What is the definition of a unit rate?

1 answer:

4 0

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. If you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.

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-6x+y=-2 x-3y=9 what is the solution set?

Anarel [89]

Mult. the 2nd eqn by 6 and then add this "new" equation to the 1st given eqn:

-6x + y = -2
6x -18y = 54
--------------------
-17y = 52, or y = -52/17. Subst. this value of y into either equation to find the value of x.

3 0

3 years ago

Pls help trig question!!

s2008m [1.1K]

$4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\$

$\sin x = \dfrac{3 - \sqrt{57}}8\\\\\implies x = n\pi + (-1)^n \sin^{-1} \left(\dfrac{3-\sqrt{57}}8\right)\\\\\\\text{ When n = 1,2 and}~ [0,2\pi]},\\\\\\x= \pi - \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)~ \text{and} ~x = 2\pi + \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)\\\\\text{In decimal,}\\\\x= 3.75~~~~ \text{and}~~~ x =5.68$

5 0

2 years ago

A filling machine puts an average of four ounces of coffee in jars, with a standard deviation of 0.25 ounces. forty jars filled

Lunna [17]

Let's attack this problem using the z-score concept. The sample std. dev. here is (0.25 oz)/sqrt(40), or 0.040. Thus, the z score representing 3.9 oz. is
3.9 - 4.0
z = -------------- = -2.5
0.040

In one way or another we must find the area under the std. normal curve that lies to the left of z = -2.5. Use a table of z-scores or a calculator with built-in statistics functions. According to my TI-83 Plus calculator, that area is

0.006. One way of interpreting this that with so small a standard deviation, most volumes of coffee put into the jars are very close to the mean, 4 oz.

4 0

4 years ago

What is not true of the construction of an angle bisector

timurjin [86]

Are there any answer choices maybe??

3 0

4 years ago

An equation is shown below: 8x + 2(x – 7) = 7x + 3x – 14 Part A: Solve the equation and write the number of solutions. Show all

marta [7]

Answer:

Infinitely Many
Distributive Property

Step-by-step explanation:

8x + 2(x - 7) = 7x + 3x - 14

8x + 2x - 14 = 7x + 3x - 14 Distributive property.

10x - 14 = 10x - 14 Combine the like terms.

-14 = -14 Subtraction.

0 = 0 Addition.

Since the statement 0 = 0 is true regardless of the value of x, there is infinitely many solutions.

7 0

2 years ago