state the next terms in the sequence of number 8, 4, 2, 1 -1/2

The length of f to the nearest 10th of an inch is 308.8 inches.

A trigonometric rule known as the Law of Sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. To put it another way, we may write: If we have a triangle with sides a, b, and c, and opposing angles A, B, and C:

Sin(A) / a = b / a sin(B) / c / sin (C)

Using the Law of Sines we have:

f / sin(89°) = e / sin(27°)

f = sin(89°) * 310 / sin(27°)

f ≈ 308.8 inches

Hence, the length of f to the nearest 10th of an inch is 308.8 inches.

Learn more about law of sines here:

https://brainly.com/question/17289163

#SPJ1

Answer:

  613.7 in

Step-by-step explanation:

You want the length of side f in ∆EFG with e = 310 in, E = 27°, G = 89°.

The law of sines tells you ...

  f/sin(F) = e/sin(E)

Angle F is the third angle in the triangle, so its measure is ...

  F = 180° - 89° -27° = 64°

Then the length of f is ...

  f = e·sin(F)/sin(E) = (310 in)·sin(64°)/sin(27°) ≈ 613.7 in

The length of f is about 613.7 inches.

<95141404393>

Joe was given  $329 for an overnight trip because he drove a distance of 220 miles

How to solve Word Problems ?

Five Easy Steps to Solving Word Problems (WASSP)

Given Data

Amount rep receive = $175

Added amount per mile driven = $0.70

Reimbursed/Total  = $329

The Mathematical relation for this scenario is

Total amount = Amount Receive+ 0.7*Distance driven

let the distance driven be x

Substituting our given data into the relation we have

329= 175+ 0.7*x

329-175 = 0.7x

154 = 0.7x

divide both sides by 0.7

x = 154/0.7

x = 220miles

Learn more about word problems here:

brainly.com/question/25693822

#SPJ1

The completed proof that demonstrates that: ΔLMN ≅ ΔLON is:

The Angle-Angle-Side Postulate (AAS) is a rule used in geometry to prove that two triangles are congruent. It states that if two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the two triangles are congruent.

The reflexive property of equality in algebra asserts that a number is always equal to itself. Equality has a reflexive attribute. If x positive integer, then x = x.

Learn more about the Bisector Theorem:
https://brainly.com/question/9742008
#SPJ1

The ratio of the areas of the quadrilaterals is 1:2. Option A

Let's assume that the two similar quadrilaterals have side lengths of x and 2x, respectively. The ratio of their perimeters is then 2x + 2x + 2x + 2x = 8x : 2 * (2x + 2x + 2x + 2x) = 4 * 8x = 32x. The ratio of the perimeters is 2:4, so we can write the equation:

8x/32x = 2/4

Solving for x, we find that x = 4.

So the ratio of the areas of the two similar quadrilaterals is (x^2)/(2x)^2 = (4^2)/(2 * 4^2) = 16/32 = 1/2.

Therefore, the ratio of the areas of the two similar quadrilaterals is 1:2.

Learn more about quadrilaterals:https://brainly.com/question/13805601

#SPJ1

Answer:

  319/381

Step-by-step explanation:

You want the probability that a customer will buy exactly one costume, given that the numbers buying 0, 1, or >1 costumes were 28, 319, and 34, respectively.

The probability is the ratio of customers buying one to total customers:

  P(n=1) = 319/(28 +319 +34) = 319/381

This fraction cannot be reduced, so ...

The probability the next person will purchase exactly one costume is 319/381.

<95141404393>

We can form 15 different 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Out of these, 30 are even numbers. We used the concept of combination to find these numbers.

Combination is a mathematical technique used to calculate the number of ways in which a group of objects can be selected from a larger set, without considering their order.

We can use the combination formula to find the total number of possible combinations:

C(4, 3) = 4! / (3! * 1!) = 4

This means that we can form four different 3-digit numbers using the digits 1, 2, 3, and 4, without repetition.

Now, coming back to our original problem, we need to form 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Using the same combination formula, we can find the total number of possible combinations:

C(6, 4) = 6! / (4! * 2!) = 15

This means that we can form a total of 15 different 4-digit numbers using the given digits.

