Kelli intends to cut a piece of ribbon 10 yards long into several pieces, each yard long. How many full pieces can she cut?

CaHeK987 [17]

Since q(x) is inside p(x), find the x-value that results in q(x) = 1/4

$\frac{1}{4} = 5 - x^2\ \Rightarrow\ x^2 = 5 - \frac{1}{4}\ \Rightarrow\ x^2 = \frac{19}{4}\ \Rightarrow \\
x = \frac{\sqrt{19} }{2}$

so we conclude that
$q(\frac{\sqrt{19} }{2} ) = 1/4$

therefore

$p(1/4) = p\left( q\left(\frac{ \sqrt{19} }{2} \right) \right)$

plug $x=\sqrt{19}/2$ into p( q(x) ) to get answer

$p(1/4) = p\left( q\left( \frac{ \sqrt{19} }{2} \right) \right)\ \Rightarrow\ \dfrac{4 - \left( \frac{\sqrt{19} }{2}\right)^2 }{ \left( \frac{\sqrt{19} }{2}\right)^3 } \Rightarrow \\ \\ \dfrac{4 - \frac{19}{4} }{ \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{8\left(4 - \frac{19}{4}\right) }{ 8 \cdot \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{32 - 38}{19\sqrt{19}} \Rightarrow \dfrac{-6}{19\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}\Rightarrow$

$\dfrac{-6\sqrt{19} }{19 \cdot 19} \\ \\ \Rightarrow -\dfrac{6\sqrt{19} }{361}$

$p(1/4) = -\dfrac{6\sqrt{19} }{361}$

3 0

3 years ago

Round to the nearest integer √10

Bingel [31]

Step-by-step explanation:

if the digit in the tenth place is less then 5, then round down, which means the units digit remains the same. If the digit in the tenth place is 5 or greater then round up which means you should increase the unit digit by one.

5 0

3 years ago

Y varies directly as x squared. y is 18 when x is 3. Find y if x is 4. Any help? thanks

stealth61 [152]

Answer:

Step-by-step explanation:

y ∝ x^2

Introducing the proportionality constant, we have

y = kx^2

Given : y= 18 when x = 3

substitute the given values in order to get the constant

i.e 18 = k x 3^2

18 = 9k

k = 2

therefore the formula connecting x and y

⇒ y = 2x^2

To find y if x is 4, just substitute x = 4 into the formula connecting x and y

i.e y = 2 x 4^2

= 2 x 16

= 32

4 0

3 years ago

An airplane flew with the wind for 2.5 hours and returned the same distance against the wind in 3.5 hours. If the cruising speed

KengaRu [80]

Answer:

60 miles per hour.

Step-by-step explanation:

Let r represent speed of wind blowing in miles per hour.

We have been given that the cruising speed of the plane was a constant 360 mph in air. The speed of the plane is the direction of wind would be $360+r$ .

The speed of the plane is the opposite direction of wind would be $360-r$ .

$\text{Distance}=\text{Speed}\times \text{Time}$

Distance covered in the direction of wind would be $2.5(360+r)$ .

Distance covered in the opposite direction of wind would be $3.5(360-r)$ .

Since both distances are same, so we will get:

$2.5(360+r)=3.5(360-r)$

$900+2.5r=1260-3.5r$

$900-900+2.5r+3.5r=1260-900-3.5r+3.5r$

$6r=360$

$\frac{6r}{6}=\frac{360}{6}$

$r=60$

Therefore, the wind is blowing at a rate of 60 miles per hour.

6 0

3 years ago

SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below

kvasek [131]

Answer:

The value of test statistics is 25.

Step-by-step explanation:

We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;

380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560

Let $\sigma$ = population standard of the reading and writing section SAT score of the students in this school

So, Null Hypothesis, $H_0$ : $\sigma \leq$ 100 {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}

Alternate Hypothesis, $H_A$ : $\sigma$ > 100 {means that the reading and writing section SAT score of the students in this school is higher than 100}