What is the area of polygon XYZ?

Answer:

320

Step-by-step explanation:

Total no of employees = 1600

% of employees attended the training = 80%

no. of employee who attended the training = 80/100* 1600 = 1280

No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training =  1600-1280 = 320

Thus, 320 employees have yet to attend the training

Answer: Amount in 5 years( if compounded quarterly) = $11,768.40

Amount in 5 years( if compounded monthly = $11782.54

Step-by-step explanation:

Formula for accumulated amount in t years at annual rate of r% compounded quarterly: [tex]A=P(1+\dfrac{r}{4})^{4t}[/tex]

Formula for accumulated amount in t years at annual rate of r% compounded monthly: [tex]A=P(1+\dfrac{r}{12})^{12t}[/tex], where P= principal amount.

Given: P= $9000, r= 5.4%= 0.054, t= 5 years

Amount in 5 years if compounded quarterly =[tex]9000(1+\dfrac{0.054}{4})^{4\times5}[/tex]

[tex]=9000(1.0135)^{20}\\\\=9000(1.30760044763)\approx11768.40[/tex]

i.e. Amount in 5 years( if compounded quarterly) = $11,768.40

Amount in 5 years if compounded monthly =[tex]9000(1+\dfrac{0.054}{12})^{12\times5}[/tex]

[tex]=9000(1.0045)^{60}\\\\=9000(1.309171267)\approx11782.54[/tex]

i.e.  Amount in 5 years( if compounded monthly = $11782.54

Answer:

The 95 percent Confidence Interval is for the population is (38.911 , 41.089)

Step-by-step explanation:

To solve the above question, we would be making use of the confidence interval formula:

Confidence Interval = Mean ± z score × σ/√n

In the above question,

Mean = 40

σ = Standard deviation = 5

n = number of samples = 81

Confidence Interval = 95%

The z score for a 95% confidence interval = 1.96

Therefore, the confidence interval =

= 40 ± 1.96 (5/√81)

= 40 ± 1.96(5/9)

= 40 ± 1.0888888889

Confidence Interval

a)40 + 1.0888888889

= 41.0888888889

Approximately = 41.089

b ) 40 - 1.0888888889

= 38.911111111

Approximately = 38.911

Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)

Answer:

60%

Step-by-step explanation:

9/20 is 45%

Answer:

60 %

Step-by-step explanation: If you divide 9/20, it equals to 0.45, makes it 45% and the number 45 in general is smaller than 60. Thus, 60% is greater than 9/20. I hope this helps.

Answer:

32

Step-by-step explanation:

Everyone added together = 68

Four years ago, they were 68 -16 = 52

But the question told 54 years.

So there was a girl who was 2 years.

Girl = 2

Boy = 2 +3 = 5

Husband = 3 +w

Wife =w

3 +w +w + 5 + 2 = 68

10 + 2w = 68

2w = 58

w = 29

Wife = 29

Husband = 29 +3 =32

Husband = 32 years

Answer:

[tex]\large \boxed{\sf \bf \ \ 32 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We know that "All together they are 68 years old." and "Four years ago, all together the family was 54 years old."

If all the family was alive four years ago, it means that four years ago the sum of their ages was 68 - 4 - 4 - 4 - 4 because they are four members, so it gives 68 - 16 =52 which is different from 54, right ?

It means that we have the daughter in between, 54- 52 = 2, so the daughter's age is 2, and then the son's age is 5.

The husband is 3 years older than the wife. Let's note W the wife's age, we can write W + 3 + W + 5 + 2 = 68

2 W + 10 = 68

2 W = 68 - 10 = 58 so W = 29

and then the husband's age is 29 + 3 = 32.

And we can verify that 32 + 29 + 5 + 2 = 68, and four years ago, 28 + 25 + 1 + 0 = 54.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

positive integer divisible by 3 includes

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...

less than highest possible value is 42

The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)

The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80

This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%

We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.

The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)

=========================================

In summary, we have these answers

Answer: The length is 4 centimeters and the width is 6 centimeters.

Step-by-step explanation:

If the length of the  rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 .   And we know that to find the area of a rectangle we multiply the length by the width  and they've already given the area  so we will represent the width by w since it is unknown.

Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.

w(2w-8) = 24

2[tex]w^{2}[/tex] - 8w = 24     subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.

2[tex]w^{2}[/tex] - 8w -24 = 0      divide each term by 2.

[tex]w^{2}[/tex] - 4w - 12 = 0          Five two numbers that multiply to get -12 and to -4

[tex]w^{2}[/tex] +2w - 6w - 12 = 0    Group the left hand side and factor.

w(w+2) -6( w + 2) = 0   factor out w+2

(w+2)(w-6) = 0         Set them both equal zero.

w + 2 =0      or w - 6 = 0  

    -2  -2                + 6   +6

w= -2       or   w=6  

Since we are dealing with distance -2 can't represent a distance so the wide has to 6.  

