcsin(0) + π + 2nπ

… … … … …   ==>   2x = 2nπ   or   2x = (2n + 1)π

… … … … …   ==>   x = nπ   or   x = (2n + 1)π/2

cos(2x) = -1/2   ==>   2x = arccos(-1/2) + 2nπ   or   2x = -arccos(-1/2) + 2nπ

… … … … … …    ==>   2x = 2π/3 + 2nπ   or   2x = -2π/3 + 2nπ

… … … … … …    ==>   x = π/3 + nπ   or   x = -π/3 + nπ

(where n is any integer)

Step-by-step explanation:

X +1 + X + 2

X + X + 1 + 2

2x + 3

Therefore it's 2x + 3

Answer:

0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Person has diabetes.

Probability of a positive test:

0.95 out of 0.1(person has diabetes).

0.007 out of 1 - 0.1 = 0.9(person does not has diabetes). So

[tex]P(A) = 0.95*0.1 + 0.007*0.9 = 0.1013[/tex]

Probability of a positive test and having diabetes:

0.95 out of 0.1. So

[tex]P(A \cap B) = 0.95*0.1 = 0.095[/tex]

What is the probability that a randomly selected person has diabetes, given that his test is positive?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.095}{0.1013} = 0.9378[/tex]

0.9378 = 93.78% probability that a randomly selected person has diabetes, given that his test is positive.

Answer:

Step-by-step explanation:

y = ½(x-4)² + 13

y = ½(x² - 8x + 16) + 13

y = ½x² - 4x + 21

Answer:

x=−5+√29 or x=−5−√29

Step

Let's solve your equation step-by-step.

x2+10x+10=14

Step 1: Subtract 14 from both sides.

x2+10x+10−14=14−14

x2+10x−4=0

For this equation: a=1, b=10, c=-4

1x2+10x+−4=0

Step 2: Use quadratic formula with a=1, b=10, c=-4.

x=

−b±√b2−4ac

2a

x=

−(10)±√(10)2−4(1)(−4)

2(1)

x=

−10±√116

2

x=−5+√29 or x=−5−√29

Answer:

x+3

---------------

(x-3)(x-2)(x-4)

Step-by-step explanation:

x+4             x^2 -16

---------------÷ -------------

x^2 - 5x+6     x+3

Copy dot flip

x+4                x+3

--------------- * -------------

x^2 - 5x+6     x^2 -16

Factor

x+4                x+3

--------------- * -------------

(x-3)(x-2)     (x-4)(x+4)

Cancel like terms

1                   x+3

--------------- * -------------

(x-3)(x-2)     (x-4)1

x+3

---------------   x cannot equal 3,2,4 -4

(x-3)(x-2)(x-4)

Answer:

Diameter = 2 × Radius

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diameter of a circle is the length of the line through the center and touching two points on its edge. In the figure above, drag the orange dots around and see that the diameter never changes. The diameter is also a chord.

Answer:

A. 4000 meters because

1 km = 1000 meters

and 4 km = 1000 × 4 = 4000

............

Answer:

12

Step-by-step explanation:

120 divided by 100 =1.2 x 10