Use double-angle identities to write each expression, using trigonometric functions of θ instead of 4θ .
tan 4θ

Using greatest common factor (GCF), Mr. Raymond should put 6 students in each group. If that happens, he will have 3 groups of 6th graders and 4 groups of 7th graders.

The greatest common factor (GCF) of a set of numbers is defined as the largest common positive integer that divides each number into equal parts with zero remainder.

If Mr. Raymond has 18 6th graders students and 24 7th grader students he wants to put in equal groups wherein each group will have students of only one grade level, find the GCF of 18 and 24 to find how many students he will put in each group.

18 : 1, 2, 3, 6, 9, 18

24 : 1, 2, 3, 4, 6, 8, 12, 24

GCF = 6

Hence, he should put 6 students in each group.

Dividing each level of students to groups of 6.

6th graders = 18/6

6th graders = 3 groups

7th graders = 24/6

7th graders = 4 groups

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Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|. Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.

Two expressions with equal sign is called as equation.

Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|.

Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.

Therefore Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.

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Answer:

X = 8

Step-by-step explanation:

Based on the given task content, the approximate radius of the tan circle given the area of the blue circle is 9.27 yards.

1,335 = 5x - 15

1,335 + 15 = 5x

1,350 = 5x

x = 1350/5

x = 270 square yards

Area of the tan circle = πr²

270 = 3.14 × r²

270 = 3.14r²

r² = 270 / 3.14

r² = 85.98726114649681

r = √85.98726114649681

Approximately,

r = 9.27 yards

Therefore, the approximate radius of the tan circle given the area of the blue circle is 9.27 yards.

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The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

y ≤ 3/4x − 4

The inequality symbol in the above inequality expression is

≤

This implies that the inequality expression is a less than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the bottom part is shaded

Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

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Answer: 51357

901×57=51357

Answer: free fall

Step-by-step explanation: A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name.

Answer:

12−3x

Step-by-step explanation:

12+3.4x−5.4x−x

Combine 3.4x and −5.4x to get −2x.

12−2x−x

Combine −2x and −x to get −3x.

12−3x

After simplification of given expression. We get, the value of x is 4.

To simplify this 12 + 3.4x - 5.4x - x,

12 + 3.4x - 5.4x - x = 0

3.4x - 5.4x = - 2x

12  - 2x - x

-2x - x = -3x

-3x + 12 = 0

-3x = -12,

x = 4

Therefore, the value of x is 4.

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The function g(x)= x^ square root of 1+x is neither an even function nor an odd function

The function is given as

g(x)= x^ square root of 1+x

Rewrite the above function equation properly

So, we have

g(x) = x^(√x+1)

Calculate g(-x)

So, we have

g(-x) = -x^(√-x+1)

Evaluate

g(-x) = -x^(√-x+1)

Calculate -g(x)

So, we have

-g(x) = -x^(√x+1)

In the above computations;

g(x) does not equal g(-x) and -g(x)

Hence, the function g(x)= x^ square root of 1+x is neither an even function nor an odd function

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Answer:

33

Step-by-step explanation:

Convert the percentage to a decimal.

55 ÷ 100 = 0.55

Multiply 60 by 0.55

60 × 0.55 = 33

Answer:

33

Step-by-step explanation:

55 x 60 divided by 100

= 33

The value of logarithmic expression (2logbx/3 + 3logby / 4) - 5logbz is logbx/3^2(by / 4)^3/logbz^5.

By considering the given logarithmic expression

(2logbx/3 + 3logby / 4) - 5logbz

logb(x/3)^2 +log(by / 4)^3-log(bz)^5

logb(x/3)^2(by / 4)^3-logbz^5

logbx/3^2(by / 4)^3/logbz^5

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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The interest the friend will have after her college graduation in 4 years is $240 and an exponential model is not reasonable for this situation.

The formula to be used to is given as :

            I = Prt (1)

where, I = simple interest

          P = principal amount or amount initially deposited.

          r = annual interest rate

         t = time

According to the question we have been given that

         P = $1000

         r = 0.06

       t = 4 years

Putting the required values in equation (1) we get

        I = 1000*0.06*4

        I = 240

Thus $240 interest the friend will have after her college graduation in 4 years.

a) the exponential model is not reasonable for this situation as simple interest is not an exponential function.

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Answer:

2/2, 6/2

Step-by-step explanation:

2/2 can be simplified as 1 and 6/2 can be simplified as 3

y = 25x / 5 is each function is an example of exponential growth or decay.

What does exponential growth look like in math?

y= 25/7(7/5) x

y = 25/5 x

y = 25x / 5

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Answer:

So There will be 2 congruent angle

The simplified form of number is 2

To find the simplified form of the number, we will find the number whose square is equal to 4. As per the known fact, only 2 is the number whose square is 4.

Firstly rewriting the number -

Number = [tex]4^{1/2}[/tex]

Now, rewriting the number with base as 2 and exponent also as 2, as stated in theory above -

Number = [tex]2^{2(1/2)}[/tex]

Cancelling 2 from the exponent as it is present in both numerator and denominator. Rewriting the number with 2 as base and 1 as exponent to find the simplified form of the number.

Number = 2

Hence, the simplified number is 2

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We must invest $6294.256 if we want exactly $ 8000 after four years.

