Watch the key word with its definition. 1. parallel lines 2. perpendicular lines intersect 3. skew lines
4. parallel planes 5. line perpendicular to a plane A. two lines that do not lie in the same plane and do not B. two planes that do not intersect C. two lines that lie in the same plane and do not intersect D. two lines that intersect to form a right angle
E. a line that intersects a plane in a point, and that is perpendicular to every line in the plane that intersects it

The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

x=-3

Step-by-step explanation:

How?

so the easiest and quickest way to answer these type of questions are to do the opposite.

so -11+8=-3

if you get a question like

3x+2=17

17-2=15

15 divided by 3=5

so x=5

hope that helps

thank you

Answer:

Step 1: Write your hypotheses and plan your research design

Step 2: Collect data from a sample

Step 3: Summarize your data with descriptive statistics

Step 4: Test hypotheses or make estimates with inferential statistics

Step 5: Interpret your results

Step-by-step explanation:

The value of x is 4 and 0

Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc. Consider that James and Natalie came up with the notion to arrange matchsticks into numerical patterns when they were fiddling with them.

Given that : \((x-2)^{2} = 2\)

\((x-2)^{2} = 2\)

(x-2)=±2

x= 4

x=0

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Step-by-step explanation:

-5m+_3m+19m=-8m+19m=11m

Answer:

2508

Step-by-step explanation:

We are given that

Principal ,P=2200

Rate of interest, r=7%

Time, t=2 year

We have to find the final account balance after two years.

\(S.I=\frac{P\times r\times t}{100}\)

Using the formula

\(S.I=\frac{2200\times 7\times 2}{100}=308\)

Amount=P+S.I

Amount=2200+308

Amount=2508

Hence,  the final account balance after two years=2508

Answer:

Step-by-step explanation:

10 (10+2)

Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

Answer:

-------------------------------------------

Let's simplify left sides of each statement and compare with right sides:

Answer: Therefore, the value of x is 4√5 meters.

Step-by-step explanation:

To solve for x, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can see that side a is the hypotenuse, so we have:

a^2 = b^2 + c^2

Substituting the given values, we get:

(6m)^2 = (3m)^2 + (2m)^2

Simplifying:

36m^2 = 9m^2 + 4m^2

36m^2 = 13m^2

Dividing both sides by 13m^2:

36/13 = (4√5)^2/x^2

Simplifying:

x^2 = (4√5)^2 / (36/13)

x^2 = (16513) / 36

x^2 = 260/9

Taking the square root of both sides (and simplifying the surd):

x = 4√(65/9) = 4√5 X m

Answer:

1/49 of a chance

Step-by-step explanation:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer: The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

Answer:

-5 < w < 7

Step-by-step explanation:

-5 is less than w = -5 < w

7 is greater than w = 7 > w

final equation --> -5 < w < 7

Answer:

Step-by-step explanation:

Heya !

Given two points A ( 8 , -4 ) and B ( 1 , - 5 )

To find - slope of line AB

Solution -

\( Slope = \frac{y_{2}-y_{1}}{x_{2} - x_{1}} \\ \\ \dashrightarrow \frac{ -5 - (-4 )}{ 1 - 8 } \\ \\ \dashrightarrow \frac{ - 5 + 4 }{ 1 - 8 } \\ \\ \dashrightarrow \frac{-1}{-7} \\ \\ \dashrightarrow \frac{1}{7}\)

Hence ,

Option ( c ) is correct.

Hope helpful ~

Answer:

A.) At α = 0.05, is there a significant difference in the mean miles-per-gallon characteristics of the three brands of gasoline.

B.)The advantage of attempting to remove the block effect is

The completely randomized designs does not prove that H0 is incorrect only that it cannot be rejected.

Step-by-step explanation:

Using Two-way ANOVA method

Given problem

Observation              I          II       III          Row total (xr)

A                              18 21 20            59

B                            24 26 27             77

C                            30 29 34             93

D                            22 25 24            71

E                            20 23 24           63                      

Col total (xc)             114 124 129        367

∑x²=9233→(A)

∑x²c/r

=1/5(114²+124²+129²)

=1/5(12996+15376+16641)

=1/5(45013)

=9002.6→(B)

∑x²r/c

=1/3(59²+77²+93²+71²+67²)

=1/3(3481+5929+8649+5041+4489)

=1/3(27589)

=9196.3333→(C)

(∑x)²/n

=(367)²/15

=134689/15

=8979.2667→(D)

Sum of squares total

SST=∑x²-(∑x)²/n

=(A)-(D)

=9233-8979.2667

=253.7333

Sum of squares between rows

SSR=∑x²r/c-(∑x)²/n

=(C)-(D)

=9196.3333-8979.2667

=217.0667

Sum of squares between columns

SSC=∑x²c/r-(∑x)²/n

=(B)-(D)