Now it says that the length is 8 less that twice the width.

So  2(6) - 8 = 12 -8 = 4  So the length in this care is 4.

Check.

6 * 4 = 24

24 = 24

Step-by-step explanation:

Hi, there!!!

It's so simple..

Let me clear you, alright.

Here, On the fig line, OE is just a confusing line. If you look it in simple way,

AB and CD are interested at a point O.

so, angle AOD and angle COB are equal.{ because they are vertically opposite angle}

so, angle AOD= angle COB

or, 4x°=45°+15°

or, 4x°= 60°

or, x= 60°/4

Therefore, x= 15°.

Hope it helps....

Answer:

716.75 m^3

Step-by-step explanation:

Volume of a cylinder:

=> PI x R^2 x H

H = Height

R = Radius

=> PI x 3.9^2 x 15

=> PI x 15.21 x 15

=> PI x 228.15

=> 228.15 PI

           or

=> 228.15 x 3.14159

=> 716.75 m^3

Answer:

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

  y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

  y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

__

B) The continuous decay rate is the natural log of the growth factor, so is ...

  ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

__

C) For y=.10 (1/10 of the original amount) we find x to be ...

  .1 = .5^(x/30)

  ln(.1) = (x/30)ln(.5) . . . . . take the natural log

  30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

__

D) As x goes to infinity, y goes to zero.

_____

The relationship between growth rate and growth factor is ...

  growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

Answer:

x=3mod4

Means that when x is divided by 4 it gives an unknown integer and a remainder of 3.

x/4 = Z + 3/4

Z= (x-3)/4

Where Z is the integer

x=5 mod6

x/6 = Y + 5/6

Y = (x-5)/6

Where Y is the integer

Z-Y must be an integer on equal to zero

(x-3)/4 - (x-5)/6

3(x-3)/12 - 2(x-5)/12

(3x-9-2x+10)/12

(x+1)/12

If it is equal to 0

x=-1. But x should be positive

If it is equal to 1

x=11

Hence the smallest possible number is 11

Answer:

74

Step-by-step explanation:

The average score of boys and girls is 68 and boys is 62

Think of it as an equation (62 + x)/2 = 68, where x is the average score of girls

First multiply each side by 2 making the equation 62 + x = 136

Now subtract each side by 62, which will make the average score for girls 74

(x = 74)

Answer:

option C . 5

Step-by-step explanation:

For two points (x1,y1) and (x2,y2) divided by a point p in ratio m:n then coordinates of that point is given by

p    :  (nx1+mx2)/(m+n),  (ny1+my2)/(m+n),  

Given

x coordinate of P (-3)

x  coordinate of Q (a) since we have to find it , let it be a

x coordinate of R(-1)\

ratio = 1:3

_______________________________________

Using the above formula to find the point of division

we can get value of x coordinate for point Q

x  coordinate of R = 3*-3 + 1*a/(1+3)

-1 = (-9 + a)/4

=> -4 = -9 +a

=>a = -4+9 = 5

Thus, x  coordinate of Q is 5

Answer:

B) 9.2

Step-by-step explanation:

tan(57)=x/6 multiply 6 on both sides

6.tan(57)=x use calculator to find answer

9.2 rounded

Answer:9.2 is correct

Step-by-step explanation:

Answer:

6.25

Step-by-step explanation:

(x-a)^2=x^2-2ax+a^2

2a=5

a=2.5

2.5 ^ 2 = 6.25

Answer:

x^2 +3x -3

Step-by-step explanation:

f(x) = 3х – 5

g(x) = х^2+ 2,

(f+g)(x) = 3х – 5 +х^2+ 2

Combine like terms

         = x^2 +3x -3

Answer: 3.2 feet.

Step-by-step explanation:

Given: The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation[tex]f(x) = -0.3x^2 + 2x[/tex], where [tex]f(x)[/tex] is the height of the path of the water above the ground, in feet, and [tex]x[/tex] is the horizontal distance of the path of the water from the end of the hose, in feet.

At x= 4 , we get

[tex]f(x) = -0.3(4)^2 + 2(4)=-0.3(16)+8 =-4.8+8=3.2[/tex]

Hence, when the water was 4 feet from the end of the hose,  its height above the ground is 3.2 feet.

Answer:

3.2 feet.

Step-by-step explanation:

Answer:

8)  1.962 miles

9)  (-2, -1.5)

10) 0.515 miles

Step-by-step explanation:

√(-9 - 5)² + (1 - -4)² = 14.866

14.866 x .132 = 1.962

(-9+5)/2, (1 + -4)/2

-4/2, -3/2

-2, -3/2

√(-2 - 1)² + (-3/2 - -4)² = 3.905

3.905 x .132 = 0.515 miles

Answer:

the like terms are:

3x+8x+x+y+8

12x+y+8

Answer:

The like terms are

3x, 8x, x

Step-by-step explanation:

3x+8x+y+x+8

The like terms are

3x, 8x, x

They are the terms that are in terms of the first power of x

Answer:

Step-by-step explanation:

y varies direcrtly with √(x+5) wich can be expressed mathematically as:

● y = k*√(x+5)

Let's calculate k khowing that y=4 and x=-1

● 4 = k*√(-1+5)

● 4 = k*√(4)

● 4 = k * 2

● k = 4/2

● k = 2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's calculate y khowing that x = 11

● y = k*√(x+5)

● y = 2×√(11+5)

● y = 2× √(16)

● y = 2× 4

● y = 8

Answer:

The value of y is 8.

Step-by-step explanation:

Given that y is directly proportional to √(x+5) so the equation is y = k√(x+5) where k is constant. First, you have to find the value of k with given values :

[tex]y = k \sqrt{x + 5} [/tex]

[tex]let \: x = - 1,y = 4[/tex]

[tex]4 = k \sqrt{ - 1 + 5} [/tex]

[tex]4 = k \sqrt{4} [/tex]

[tex]4 = k(2)[/tex]

[tex]4 \div 2 = k[/tex]

[tex]k = 2[/tex]

So the equation is y = 2√(x+5). In order to find the value of y, you have to substitute x = 11 into the equation :

[tex]y = 2 \sqrt{x + 5} [/tex]

[tex]let \: x = 11[/tex]

[tex]y = 2 \sqrt{11 + 5} [/tex]

[tex]y = 2 \sqrt{16} [/tex]

[tex]y = 2(4)[/tex]

[tex]y = 8[/tex]

Answer:

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

Step-by-step explanation:

(x-h)^2 = 4p(y-k)

P is the distance between the focus and vertex

P = 1 --> used distance formula for the points of -3,2 -3,3

Vertex is -3,3 --> according to picture

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

P is negative since it goes downwards in the picture.

Answer:

Step-by-step explanation:

Given that:

Let sample size of women be [tex]n_1[/tex]  = 1000

Let the proportion of the women be [tex]p_1[/tex] = 0.65

Let the sample size of the men be [tex]n_2[/tex] = 1000

Let the proportion of the mem be [tex]p_2[/tex]  = 0.60

The null and the alternative hypothesis can be computed as follows:

[tex]H_0: p_1 = p_2[/tex]

[tex]H_0a: p_1 \neq p_2[/tex]

Thus from the alternative hypothesis we can realize that this is a two tailed test.

However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]

p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]

p = [tex]\dfrac{650+600 } {2000}[/tex]

p = 0.625

The standard error of the test can be computed as follows:

[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]

[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]

[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]

[tex]SE = \sqrt{0.234375 (0.002)}[/tex]

[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]

[tex]SE = 0.02165[/tex]

The test statistics is :

[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]

[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]

[tex]z =\dfrac{0.05}{0.02165}[/tex]

[tex]z =2.31[/tex]

At level of significance of 0.05  the critical value for the z test will  be in the region between - 1.96 and 1.96

Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96

Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that  the percentage of men and women favoring a higher legal drinking age is different.

Answer:

3 =x

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

3x(x+1) = 4x*x

Divide each side by x

3(x+1) = 4x

Distribute

3x+3 = 4x

Subtract 3x from each side

3x-3x +3 = 4x-3x

3 =x

Hello, please consider the following.

We know the following, right ?

[tex](\forall a, b \in \mathbb{R}) \left( sin(a+b)=sin(a)sin(b)+cos(a)cos(b) \right)[/tex]

So, here, it gives.

[tex]Asin(\omega t+\phi)=Asin(\phi){\sf \bf sin(\omega t)}+Acos(\phi){\sf \bf cos(\omega t)}\\\\=c_2{\sf \bf sin(\omega t)}+c_1{\sf \bf cos(\omega t)}\\\\\text{ *** where }c_2=Asin(\phi) \text{ and } c_1=Acos(\phi) \text{ ***}[/tex]

Do not hesitate if you need further explanation.

Answer:

the value of the 3 is 30

Step-by-step explanation:

the second digit to the left of a decimal is always tens column

Answer:

x² + 7x + 49/4 = (x + 7/2)²

Step-by-step explanation:

x² + bx + c is a perfect square when c = (b/2)².

b = 7, c = (7/2)² = 49/4.

x² + 7x + 49/4 = (x + 7/2)²

Answer:

x² + 7x + 12.25 = (x+3.5)²

Step-by-step explanation:

(a+b)² = a²+ 2ab + b²

then:

7x = 2ab

7/2 = 3.5

then:

(x+3.5)² = x² + 2*3.5*a + 3.5²

x² + 7x + 12.25 = (x+3.5)²

Answer:

84 pounds

Step-by-step explanation:

If 1/3 of a book is equal to 28 pounds then 28*3 will give you your answer

Answer:

D) 60 degree

Step-by-step explanation:

Let's connect the remaining diagonal, which forms a triangle containing angle x.

As a property of regular hexagon, all diagonals are equal.

=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.