4. Write 3x(x + 4)(x - 1) in standard form.
3x3 + 9x2 - 12x
3x3
- 12x + 9x2
3x3 + 9x2 - 12x + 1
1 - 12x + 9x2 + 3x3

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.

Answer:

33 years

Step-by-step explanation:

Given the quadratic model :

P=0.006A2−0.02A+120

P = blood pressure ; A = Age

Given a blood pressure value of 126 mmHg ; the age, A will be ;

The equation becomes :

126 = 0.006A2−0.02A+120

0.006A² - 0.02A + 120 - 126 = 0

0.006A² - 0.02A - 6 = 0

Using the quadratic formula :

-b ± (√b²-4ac) / 2a

a = 0.006 ; b = - 0.02 ; c = - 6

Using calculator :

The roots are :

a = 33.333 or a = - 30

Age cannot be negative, hence, the age, A will be 33.333

Total the nearest year ; Age = 33 years

ANSWERS:

a) 16 students

b) 25 students

c) 2 students

STEP BY STEP:

There are 42 students in total. This question can be solved by "Principal of Inclusion and Exclusion"

Question a)

The students that studied on Sunday in total with overlaps is 30. To figure out the students that ONLY studied on Sunday you need to first minus the overlaps in the combos:

the combos:

3, 10, 6, 2

Since the last combo included all of the other dates, we need to minus it:

1, 8, 4, 2

Now we can use the total of Sunday and minus the combos that includes Sunday:

30 - (4 + 2 + 8)  = 16 students

Question b)

To figure out all the students that only studied on ONE day, not 2 not 3, just one day. We need to figure out the students that studied for Saturday and Friday using the same method before for figuring out Sunday:

Friday: 9 - 4 - 1 -2 = 2 students

Saturday: 18 - 1 - 2- 8 = 7 students

and now add them all together: 2 + 7 + 16 = 25 students

That is the total number of students that studied on one day.

Question c)

Now for the numbers of students that didn't study... We can just use the total to minus everything else!

42 - (25 + 1 + 4 + 8 + 2) = 2 students!!!

And thats all done!  If you still don't get it, please ask!

Answer:

Hence the probability that the mean of their utility bills will be less than $75 = P(X < 75) is 0.9736.

Step-by-step explanation:

Now,  

Population mean electric bill, [tex]\mu =[/tex]  $72  

Population standard deviation, [tex]\sigma =[/tex]  $6  

Standard error of the mean[tex]= \sigma / \sqrt{n} = 6 / \sqrt{15} = 1.5492[/tex]

The probability that the mean of their utility bills will be less than $75 = P(X < 75)

= P[Z < (75 - 72) / 1.5492]

= P[Z < 1.9365]

= 0.9736 (Using Z table)

Answer:

7x - 63y

Step-by-step explanation:

Given

7(x - 9y) ← multiply each term in the parenthesis by 7

= 7x - 63y

Answer:

rectangle- 2 lines of reflection

trapezoid- 0 lines of reflection

regular pentagon- 5 lines of reflection

square- 4 lines of reflection

Step-by-step explanation:

Step-by-step explanation:

here is the ans

the perimeter= 130m

hope so this might help you

Answer:

its the first square one that says "6 inch, 5 inch"

Step-by-step explanation:

Because 6+6=12 and 5+5=10, so 12+10=22

Answer:

6 and 5 inch

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

You need to find the average number of students

Add up all the students

27+31+28+33+26

145

Divide by the number of classes

145/5

29

The average is 29

32

Step-by-step explanation:

answer of number 30 is 32

Answer:

A the answer is A if you look at it .

Answer:

The first one is B) point D

The second one is D) (0,0)

Hope this helps!

btw, coordinates are in (x,y) form, so the other answer above me is wrong.

