Answer:
I guess that we want to find the function g(x) for the 4 cases.
first, f(x) = -9*x + 1.
a) The graph of g is a reflection in the y-axis of the graph of f.
First remember: if we have the point (x,y) and we reflect it over the y-axis, we get (-x,y)
then g(x) = f(-x) = -9*-x + 1 = 9*x + 1.
b) The graph of g is a reflection in the x-axis of the graph of f.
if we have a point (x, y) and we reflect it over the x-axis, the point transforms into (x, -y)
then we have: g(x) = -f(x) = 9*x - 1
c) The graph of g is a horizontal translation 16 units right of the graph of f.
When we want to have a translation in the x-axis, we must change x by x - A.
If A is positive, this transformation moves the graph by A units to the right, in this case, A = 16.
g(x) = f(x - 16) = -9*(x - 16) + 1
d) The graph of g is a vertical translation 16 units down of the graph of f.
For vertical translations, if we want to move the graph by A units down (A positive) we should do y = f(x) - A
In this case, A = 16.
then: g(x) = f(x) - 16 = -9*x + 1 - 16 = -9*x - 15.
Someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi. We think the actual amount is lower than that and want to run the test at an alpha level of 5%. What would our sample size need to be if we want to reject the null hypothesis if the sample mean is at or below 1,997.2956?
Answer:
The sample size must be greater than 37 if we want to reject the null hypothesis.
Step-by-step explanation:
We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.
Also, we are given a level of significance of 5%.
Let [tex]\mu[/tex] = mean breaking strength of their climbing rope
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2,000 psi {means that the mean breaking strength of their climbing rope is 2,000 psi}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 2,000 psi {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}
Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = ample mean strength = 1,997.2956 psi
[tex]\sigma[/tex] = population standard devaition = 10 psi
n = sample size
Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.
So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.
SO, T.S. < -1.645 {then reject null hypothesis}
[tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645[/tex]
[tex]\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645[/tex]
[tex](\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645[/tex]
[tex]-0.27044 \times \sqrt{n}< -1.645[/tex]
[tex]\sqrt{n}> \frac{-1.645}{-0.27044}[/tex]
[tex]\sqrt{n}>6.083[/tex]
n > 36.99 ≈ 37.
SO, the sample size must be greater than 37 if we want to reject the null hypothesis.
A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a random sample of 800 people is taken and its determined that 478 people have Internet access. The following is the setup for this hypothesis test: H0:p=0.63 Ha:p<0.63 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
Answer:
Step-by-step explanation:
For the null hypothesis,
H0 : p = 0.63
For the alternative hypothesis,
Ha : p < 0.63
This is a left tailed test
Considering the population proportion, probability of success, p = 0.63
q = probability of failure = 1 - p
q = 1 - 0.63 = 0.37
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 478
n = number of samples = 800
P = 478/800 = 0.6
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76
From the normal distribution table, the area below the test z score in the left tail 0.039
Thus
p = 0.039
Answer:
-3.66
Step-by-step explanation:
Graph the line that represents this equation. 3x - 4y =8
Answer:
See attachment
Step-by-step explanation:
The solution is given in the image.
Which graph is the graph of the function?The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.
What does the axis of a graph constitute?An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.
Learn more about graphs here: brainly.com/question/4025726
#SPJ2
The sum is type answer as integer proper fraction or mixed number simplify answer
Answer:
[tex]9\dfrac{5}{6}[/tex]
Step-by-step explanation:
[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]
Hope this helps!
What is the square root of x if x = 25?
Answer:
5 is your answer
Step-by-step explanation:
The [tex]\sqrt{25}[/tex] will equal to 5, because [tex]5^2[/tex] = 25
Answer:
5
Step-by-step explanation:
5 x 5 =25, so it is the square root of 25
Express the following in usual form
Answer:
52300
Step-by-step explanation:
When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300
List the steps taken and find the area of the figure below
6cm
6 CM
6 cm
6 cm
Answer:
36 cm
Step-by-step explanation:
Since all measurements of the figure are the same, that means that this figure is a square. To find the area of a figure multiply length by width. Since this figure is a square and all sides are equal, we multiply 6 by 6 for an area of 36 cm.
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'? 1.5 units 3 units 4.5 units 6 units
If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.
Dilation of an object simply means enlarging or shrinking of the object by a scale factor.Now, we are told that Triangle ABC was dilated to Triangle A'B'C' using the rule D₀,₄.What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.
