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jarptica [38.1K]

3 years ago

7

A school chorus has 90 sixth-grade students and 75/7 grade students the music director wants to make groups of performers with t

he same combination of sixth and seventh grade students in each group she wants to form as many groups as possible what is the largest number of groups that could be formed explain or show your reasoning

1 answer:

Nesterboy [21]3 years ago

3 0

Answer:

The music director can make 15 groups of performers with 6 sixth grade students and 5 seventh grade students in each group.

Step-by-step explanation:

A school chorus has 90 sixth-grade students and 75 seventh-grade students.

Factor these two numbers:

$90=2\cdot 45=2\cdot 3\cdot 15=2\cdot 3\cdot 3\cdot 5\\ \\75=3\cdot 25=3\cdot 5\cdot 5$

Find GCF(90,75):

$GCF(90,75)=3\cdot 5=15$

Now,

$90=15\cdot 6\\ \\75=15\cdot 5$

Therefore, the music director can make 15 groups of performers with 6 sixth grade students and 5 seventh grade students in each group.

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Trigonometry<br> Trigonometric Functions <br> Given: Cos θ = (3/5), Find: Csc θ

nasty-shy [4]

The value of $\csc \theta$ is $\frac{5}{4}$

Explanation:

Given that the function $cos \ \theta$ is $cos \ \theta= \frac{3}{5}$

We need to determine the value of $\csc \theta$

<u>The value of Opposite side of the triangle:</u>

The formula for $cos \ \theta$ is given by

$cos \ \theta= \frac{adj}{hyp}=\frac{3}{5}$

The value of opposite side can be determined using the formula,

$opp=\sqrt{hyp^2-adj^2$

$opp=\sqrt{5^2-3^2}$

$opp=\sqrt{25-9}$

$opp=\sqrt{16}=4$

Thus, the value of opposite side is 4

<u>The value of </u> $\csc \theta$ <u>:</u>

The formula for $\csc \theta$ is given by

$csc \ \theta=\frac{1}{sin \ \theta}$

First, we shall determine the value of $sin \ \theta$

The formula for $sin \ \theta$ is given by

$sin \ \theta= \frac{opp}{hyp}$

Substituting the values, we have,

$sin \ \theta= \frac{4}{5}$

Thus, the value of $sin \ \theta$ is $\frac{4}{5}$

Substituting the values in the formula for $\csc \theta$ , we have,

$csc \ \theta=\frac{1}{\frac{4}{5}}$

$csc\ \theta= \frac{5}{4}$

Hence, the value of $\csc \theta$ is $\frac{5}{4}$

5 0

3 years ago

Four bracelets and 6 necklaces cost $66. Six bracelets and three necklaces cost $45. How much does it cost for five bracelets an

Aleonysh [2.5K]

Answer:

$90

Step-by-step explanation:

Let B represent bracelets and N represent necklaces

4B + 6N = $66

6B + 3N = $45 mutyply second equation by -2

-2 × (6B + 3N) = $45 ➡ -12B - 6N = -$90 now add this to the first equation

4B + 6N -12B - 6N = $66 - $90 add the like terms (-6N will eliminate 6N)

-8B = -$24 ➡8B = $24 ➡ B = $3

one bracelet costs $3 ww can find the price of necklace by using this information

6B + 3N = $45 write $3 instead of B

6× $3 + 3N = $45

$24 + 3N = $45

3N = $45

N = $15 this is the price for a necklace

For five bracelets and five necklaces the cost would be 5 × $15 + 5 × $3 = $90

7 0

4 years ago

Please answer this correctly without making mistakes

Vadim26 [7]

Dale should use the $15 dollars off coupon to save the most money which costs 47.00.

25% off of 47.00 is 45.49.

$15 off of 47.00 is 32.00.

The $15 off coupon makes the DVD player cost less, so he should use that one.

4 0

3 years ago

Select the correct answer.<br><br> Which function has an inverse function?

aleksley [76]

<h2>Answer:</h2>

The function that has an inverse function is:

D. $f(x)=\dfrac{x+3}{7}$

<h2>Step-by-step explanation:</h2>

We know that <em>" A</em> <em>inverse of a function f(x) exist if it is both 1-1 and onto "</em>

A)

$f(x)=|x-4|+1$

We know that the modulus function is not 1-1.

Since, there are two different 'x' such that the function have the same value.

Take x=1

and take x= 7

In both the cases we have: f(x)=4

Hence, the function does not has a inverse.

B)

$f(x)=25x^2+70x+49$

We know that a polynomial with even degree is not 1-1.

As it is symmetric about a line x=a

Hence, option: B is incorrect.

C)

$f(x)=x^4$

Again it is a polynomial of even degree.

Hence, it does not has a inverse.

D)

$f(x)=\dfrac{x+3}{7}$

As the function is both 1-1 and onto.

Hence, the function has a inverse and the inverse function is calculated as:

$f(x)=y\\\\i.e.\\\\\dfrac{x+3}{7}=y\\\\i.e.\\\\x+3=7y\\\\i.e.\\\\x=7y-3$

Hence, the inverse function is:

$f(y)=7y-3$

The answer is:

Option: D

3 0

3 years ago

For what value of k, if any, will y = ksin (5x) + 2cos (4x) be a solution to the differential equation y'' +16y =-27sin(5x)?

emmainna [20.7K]

Answer:

c. 3

Step-by-step explanation:

y = k sin(5x) + 2 cos(4x)

y' = 5k cos(5x) − 8 sin(4x)

y" = -25k sin(5x) − 32 cos(4x)

y'' + 16y = -27 sin(5x)

(-25k sin(5x) − 32 cos(4x)) + 16(k sin(5x) + 2 cos(4x)) = -27 sin(5x)

-25k sin(5x) − 32 cos(4x) + 16k sin(5x) + 32 cos(4x) = -27 sin(5x)

-9k sin(5x) = -27 sin(5x)

k = 3

4 0

4 years ago