What is the radius of a sphere with the volume of 113.04 in.³

Suppose that 12% of test scores for the unit 1 test were above 85 and 8% were below 70. Assuming a normal

Doss [256]

Answer:

Mean = 78.2

Standard deviation = 5.8

Step-by-step explanation:

Mathematically z-score;

= (x-mean)/SD

From the question;

12% of test scores were above 85

Thus;

P( x > 85) = 12%

P(x > 85) = 0.12

Now let’s get the z-score that has a probability of 0.12

This can be obtained from the standard normal distribution table and it is = 1.175

Thus;

1.175 = (85 - mean)/SD

let’s call the mean a and the SD b

1.175 = (85-a)/b

1.175b = 85 - a

a = 85 - 1.175b ••••••••(i)

Secondly 8% of scores were below 70

Let’s find the z-score corresponding to this proportion;

We use the standard normal distribution table as usual;

P( x < 70) = 0.08

z-score = -1.405

Thus;

-1.405 =( 70-a)/b

-1.405b = 70-a

a = 70 + 1.405b ••••••(ii)

Equate the two a

70 + 1.405b = 85 - 1.175b

85 -70 = 1.405b + 1.175b

15 = 2.58b

b = 15/2.58

b = 5.81

a = 70 + 1.405b

a = 70 + 1.405(5.81)

a = 78.16

So mean = 78.2 and Standard deviation is 5.8

4 0

3 years ago

Need help ASAP! (Geometry 1)

melisa1 [442]

Answer:

The Length of third side is 52 units.

Step-by-step explanation:

Given:

Length of First side = 48

Length of second side = 20

Also given the angle between them is 90°.

Hence we can say figure shown is a right angled triangle.

For finding the third side we can use Pythagoras theorem which states that;

"If a triangle is right angled then, the Square of the hypotenuse is equal to sum of the square of the other two sides."

$Third \ side ^2=First \ side^2+Second \ side^2$

Hence substituting the values we get;

$Third\ side^2= 48^2+20^2 = 2304+400 =2704$

Now taking Square root on both side we get;

$\sqrt{Third \ side^2} = \sqrt{2704}\\ Third \ side = 52 \ units$

Hence Length of Third side is 52 units.

3 0

3 years ago

Use synthetic substitution to evaluate the polynomial P(x) = x^3-3x^2+4x-7 for x=3

Zina [86]

Answer:

$\frac{x^3-3x^2+4x-7}{x-3} =(x^2+4)+\frac{5}{x-3}$

Step-by-step explanation:

We are given polynomial as

$P(x)=x^3-3x^2+4x-7$

and it is divided by x=3 or x-3

we can use synthetic division

so, we got

Remainder =5

Quotient is

$=x^2+0x+4$

$=x^2+4$

we can write as

$\frac{x^3-3x^2+4x-7}{x-3} =(x^2+4)+\frac{5}{x-3}$

3 0

2 years ago

Stacie is choosing between two careers. Working for company A, Stacie will make $45,000 the first year and will receive an addit

fomenos

The expression in company B represents that is is in arithmetic progression where first term is 42000 and common difference is 1800 . So we have to use the formula of sum of n terms which is

$S=\frac{n}{2}(2a +(n-1)d)$

Where a is the first term, n is the nth term, d is the common difference

On substituting there values,we will get

$S =\frac{30}{2}(2*42000+(30-1)1800)$

= 15(84000+52200) = 15*136200 =2043000

And for company A, it is

$S= \frac{30}{2}(2*45000+(30-1)1500 ) = 15(90000+43500)=2002500$

Difference between them =2043000-2002500= 40500

So the correct option is the second option .

6 0

3 years ago

PLEASE HELP!!!!!!!

posledela

90° = complimentary

middle one = is neither

3rd one is supplementary

8 0

1 year ago