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4 years ago

Tracy drove 312 miles in about 5 hours. What is the best underestimate of Tracy's rate of speed?

Mathematics

2 answers:

slavikrds [6]4 years ago

8 0

Tracy average speed is 62.4 miles per hour

sergeinik [125]4 years ago

5 0

Tracy average speed is 62.4 mph

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“76 is 60% of what?” Help!

kipiarov [429]

126.67

Hope this helps!

5 0

3 years ago

Solve the equation by using the quadratic formula. x^2+2x=6

katrin [286]

Answer:

$\Huge \boxed{{x=-1\pm \sqrt{7}}}$

Step-by-step explanation:

x² + 2x = 6

Subtract both sides by 6.

x² + 2x - 6 = 0

ax²+bx+c=0

a=1, b=2, and c=-6

We can apply the quadratic formula.

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plug in the values.

$\displaystyle x=\frac{-2\pm\sqrt{2^2-4(1)(-6)}}{2(1)}$

Evaluate.

$\displaystyle x=\frac{-2\pm\sqrt{4-(-24)}}{2}$

$\displaystyle x=\frac{-2\pm\sqrt{28}}{2}$

$\displaystyle x=\frac{-2\pm 2\sqrt{7}}{2}=-1 \pm \sqrt{7}$

6 0

3 years ago

Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

Step 4: Integrate Pt. 2

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

7 0

3 years ago

Jane is trying to estimate the average electric bill amount of people who live in Las Cruces in summer time. She randomly select

Lina20 [59]

Answer:

The estimated average electric cost amount of all residents in Las Cruces = 182.9

Step-by-step explanation:

The bill amounts from the electric company for the month of July for 10 randomly selected houses from the map was obtained to be

135 265 215 103 156 203 125 156 230 241

Using the Central Limit theory, the mean of a sample extracted randomly from an independent distribution is approximately equal to the population mean of the independent distribution.

This means that the sample mean of a random sample extracted from the population is a good estimate of the population mean.

Sample mean ≈ Population mean

μₓ = μ

Mean = = (Σx)/N

The mean is the sum of variables divided by the number of variables

x = each variable

N = Sample size = 10

Σx = (135+265+215+103+156+203+125+156+230+241) = 1,829

Sample mean = (1,829/10) = 182.9

Population mean ≈ sample mean

Population mean ≈ 182.9

Hope this Helps!!!

8 0

3 years ago

Find the value of x that makes m\ \n.

Fofino [41]

Answer:

x = 15

Step-by-step explanation:

These angles are supplementary so you'd set up an equation like 3x -15 +150 = 180 then solve for x from there.

5 0

3 years ago