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PSYCHO15rus [73]

2 years ago

6

Laura Bernett is 5 ft-4 inches tall. She stands 12 feet from a streetlight and casts a 5-foot-long shadow. How tall is the stree

tlight? Give your answer to the nearest hundredth.

1 answer:

Sidana [21]2 years ago

6 0

Answer: the height of the streetlight is 19.47 feet

Step-by-step explanation:

The height of Laura Bernett is 5 ft-4 inches.

12 inches = 1 foot

4 inches = 4/12 = 1/3 foot

Therefore, her height is

5 + 1/3 = 16/3 foot

The diagram of the scenario is shown in the attached photo

The right angle triangle ABC and EBD formed are similar.

h represents the height of the streetlight

Total length of AB = 12 + 5 = 17 feet

Considering triangle BDE,

To determine the angle formed, θ, we would apply trigonometric ratio

Tan θ = opposite side/adjacent side

Tan θ = (16/3)/5 = 1.067

θ = 46.86 degrees

Considering triangle ABC,

Tan θ = h/AB

Tan 48.86 = h/17

h = 17tan48.86 = 17 × 1.145

h = 19.465

To the nearest hundredth,

h = 19.47 feet

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According to the Rational Root Theorem, the following are potential fox) 2x2 +2x 24.roots of -4, -3, 2, 3, 4Which are actual roo

aksik [14]

Correct Answer: First Option

Explanation:

There are two ways to find the actual roots:

a) Either solve the given quadratic equation to find the actual roots

b) Or substitute the value of Possible Rational Roots one by one to find out which satisfies the given equation.

Method a is more convenient and less time consuming, so I'll be solving the given equation by factorization to find its actual roots. To find the actual roots set the given equation equal to zero and solve for x as given below:

$2x^{2} +2x-24=0\\ \\ 2(x^{2} +x-12)=0\\ \\ x^{2} +x-12=0\\ \\ x^{2} +4x-3x-12=0\\ \\ x(x+4)-3(x+4)=0\\ \\ (x-3)(x+4)=0\\ \\ x-3=0, x=3\\ \\ or\\\\x+4=0, x=-4$

This means the actual roots of the given equation are 3 and -4. So first option gives the correct answer.

7 0

2 years ago

Read 2 more answers

At the beginning of year 1, paolo invests $500

suter [353]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$500\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annuall, thus once}
\end{array}\to &1\\
t=years\to &t
\end{cases}
\\\\\\
A=500\left(1+\frac{0.04}{1}\right)^{1\cdot t}\implies A=500(1+0.04)^t
\\\\\\
\textit{after 5 years }t=5\qquad A=500(1.04)^5$

the example on your picture uses A(n) and n = years, but is pretty much the same, in this case is t = years.

3 0

2 years ago

Read 2 more answers

6 questions = 30 points someone please help me

eduard

Answer:

1)D

2)D

3)A

4)B

5)Cannot Answer - No data

6)C

7)C

6 Questions answered for 30 points.

Step-by-step explanation:

Answer for the 1st Question,

Area of a cylinder can be calculated by,

Area of the cylindrical part = $2\pi rL$

Area of the parts that cover the open parts of cylinder = $2\pi r^2$

Therefor Total are of the cylinder = $2\pi rL+2\pi r^2$

Area of the total cylinder = $2*3.14*6.8*14.2+2*3.14*6.8^2$

= $896.784$

<u>Therefor best estimate will be D) 923 in^2</u>

Answer for the 2nd Question,

ABC is a triangle.

By Pythagorean theorem it says,

$(AC)^2+(CB)^2=(AB)^2$

The distance from A to C = 6

The distance from C to B = 5

$(AC)^2=6^2=36$

$(CB)^2=5^2=25$

$(AC)^2+(CB)^2=(AB)^2=36+25=61$

Therefor $(AB)^2=61\\(AB)=\sqrt{61}$

<u>Therefor Answer is D) Sqr 61</u>

Answer to Question 3

To find the trend you can draw an imaginary line that fits the scatter plots.(I have attached a image drawing the imaginary lines)

Then the revenue can be calculated by calculating the area covered by the imaginary line drawn or area "under" the curve.

Area of the Store 1 = $\frac{1}{2} *(110+40)*110=8250$

Area of the Store 2= $\frac{1}{2} *110*80=4400$

Therefore Revenue from Store 1 = $8250

Revenue from Store 2 = $4400

<u>Answer is A) Store 1 has more sales revenue</u>

Answer for Question 4

$\frac{5}{12}=0.4167\\\frac{5}{11}=0.4545$

You can straight away discard answer D because it is less than both 5/12 and 5/11.

Also you can discard Answer C because 25/264 is very small (less than 1/10=0.1)

$\frac{11}{23} =0.4782$ , therefor this is not in between those two numbers.

Then it has to be $\frac{115}{264} =0.4356$

<u>Answer is B)</u>

Answer for question 6

The equation of a straight line is of the form $y=mx+c$

here m is the gradient and c is the intercept.

Find the intercept(c) by finding the y value when x value is 0, here it is +1.

Gradient (m) of the graph can be found by,

$\frac{y1-y2}{x1-x2} =\frac{7-3}{3-1} =2$

Therefor the equation of the graph is,

$y=2x+1$

<u>Answer is C</u>

Answer for question 7

$\frac{7}{8} =0.875$

$\frac{6}{9} =0.67$

We can discard answer A because the value is close to 0.5

We can discard answer B because 3/17 is a very small value (0.17)

$\frac{53}{72} =0.73$ , This falls between the above 2 numbers.

<u>Therefor answer is C</u>

5 0

2 years ago

Now let the figure show a scale drawing of a park. The scale is 1 unit : 25 meters. What is the horizontal distance across the p

insens350 [35]

The question is missing the figure. So, the figure is attached below.

Answer:

C. 350 m

Step-by-step explanation:

Given:

Scale is given as:

1 unit : 25 meters

This means that 1 unit on the grid is equivalent to 25 meters in actual.

Now, from the figure, the horizontal distance across the park is 14 units.

1 unit = 25 meter

Now, we can find the actual distance using unitary method and thus multiplying 25 and 14 to get the actual distance across the park horizontally.

∴ 14 units = $25\times 14=350$ meters.

Therefore, the horizontal distance across the park is 350 m in actual.

So, the correct option is option C.

7 0

2 years ago

Round 96.9617186007 to the nearest tenth.

Pavlova-9 [17]

if you're talking about the whole number, 100.96. if you're referring to decimal place values; 96.70.

underline the digit that you round to

circle the digit to the right

five or more goes up

four or less stays the same

everything behind becomes a zero.

6 0

2 years ago

Read 2 more answers