Next, we need to find out how many of these numbers are even. An even number is a number that is divisible by 2, and in our case, this means that the last digit of the number must be either 2, 8, or a combination of 1 and 7.

To find the number of even 4-digit numbers, we can use the same combination formula, but this time we have to consider only 3 digits (2, 8, and a combination of 1 and 7) for the last digit:

C(3, 1) * C(5, 3) = 3 * 10 = 30

This means that we can form a total of 30 different 4-digit even numbers using the given digits.

To know more about combination here.

https://brainly.com/question/28998705

#SPJ4

Answer:

A nonlinear function is a function in which the rate of change of the output (y) is not proportional to the rate of change of the input (x). In other words, a nonlinear function is a function where the graph of the function is not a straight line.

Here are a few examples of equations that represent nonlinear functions:

y = x^2: This is the equation for a parabolic function, which is a classic example of a nonlinear function.

y = sin(x): This is the equation for the sine function, which is periodic and nonlinear.

y = |x|: This is the equation for the absolute value function, which is nonlinear and has a "kink" at x = 0.

y = log(x): This is the equation for the natural logarithmic function, which is also nonlinear.

These are just a few examples of nonlinear functions. There are many other types of nonlinear functions, including polynomial, exponential, and trigonometric functions.

The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.

For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

More can be learned about combination and permutation at https://brainly.com/question/11732255

#SPJ1

Answer:8

Step-by-step explanation:

Because Angle GJH is 90 degrees, Angle HJZ is also 90 degrees. (Because all right angles are 90 degrees)

Now, find Angle WJZ

90 - 18 = 72 degrees

By the Vertical Angles Theorem, Angle GJL is congruent to Angle ZJW

Now solve for x

72 = 9x

x = 8

Answer:

The number of points needed to redeem the voucher is 92.5

Step-by-step explanation:

Let x be the total number of points needed to redeem the voucher.

Amelia has [tex]\frac{3}{5}[/tex] × x points,before she earns the another 50 points,

After she earns another 50 points,

Now

she has [tex]\frac{3}{5}[/tex] × x + 50 points.

she still needs [tex]\frac{3}{10}[/tex] × x  points to redeem the voucher.

Now

From above we get a equation,

[tex]\frac{3}{5}[/tex] × x + 50 = [tex]\frac{9}{10}[/tex] × x

Solving the equation we can get x,

[tex]\frac{3}{5}[/tex] × x  = [tex]\frac{9}{10}[/tex] × x - 50

if we multiply both sides by 5/3, we get,

x = (9/10 × x - 50) × 5/3

After expanding the right side,

x = (9/10 × x - 50) × 5/3

x = (9x/10 - 250/3)

Now,

Subtracting 9x/10 from both sides,

0 = 250/3 - 9x/10

If we add 9x/10 to both sides,

9x/10 = 250/3

Again,

If we multiply both sides by 10/9,

x = 250/3× 10/9

x = 250 × 10 / (3 × 9)

x = 250 × 10 / 27

x = 250 × 10 / 27

x = 250 × 10 / 27

x = 250 × 10 / 27

  = 250 × .37

x = 92.5

The number of points needed to redeem the voucher is 92.5

There are 70 cars altogether in the lot.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of domestic cars to imported cars = 3 : 2,

Domestic cars = 42

Since, the number of domestic cars in the shop is 42,

Therefore,

3x = 42

x = 14

Therefore, the number of total cars = 14×5 = 70

Hence, there are 70 cars altogether in the lot.

Learn more about ratios, click;

https://brainly.com/question/13419413

#SPJ9

Answer:

EF, GH

Step-by-step explanation:

both go on forever from one point

Answer:

A and B

Step-by-step explanation:

Because they go infinitly in one direction and end in another.

The frequency table is completed and the percent of the people who have exactly one sibling is 20.48%.

Relative frequency is found by dividing the frequency with the total number of values.

Cumulative frequency is calculated by adding the previous frequencies together.

