What are the possible solutions to this system?

The fundamental period of the function 2 cos(3x) is (A) 2.

In general, for a function of the form cos(kx), where k is a constant, the fundamental period is given by 2π/k. In this case, the constant k is 3, so the fundamental period is 2π/3. However, we can simplify this further to 2/3π, which is equivalent to approximately 2.094. Therefore, the fundamental period of 2 cos(3x) is approximately 2.

To understand why the fundamental period is 2, we need to consider the behavior of the cosine function. The cosine function has a period of 2π, meaning it repeats its values every 2π units. When we introduce a coefficient in front of the x, it affects the rate at which the cosine function oscillates. In this case, the coefficient 3 causes the function to complete three oscillations within a period of 2π, resulting in a fundamental period of 2.

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Answer:

-30

Step-by-step explanation:The answer is -30. Hope this helps.

Answer:

9.311, < 9.345, < 9.35, < 9.37, < 9.4, < 9.433 written as an inequality statement

Step-by-step explanation:

Look at the hundreths and thousanths place and compare/contrast them between two numbers. The tenths can sometimes trick you!

Answer:

\(\boxed{9.311} , ~ \boxed{9.345},~ \boxed{9.35},~ \boxed{9.37},~ \boxed{ 9.4}, ~\boxed{ 9.433}\)

Step-by-step explanation:

\(9.311 < 9.345 < 9.35 < 9.37 < 9.4 < 9.433\)

Answer:

72x430/43

Step-by-step explanation:

The key features include random assignment of participants into two groups (drug A and placebo), administration of the drug or placebo without participants knowing which one they received, and comparison of outcomes (number of pain episodes) between the groups at the end of the treatment period.

This is a randomized controlled trial (RCT). An RCT is a type of research study where participants are randomly assigned to receive either the treatment (drug) or a placebo, and then the outcomes of both groups are compared. In this case, the study was conducted by the National Institutes of Health to investigate whether drug A can reduce the pain associated with sickle-cell disease. 150 sickle-cell sufferers were randomly assigned to receive the drug and another 150 were given placebos. The researchers took great care to ensure that the participants did not know whether they were receiving the drug or the placebo. At the end of the treatment period, the number of episodes of pain reported by each subject was counted. This study is important in helping researchers and healthcare professionals understand the effectiveness of the drug in reducing the pain associated with sickle-cell disease.

This study is a double-blind randomized controlled trial (RCT).

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The equivalent equation for the given equation is 5n+10d=365. Therefore, option A is the correct answer.

The given equation is 0.05n + 0.1d = 3.65.

Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

Now, multiply by 100 on both sides of the given equation.

That is, 100(0.05n + 0.1d) = 3.65×100

⇒ 0.05n×100+0.1d×100=365

⇒5n+10d=365

The equivalent equation for the given equation is 5n+10d=365. Therefore, option A is the correct answer.

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Answer:

V(0)=$537,000

b=0.83

t=9

v (9)=100,386.92

Value after 9 years of depreciation at 17% per year

b = 1- r

b = 1 - 17% b = 0.83

Step-by-step explanation:

V (t)=V(0) (b)^t

V (t) future value ?

Vo present value $537,000

b=0.83

T time =9 years

V (9)=537,000×(0.83)^(9)

v (9)=100,386.92

Value after 9 years of depreciation at 17% per year

b = 1- r

b = 1 - 17% b = 0.83

Answer:

-32

Step-by-step explanation:

sol`n:

a/c to the question,

41+3z=-55

then,

3z=-55-41

3z=-96

z=-96/3

z=-32

Answer:

z equals -32

Step-by-step explanation:

We need to solve for z.  Start by isolating the 3z term:  subtract 41 from both sides of the given equation, obtaining 3z = -96.

Finally we divide both sides of this result by 3 to isolate z:

        -96

z = -----------  = -32

            3

z equals -32

Answer:

17×6=102 because he gave 2 boxes to his brother so he have 6 boxes

Answer:

22.50

Step-by-step explanation:

25 percent 30

= (25/100)30

= (25*30)/100

= 750/100 = 7.50

$30 - $7.50 = $22.50

Therefore, the total number of possible(probability) license plates is:

1296 × 676 + 1296 × 100 = 1,005,696.

A number can be viewed as a measurement, like John Cena's weight of 275 lbs, or as a count, like when we yell "3, 2, 1, GO!" during a race. Moreover, there are fractions like 22/7 and decimals like 3.14.

There are two cases to consider: when the characters are pairs of letters, and when they are pairs of numbers.