The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously, after t years is-

[tex]A = Pe^{rt}[/tex]

Here, we are given that rate of interest = 6% and we need exactly $8000 after four years.

Thus r = 6/100 = 0.06 and t = 4

Putting the values in the compound interest formula we get,

8000 = P[tex]e^{(0.06*4)}[/tex]

8000 = P[tex]e^{(0.24)}[/tex]

P[tex]e^{(0.24)}[/tex] = 8000

[tex]e^{(0.24)}[/tex] = 1.271

⇒  1.271P = 8000P

= 8000/ 1.271P

= 6294.256

Thus, we must invest $6294.256 if we want exactly $ 8000 after four years.

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Answer:1.  

Step-by-step explanation: 1.  because ,  and Step-by-step explanation:We have been given two triangles  and . We are asked to find the relationship between these triangles.By angle sum property let us find measure of angle C of triangle ADC.Let us find measure of angle T of triangle RTS.We can see that ,  and . Therefore,  and 1st option is the correct choice.

We have expression ln 9+ln 2 as a single natural logarithm ln 18

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

We have been asked to express ln 9+ln 2 as a single natural logarithm.

⇒ ln 9 + ln 2

⇒ ln (9) = ln (2)

Use the quotient property of logarithms

⇒ ln (9 × 2)

⇒ ln 18

Finally, we have expressed ln 9+ln 2 as a single natural logarithm ln 18

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Answer:

Step-by-step explanation:

0.75

The domain of the function is [-2, 2] and the range of the function is [-1, 2].

If there is a function y = x + a, then the domain is the set of all values that x can take and the range is the set of all the values that y can take for the function to exist.

Here, we are given a function as shown in the graph.

As we can see the function is defined only for the given points, that is, it has 2 endpoints.

Just by looking at the graph we can see that x can take values from -2 to 2. Thus, the domain of the function is [-2, 2].

We use closed brackets as x can be -2 and 2 as well. Similarly, we can see that y can take values from -1 to 2.

Thus, the range of the function is [-1, 2].

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The ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.

According to the question we have been given that,

 Total number of championship = 41

  Total number of championship won by Australia = 6

Thus we need to find the ratio that compares the championship won by Australia to the total number of championship.

For this the ratio will be :   [tex]\frac{number of championship won by Australia}{Total number of championship }[/tex]

                                       = 6/41

Hence the ratio that compares the championship won by Australia to the total number of championship is 6/41 which means that of the total 41 championship Australia has won 6 of the championship.

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Answer:D

Step-by-step explanation:Hope that helped

Hence , the missing value y  in x^2 y^8 times x²y⁸ x³ y = x⁵ y⁵ is -3 .

Definition of law of exponents

- one in every of a collection of rules in algebra: exponents of numbers are additional once the numbers are increased, subtracted once the numbers are divided, and increased once raised by still another exponent: a^m × aⁿ = a^(m+n)

We have given an expression x²y⁸ x³ y = x⁵ y⁵ .

LHS  = x²y⁸ x³ yⁿ

Let the power of y in LHS be "n" .

On using exponents rule , we get

LHS  = x⁵y⁹⁺ⁿ

RHS =  x⁵ y⁵

As LHS = RHS

x⁵y⁹⁺ⁿ =  x⁵ y⁵

On comparing power of y  , we get

 9 + n = 5

      n = -3

Hence , the power of y in LHS is -3 .

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Tax levied is $4.17 if the price of album is $27.80.

Kathy will get $3.03 after buying the album and paying the tax.

A tax is a mandatory financial charge or other sort of levy that is placed on a taxpayer by a governmental entity in order to pay for public services and other expenses.

The total amount is calculated by adding the tax on the cost of product or service.

The pre-tax price of an item must first be multiplied by the sales tax percentage once it has been translated to a decimal form in order to determine the amount of sales tax that will apply to the purchase. To determine the item's Total Amount, the sales tax must be computed and then added to the pre-tax price.

a) Given data: Tax%=0.15 of cost of album

Selling Price=$27.80.

Tax=Tax%×Selling Price

=0.15×27.80

=$4.17

b) Given data: Amount given by Kathy = $35

Tax=$4.17

Total Amount = Selling Price + Tax

=$4.17+$29.80

=$31.97

Amount left can be calculated by subtracting the amount given by Kathy from the Total Amount.

Amount=$35-$31.97

=$31.97

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The simplified form is -0.3.

As an instance, 3√(8) method to locate the diced root of 8. If there may be no superscript range, the novel expression is asking for the rectangular root. The term underneath the unconventional image is referred to as the radicand.

An intensive expression is an expression containing a rectangular root. Radicand - a variety of expressions in the radical symbol. Radical equation - An equation containing radical expressions with variables inside the radicands.

A few examples of radicals are √7, √2y+1, etc. an intensive also can be associated with the subsequent terms: An equation this is inside a radical is referred to as a thorough equation. An expression that lies interior a rectangular root is referred to as an intensive expression.

Applying radical rule,

[tex]\sqrt[n]{-a} =-\sqrt[n]{a} \\\sqrt[3]{-0.027}=-\sqrt[3]{0.027}\\ = -0.3[/tex].

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Answer: 6

Step-by-step explanation:

Answer: D

Step-by-step explanation: