Roll a dice six times. Find the probability that :
a . The back of the dot appears exactly 4 times ;

Answer:

[tex] Area = 240 m^2 [/tex]

Step-by-step explanation:

The area of the right triangle above = [tex] \frac{1}{2}*base*height [/tex].

Where,

base = 16 m

height = 30 m

Plug in the above values into the area formula:

[tex] Area = \frac{1}{2}*16*30 [/tex]

[tex] Area = 8*30 [/tex]

[tex] Area = 240 m^2 [/tex]

Refer to the attachment for solution.

Answer:

No, they aren't perpendicular

Step-by-step explanation:

Two lines are perpendicular if the product of their slope is - 1. The slope of line AB=(-1-10)/(0-(-1))=-11 and the slope of the line AC=(2-10)/(-3-(-1))=4. Since the product of their slope isn't - 1. They aren't perpendicular.

Answer:

Sample size n [tex]\simeq[/tex] 1269.15

Step-by-step explanation:

From the information given ,

At 99% of confidence interval,

the level of significance ∝ = 1 - 0.99

the level of significance ∝ =  0.01

the critical value for 99% of confidence interval is:

[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]

= 0.005

[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]

The value for z from the standard normal tables

= 2.58

The Margin of error E= 3% = 0.03

The formula to  determine the sample size n used can be expressed as follows:

[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]

where;

[tex]\mathtt{\hat p }[/tex] = 22% = 0.22

Then:

[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]

[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]

[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]

n = 1269.1536

Sample size n [tex]\simeq[/tex] 1269.15

Answer:

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Answer:

true

Step-by-step explanation:

there is 100 candies. That means we can easily turn the amount of each type of candy into a percent. there was 30 butterscotch which means that is 30 percent. There was 15 strawberry which means that is 15 percent. add that and you get 45. This is a shortcut and i advise you use the way your teacher taught you.

[tex]|\Omega|=100\\|A|=30+15=45\\\\P(A)=\dfrac{45}{100}=0.45[/tex]

So TRUE

Answer:

x = 34° and y = 62°

Step-by-step explanation:

Complementary angles sum to 90°, therefore 90 = 56 + x which means that x = 34°. The angles formed by an angle bisector are congruent and so are vertical angles; this means that ∠SOR = ∠POU = 56° and ∠POQ = ∠QOR = y. Since POS is a straight line, straight lines have a measure of 180° and because ∠POS = ∠POQ + ∠QOR + ∠SOR, we know that 180 = y + y + 56 → 180 = 2y + 56 → 180 → 2y = 124 → y = 62°.

Answer:

positively skewed to the right

Step-by-step explanation:

The measure of the central tendency is a profound way to describe the mean, median and mode. The measure of central tendency indicates where the center of distribution tends to be. The measure of central tendency provide a validity and answers whether the scores are high or generally low.

In this measure,The mean is usually pulled to the tail. The skewed is determined by where the tail goes, to the right side , it is positively skewed  and to the left side , it is known as negatively skewed distribution.

Given that:

In a frequency of distribution of 290 scores,

the mean  = 99

the median = 86

One would expect this distribution to be; positively skewed to the right  since the mean value is greater than the median value.

Answer:

The answer is

Step-by-step explanation:

To find the equation of the line we must first find the slope (m)

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

So the slope of the line using points

(-8,6) (-9,-9) is

[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]

So the equation of the line using point (-8,6) and slope 15 is

y - 6 = 15( x + 8)

y - 6 = 15x + 120

Writing the equation in the form

Ax+By=C

We have

15x - y = -120-6

The final answer is

Hope this helps you

Answer:

no

Step-by-step explanation:

2(4+10)+20

2(14)+20

28+20

48

Answer:

Step-by-step explanation:

Answer:

A. The point that splits a line segment into two equal parts.

Step-by-step explanation:

A. The point that splits a line segment into two equal parts.

Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.

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Answer:

-3

Step-by-step explanation:

The length of a segment is

sqrt( ( y2-y1)^2 + (x2-x1) ^2) = 2 sqrt(10)

sqrt( ( a-4 - -1)^2 + (2a -4) ^2) = 2 sqrt(10)

sqrt( ( a-4 +1)^2 + (2a -4) ^2) = 2 sqrt(10)

Combine like terms

sqrt( ( a-3)^2 + (2a -4) ^2) = 2 sqrt(10)

Square each side

( a-3)^2 + (2a -4) ^2) = 4 *(10)

FOIL the left side

a^2 -6a +9   + 4a^2 -16a +16 = 40

Combine like terms

5a^2 -22a +25 = 40

Subtract 40 from each side

5a^2 -22a -15 =0

Factor

(a - 5) (5 a + 3) = 0

Using the zero product property

a-5 =0   5a +3 = 0

a = 5       5a = -3

a=5     a = -3/5

The product of the terms is

5 * -3/5 = -3

Answer:

16/3 hours  5 1/3

Step-by-step explanation:

Answer: 5 1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

$7,415.99

Step-by-step explanation:

Hello, please consider the following.

[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]

So it gives $7,415.99

Thank you.

Step-by-step explanation:

Tan² theta = sec² theta - 1

Cot² theta = cosec² theta - 1

Tan²+Cot² = sec²-1+cosec²-1

= sec²+cosec²-2

Please find attached herewith the solution of your question.

If you have any doubt, please comment.

Make sure everyone participates. Therefore, option B is the correct answer.

This violates rule b) Make sure everyone participates. Michael has convened a large group, however only a few people are driving the conversation. In order to have a successful brainstorming session, everyone must participate and all ideas should be heard. This will ensure that all ideas are taken into account and that the team can come up with the best solutions.

Therefore, option B is the correct answer.

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9514 1404 393

Answer:

  210

Step-by-step explanation:

The number of combinations of 10 things taken 6 at a time is ...

  10!/(6!(10-6)!) = 210

210 bit strings of length 10 will have 6 1-bits.

Using combination

[tex]\\ \sf\longmapsto {}^{10}C_6[/tex]

We know

[tex]\boxed{\sf {}^nC_r=\dfrac{n!}{r!(n-r)!}}[/tex]

[tex]\\ \sf\longmapsto \dfrac{10!}{6!(10-6)!}[/tex]

[tex]\\ \sf\longmapsto \dfrac{10!}{6!(4!)}[/tex]

[tex]\\ \sf\longmapsto 210[/tex]

The value of x using complete sentences is 40 degrees.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees. A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

We are given that;

The measure of angles 75,50 and 85

Now,

In triangle 1

50+75+y=180

y=180-125

y=55

In triangle 2

55+85+x=180

140+x=180

x=40

Therefore, by angle sum properties of triangle answer will be 40 degrees.

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Hi

Income tax is  progressive

So with  50 000  we have  :  

0.02*3000 + 0.03 ( 5000 -3001) + 0.05 ( 17 000-5001) + 0.0575 ( 50 000 - 17 001) =  60+ 59.97+599.95 + 1897.44 =  2617.36

tax is = 2617.36

Step-by-step explanation:

To solve for x, we set up our equation like this:

7x - 7 = 4x + 14

Next, we subtract 4x from the right side to cancel it out and then subtract 4x from the left side.

7x (-4x) - 7 = 4x (-4x) + 14

3x - 7 = 14

Then, we add 7 on both sides (to cancel the -7 out and place it on the right)

3x - 7 (+7) = 14 + 7

3x = 21

Finally, we divide both sides by 3 to isolate our variable, x.