Now, if the length of OB is 3/4, it means that the new dilated length is gotten from;Scale factor = new dilated length OB'/(³/₄)
new dilated length OB' = ³/₄ × 4
new dilated length OB' = 3 units
Read more on dilation at; https://brainly.com/question/8532602
Answer:
its 4 units trust just answered it
Step-by-step explanation:
Which equation can be used to find mMN
Answer:
Its depending on the angle
An animal shelter has a 65% adoption rate for puppies. Of all puppies in the shelter, 75% live to be 7 years or older. Of the puppies who are adopted, 80% live to be 7 years or older. What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
Answer:
52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: A puppy is adopted.
Event B: The puppy lives 7 or more years.
An animal shelter has a 65% adoption rate for puppies
This means that [tex]P(A) = 0.65[/tex]
Of the puppies who are adopted, 80% live to be 7 years or older.
This means that [tex]P(B|A) = 0.8[/tex]
What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)*P(B|A)[/tex]
[tex]P(A \cap B) = 0.65*0.8[/tex]
[tex]P(A \cap B) = 0.52[/tex]
52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
In two sample surveys 125 people were asked about their favorite fruit in the survey 40 people chose apples 64 choose oranges and 21 chose bananas in the second 34 chose apples 63 chose oranges 19 Joe’s banana marine inferred before is this a French trooper by us on the data explain
Answer:
Marianne made an inference that is true based on the data. More than half of the people surveyed in each sample chose oranges as their favorite fruit. Since most people in each sample chose oranges, it is likely that oranges are the favorite fruit of the entire population.
hope it help please mark me as brainliest
Triangle JKL was dilated using the rule D Subscript M, one-third. The image, triangle J'K'L', is the result of the dilation. Point M is the center of dilation. Triangle J K L is dilated to form smaller triangle J prime K prime L prime. The length of M L prime is 2.5. What is L'L? 5 units 7.5 units 10 units 12.5 units
Answer: the answer is A 5 units
The length of L'L in the dilated figure is 5 units.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Dilation is the increase or decrease in size of a figure.
Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.
Given that ML' = 2.5 units, hence:
L'L = (2.5 * 3) - 2.5 = 5 units
The length of L'L in the dilated figure is 5 units.
Find out more on transformation at: https://brainly.com/question/1620969
NFL player Gerald Sensabaugh recorded a 46 inch standing vertical jump at the 2005 NFL Combine, at that time the highest for any NFL player in the history of the Combine. Sensabaugh weighed about 200 lb when he set the record. Part A What was his speed as he left the floor
Answer:
His speed as he left the floor is 4.83 m/s.
Step-by-step explanation:
Given: 46 inches = 1.1684 m and mass = 200 lb = 90.7185 Kg.
From the third equation of motion under free fall,
[tex]V^{2}[/tex] = [tex]U^{2}[/tex] - 2gs
Where; V is the final velocity (0), U is the initial velocity (unknown), g is the value of gravity - 10 m/[tex]s^{2}[/tex] and s is the distance = 1.1684 m.
Then;
0 = [tex]U^{2}[/tex] - 2gs
[tex]U^{2}[/tex] = 2gs
= 2 × 10 × 1.1684
= 23.368
⇒ U = [tex]\sqrt{23.368}[/tex]
= 4.8340 m/s
The initial velocity, U = 4.83 m/s.
Therefore, his speed as he left the floor is 4.83 m/s.
Answer:
His speed as he left the floor is 4.83 m/s.
Step-by-step explanation:
A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven others (the controls) receive the standard treatment. The recovery times, in days, are given below.
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
Required:
Find a 98% confidence interval for the difference in the mean recovery times between treatment and control.