For the first two positions (xx and yy), there are 26 letters and 10 digits to choose from. Since repetition is allowed, there are 36 choices for each position. Therefore, there are 36 × 36 = 1296 possible combinations for xx-yy.

For the last position (zz), there are two probability: either two letters or two numbers. If zz is a pair of letters, there are 26 choices for each position, giving a total of 26 × 26 = 676 combinations. If zz is a pair of numbers, there are 10 choices for each position, giving a total of 10 × 10 = 100 combinations.

Therefore, the total number of possible license plates is:

1296 × 676 + 1296 × 100 = 1,005,696.

So there are 1,005,696 different license plates of this form possible in the Netherlands.

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Answer:

8 CDs for $14.50

Step-by-step explanation:

We have to divide both of the numbers by the number of CDs. Our formula is:

(price) ÷ (number of CDs) = price per CD

When we divide both of the prices by the number of CDs, we see that 6 CDs for 12.00 is worse because it is 2.00, whereas the inflation is lower when you compare to the other rate. You get $1.81.

Answer:

Step-by-step explanation:

1) ∠WVZ and ∠VWX are right angles & VX = = WZ      Given

2) WV = VW                                                                      Reflexive property

3) ΔWVZ ≅ ΔVWX                                                           HL

4) ∠Z = ∠X                                                                       CPCT

CPCT --> Corresponding parts of congruent triangle.

Answer:

6 miles

Step-by-step explanation:

20.00 - 2.00 = 18

18/3 = 6

she can travel 6 miles

Answer:

Step-by-step explanation:

the formula for an arithmetic sequence is

a, a+d,a+3d,a+3d etc, where d is the common difference

we have the terms -6, 13,23

first term is -6

-6+19=13

however, 13+10=23

this is not an arithmetic sequence

The equation of the trend line in the graph can be found to be y = 5 x + 15

The equation of the trend line takes the form :

y = Slope ( x ) + y intercept

From the diagram, we know the y - intercept is 15 as this is where the line intercepts the y - axis.

The slope can be found by picking a point and using the formula. We will pick ( 1, 20 ).

The slope is:

20 = Slope ( 1 ) + 15

Slope = 20 - 15

Slope = 5

The equation is:

y = 5 x + 15

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Answer:

first exercise:

24

10

0

-2

-8

-11

exercise two:

neither of them

Step-by-step explanation:

start with the greater number which is not negative numbers = 24, and so on, last is -11

neither of them is true

Answer:

$40.95

Step-by-step explanation:

Original price = $65.00

If the jacket is on sale for 40% off, then it is now 60% of the original price.

60% = 60/100 = 0.6

⇒ 60% of $65.00 = 0.6 × 65

                              = $39

If we have to pay 5% sales tax, then this means that the final price will be 105% of the sale price.

105% = 105/100 = 1.05

⇒ 105% of $39 = 1.05 × 39

                         = $40.95

Discount:-

\(\\ \rm\rightarrowtail 0.40(65)=26\$\)

Now

So

Sales tax is 5%

Total price=39+0.05(39)=40.95$

Answer:

3.5

Step-by-step explanation:

ΔABC ≅ ΔHJK

This means that sisde AB is congruent to side HJ

Side BC is congruent to JK

and side CA is congruent to KH

I AB is 3.5 then HJ=3.5

Answer:

3.5 cm

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The magnitude of -v is \(\sqrt{(89)}\)

In physics and mathematics, magnitude refers to the size or quantity of a physical or mathematical property. It can be represented by a scalar value or a vector with a scalar magnitude.

In the case of scalar magnitude, it represents a property's absolute value, which is always positive. For example, the magnitude of a force, velocity, or acceleration represents its absolute value without any direction.

In contrast, vector magnitude represents the length or size of a vector, including both its magnitude and direction. It can be calculated using the Pythagorean theorem, where the magnitude of a vector V with components (Vx, Vy, Vz) is:

\(|V| = sqrt(Vx^2 + Vy^2 + Vz^2)\)

The magnitude of a vector is always positive and can be used to determine the distance between two points in space.

Overall, magnitude is an essential concept in many fields, including physics, mathematics, engineering, and computer science, and it plays a crucial role in understanding various physical and mathematical phenomena.

The magnitude of a vector is its length, which is calculated using the Pythagorean theorem. For a vector v = (a, b), the magnitude is given by:

\(|v| = sqrt(a^2 + b^2)\)

The negative of a vector simply reverses its direction, but not its magnitude. Therefore, the magnitude of -v is the same as the magnitude of v.