Answer:

[tex]{ \bf{formular : \: { \tt{volume = \frac{4}{3} \pi {r}^{3} }}}} \\ { \tt{volume = \frac{4}{3} \times 3.14 \times {( \frac{5}{2}) }^{3} }} \\ { \tt{volume = 65.4 \: cubic \: inches}}[/tex]

Answer:

65

Step-by-step explanation:

formula =   4/3 * 3.14* r^3

               = 4/3 * 3.14 * 2.5^3 (radius is half of the diameter)

                    = 65.44985

                     rounded to 65

Step-by-step explanation:

[tex] \frac{ \frac{6}{7} }{ \frac{9}{14} } [/tex]

[tex] = \frac{6}{7} \times \frac{14}{9} [/tex]

[tex] = \frac{2}{1} \times \frac{2}{3} [/tex]

[tex] = \frac{4}{3} = 1 \frac{1}{3} (Ans) [/tex]

[tex] \frac{18}{x} = \frac{6}{10} [/tex]

[By cross multiplication]

=> 18 × 10 = 6 × x

[tex] = > \frac{18 \times 10}{6} = x[/tex]

=> 3 × 10 = x

=> x = 30 (Ans)

Answer:

[tex]5\sqrt{2} \\45[/tex]

Step-by-step explanation:

just multiply

Answer:

a) 5√2

b) 135

Step-by-step explanation:

√5·√10 is equivalent to √50, which in turn is equivalent to √25·√2, or 5√2.

√27·√75 can be simplified by factoring:

√3·√9·√3√25, or (because √3·√3 = 3):

(3)(9)(5) = 135

Answer:

The correct answer is "50%".

Step-by-step explanation:

The given values are:

Gravel,

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

Water,

= [tex]\frac{1}{2}[/tex]

Cement,

= 1

Sand,

= 2

Now,

The total mixture will be:

= [tex]Gravel+Water+Cement+Sand[/tex]

By substituting the values, we get

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

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

= [tex]4 \ cubic \ feet[/tex]

hence,

The percentage of sand will be:

= [tex]\frac{Sand}{Total}\times 100[/tex]

= [tex]\frac{2}{4}\times 100[/tex]

= [tex]50[/tex]%

Answer:

The correct answer will be "-1.66".

Step-by-step explanation:

Let z₀ be,

[tex]P(z<z_0)=4.8 \ percent[/tex]

                [tex]=0.048[/tex]

⇒ [tex]\Phi (z_0)=0.048[/tex]

Now,

⇒ [tex]\Phi (-1.6646)=0.048[/tex]

   [tex]z_0=-1.6646[/tex]

       [tex]\simeq -1.66[/tex]

Thus the above is the right answer.

Answer:

x≤9/2

Step-by-step explanation:

8x+15≤51

Subtract 15

8x+15-15≤51-15

8x+≤36

Divide by 8

8x/8≤36/8

x≤9/2

Given that,

The angles in a triangle are represented by x, x+10, and x+50.

We had to,

find the measure of the largest angle.

Let's start to solve,

→ x + (x+10) + (x+50) = 180°

→ x + x + x = 180° (-50 -10)

→ 3x = 180° -60

→ 3x = 120

→ x = 120/3

→ x = 40°

Then the value of x + 10,

→ x + 10

→ 40 + 10

→ 50°

Then the value of x + 50,

→ x + 50

→ 40 + 50

→ 90°

The measure of the largest angle is,

→ D. 90 degrees

Hence, option (D) is correct answer.

Step-by-step explanation:

good of you and good workings

Answer:

[tex]y-3=\frac{3}{4} (x-5)\\\\y-3=\frac{3}{4}x-\frac{3}{4}(5)\\\\y=\frac{3}{4} x+3-\frac{15}{4} \\\\y=\frac{3}{4} x+\frac{12}{4} -\frac{15}{4} \\\\y=\frac{3}{4} x-\frac{3}{4}[/tex]

Is this standard form? :\

Answer:

3x-4y=3

Step-by-step explanation:

Hi there!

We are given the equation y-3=[tex]\frac{3}{4}(x-5)[/tex], and we want to write it in standard form

Standard form is given as ax+by=c, where a, b, and c are integer coefficients, a CANNOT be 0 and CANNOT be negative, and b also CANNOT be 0

So let's expand the parentheses in the equation

Do the distributive property

y-3=[tex]\frac{3}{4}x-\frac{15}{4}[/tex]

Add 3 to both sides

y=[tex]\frac{3}{4}x-\frac{3}{4}[/tex]

We expanded the parentheses, but the equation is now in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)

Remember that we want it in standard form, which is ax+by=c

Subtract [tex]\frac{3}{4}x[/tex] from both sides

[tex]\frac{-3}{4}x+y=\frac{-3}{4}[/tex]

Remember that the coefficients of a, b, and c need to be integers, and also that a (the coefficient in front of x) CANNOT be negative

So multiply both sides by -4

[tex]-4(\frac{-3}{4}x+y)=-4(\frac{-3}{4})[/tex]

Distribute -4 to every number

[tex]-4(\frac{-3}{4}x)+-4(y)=-4(\frac{-3}{4})[/tex]

Multiply

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

Simplify

3x-4y=3

There's the equation in standard form

Hope this helps!

Answer:

i think its 2 1

Step-by-step explanation:

Answer:

y =2/3x-1

Step-by-step explanation:

First find the slope

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

   = ( 3-1)/ (6-3)

   = 2/3

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2/3x +b

Using a point

3 = 2/3(6)+b

3 = 4+b

3-4 =b

-1=b

y =2/3x-1

Answer:

y= -3x +40

Step-by-step explanation:

Properties of perpendicular bisector:

• perpendicular to the given line

• cuts through the center of the given line

The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y -intercept.

Let's find the gradient of the given line first.

[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]

Gradient of given line

[tex] = \frac{6 - 2}{18 - 6} [/tex]

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

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

The product of the gradients of perpendicular lines is -1.

m(⅓)= -1

m= -1(3)

m= -3

Substitute m= -3 into the equation:

y= -3x +c

To find the value of c, substitute a pair of coordinates in which the perpendicular bisector passes through into the equation. Since perpendicular bisectors passes through the center of the segment, we can find the point in which the perpendicular bisector passes through using the mid- point formula.

[tex]\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )}[/tex]

Midpoint

[tex] = ( \frac{6 + 18}{2} , \frac{6 + 2}{2} )[/tex]

[tex] = ( \frac{24}{2} , \frac{8}{2} )[/tex]

[tex] = (12,4)[/tex]

y= -3x +c

when x= 12, y= 4,

4= -3(12) +c

4= -36 +c

c= 4 +36

c= 40

Thus, the equation of the perpendicular bisector is y= -3x +40.

Answer:

9cm

Step-by-step explanation:

Circumference formula = 2piR

To calculate radius

The equation becomes

2piR = 18pi

R = 18pi/2pi

= 9cm

Answer:

Maybe

1/8 is the probability that the first two assignments Ms.patel collected were completed in pencil

Answer:

1 3 5 7 9 11

Step-by-step explanation:

same like this do the question the answer will come

Answer:

A. Total=520 loaves

B. Estimate= 180 rolls

Step-by-step explanation:

Answer:

its 1900 Bc. Because BC stand for before chirst

Step-by-step explanation:

Answer:

54 cm

Step-by-step explanation:

27:9=3

4+5+9=18

3×18=54

Answer:

78 cm²

42 cm

Step-by-step explanation:

To obtain the area of the shape given :

The figure is divide into three different rectanglular parts :

Recall, area of a rectangle = Length x width :

Rectangle 1 : 9* 6 = 54 cm²

Rectangle 2 = 6 * 2 = 12 cm²

Rectangle 3 = 4 * 3 = 12 cm²

Total area = (54 + 12 + 12). = 78 cm²

Perimeter = sun of the exterior sides of the shape

Perimeter = (9 + 8 + 3 + 4 + 3 + 6 + 3 + 6) = 42 cm

Answer:

Step-by-step explanation:

first athlete =28.65

second athlete=24.25

the first athlete jump - second athlete jump

28.65-24.25

= 4.40

the first athlete long jump then the second athlete

Answer:

Here is your answer.....

Hope it helps....

The value of given function f(x) - g(x) is 2x² + 2x + 1.

Given,

                  f(x) =3x² + 2x + 1

                  g(x) = x² - 6x + 3

f(x) - g(x) = ( 3x² + 2x + 1) - ( x²- 6x + 3)

              = 3x² + 2x +1 - x² + 6x - 3

              = 2x² +8x - 2

Therefore , the value of given function f(x) - g(x) is 2x² + 2x + 1.

Learn more about function brainly.com/question/11963913

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