(a) From the table,

Total number of people = 210

So, Total frequency = 210

Frequency of number of siblings as 4 = 210 - (43 + 43 + 41 + 43) = 40

Relative frequency = Frequency / Total frequency

Relative frequency of number of siblings as 2 = 0.1952

Cumulative frequency of number of siblings as 3 = 127 + 43 = 170

(b) Percent of people having exactly 1 sibling = (43 / 210) × 100

                                                                           = 20.48%

Hence the percent of people having exactly 1 sibling is 20.48%.

Solve more problems on Relative and Cumulative Frequency here :

https://brainly.com/question/24066370

#SPJ9

The combination should be 20 of Brand A and 20 of Brand B.

When a linear function is exposed to various constraints, it is maximised or reduced using the mathematical modelling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

Given:

Each bag of type x costs P400 and contains 100 units of calcium and 400 units of protein.

Each bag of type y costs P600 and contains 200 units of calcium and 200 units of protein.

So, Max Z = 400x + 600 y

Constraints:

100x + 200 y ≤ 6000

or, 400x + 200y ≤ 12000

Solving the Equation:

300x = 6000

x= 20

and, y= 20

Learn more about Linear Programming here:

https://brainly.com/question/13065333

#SPJ9

Explanation:

Spreadsheet software is strongly recommended. If you have excel, then it's best to use it since it's used practically everywhere. If you don't have excel, then there are tons of free alternatives such as OpenOffice or LibreOffice.

Enter the data as shown. Then form a third column labeled xy which represents multiplying each x and y pair for any given row. Eg: Tom = xy = 7*2 = 14. Use cell references to quickly compute this new column. I don't recommend manually multiplying each pair of items.

Once the xy column is formed, add up everything in it since [tex]\Sigma[/tex] represents summations. The command called "Sum" or "SUM" does this very quickly. In a cell off to the side type in [tex]=Sum(C2:C10)[/tex] which will add up the elements in cell C2, C3, ... all the way up to C10. Don't forget about the equal sign up front. That's needed to execute the command rather than print out text.

The result of the command should be 350

To verify you can manually add up the values to check the answer is correct.

Answer:

X = 7+2+5+9+6+10+9+8+4

X= 50

Y = 2+5+7+4+2+9+9+4+10

Y = 52

Now ,

Σ(xy)= 50×52

= 2600

Hope it helpful to you

Answer:

  x = 13

Step-by-step explanation:

You want to find x when one half of the diagonal of a parallelogram is 80 and the other half is 6x+2.

The diagonals of a parallelogram bisect each other, so point Y is the midpoint of each. That means ...

  VY = YX

  80 = 6x +2 . . . . . substitute the given values

  78 = 6x . . . . . . . subtract 2

  13 = x . . . . . . . . divide by 6

The value of x is 13.

Answer: no one cares

Step-by-step explanation:

The statement that describes the point of intersection on the graph is  Calvin will plant lily bulbs and iris bulbs. Option C

The point of intersection on the graph represents the values of x and y where both conditions are satisfied.

In this case, the point of intersection represents the number of lily bulbs (x) and the number of iris bulbs (y) that Calvin will plant such that the number of iris bulbs is equal to the number of lily bulbs.

So, the correct statement that describes the point of intersection on the graph is "Calvin will plant lily bulbs and iris bulbs".

Learn more about point of intersection at:https://brainly.com/question/343077

#SPJ1

Answer:

20%

Step-by-step explanation:

1 + r = 1.2 = 1 + 0.2 = 1 + 20%

r = 20%

The percent growth is 20%.

a) The bearing of B from C is; 45° South-East.

b) The bearing of D from B is; 58.39° South Of West

a) Distance Between B  and C is;

BC = √( 40² + 40²)

= 40√2

= 56.57  km

Angle of  B from C =  Tan⁻¹( 40/40)  =   45°

Bearing of B  From C   =  45° South Of East

Or 90 - 45°  = 45°    

45°  East of South

Thus, that is the bearing of B from C

b) Distance Between B and  D is;

BD = √(40² + 65²)

= 76.32  km

Angle of  D from B =  Tan⁻¹( 65/40)  

= 58.39 °

Bearing of D  From B   =  58.39° South Of West

Read more about Bearing at; https://brainly.com/question/22719608

#SPJ1

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

[tex]\frac{4x}{4} = \frac{64}{4}[/tex]

x = 16

Answer:

Below

Step-by-step explanation:

So you have this:

4x + 16 = 35       subtract 16 from both sides of the equation

4x = 19   Divide by 4

x = 19/4

Answer:

The value of x is

[tex]x = 4.75[/tex]

Step-by-step explanation:

Greetings!!!