Using this information, we can calculate the magnitude of -v as follows:

\(|-v| = |-( -5, 8)| = |(5, -8)|\\\|-v|\ = \sqrt{(5^2 + (-8)^2)} = \sqrt{(25 + 64) }= \sqrt{(89)}Therefore, the magnitude of -v is \sqrt{(89)}\)

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Answer:

-11  321/770

Step-by-step explanation:

-7+9/10+3/7-5+5/11-6/5

Answer:

Number of pennies = 11

Number of dimes = 11

Number of quarters = 8

Step-by-step explanation:

Given:

Total number of coins = 30

Number of pennies = Number of dimes

Total value = $3.21 = 321 penny

Computation:

Assume:

Number of pennies = x

So,

Number of dimes = x

Number of quarters = 30 -x- x = 30 - 2x

Value of pennies = x

Value of dimes = 10 x

Value value of quarters = 25[30 - 2x] = 750 - 50 x

Total value = x + 10x + 750 - 50x

39x = 429

x = 11

Number of pennies = 11

Number of dimes = 11

Number of quarters = 30 - 11 -11 = 8

Answer:

THE ONLY STATEMENT THAT IS FALSE IS THE NUMBER 5.

Step-by-step explanation:

Table of ordered data

number of       value

data

1                      62

2                      88

3                      89

4                      90

5                      92

6                      95

7                      96

8                      98

9                    100

10                  100

Range of scores: 100 - 62 = 38

Oulier: 62 => Range without the outlier = 100 - 88 = 12

Interquartile range, IQR, = difference between third quartile and first quartile: IQR = Q3 - Q1

Quartlies of all the data:

1                      62

2                      88

3                      89 ---------------   first quartile, Q1 = 89

4                      90

5                      92

------------------------------------------ median, Q2 = (95 + 92) / 2 = 93.5

6                      95

7                      96

8                      98 ---------------- third quartile, Q3 = 98

9                    100

10                  100

=> IQR = 98 - 89 = 9 : the interquartle range is 9

Quartlies without the outlier:

2                      88

3                      89

------------------------------------- first quartile, Q1 = (89 + 90) / 2 = 89.5

4                      90

5                      92

6                      95 --------------- median, Q2 = 95

7                      96

8                      98

------------------------------------ third quartile, Q3 = (98 + 100) / 2 = 99

9                    100

10                  100

=> IQR = Q3 - Q1 = 99 - 89.5 =  : the interquartle range without the outlier is 9.5

Therefore, the outlier impacts more the range than it impacts the IQR.

THE ONLY STATEMENT THAT IS FALSE IS THE NUMBER 5.

Since each serving contains 2/5 of a pound, then, the total weight of x servings would be:

If the total weight of x servings should be equal to the weight of the turkey, then:

Multiply both sides of the equation by 5/2:

Simplify the expressions on both sides of the equation:

Therefore, the number of adult servings from a 10 pound turkey, will be 25.

Answer:

I also need the answer

Step-by-step explanation:

Three options for the given area of a rectangular room is 750 square feet and the relation between width and length is equal to :

b. y² -5y =750

c. 750 – y(y – 5) = 0

e. (y + 25)(y – 30) = 0

As given in the question,

Given area of a rectangular room  =  750 square feet

Let y be the length of the rectangular room ,

Then width of the rectangular room = y -5

Area of rectangular room = length × width

⇒ 750 = y (y -5)

Option which are same as the required equation are :

a.  y(y + 5) = 750

Here y +5 is used .Not a valid option

b. y² -5y =750

⇒y(y-5) =750

Valid option.

c. 750 – y(y – 5) = 0

⇒y(y-5) =750

Valid option.

d. y(y – 5) + 750 = 0

⇒ y(y-5) =-750

Not valid option

e. (y + 25)(y – 30) = 0

⇒y² -30y +25y-750 =0

⇒y² -5y =750

⇒ y(y-5) =750

Valid option.

Therefore, three options for the given area of a rectangular room is 750 square feet and the relation between width and length is equal to :

b. y² -5y =750

c. 750 – y(y – 5) = 0

e. (y + 25)(y – 30) = 0

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Answer:

76% of the student body are not seniors

Step-by-step explanation:

450-108=342 (to find how many students are not seniors)

342/450=0.76 (to find the percentage of non seniors against the whole student body)

0.76x100= 76

Therefore, 76% of the student body are not seniors.

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Work Shown:

15n+30 = 75

15n+30-30 = 75-30 ... subtract 30 from both sides

15n = 45

15n/15 = 45/15 .... divide both sides by 15

n = 3