If cos x = 2 / 3 and x is in quadrant 4, find:

a. sin(x / 2)

b. cos(x / 2)

c. tan(x / 2)

Answer:

no solution

Step-by-step explanation:

Given

- 3 | 6n - 2 | + 5 = 8 ( subtract 5 from both sides )

- 3 | 6n - 2 | = 3 ( divide both sides by - 3 )

| 6n - 2 | = - 1

The absolute value always returns a positive value and so

| 6n - 2 | ≠ - 1

Hence there is no solution to the equation

Answer:

x = ±√2

Step-by-step explanation:

         x - 1 =     1/(x + 1)

(x -1)(x + 1) =     1     Multiplied each side by x + 1

       x² - 1 =     1     Difference of two squares

           x² =     2     Add 1 to each side

           x  = ±√2

x-1 is the reciprocal of x+1 when x = -√2 or x = √2.

Check:

(a) x = -√2

  -√2 - 1 = 1/(-√2 + 1)

-(√2 + 1) = (√2 +1)/[(-√2 +1)(√2 + 1)]

-(√2 + 1) = (√2 +1)/(-2 +1)

-(√2 + 1) = (√2 +1)/(-1)

-(√2 + 1) = -(√2 +1)

(b) x = √2

√2 - 1 = 1/(√2 + 1

√2 - 1 = (√2 - 1)/[(√2 + 1)(√2 - 1) ]

√2 - 1 = (√2 - 1)/(2 - 1)

√2 - 1 = (√2 - 1)/1

√2 - 1 = √2 - 1

OK.

Answer:x = ±√2

Step-by-step explanation: this is because reciprocal means the numerator and denominator switches

So the equation is x-1=1/(x+1)

And you solve for it thats how u get the answer

Answer:

[tex]\large\boxed{x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{3}x-2=7\qquad\text{add 2 to both sides}\\\\\dfrac{2}{3}x-2+2=7+2\\\\\dfrac{2}{3}x=9\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x=3\cdot9\\\\2x=27\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{27}{2}\\\\x=\dfrac{27}{2}\to x=13\dfrac{1}{2}\to x=13.5[/tex]

Answer:

There are 16 terms in the sequence.

Step-by-step explanation:

The given sequence is

14348907, ..., 9, 3, 1

The first term of the sequence is

[tex]a_1=14348907[/tex]

The last term of the sequence is [tex]l=1[/tex]

The common ratio is [tex]r=\frac{1}{3}[/tex]

The nth term of this sequence is;

[tex]a_n=a_1(r)^{n-1}[/tex]

We plug in the common ratio and the first term to get;

[tex]a_n=14348907(\frac{1}{3})^{n-1}[/tex]

The find the number of terms in the sequence , we plug in the last term of the sequence.

This implies that;

[tex]1=14348907(\frac{1}{3})^{n-1}[/tex]

[tex]\frac{1}{14348907}=(\frac{1}{3})^{n-1}[/tex]

[tex]\Rightarrow 3^{-15}=3^{-(n-1)}[/tex]

Since the bases are the same, we equate the exponents;

[tex]-15=-(n-1)[/tex]

[tex]15=n-1[/tex]

[tex]15+1=n[/tex]

[tex]n=16[/tex]

Answer:

There are 21 luxury vehicles in 3 shipments sent to a dealership . Which of the following expresses the ratio of shipments to luxury vehicles?

A. 21/3

B. 21 to 3

C. 21:3

D. 3:21

Step-by-step explanation:

Answer:

The answer is D. 3:21 Hope this helps!

Answer:

15  cookies

Step-by-step explanation:

We have 20 cookies and we know that three quarters of them were burned. To find the number of cookies burned, divide the 20 cookies into 4 equal parts.

This will give you 4 parts of 5 cookies.

[5] + [5] + [5] + [5]

Then they tell us that 3 quarters were burned. This means that of these 4 parts [5] + [5] + [5] + [5], 3 were burned. Then take 3 of these parts and add them.

[5] + [5] + [5] = 15 cookies.

This is the same as multiplying:

[tex]20 * \frac{3}{4} = 15[/tex]

Answer:

The slope is undefined

Step-by-step explanation:

x = -4 is a vertical line.  Slope is defines as the change in y divided by the change in x.  

(change in y)/(change in x)

All the points on this line have the same x value, so the change in x is zero.  This means we have

(change in y)/0, which is undefined.

Answer:

UNDEFINED

Step-by-step explanation:

Any initial value set to equal x is considered an undefined rate of change [slope], which is a vertical line.

I am joyous to assist you anytime.

Answer:

D.

Step-by-step explanation:

50-20=30 (because of the initial cost)

Then multiply 30*0.5=60

so she can buy less than or equal to 60

Answer:

D. S ≤ 60

Step-by-step explanation:

Ella has $50.00 and the registration fee is $20. This means that she would have $30.00 to buy songs and each song costs $0.50, so:

$30.00/$0.50= 60

The number of songs that she would be able to buy is 60.

According to this, the inequality that gives the maximum number of songs that she can buy is S ≤ 60 as it indicates that the maximum number of songs (s) that she can buy is less than or equal to 60.

Answer:

56 in.

Step-by-step explanation:

By proportion  8/5 = L/35  where L is the length of the picture.

5L = 8*35

L = 8*35/5

L = 56 in.

The length of a similar picture frame is Option (a) 56 in.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A ratio indicates how many times one number contains another. It is expressed as a:b where a and b are parameters for any given set of relation.

Given length to width ratio is 8:5.

We have to find the length of similar picture frame which has a width of 35 inches.

Let length of the picture frame be L inches.

Using ratio equation for solving, we have

   8:5 = L:35

⇒ 8/5 = L/35

∴  L = (8/5) * 35 = 56 inches.

Therefore the length of a similar picture frame is Option (a) 56 in.

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To assess the evidence of Hypothesis testing, the students need to determine the likelihood of the proportion of Millennial students at their campus that live at home with their parents being 36% or higher.

The question here is regarding the testing of a population proportion using statistical hypothesis testing, specifically a one-sample z-test. The null hypothesis (H0) is that the population proportion is equal to a specified value, in this case, 36%). The alternative hypothesis (Ha) is that the population proportion is greater than the specified value (more than 36%).

The question we need to answer is 'If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?'

The scenario suggests an indication towards a right-tailed z-test as we're looking to see if the data indicates a proportion >36%. However, as with all statistical tests, one should be cautious about drawing definitive conclusions without additional context and understanding the potential for sampling variability and error.

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➷ The data set is not approximately periodic

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

Step-by-step explanation:

The given data doesn't show any periodic pattern, the change is not constant, and it doesn't simulate any simple pattern because the increase is like random, the first increase is for 1.35, the second is for 0.13, the third one is for 0.65, it doesn't show any periodic behaviour.

In addition, the variables involved aren't periodic, because it's about stocks, which it changes randomly.

Therefore, the right answer is the first option.

Answer: form by math and can multiply two numbers or divide your choice

Step-by-step explanation:

Answer:

The correct option is D) All real numbers.

Step-by-step explanation:

Consider the provided function.

Range: Range is the set of output value produce by the function, or the range is the set of all possible y values.

Now consider the provided graph of the function.

The graph of the function is a straight line and function produces the positive and negative value of y.

By interpreting the graph it can be concluded the the range of the function is all real numbers.

Thus, the correct option is D) All real numbers.

he has 84 hockey cards total

Answer:

264 cubic meters

Step-by-step explanation:

The sea turtle habitat at the zoo has a total volume of 264 cubic meters.

To find the total volume of the sea turtle habitat, which consists of two connected aquariums, you can calculate the volume of each aquarium separately and then add them together.

For the first aquarium:

- Length = 6 meters

- Width = 4 meters

- Height = 2 meters

The volume of the first aquarium is calculated as:

Volume_1 = Length * Width * Height

Volume_1 = 6 m * 4 m * 2 m

Volume_1 = 48 cubic meters

For the second aquarium:

- Length = 8 meters

- Width = 9 meters

- Height = 3 meters

The volume of the second aquarium is calculated as:

Volume_2 = Length * Width * Height

Volume_2 = 8 m * 9 m * 3 m

Volume_2 = 216 cubic meters

Now, to find the total volume of the sea turtle habitat, you add the volumes of the two aquariums together:

Total Volume = Volume_1 + Volume_2

Total Volume = 48 cubic meters + 216 cubic meters

Total Volume = 264 cubic meters

So, the total volume of the sea turtle habitat at the zoo is indeed 264 cubic meters, as provided.

