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Lera25 [3.4K]
2 years ago
11

The University of Central Florida is planning to build a new access ramp for wheelchairs at its education building. The main ent

rance to the building is 4 feet above the sidewalk level. The angle of elevation from where the ramp and sidewalk would meet is 8.1°. Determine the length of the ramp to the nearest tenth of a foot.
Mathematics
1 answer:
forsale [732]2 years ago
6 0

Answer:

0.6 feet

Step-by-step explanation:

We solve this question using the Trigonometric function of Tangent.

tan θ = Opposite/Adjacent.

Where:

Opposite = Height /Length of the ramp = ?

Adjacent = Distance from the base of the ramp = 4 feet

θ = 8.1°

Therefore,

tan 8.1° = x/4

Cross Multiply

x = tan 8.1 × 4

x = 0.5692843028 feet

Approximately = 0.6 feet

Length of the ramp = 0.6 feet.

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8. If 30 cents out of every 1 dollar goes to taxes and the rest is net income, what's the
aniked [119]

Answer:

  • D. 3:7

Step-by-step explanation:

1 dollar = 30 cents tax + 70 cents net income

<u>The ratio of taxes to net income:</u>

  • 30 : 70 =
  • 3 : 7

Correct choice is D

4 0
2 years ago
Read 2 more answers
Dr. Caras was characterizing a cytochrome (an iron containing protein) from a new strain of bacteria. He obtained the following
olya-2409 [2.1K]

Answer:

0.5613

Step-by-step explanation:

Here mean strain of bacteria x = sum of all numbers/ total numbers = 0.5514 %

Standard deviation s = 0.0040 %

Test statistic

G = (x_{max} -x)/s = (0.5613 - 0.5514)/ 0.0040 = 2.475

95% confidence value for outlier for n = 8 and alpha = 0.05

G_{critical} = 2.1266

so here we see that G > G_critical , so we reject that the there is no outlier . the value of 0.5613 is and outlier.

7 0
2 years ago
Given the geometric sequence where a1 = 3 and r = √2 find a9
Zigmanuir [339]

Answer:

a_9=48

Step-by-step explanation:

we are given

sequence is geometric

so, we can use nth term formula

a_n=a_1(r)^{n-1}

we have

a_1=3

r=\sqrt{2}

we have to find a9

so, we can plug n=9

we get

a_9=3(\sqrt{2})^{9-1}

a_9=2^4\cdot \:3

a_9=48

8 0
3 years ago
Find the discriminant of the following equation.<br> 4x2 + 16x + 16 = 0 ...?
kenny6666 [7]

Discriminant = b^2 - 4ac

a = 4

b = 16

c = 16

16^2 - 4(4 x 16)

256 - (4x64)

256 - 256 = 0

Therefore it only has one root

7 0
2 years ago
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, So
tatyana61 [14]

Answer:

The probability that at least 13 flights arrive late is 2.5196 \times 10^{-6}.

Step-by-step explanation:

We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.

A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.

The above situation can be represented through binomial distribution;

P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........

where, n = number of trials (samples) taken = 18 Southwest flights

           r = number of success = at least 13 flights arrive late

          p = probability of success which in our question is probability that

                flights arrive late, i.e. p = 1 - 0.80 = 20%

Let X = <u><em>Number of flights that arrive late</em></u>.

So, X ~ Binom(n = 18, p = 0.20)

Now, the probability that at least 13 flights arrive late is given by = P(X \geq 13)

P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)

= \binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}

= \binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}

= 2.5196 \times 10^{-6}.

7 0
3 years ago
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