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3 years ago

Lindsay drove for 5 1 /2 hours at 60 miles per hour. How much distance did she travel?

Mathematics

1 answer:

GaryK [48]3 years ago

5 0

let's firstly convert the mixed fraction to improper, and then check.

$\bf \stackrel{mixed}{5\frac{1}{2}}\implies \cfrac{5\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{11}{2}}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\begin{array}{ccll}
miles&hours\\
\cline{1-2}
60&1\\[0.8em]
m&\frac{11}{2}
\end{array}\implies \cfrac{60}{m}=\cfrac{~~1~~}{\frac{11}{2}}\implies \cfrac{60}{m}=\cfrac{~~\frac{1}{1}~~}{\frac{11}{2}}\implies \cfrac{60}{m}=\cfrac{1}{1}\cdot \cfrac{2}{11}
\\\\\\
\cfrac{60}{m}=\cfrac{2}{11}\implies 660=2m\implies \cfrac{660}{2}=m\implies 330=m$

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You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

3 years ago

a random sample of 4 claims are selected from a lot of 12 that has 3 nonconforming units. using the hypergeometric distribution

Sloan [31]

Answer:

The probability that the sample will contain exactly 0 nonconforming units is P=0.25.

The probability that the sample will contain exactly 1 nonconforming units is P=0.51.

Step-by-step explanation:

We have a sample of size n=4, taken out of a lot of N=12 units, where K=3 are non-conforming units.

We can write the probability mass function as:

$P(x=k)=\frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}$

where k is the number of non-conforming units on the sample of n=4.

We can calculate the probability of getting no non-conforming units (k=0) as:

$P(x=0)=\frac{\binom{3}{0}\binom{9}{4}}{\binom{12}{4}}=\frac{1*126}{495}=\frac{126}{495} = 0.25$

We can calculate the probability of getting one non-conforming units (k=1) as:

$P(x=1)=\frac{\binom{3}{1}\binom{9}{3}}{\binom{12}{4}}=\frac{3*84}{495}=\frac{252}{495} = 0.51$

5 0

4 years ago

write the equation of the line in slope - interact firm given the slop and the coordinates of the y-intercept. m=3/5; (0,1/6)

brilliants [131]

Y - y₁ = m(x - x₁)
y - ¹/₆ = ³/₅(x - 0)
y - ¹/₆ = ³/₅(x) - ³/₅(0)
y - ¹/₆ = ³/₅x - 0
 + ¹/₆ + ¹/₆
 y = ³/₅x + ¹/₆
 y = ³/₅(0) + ¹/₆
 y = 0 + ¹/₆
 y = ¹/₆

5 0

3 years ago

Read 2 more answers

3x * -2y= -100 Solve for y and x.

Sedbober [7]

Answer:

x=50/3y

y=50/3x

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

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3 years ago

Store A sells 11 bagels for 9.57 Store B sells bagels for 3.52. How do the unit rates compare?

Sloan [31]

First you put the numbers in this form:

11 Bagels = $9.57
________ _______
? Bagels = $3.52

Now they look like fractions but you have to cross multiply them like this: 11 x $3.52 which makes $38.72 then you divide $38.72 by $9.57 which makes the answer that you have to find which is 4.04597701 or just to round 4 and then that will be your answer.

4 0

3 years ago