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3 years ago

A painter leans a 10 ft ladder against a building.

Mathematics

1 answer:

Katarina [22]3 years ago

8 0

Answer:

<h2>7.14 ft </h2><h2>I hope it helps :)</h2>

Step-by-step explanation:

$Hypotenuse = 10\\Opposite = 7\\Adjacent = x\\ \\Using Pythagoras theorem ;\\Hyp^{2} =opp^{2} +adj^{2} \\10^{2} = 7^{2} +x^{2} \\100 = 49+x^{2} \\x^{2} =100-49\\x^{2} =51\\\sqrt{x^{2} } =\sqrt{51} x = 7.14 ft$

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Find all solutions in the interval [0, 2π) sin2x + sin x = 0

Molodets [167]

Sin 2 x + sin x = 0
( sin 2 x = 2 sin x cos x )
2 sin x cos x + sin x = 0
sin x ( 2 cos x + 1 ) = 0
sin x = 0
x 1 = 0
x 2 = π
or: 2 cos x + 1 = 0
2 cos x = - 1
cos x = -1/2
x 3 = 2π/3
x 4 = 4π/3

3 0

3 years ago

A golf association sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250

Oksanka [162]

Answer:

In this context 38% represents that if the mean speed of ball is 250 ft/sec, then there is 34% chance of obtaining a similar or more extreme value related to test statistics.

Step-by-step explanation:

We are given that the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the association.

Based on the mean speed in the sample, the association comes up with a P-value of 0.38.

Let $\mu$ = <u><em>mean speed of the ball</em></u>

So, Null Hypothesis, $H_0$ : $\mu$ = 250 ft/sec

Alternate Hypothesis, $H_A$ : $\mu$ > 250 ft/sec

Now, the P-value given to us is 0.38.

P-value basically tells us the exact percentage where our test statistics lie. Also, it is the probability of obtaining the value that is more extreme, given that null hypothesis is true,

So, in this context 38% represents that if the mean speed of ball is 250 ft/sec, then there is 34% chance of obtaining a similar or more extreme value related to test statistics.

7 0

4 years ago

Please solve and show the steps. 2/3z +3 =7

USPshnik [31]

Subtract 3 from both sides:

2/3z=4

divide by 2/3 on both sides (multiple 3/2 on both sides)

z= 6

4 0

3 years ago

Read 2 more answers

Solve for 2cos^2theta + 13costheta = -6. theta is >= 0 and < 360 degrees

LiRa [457]

$\\ 2cos^2 \theta+13cos \theta=-6 \\ 2cos^2 \theta+13cos \theta+6=0 \\ 2cos^2 \theta+12cos \theta+1cos \theta+6=0 \\ 2cos \theta(cos \theta+6)+1(cos \theta+6)=0 \\ (2cos\theta +1)(cos\theta+6)=0 \\$

$cos\theta+6=0 \\ cos\theta=-6 \\ \\ cos(x)=|a| \leq 1 \\ |-6| \geq 1 \\ \\$

$2cos \theta+1=0 \\ 2cos \theta=-1 \\ cos \theta=- \frac{1}{2} \\ \theta= \frac{ 2\pi }{3} +2 \pi k~~~k \in Z \\ \\ 0 \leq \theta \ \textless \ 360^{а} \\ 0 \leq \theta \ \textless \ 2 \pi \\ \theta = \frac{2 \pi }{3} \\ \theta = \frac{2 \pi }{3} , \frac{4 \pi }{3}$

7 0

3 years ago

200 reduced by 2 times my age equals 16

Komok [63]

Ok, so since it doesn't give a value for "my age", we'll call it x. So the sentence translates into an equation...

200 reduced means... 200 -
by 2 times my age means... 2x
equals 16 means... = 16

200 - 2x = 16

Now let's solve for x to find "my age"

First subtract 200 from each side to begin to isolate x

-2x = -184

Divide each side by -2 to isolate x

x = -184/-2
x = 92

I'm 92 years old!

8 0

3 years ago