Simplify: –3(y + 2)2 – 5 + 6y.

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the coordinate of A is not given.

However, the rule to follow has been stated in the question.

i.e.

[tex](x,y) \to (-x,y)[/tex]

Assume that:

[tex]A = (2,5)[/tex]

After reflection, A will be:

[tex]A =(-2,5)[/tex]

Given:

Probability distribution table is:

Household Size :   1            2          3           4          5         6         7          8

Probability          : 0.04     0.09     0.14     0.20     0.29    0.14    0.08   0.02

To find:

The probability that there are less than 5 members in a household in India.

Solution:

Let x be the number of members in a household. The probability that there are less than 5 members in a household in India is:

[tex]P(x<5)=P(x=1)+P(x=2)+P(x=3)+P(x=4)[/tex]

[tex]P(x<5)=0.04+0.09+0.14+0.20[/tex]

[tex]P(x<5)=0.47[/tex]

Therefore, the probability that there are less than 5 members in a household in India is 0.47.

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

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.

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Answer:

e=2

Step-by-step explanation:

7(2e−1)−3=6+6e

Distribute

14e -7 -3 = 6+6e

14e -10 = 6+6e

Subtract 6e from each side

14e-6e -10 = 6+6e-6e

8e -10 =6

Add 10 to each side

8e -10+10 = 6+10

8e = 16

Divide by 8

8e/8 = 16/8

e=2

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:

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:

3/2

Step-by-step explanation:

We can use the slope formula

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

    = ( -4-2)/(5-9)

    = -6/-4

    =3/2

Answer:

p = 18

Step-by-step explanation:

4(p – 7) = 44

Divide each side by 4, using the division property of equality

4(p – 7)/4 = 44/4

p-7 = 11

Add 7 to each side using the addition property of equality

p-7+7 = 11+7

p = 18

Answer:

he is right the guy above me

Step-by-step explanation:

Answer:

A. Total=520 loaves

B. Estimate= 180 rolls

Step-by-step explanation:

Answer:

9cm

Step-by-step explanation:

Circumference formula = 2piR

To calculate radius

The equation becomes

2piR = 18pi

R = 18pi/2pi

= 9cm

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:

13/4

Step-by-step explanation:

Subtract 2 from both sides. Now we have 4x=13. Divide by 4. We have our answer: x=13/4.

Answer:

3+3=6×2=12+4=16÷2=8-3=5

Step-by-step explanation:

b

Answer:

X=1.2/1.3

answérica is 1.25, depends on how you want to round

Step-by-step explanation:

Answer:

Five and thirty-nine thousandths in standard decimal form is

5.039

Hope This Helps!!!

Answer:

7x - 63y

Step-by-step explanation:

Given

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

= 7x - 63y

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:

You should get 21 odds

Step-by-step explanation:

There are 6 possible outcomes on a fair die

1,2,3,4,5,6

3 of the outcomes are odd

1,3,5

P(odd) =  odd outcomes/ total = 3/6 =1/2

Rolling 42 times

number of times * P(odd)

42*1/2 = 21

You should get 21 odds

Answer:

54 cm

Step-by-step explanation:

27:9=3

4+5+9=18

3×18=54

Answer:

Subtractive Property of equality

Step-by-step explanation:

Since x = y, When you subtract anything from x, you must do the same to y for them to stay equal.

Answer:

Subtraction property of equality

Answer:

30x³

Step-by-step explanation:

2x×3x=6x²

6x²×5x=30x³

2x-3y+6=0 has an x intercept of 2 and a y intercept of -3.

That means the 2 sides of the right triangle are 2 and -3

Area of triangle= 1/2×base×height

                         = 1/2×-3×2

                         =-3

∴ Area of the triangle=-3

The area of the asked triangle is 3 sq units.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a triangle is formed by the line 2x – 3y +6=0 and the coordinate axis.

When we plot the graph of the line, we get, y-intercept = 2 and x-intercept = -3

Hence, the height and base of the triangle will be 2 and 3 respectively.

Area of a triangle = 1/2 (base) (height)

Area = 1/2 (2)(3)

Area = 3

Hence, the area of the asked triangle is 3 sq units.

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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

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:

The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Male undergraduates:

670, 388 were employed. So

[tex]p_M = \frac{388}{670} = 0.5791[/tex]

[tex]s_M = \sqrt{\frac{0.5791*0.4209}{670}} = 0.0191[/tex]

Female undergraduates:

Of 617, 323 were employed. So

[tex]p_F = \frac{323}{617} = 0.5235[/tex]

[tex]s_F = \sqrt{\frac{0.5235*0.4765}{617}} = 0.0201[/tex]

Distribution of the difference:

[tex]p = p_M - p_F = 0.5791 - 0.5235 = 0.0556[/tex]

[tex]s = sqrt{s_M^2+s_F^2} = \sqrt{0.0201^2 + 0.0191^2} = 0.0277[/tex]

Confidence interval:

The confidence interval is given by:

[tex]p \pm zs[/tex]

In which

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

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower bound of the interval is:

[tex]p - zs = 0.0556 - 1.645*0.0277 = 0.01[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.0556 + 1.645*0.0277 = 0.1012[/tex]

The 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer is (0.01, 0.1012).