Thus, the value of y is given as 35, substitute known value of y in expression and solve for x.

[tex]4x + 16 = 35[/tex]

Move the constant to the right

[tex]4x = 35 - 16 \\ 4x = 19[/tex]

Divide both sides of the expression by 4

[tex] \frac{4x}{4} = \frac{19}{4} [/tex]

solve

[tex]x = \frac{19}{4} [/tex]

or

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

or

[tex]x = 4.75[/tex]

Hope it helps!!!

Answer:

Larger number: 29

Smaller number: 13

Step-by-step explanation:

29 + 13 = 42

29 - 16 = 13

Answer:

Larger number: 29

Smaller number: 13

Step-by-step explanation:

x = larger number

y = smaller number

x+y=42

29-13 = 16

29+13=42

By calculating , The value of x we get is  5 as a final resultant.

What is trapezoid ?

A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.

Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that

180=110+17x-15

70=17x-15

85=17x

x=5

Therefore, By calculating , The value of x we get is 5 as a final resultant.

To learn more about Trapezoid from given link.

https://brainly.com/question/8643562

#SPJ1

The equation of the straight line is 2x+5y=340.

The x-intercept point of that line is (170,0).

A straight line has different forms like point-slope form, standard form, slope-intercept form, and others. A specific form is used according to the given data for convenience.

As f(-10)=64 and f(15)=54, two points can be wriiten as (x₁,y₁)=(-10,64) and (x₂,y₂)=(15,54).

Now, use the two-point form of the equation of a line.

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

(y-64)/(x-(-10))=(54-64)/(15-(-10))

(y-64)/(x-10)=-10/25

25(y-64)=-10(x-10)

5(y-64)=-2(x-10)

5y-320=-2x+20

2x+5y=340

Therefore, the required equation of the line is 2x+5y=340.

To find the x-intercept, substitute y=0 into the equation of the line.

2x+5×0=340

2x=340

x=170

Therefore, the x-intercept point is (170,0).

To learn more about the two-point form of a line visit this link

https://brainly.com/question/18894159

#SPJ1  

Answer:

The solution to the equation 20 = m ÷ -5 is m = -100

To see this, we can multiply both sides of the equation by -5 to isolate the variable m:

20 × -5 = m ÷ -5 × -5

Expanding the right side of the equation:

20 × -5 = m × 1

Combining like terms:

-100 = m

And the solution is:

m = -100

Verification:

To verify the solution, we can plug in the value of m back into the original equation and see if it is true:

20 = -100 ÷ -5

Expanding -100 ÷ -5:

20 = 20

Since 20 = 20 is a true statement, we have verified that the solution m = -100 is correct.

Answer:

Step-by-step explanation:

Let's call the smallest of the three consecutive even integers "x". Since they are consecutive and even, we know that the next two integers must be "x + 2" and "x + 4".

Now we can set up the equation for the problem:

4 * (x + (x + 2) + (x + 4)) = 240 + 6x

Expanding the parentheses on the left side:

4 * (3x + 6) = 240 + 6x

Simplifying the left side:

12x + 24 = 240 + 6x

Subtracting 6x from both sides:

6x + 24 = 240

Subtracting 24 from both sides:

6x = 216

Dividing both sides by 6:

x = 36

So the smallest of the three consecutive even integers is 36, and the others are 38 and 40.

Answer:

y = ( x - 4 )² - 4

Step-by-step explanation:

a² ± 2ab + b² = ( a ± b )²

~~~~~~~~~~~~

y = x² - 8x + 12

y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4

y = ( x - 4 )² - 4