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11111nata11111 [884]

3 years ago

14

You start driving north for 24 miles, turn right, and drive east for another 10 miles. At the end of driving, what is your strai

ght line distance from your starting point?

1 answer:

yawa3891 [41]3 years ago

8 0

Answer:

26 miles

Step-by-step explanation:

Given: 24 miles drive to north.

10 miles drive to east.

Driving pattern form a right angle triangle, which has three leg including straight line distance from starting point (hypotenous).

Now, using Pythogorean theoram to find straight line distance from starting point.

h²= a²+b²

Where, h is hypotenous

a is opposite leg

b is adjacent leg.

⇒h²= $24^{2} + 10^{2}$

⇒ $h^{2} = 576+100$

⇒ $h^{2} = 676$

Taking square root on both side, remember; √a²= ±a

⇒ $h=\sqrt{676}$

∴ $h= \pm 26$

Ignoring -26 as distance cannot be negative.

Hence, 26 miles is the straight line distance from starting point.

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Function P is defined as P (x) = x ^2 . Explain why P (2) + P (3) isn't equal to P (5) .

diamong [38]

Answer:

P(x) = x + 2

Piden: A = P(P(P(P(3))))

P(3); x = 3

P(3) = 3 + 2 = 5

A = P(P(P(P(3))))

A = P(P(P(5)))

P(5); x = 5

P(5) = 5 + 2 = 7

A = P(P(P(5)))

A = P(P(7))

P(7); x = 7

P(7) = 7 + 2 = 9

A = P(P(7))

A = P(9)

P(9); x = 9

P(9) = 9 + 2 = 11

→ A = P(P(P(P(3)))) = 11

Step-by-step explanation:

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4 0

3 years ago

Based on the survey results from 300 selected students in the Burbank School District (BSD), the 98% confidence interval used to

Pavlova-9 [17]

Answer:

follows are the solution to this question:

Step-by-step explanation:

Please find the correct question in the attached file:

The formula for calculating the Confidence interval of proportion:

$\to CI=\hat{p} \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to \hat{p}=\frac{\text{lower limit +upper limit}}{2}\\$

$=\frac{0.48+0.60}{2}\\\\=\frac{1.08}{2}\\\\=0.54$

The number of learners with access to working at home on a computer:

$= 0.54 \times 300 \\\\=162$

Lower limit =0.48

upper limit = 0.60

$\to margin \ error = \frac{\text{upper limit - lower limit}}{2}\\$

$=\frac{0.60-0.48}{2}\\\\=\frac{0.12}{2}\\\\= 0.06$

5 0

3 years ago

Is 6 rational or irrational

swat32

Answer:

-6 is a rational number

Step-by-step explanation:

because it can be expressed as a fraction where the numerator and denominator are integers and the denominator doesn't equal 0.

3 0

3 years ago

A cable hangs between two poles of equal height and 35 feet apart. At a point on the ground directly under the cable and x feet

gayaneshka [121]

Answer:

293.38 pounds

Step-by-step explanation:

We are given that

Distance between poles=35 feet

$h(x)=10+0.1(x^{1.5})$

Weight of cable=10.4 per linear foot

We have to find the weight of the cable.

Differentiate w.r.t

$h'(x)=0.1(1.5)x^{0.5}=0.15x^{0.5}$

$s=2\int_{0}^{17.5}\sqrt{1+(h'(x))^2}dx$

$s=2\int_{0}^{17.5}\sqrt{1+(0.15x^{0.5})^2}dx$

$s=2\int_{0}^{17.5}\sqrt{1+0.0225x}dx$

Let $1+0.0225x=t$

$dx=\frac{1}{0.0225}dt$

$s=\frac{2}{0.0225}\int_{0}^{17.5}\sqrt{t}dt$

$s=\frac{2}{0.0225}\times\frac{2}{3}[t^{\frac{3}{2}}]^{17.5}_{0}$

$s=2\times \frac{2}{3\times0.0225}[(1+0.0255x)^{\frac{3}{2}]^{17.5}_{0}$

$s=\frac{4}{3\times 0.0225}((1+0.0225(17.5))^{\frac{3}{2}-1)$

s=28.21

Weight of cable= $28.21\times 10.4=293.38$ pound

8 0

3 years ago

7 times as much as the sum of 1/3 and 4/5

Jet001 [13]

First of all, you add 1/3 and 4/5, so you get:
$\frac{1}{3} + \frac{4}{5}$

To add 2 fractions, they need to have the same denominator. Since 3 and 5 don't have a common factor, so you multiply 1/3 by 5, and 4/5 by 3, so you get:
$\frac{1*5}{3*5} + \frac{4*3}{5*3}$
$\frac{5}{15} + \frac{12}{15}$

Now, the two fractions got the same denominator, and you can add them by adding the numerators over the same denominator. (You don't add denominators in addition) so you get:
$\frac{5+12}{15}$
$\frac{17}{15}$

That's the sum of 1/3 + 4/5.

Now, they want the sum of the 2 fractions 7 times. So you multiply 17/15 by 7. And as you know, 7 = 7/1. So you get:
$\frac{17}{15} * \frac{7}{1}$

In multiplication no need to have the same denominator. You multiply nominators by nominators and denominators by denominators. So you get:
$\frac{17*7}{15*1}$
$\frac{119}{15}$

Since 119 and 15 don't have a common factor, so they can't be simplified.
So, the answer is 119/15.

Hope this Helps! :D

7 0

3 years ago

Read 2 more answers