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I am thinking the answer is 225. Sorry if I'm wrong!

Answer:

280 degrees.

Step-by-step explanation:

To convert radians to degrees we multiply by 180/pi:

angle O = 14pi/ 9 * 180 / pi

=  14*180 / 9

=  280 degrees.

The angle 0=14pi/9 radians can be converted to degrees by using the conversion factor 1 radian = 57.3°. Multiplying the given angle in radians by the conversion factor results in an equivalent angle of 280° in degrees.

To convert the angle from radians to degrees, we use the conversion factor 1 rad = 57.3°. The problem provides the angle 0 = 14pi/9 radians. By using the conversion factor, the process of conversion would be as follows:

Therefore, the angle 0=14pi/9 radians is equal to 280° in degrees.

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Answer:

P(n) = 0.5

Step-by-step explanation:

For two events which are independent, we use the multiplication rule which states P (A and B) = P(A) * P(B). Substitute P(m) = 0.4 and P(m and n) = 0.2 into this formula.

P (m and n) = P(m) * P(n)

0.2 = 0.4*P(n)

Divide by 0.4 on both sides.

0.2 / 0.4 = P(n)

0.5 = P(n)

It’s a if the quotation is bigger than the dividend the answer is just a mixed number

Divide 7.8 by 1.18:

7.8 / 1.18 = 6.61 = 6.6 rounded to the nearest tenth.

When you divide scientific notation, subtract the exponents: 20 - 13  =7

The answer becomes 6.6 x 10^7

Division is one of the four fundamental arithmetic operations. The number of times the milk way is wider than the solar system is 6.61 × 10⁷.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that our solar system is 1.18 × 1013 meters in diameter, and the Milky Way galaxy is 7.8 × 1020 meters in diameter. Therefore, the number of times the milk way is wider than the solar system is,

Number of times = (Diameter of MIlky way)/(Diameter of Solar System)

                            = 7.8 × 10²⁰ meters/ 1.18 × 10¹³ meters

                            = 6.61 × 10⁷

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5y+2x=10y=−25x+2246810−2−4−6−8−10246810−2−4−6−8−10Let's solve for x.5y+2x=10Step 1: Add -5y to both sides.2x+5y+−5y=10+−5y2x=−5y+10Step 2: Divide both sides by 2.2x2=−5y+102x=−52y+5Answer:x=−52y+5

Do make the intercepts twice as big, you simple divide the function by 2, but leave it =10.

The function 5y+2x=10 has intercepts (0,2) and (5,0)

Therefore by dividing by 2 we get 2.5y+x=10 which is your answer. It has intercepts (0,4) and (10,0)

Answer:

  72

Step-by-step explanation:

1 out of 10 do not recommend naps, so 9 times as many do recommend naps.

  9 × (8 doctors) = 72 doctors . . . . . recommend naps

Answer: 6 teaspoons of sugar

Step-by-step explanation: Create a proportion

4 ounces of frosting = 2 teaspoons of sugar

8 ounces of frosting = 4 teaspoons of sugar

12 ounces of frosting = 6 teaspoons of sugar

To make 12 ounces of frosting, you would need 6 teaspoons of sugar.

To find out how much sugar is needed to make 12 ounces of frosting, we can set up a proportion using the given information. The recipe calls for 2 teaspoons of sugar for 4 ounces of frosting. We can set up the proportion: 2 teaspoons / 4 ounces = x teaspoons / 12 ounces.

To solve the proportion, we can cross multiply and divide. So, (2 teaspoons)(12 ounces) = (4 ounces)(x teaspoons). This simplifies to 24 = 4x. Dividing both sides by 4, we find that x = 6 teaspoons.

Therefore, you would need 6 teaspoons of sugar to make 12 ounces of frosting.

Answer:

For a unique solution, there must be as many consistent, independent equations as there are variables.

Step-by-step explanation:

Each equation lets you write an expression for one variable in terms of the others in that equation. That expression can be substituted throughout the system, reducing the number of equations and variables by one each.

After n-1 such substitutions in a system of n equations, there will be one equation left. If that is an equation in one variable, then the solution to the system can be easily found. If more than one variable remains (> n variables in n equations), then the system cannot be solved for definitive values of each of the variables.

___

If the equations are inconsistent, there is no solution. If the equations are dependent, then there is no unique solution.

