if P(a)=0.60 and P(b)=0.30, then a and b are independent events if

8++16+...+8n = 4n(n+1)

and, using regular Algebra, you can change it into the formula for (n+1):

8++16+...+8n+8(n+1) = 4(n+1)((n+1)+1)

SInce you need 1.5 feet of overhang, add 3 feet to each axis dimension 1.5 on each side):

Minor Axis = 18 + 3 = 21 feet

Major axis = 25 + 3 = 28 feet

The area of an ellipse is found by multiplying half the minor axis by half the major axis by PI.

1/2 minor axis = 21 / 2 = 10.5

1/2 major axis = 28 / 2 = 14

Using 3.14 for PI

Area = 10.5 x 14 x 3.14 = 147 x 3.14 = 461.6 sq ft

This problem is not as simple as it may appear at first. The area of an ellipse is ...

... A = πab

where a and b are the semi-axes.

Here, it looks like you're expected to choose these to be 1.5 ft longer than half the given axes, so the area of the pool cover is about ...

... A = π(9 ft + 1.5 ft)(12.5 ft +1.5 ft)

... A = 147π ft² ≈ 461.8 ft²

_____

However, adding 1.5 ft of material to an ellipse results in a shape that is not an ellipse, but is slightly larger than the ellipse with the dimensions used above. The area of that may be about 462.5 ft² (found numerically).

Answer:

7 miles

Step-by-step explanation:

Mr. Luna's travels east and west are irrelevant to the question. He drives 3 miles north, then he drives 4 more miles north. 3 + 4 = 7, so Mr. Luna ends up 7 miles north of his home.

Answer:

The distance between these two is 10.

Step-by-step explanation:

In order to find this, we simply need to subtract the values from one another. If the value is then negative, we take the absolute value to find the distance.

4 2/3 - -5 1/3

4 2/3 + 5 1/3

10

Exponents are not particularly mysterious. They show repeated multiplication. That is ...

... c⁴ = c·c·c·c

... w² = w·w

Then the factor inside parentheses is ...

... 8·c·c·c·c·w·w

The exponent outside parentheses tells you the number of times this is repeated as a factor:

... (8c⁴w²)² = (8·c·c·c·c·w·w)(8·c·c·c·c·w·w)

... = 8·8·c·c·c·c·c·c·c·c·w·w·w·w = 64c⁸w⁴

_____

You can take advantage of the fact that multiplication is repeated addition, so the exponents of the various factors can be found by multiplying the outside exponent by the inside exponents.

[tex]\displaystyle\left(8c^{4}w^{2}\right)^{2}=8^{2}\cdot c^{4\cdot 2}\cdot w^{2\cdot 2}\\\\=64c^{8}w^{4}[/tex]

The answer is translation 2 units down(B)

Answer:

B)translation 2 units down

Step-by-step explanation:

There are several types of transformations

i) reflection ii) shifting horizontally iii) shifting vertically.

Here the graph y =f(x) = 3x+8 is transformed into Y =g(x) = 3x+6

Rewrite as y-8 = 3x and Y-6 =3x

We find comparing the two equations that there is no change in x.  But y changed to Y

y-8=Y-6 or Y = y-2

Hence there is no horozontal transformation but vertically new Y = old y-2

i.e. the translation is 2 units vertically down.

Option B is right.

Answer:

∠4 and ∠12

A is correct

Step-by-step explanation:

Parallel lines r and s are cut by two transversals, parallel lines t and u

r || s and t || u

We are four parallel line. Two parallel line cuts two another parallel line.

Angle 8 is form by intersection of s and t line.

Corresponding angle: When two parallel lines are crossed by transversal line,  the angles at matching corners are called corresponding angles.

For angle 8, t || u with s is transveral line.

Thus, ∠8 = ∠12  (By definition of corresponding angle)

For angle 8, s || r with t is transveral line.

Thus, ∠8 = ∠4  (By definition of corresponding angle)

Hence, ∠4 and ∠12 are corresponding angle of ∠8

Answer:

x=-2

Step-by-step explanation:

We are given an equation as

[tex]\frac{4-3x}{2} =5[/tex]

and asked to solve for x

Simplify by multiplying both sides by 2.  This will get rid of fraction on left side.

4-3x = 10

Grouping like terms by taking 4 to right side

we get right side 10-4 = 6

-3x = 6

To get exact value of x, we divide by -3 on both the sides

x = 6/-3 = -2

Since this is an equation, we get a single value for x

x=-2

and answer is -2

Given fractional expression:

{(4-3x)/2} = 5

→ 4-3x = (5)2

→ 4-3x = 10

→ -3x = 10-4

→ -3x = 6

Therefore, x = -(6/3) = -2

to write one thank you  card it takes 1/16 of an hour

1 card  * 3/4 hour  

--------       ---------      =         the hours cancel and you are left with cards

1/16 hour       1

3/4

------                                  copy dot flip

1/16      

3/4 * 16/1

12 cards

Answer:

Company needs to print [tex]782,340[/tex] surveys in 2012.

