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Novosadov [1.4K]

3 years ago

6

Jennifer bought 3 shirts for $48.00. At the same rate, how much would Jennifer pay for 10 shirts?HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

2 answers:

vodka [1.7K]3 years ago

5 0

Answer:

$160

Step-by-step explanation:

48/3=16

16*10=160

n200080 [17]3 years ago

3 0

Answer:

$160

Step-by-step explanation:

We can solve this by setting up equivalent proportions and cross-multiplying:

3/48=10/x

Cross-multiply:

480=3x

Divide by 3:

x=160

HTH :)

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Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

I have many students are represented in the data set?

nalin [4]

Answer:

a) 19 students

b) the mean 3 9/19

the median 3

the mode 3

c) the range 6

Step-by-step explanation:

The data set shows that

0 points gets 1 student,

1 point gets 1 student,

2 points get 2 students,

3 points get 6 students,

4 points get 4 students,

5 points get 3 students and

6 points get 2 students.

a) There are 1+1+2+6+4+3+2=19 students.

b) The mean is

$\dfrac{1\cdot 0+1\cdot 1+2\cdot 2+6\cdot 3+4\cdot 4+3\cdot 5+2\cdot 6}{19}=\dfrac{66}{19}=3\dfrac{9}{19}.$

The average score is 3 9/19 points.

The median is 10th term in the data set - 3 points (means the middle score in the data set)

The mode is 3 points (means most happened score)

c) The range of the data is 6-0=6 points.

7 0

3 years ago

3/6x4/9 plz help meeeeee

Aleonysh [2.5K]

Answer:

12/54

Step-by-step explanation:

4x3=12

6x9=54

3 0

3 years ago

Read 2 more answers

The midpoint of line XZ is (2,-5). One endpoint is X(12,-5). Find the coordinates of the other endpoint Z

Inga [223]

Answer: (-8,-5)

Step-by-step explanation:

6 0

3 years ago

11 1/2 and 13 3/4 is?

Tpy6a [65]

This would depend on what you are asking for.

If you are adding the two numbers(which the word and is implying) you’re answer is 25 1/4.

You get this by finding a common denominator. In this case, that can be 4.

Turn 1/2 in to 2/4.

Next, you add 11 and 13 to get 24.

Then, you’ll add 2/4 and 3/4. You will get 1 1/4

Add 24 and 1 1/4. You have your answer of 25 1/4

5 0

3 years ago