3x ÷ 3 = x

21 ÷ 3 = 7

Our final answer: x = 7

Answer:

3/4

Step-by-step explanation:

First find the number that are not seniors

80 -20 = 60

60 are not seniors

The ratio of not seniors to total

60/80

Divide top and bottom by 20

3/4

Answer:

60 students

Step-by-step explanation:

80 -20 = 60

Answer:

JK=12

KI=16

Step-by-step explanation:

[tex]K\in\ [JI]\ \Rightarrow\ |JK|+| KI |=|KI|\\\\x^2-4x+3x-2=28\\\\\Longleftrightarrow\ x^2-x-30=0\\\\\\\Longleftrightarrow\ x^2+5x-6x-30=0\\\\\\\Longleftrightarrow\ x(x+5)-6(x+5)=0\\\\\\\Longleftrightarrow\ (x+5)(x-6)=0\\\\x=-5\ (excluded)\ or\x=6\\\\\\\Longleftrightarrow\ \\|JK|=x^2-4x=6^2-4*6=36-24=12\\|KI|=3x-2=3*6-2=18-2=16\\\\Proof: 12+16=28\\[/tex]

Answer:

Step-by-step explanation:

Given

2^x [(x+1)³ -1] = 2^x - (x+1)³ + 1

Lep p = 2^x, and q = (x+1)³ - 1

Then the original equation becomes

pq = p - q

p - q - pq = 0

p(1 - q) - q = 0

p = q/(1 - q)

2^x = [(x+1)³ - 1]/[-(x+1)³]

2^x = [1 - (x+1)³]/[(x+1)³]

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

Answer:

Slope of the tangent line (m) = 1 / 2

Step-by-step explanation:

Given:

Point A = (4,2)

Origin point = (0,0)

Find:

Slope of the tangent line (m)

Computation:

Slope of the tangent line (m) = (y2-y1) / (x2-x1)

Slope of the tangent line (m) = (2-0) / (4-0)

Slope of the tangent line (m) = 2 / 4

Slope of the tangent line (m) = 1 / 2

Answer:

2

Step-by-step explanation:

g(x) = 2x-1

g(-3)+5

2(-3)-1 +5

-6-1+5

-7+5

-2

ertificates 6.00% per annum ---x

AA bond 11.00% per annum ---y

x + 1 y= 160000 ------------------------1

6.00% x + 11.00% y= 15600

Multiply by 100

6 x + 11 y= 1560000.00 --------2

Multiply (1) by -6

we get

-6 x -6 y= -960000.00

Answer: It's B

Step-by-step explanation:

The table that represents the double number line is (b)

On the double number line, we have the following points

x: 0    1

y: 0    25

This means that as x increases by 1, y increases by 25.

So, we have:

x: 0  1    2    3   4

y: 0 25  50 75 100

The above is represented by the second table

Hence, the table that represents the double number line is (b)

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Answer: 200 ways

Step-by-step explanation:

From the given information:

Total number of roads leading from Bluffton to​ Hardeeville = 4

Total number of roads leading from Hardeeville to​ Savannah = 10

Total number of roads leading from Savannah to Macon = 5

We need to find the total number of ways to get from Bluffton to​ Macon.

Total number of ways to get from Bluffton to​ Macon = 4 * 10 * 5

= 200

Therefore, there are 200 required number of ways to get from Bluffton to​ Macon.

Answer:

720 different ways.

Step-by-step explanation:

Permutation has to do with arrangement. For example, in order to arrange 'n' objects in any order, this can only be done in n! ways since there is no condition or restriction on how to arrange the objects.

n! = n(n-1)(n-2)... (n-r)!

If there are 3 statistics books, 2 math books, and 1 computer science book on your bookshelf, the total number of books altogether is 3 + 2 + 1 = 6 books.

The number of ways that 6 books can be arranged in any order is 6!.

6! = 6(6-1)(6-2)(6-3)(6-4)(6-5)

6! = 6*5*4*3*2*1

6! = 120*6

6!= 720 different ways.

Hence, the books on your shelf can be arranged in 720 different ways.