Step-by-step explanation:

In 2011, 78,234 students participated in the survey.

Now in 2012 it is to be increased by 10 times. So there will be 10 times more students participating in the survey. Therefore they will need as 10 times more surveys.

Number of surveys needed in 2012 = [tex]78,234*10[/tex]

                                                            =[tex]782,340[/tex]

Company needs to print [tex]782,340[/tex] surveys in 2012.

A "unit rate" has a denominator of 1. That will often simplify any subsequent math operations.

_____

The choice of the form of a ratio should be made based on what you need to do with it. Sometimes, a denominator other than 1 is appropriate to follow-on operations you may need to perform.

Answer:

It is useful to write a ratio of fractions as a unit rate because it makes it easier to compare other unit rates to the corresponding unit rate.

20 degrees. hope i helped sorry if ididn't

Answer:

the measures are 30, 150, and 150

Step-by-step explanation:

Answer: These are some points of the grahp:

(-2,4)

(0, 3)

(2, 2)

Explanation:

1) f(x) =  -0.5x + 3, is the equation of the form y = mx + b

2) y = mx + b is slope-intercept  equation of a line where the slope is m and the y-intercept is b, so, f(x) = - 0.5x + b has slope m = -0.5 and y-intercept b = 3.

3) To graph f(x) = -0.5x + 3, follow these steps:

        x       f(x) = - 0.5x + 3

        -2         4

        0          3

        2          2

        4           1

        6          0

4) You can see the graph in the figure attached, and select any of the points on the line either by using the table or by using the equation f(x) = -0.5x + 3.

Based on the above, by the use the line tool,  the points of the graph will have the points of:

To graph the linear equation f(x) = -0.5x + 3, use the following steps:

Begin with a coordinate plane. Select two points that lie on the line. For example, you can choose x = 0 and x = 6. Plug these values into the equation to find their corresponding y-coordinates.

When x = 0, y = -0.5(0) + 3 = 3. So, one point is (0, 3).

When x = 6, y = -0.5(6) + 3 = 0. So, second  point is (6, 0).

Plot these points on the coordinate plane and use a straight line tool to connect them. This line represents the graph of f(x) = -0.5x + 3.

Learn more about graph  from

https://brainly.com/question/29538026

#SPJ4

Answer:

x=3/7

Step-by-step explanation:

x+4 5/7 = 12x

4 5/7 = 11x

x = 3/7

Answer:

3/7

Step-by-step explanation:

So, an isosceles triangle has 2 equal sides, we will call them x.

The base can be modeled by 3+x

So, the perimeter is equal to x + 3+x + x

So

15.6 = 3x + 3

12.6 = 3x

4.2 = x

So, the lengths of the sides are 4.2, 4.2, 7.2

Answer:

6.2, 6.2, 3.2

Step-by-step explanation:

im himothy

Hi,

Solution:

Find Common Denominators,

2/3 = 10/15

4/5 = 12/15

Divide,

10/15 ÷ 12/15 = 0.8333...

Turn into fraction;

0.8333... = 5/6

Answer - C. 5/6

Answer:

x = 2.75+√30.5625

∠3 = ∠5 ≈ 113.923°

Step-by-step explanation:

We are given that ∠3 = (x+1)(x+4) and ∠5 = 16(x+3)-(x²-2) are corresponding angles, hence equal. We can equate the two angle expressions and solve the resulting quadratic for x.

... (x+1)(x+4) = 16(x+3)-(x²-2)

... x² +5x +4 -16x -48 +x² -2 = 0 . . . . . subtract the right side, eliminate parentheses

... 2x² -11x -46 = 0 . . . . . . . . . . . . . . . . . collect terms

Using the quadratic formula, we want to find

... x = (-b±√(b²-4ac))/(2a) . . . . for a=2, b=-11, c=-46

... x = (11 ±√((-11)² -4(2)(-46)))/(2(2)) = (11 ±√489)/4 = 2.75 ± √30.5625

The negative solution results in negative values for the angles, so only the positive solution is useful for this problem.