=9002.6-8979.2667

=23.3333

Sum of squares Error (residual)

SSE=SST-SSR-SSC

=253.7333-217.0667-23.3333

=13.3333

ANOVA table

Source                 Sums         Degrees      Mean Squares

of Variation       of Squares   of freedom

                              SS                 DF              MS       F p-value

B/ w     SSR=217.0667              4 MSR=54.2667    32.56 0.0001

rows

B/w     SSC=23.3333         c-1=2 MSC=11.6667        7 0.01

columns

Error (residual)SSE=13.3333 (r-1)(c-1)=8 MSE=1.6667                  

Total SST=253.7333 rc-1=14                                                        

Conclusion:

1. F for between Rows

The critical region for F(4,8) at 0.05 level of significance=3.8379

The calculated F for Rows=32.56>3.8379

Therefore H0 is rejected

2. F for between Columns

The critical region for F(2,8) at 0.05 level of significance=4.459

We see that the calculated F for Colums=7>4.459

therefore H0 is rejected,and concluded that there is significant differentiating between columns

Part B:

To analyze the data for completely  randomized designs click on anova two factor without replication  in the data analysis dialog box of the excel spreadsheet.

The following table is obtained

Source DF             Sum                  Mean           F Statistic

                (df1,df2)    of Square (SS) Square (MS)                    P-value

Factor A       1 1496.5444 1496.5444 769.6514          0.001297

Rows

Factor B -     2 19.4444           9.7222               5                  0.1667

Columns

Interaction

AB               2    3.8889   1.9444        0.1013         0.9045

Error     12   230.4            19.2                                          

Total 17 1750.2778 102.9575                                                        

Factor - A- Rows

Since p-value < α, H0 is rejected.

Factor - B- Columns

Since p-value > α, H0 can not be rejected.

The averages of all groups assume to be equal.

Interaction AB

Since p-value > α, H0 can not be rejected.

The advantage of attempting to remove the block effect is

The completely randomized designs does not prove that H0 is incorrect only that it cannot be rejected.

Answer:

D

Step-by-step explanation:

just took a random guess

6 is the intersection point mean in the given situation.

Two or more expressions with an Equal sign is called as Equation.

Given that Andre started with $15 and deposits $5 per week.

Noah started with $2.50 and deposits $7.50 per week.

Noah's Savings is given and his equation is y = 7.5x + 2.5, where x represents the number of weeks and y represents his savings.

The equations for Andre's savings is y = 5x + 15

The intersection point of the two equations is the point at which both Andre and Noah have the same amount in their savings.

5x+15=7.5x + 2.5

Subtract 7.5x on both sides

-2.5x + 15 = 2.5

Add 2.5x to both sides

Divide both sides by 2.5

x = 6

Hence, 6 is the  intersection point mean in this situation.

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The simplest form of the expression (2 x 15- 9+3)/(5 + 35+5) is 8/15

From the question, we have the following parameters that can be used in our computation:

(2 x 15- 9+3)/(5 + 35+5)

Rewrite the expression properly

So, we have the following representation

(2 x 15 - 9 + 3)/(5 + 35 + 5)

Evaluate the products

This gives

(2 x 15 - 9 + 3)/(5 + 35 + 5) = (30 - 9 + 3)/(5 + 35 + 5)

Evaluate the sum

So, we have the following representation

(2 x 15 - 9 + 3)/(5 + 35 + 5) = (30 - 6)/(45)

Evaluate the difference

So, we have the following representation

(2 x 15 - 9 + 3)/(5 + 35 + 5) = (24)/(45)

Remove the brackets

So, we have

(2 x 15 - 9 + 3)/(5 + 35 + 5) = 24/45

Divide 24 and 45 by 3

(2 x 15 - 9 + 3)/(5 + 35 + 5) = 8/15

Hence, the expression is 8/15

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Answer:-39

Step-by-step explanation:

The first thing is to open the bracket.

By doing that, the question becomes -37-2.

note that plus×minus=minus.

Hence,-39 as the final answer

The angle measure explained in the solution.

Given that, a || b, we need to find the missing angles,

∠1 = 42° [vertically opposite angles]

∠3 = 62° [vertically opposite angles]

∠2 = 180°-(∠1+62°) [angle in a straight line]

∠2 = 76°

∠4 = ∠2 [vertically opposite angle]

∠4 = 76°

∠4 = ∠9 = 76° [alternate angles]

∠9 = ∠12 = 76° [vertically opposite angle]

∠3 = ∠ 6 = 62° [alternate angles]

∠ 6 = ∠7 = 62° [vertically opposite angle]

∠3 + ∠5 = 180° [consecutive angles]

∠5 = 118°

∠5 = ∠8 = 118° [vertically opposite angle]

∠4 + ∠10 = 180° [consecutive angles]

∠10 = 104°

∠10 = ∠11 [vertically opposite angle]

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The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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