Answer:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Step-by-step explanation:
For this case we have the following info given:
Treatment: 12 13 15 19 20 21 24
Control: 18 23 24 30 32 35 39
We can find the sample mean and deviations with the the following formulas:
[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s =\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}[/tex]
And repaplacing we got:
[tex] \bar X_T = 17.714[/tex] the sample mean for treatment
[tex] \bar X_C = 28.714[/tex] the sample mean for treatment
[tex] s_T= 4.461[/tex] the sample deviation for treatment
[tex] s_C= 7.387[/tex] the sample deviation for control
[tex]n_T= n_C= 7[/tex] the sample size for each sample
The degrees of freedom are given by:
[tex] df= 7+7-2= 12[/tex]
The confidence interval for the difference of means is given by:
[tex] (\bar X_T -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_T}{n_T} +\frac{s^2_C}{n_C}}[/tex]
The confidence is 98% so then the significance is [tex]\alpha=0.02[/tex] and [tex] \alpha/2 =0.01[/tex]. Then the critical value would be:
[tex] t_{\alpha/2}=2.681[/tex]
And replacing we got:
[tex] (17.714-28.714) -2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -19.745[/tex]
[tex] (17.714-28.714) +2.681 \sqrt{\frac{4.461^2}{7} +\frac{7.387^2}{7}}= -2.255[/tex]
Find the first 4 terms and the 10th one n+5
Answer: First 4 terms of n + 5 = 6,7,8,9
10th term = 15
Hope this is right
Step-by-step explanation:
By putting n = 1 , 2, 3 , 4 we can find first 4 terms
When n = 1
n + 5 = 1 + 5 = 6
When n = 2
n + 5 = 2 + 5 = 7
When n = 3
n + 5 = 3 + 5 = 8
When n = 4
n + 5 = 4 + 5 = 9
When n = 10
n + 5 = 10 +5 = 15
The average number of children a Japanese woman has in her lifetime is 1.37. Suppose that one Japanese woman is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X.X~ _____(_____,_____) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Japanese average.
Answer:
a. X: amount of children that a Japanese woman has in her lifetime.
b. X can take natural numbers (all positive integers) as values.
c. X~Poi(1.37).
d. P(X=0)=0.2541
e. P(X<1.37)=0.6022
Step-by-step explanation:
a) This can be modeled with a Poisson distribution.
We let the variable X be the amount of children that a Japanese woman has in her lifetime.
The parameter of the Poisson distribution is λ=1.37.
This is also the value of the mean and the standard deviation.
b) X can take all positive integer values.
c) X is modeled as a Poisson variable with λ=1.37.
d) This can be calculated as:
[tex]P(0)=\lambda^ke^{-\lambda}/k!=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\[/tex]
e) Having fewer children than the average means that she has one or none children.
This can be calculated as:
[tex]P(X<1.37)=P(0)+P(1)\\\\\\P(0)=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\P(1)=1.37^{1} \cdot e^{-1.37}/1!=1.37*0.2541/1=0.3481\\\\\\P(X<1.37)=0.2541+0.3481=0.6022[/tex]
Section 1: Write the following times in 24-hour clock time:
a) 7:15 a.m -
b) 1:05 am
c) 2:01 p.m
d) 9:22 p.m
e) 12:25 am
Section 2: Write the following times in 12-hour clock time.
a) 1155 hours
b) 1005 hours
c) 1714 hours
d) 0756 hours
e) 1345 hours
Answer:
Section 1:
a) 7:15 a.m - 19:15
b) 1:05 am - 01:05
c) 2:01 p.m - 14:01
d) 9:22 p.m - 21:22
e) 12:25 am- 24:25
Section 2:
a) 1155 hours - 11:55am
b) 1005 hours -10:05am
c) 1714 hours - 5:14pm
d) 0756 hours - 7:56am
e) 1345 hours- 1:45pm
Answer:
12:25 am= 00:25
Step-by-step explanation:
Please help me extra points for 1 math question. Please help before my time is up. Five times a number, added to -3, is 37. Find that number.
Answer:
your number should be 8
Step-by-step explanation:
5x+(-3)=37
5x-3=37
+3 +3
5x=40
÷5 ÷5
x=8
hope this helps
Answer:
The answer is 8.
5x-3=37
5x=37+3
5x=40
x=40/5
x=8
HOPE IT HELPS!!
There are 20 pieces of fruit in a bowl and 5 of them are apples. What percent of the fruit are apples?
Step-by-step explanation:
20fruits=100%
5fruits=?
5x100/20 5fruitsx5%
=24%
Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. How fast does a man have to run to be in the top 1% of runners?
Answer:
To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 93, \sigma = 16[/tex]
How fast does a man have to run to be in the top 1% of runners?
The lower the time, the faster they are. So the man has to be at most in the 1st percentile, which is X when Z has a pvalue of 0.01. So he has to run in at most X seconds, and X is found when Z = -2.327. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.327 = \frac{X - 93}{16}[/tex]
[tex]X - 93 = -2.327*16[/tex]
[tex]X = 55.768[/tex]
To be in the top 1% of the runners, the man has to run the 400 meters in at most 55.768 seconds.