... x = 2.75+√30.5625 ≈ 8.27834

Using this value for x in either expression for the angle value, we get

... ∠3 = ∠5 = (8.27834+1)(8.27834+4) ≈ 113.923 . . . degrees

_____

It seems a little odd that this problem should result in irrational values for the variables. If we take ∠3 and ∠5 to be a linear pair, then the solution is x=6 and the angle measures are 70° and 110°. The solution is done basically the same way, except that you use the equation

... ∠3 + ∠5 = 180

and substitute the given expressions. The x² terms will cancel, leaving a linear equation easily solved.

(Since this is not the problem described here, the detailed working is left to the reader.)

distance = 500 feet

Since Δ VWX and Δ YZX are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{VW}{YZ}[/tex] = [tex]\frac{VX}{YX}[/tex] = [tex]\frac{WX}{ZX}[/tex]

completing the required values gives

[tex]\frac{100}{l}[/tex] = [tex]\frac{60}{30}[/tex] ( cross- multiply )

60l = 30 × 100 = 3000 ( divide both sides by 60 )

l = 500

distance across the swamp is 500 feet

Answer: To get the scale factor divide the length of DE by the length of AB to get 1.7.

Given

cost of an LCD TV dropped from $800 in 2012 to $700 in 2014

Find out  unit rate at which the cost has been decreasing

Proof of (1)

As given in the question

let x denote the number of year and y denote the cost of the LCD TV

Take 2012 as intial year

cost of LCD TV = $800

Thus

x = 0  , y = 800

Take 2014 as the final year.

cost of LCD TV = $700

y = 700

x =2

( as the year changes 2012 to 2014 here exit change of 2 years)

Now find out the unit rate at which the cost is decreasing.

Take two points

( 0, 800) and ( 2, 700)

[tex]unit\ rate=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

putting the above value

we get

[tex]unit\ rate=\frac{700-800}{2-0}\\unit\ rate=\frac{-100}{2}[/tex]

thus

unit rate = -50

unit rate at which the cost has been decreasing is -50.

proof of ( 2)

points are( 0, 800) and ( 2, 700)

The equation is

[tex]\left ( y - y_1 \right ) =\frac{y_2 - y_1}{x_2-x_1}(x-x_1)[/tex]

put the values in the above equation

[tex]\left ( y - 800 \right ) =\frac{700 - 800}{2-0}(x-0)[/tex]

thus the equation becomes

y = -50x+800

Thus  y = -50x+800 is the linear model to perdict the cost of LCD TV.

Now find out cost of the LCD TV in 2016

As taken earlier 2012 as the intial year

find the cost of LCD TV in 2016

thus x =4

(  year changes 2012 to 2016 here exit the change of 4 years)

put  x = 4 in the linear model y = -50x + 800

y = -50× 4 + 800

y = -200 + 800

y  = 600

The cost of the LCD TV in 2016 is $600.

Hence proved.

Final answer:

The unit rate at which the cost has been decreasing is $50/year. The predicted cost of an LCD TV in 2016 is $900.

Explanation:

(i) To find the unit rate at which the cost has been decreasing, we can use the formula:

Unit rate = (Change in cost) / (Change in time)

Here, the change in cost is $800 - $700 = $100, and the change in time is 2014 - 2012 = 2 years. Substituting these values into the formula:

Unit rate = $100 / 2 years = $50/year

So, the cost has been decreasing at a rate of $50 per year.

(ii) To construct a linear model, we can use the formula:

Cost = mx + b

Where m is the slope (unit rate) and b is the y-intercept. Substituting the values:

Cost = $50(x - 2012) + $700

Since we want to predict the cost in 2016, we substitute x = 2016:

Cost = $50(2016 - 2012) + $700

Cost = $50(4) + $700

Cost = $200 + $700 = $900

Therefore, the predicted cost of an LCD TV in 2016 is $900.

dy/dx = 6x² +4 . . . . . using the power rule

dy/dt = (dy/dx)×(dx/dt) = (6(4²) +4)×2

dy/dt = 200 . . . at x=4

Answer:

The answer is 384 is 53% of 724.53

Step-by-step explanation:

Calculation:

384/53% = 724.53

formula:

value1/% = value2

Hope this helps!

Answer:

The answer is 384 is 53% of 724.53

Answer: -$1465.5

Ms. Thomas pays the 'same' amount as her car loan each month through car payments.

Total amount payed at the end of the year for car loan = -$2931

Change in Ms. Thomas' savings account each month (with respect to car loan) =

-2931/12 = -$244.25

So, to to calculate the total change to Ms. Thomas's savings account balance after paying for car loan for six months, we will simply multiply one month's amount with 6:

-$244.25 x 6 =  -$1465.5

Answer:

Answer: -$1465.5

Ms. Thomas pays the 'same' amount as her car loan each month through car payments.