To solve a system of linear equations, one generally requires the same number of equations as there are variables for a unique solution, otherwise the system may have either an infinite number of solutions or none.

To solve a system of linear equations, you generally need as many equations as there are variables. If you have two variables, you should have two linear equations to find a unique solution. For example, the equations 3x - 2y = 24 and 3x + 9y = 30 form a system that can be solved because there are two equations with two variables (x and y).

If there are more variables than equations, then you may either have infinitely many solutions or no solution, depending on the equations' consistency. If you have fewer equations than variables, as in the case of three variables with only two equations, you typically have an undetermined system where you can choose one variable as a parameter and express the others in terms of it, leading to an infinite number of solutions.

For homogeneous equations where the vector b is zero (Ax = 0), the solutions form a subspace of the vector space, and nontrivial solutions exist if the system is not of full rank.

Slope = (y2-y1)/(x2-x1)

Slope = (3-2)/(4-0)

Slope = 1/4

Answer:

[tex]\large\boxed{the\ slope=\dfrac{1}{4}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (0, 2) and (4, 3). Substitute:

[tex]m=\dfrac{3-2}{4-0}=\dfrac{1}{4}[/tex]

Answer:

230.4

feet

Explanation:

arc length  

=

circumference  

×

fraction of circle

×

×

×

×

=

2

π

r

×

165

360

×

×

×

×

=

2

×

π

×

80

×

165

360

×

×

×

×

=

230.4

feet to nearest tenth

Step-by-step explanation:

The length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

Since the distance between the two cars is the length of an arc, we need to know what the length of an arc is.

The length of an arc is given by L = Ф/360 × 2πr where

Given that for the ferris wheel

Substituting the values of the variables into the equation, we have

L = Ф/360 × 2πr

L = 140°/360 × 2π × 30 ft

L = 14/36 × 60π ft

L = 14/3 × 5π ft

L = 70π/3 ft

L = 219.91 ft/3

L = 73.3 ft

So, length of the intercepted arc between those two cars on the Ferris wheel is 73.3 ft

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Answer:

  y = 116

Step-by-step explanation:

The central angle is double any inscribed angle that intercepts the same arc.

Inscribed angle HGF intercepts arc HF, so central angle HOF will be double the value of HGF.

  2×58° = 116° = y°

  y = 116

Answer:

Step-by-step explanation:

First att all, let's take angle B... It's bigger than 180° and smaller than 360. Then: 180 < 6x < 360. So 6x = 288°. The only alternative what's correct is the first one.

I hope I helped you

find the radius:

r = C/2pi

r= about 7 (6.99645)

find the area:

A = pi(r)^2

A = about 153.78194 inches^2

Answer: The area of the circle in inches is A= 153.64 inches²

Step-by-step explanation:

This problem bothers on the calculations on shapes

In this Case a circle

The circumference of a circle is given by

C=2πr

Given that C =43.96 inches

We need to solve for the radius, because we also need the radius to solve for the area

43.96= 2*3.142*r

43.96=6.284r

r= 43.96/6.284

r=6.99 inches

Now back to the area of a circle which is given by

A=πr²

Substituting our value for Pi we have

A= 3.142*6.99²

A=3.142*48.89

A= 153.64 inches²

Answer:

Step-by-step explanation:

Yesterday, her rate was 8mph, her time was x hours.

Today, her rate was 13mph, her time was 13 - x hours.

So the total distance she biked on the two days is

d = 8x + 13(13 - x), or 169 - 5x

Answer:

[tex]8x+13(9-x)[/tex] or [tex]-5x+117[/tex] miles.

Step-by-step explanation:

Let x represent number of hours Carmen biked yesterday.

[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]

We have been given that yesterday Carmen's average speed was 8

miles per hour. So distance covered in x hours would be [tex]8x[/tex].

We are also told that Carmen biked for a combined total time of 9

hours. So the number of hours biked second day would be [tex]9-x[/tex]. The distance covered in [tex]9-x[/tex] at a speed of 13  miles per hour would be [tex]13(9-x)[/tex].

Total distance covered by Carmen would be: [tex]8x+13(9-x)[/tex]

[tex]8x+117-13x[/tex]

[tex]8x-13x+117[/tex]

[tex]-5x+117[/tex]

Therefore, the total distance covered by Carmen in the two days would be [tex]-5x+117[/tex] miles.