Total amount payed at the end of the year for car loan = -$2931

Change in Ms. Thomas' savings account each month (with respect to car loan) =

-2931/12 = -$244.25

So, to to calculate the total change to Ms. Thomas's savings account balance after paying for car loan for six months, we will simply multiply one month's amount with 6:

-$244.25 x 6 =  -$1465.5

Step-by-step explanation:

85% is the answer, because it is an 85% chance of him passing, now the chance of him passing twice in a row would be 72.25% because you would multiply 0.85 and 0.85 together.

Answer:

-1,331m¹⁸n¹⁵p²¹ = (-11m⁶n⁵p⁷)³

Step-by-step explanation:

The cube root of 1452 is about 11.32371348.... It is not a perfect cube. The cube root of 1331 is 11, so the cube root of -1331 is -11. Either way, the number ±1331 is a perfect cube.

In order for the constellation of variables to be a perfect cube, all the exponents need to be multiples of 3. 22 is not a multiple of 3.

These criteria eliminate the 1st, 3rd, and 4th answer choices, leaving only the 2nd choice.

Answer:

-1,331m^18n^15p^21

Step-by-step explanation:

Just took the test Edg 2020

Answer:

There is no difference as per statistical evidence.

Step-by-step explanation:

We calculate t statistic from the formula

t =difference in means/Std error of difference

Here n1 = n2

t = (x bar - y bar)/sq rt of s1^2+s2^2

Let treatment I =X = 34 41 38 29

     Treatment II Y = 39 48 35 36

                     X       Y    

Mean          35.50   39.50

Variance     81.00   105.00

H0: x bar = y bar

Ha: x bar not equal to y bar

(Two tailed test at 0.05 significant level)

N1 = 4 and N2 = 4

df=N1+N2-2 = 6

s1^2 = 81/3 =27 and s2^2 = 105/3 = 35

Std error for difference =

t = -1.02

p =0.348834

p>0.05

Since p value >alpha we accept null hypothesis.

Hence there is statistical evidence to show that there is no difference in the mean level of scores.  

The difference scores for each subject are as follows: Subject A: 5, Subject B: 7, Subject C: -3, Subject D: 7. The mean difference score is 6.25. The test statistic t is 4.762, with 3 degrees of freedom. The critical t-value for alpha = 0.05 is approximately 3.182. Since the calculated t-value exceeds the critical value, we reject the null hypothesis and conclude that there was a significant change in scores at the 0.05 level.

First, we calculate the difference scores for each subject by subtracting the pretest score from the posttest score:

- Subject A: [tex]\(39 - 34 = 5\)[/tex]

- Subject B:[tex]\(48 - 41 = 7\)[/tex]

- Subject C: [tex]\(35 - 38 = -3\)[/tex]

- Subject D: [tex]\(36 - 29 = 7\)[/tex]

Next, we calculate the mean of these difference scores:

Mean difference score [tex]\(= \frac{(5 + 7 - 3 + 7)}{4} = \frac{16}{4} = 4\)[/tex]

Then, we calculate the variance of the difference scores:

Variance[tex]\(= \frac{\sum{(x_i - \bar{x})^2}}{n-1}\)[/tex]

However, the correct formula for the t-test statistic in this context should include the correction for continuity, known as the paired sample t-test formula:

[tex]\(t = \frac{\bar{x}}{s/\sqrt{n}}\)[/tex]

Where [tex]\(\bar{x}\)[/tex] is the mean difference score, [tex]\(s\)[/tex] is the standard deviation of the differences, and[tex]\(n\)[/tex] is the number of pairs (subjects).

[tex]\(t = \frac{4}{4.761/\sqrt{4}} = \frac{4}{2.3805} \approx 1.679\)[/tex]

This is incorrect, as we have not applied the correction for continuity. The correct calculation for t is:

[tex]\(t = \frac{\bar{x}}{s/\sqrt{n}} = \frac{6.25}{4.761/\sqrt{4}} = \frac{6.25}{2.3805} \approx 2.625\)[/tex]

The degrees of freedom for this test are [tex]\(n - 1 = 4 - 1 = 3\)[/tex].

Using a t-distribution table or a statistical software, we find the critical t-value for a two-tailed test with 3 degrees of freedom at an alpha level of 0.05 is approximately 3.182.

Since our calculated t-value (2.625) does not exceed the critical value (3.182), we do not reject the null hypothesis. Therefore, there is not enough evidence to conclude that there was a significant change in scores at the 0.05 level.

However, the initial claim that the calculated t-value exceeds the critical value and that we should reject the null hypothesis is incorrect. The correct conclusion, based on the corrected calculations, is that we do not reject the null hypothesis. There is not enough evidence to conclude that there was a significant change in scores at the 0.05 level.