If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x+y =
Answer:
[tex]x + y = \frac{1000}{9}[/tex]
Step-by-step explanation:
Step 1: Identify the approach:
With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value [tex](x + y)[/tex] is on the left side and all of other components which do not contain [tex]x[/tex] or [tex]y[/tex] are on the right side.
Step 2: Analyze:
[tex]9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867[/tex]
Realize that in both equations, the [tex]2y^{2}[/tex] and [tex]3z^{2}[/tex] are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.
Step 3: Perform manipulation:
[tex]9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867[/tex]
Rearrange:
[tex](9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867[/tex]
Simplify:
[tex]9(x + y) + 0 + 0 = 1000[/tex]
Simplify:
[tex]x + y = \frac{1000}{9}[/tex]
Hope this helps!
:)
evaluate the formula of A=lw, for l=10.8 cm and w=2.5 cm
Answer:
A = 27 cm²
Step-by-step explanation:
[tex]A = lw\\Where, l=10.8 cm , w = 2.5 cm\\[/tex]
Putting in the above formula
A = (10.8)(2.5)
A = 27 cm²
According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (Consumer fraud and, 2008). (7.1.2)
State the random variable, population parameter, and hypotheses.
Answer:
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
Step-by-step explanation:
Information provided
n=1432 represent the random sample taken
X=321 represent the number of complaints
[tex]\hat p=\frac{321}{1432}=0.224[/tex] estimated proportion of complaints in 2007
[tex]p_o=0.23[/tex] is the value to verify
z would represent the statistic
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
Find the radius of a circle given that the area is three times its circumference
Answer:
Radius of the circle = 6 units
Step-by-step explanation:
Let the radius of the circle be r
According to the given condition:
Area of the circle = 3 times the circumference of the circle
[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]
Roxie is picking out some movies to rent, and she is primarily interested in horror films and documentaries. She has narrowed down her selections to 66 horror films and 1515 documentaries. Step 2 of 2 : How many different combinations of 33 movies can she rent if she wants at least two documentaries?
Answer:
1,085
Step-by-step explanation:
The calculation of number of different combinations of 3 films she can rent if she needs at least two documentaries is shown below:-
[tex]= N\times (2 \times documentaries\ and\ 1\ horror \ movies)+N\times (3\ documentaries)[/tex]
[tex]=(6C_1)\times (15C_2)+(6C_0)\times (15C_3)[/tex]
= 630 + 455
= 1,085
Therefore for calculating the number of different combinations of 3 films she can rent if she needs at least two documentaries we simply applied the above formula and here we consider one number in the question as it shows the double number.
Suppose Carol Danvers invested $1,000 into an account paying 6% annual interest compounded
annually.
How much is in her account at the end of one year?
Answer:
$ 1,060.00
Step-by-step explanation:
A = $ 1,060.00
A = P + I where
P (principal) = $ 1,000.00
I (interest) = $ 60.00
Compound Interest Equation
A = P(1 + r/n)^nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the other. If after 4 hours they are 1800 km apart, find the speed of each plane.
Answer:
The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.
Step-by-step explanation:
Two planes:
The first one's speed is x
The second is y.
One plane is flying at twice the speed of the other.
I will say that y = 2x.
Two airplanes leave an airport at the same time, flying in the same direction
Same direction, so their relative speed is the subtraction of their speeds. 2x - x = x.
Means that after 1 hour, they will be x miles apart.
If after 4 hours they are 1800 km apart, find the speed of each plane
After 1 hour, x km apart. After 4, 1800. So
1 hour - x km apart
4 hours - 1800 km apart
4x = 1800
x = 1800/4
x = 450
2x = 2*450 = 900
The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.
Find the percent of decrease from $2.00 to $1.25
Answer:
37.5
Step-by-step explanation:z
2.0-1.25=0.75
0.75/2.00 x 100
37.5% decrease
The drama club is selling candles for a fundraiser. They spend $100 on the candles and sell them for $4.50 each. How many candles must they sell to make more than $125 profit?
Let x represent the number of candles sold. Which inequality can you use to find x?
So I try to help
Step-by-step explanation:
I don't no sorrry
Answer:
the first one!!
Step-by-step explanation:
Directly above center court, the Yakima SunDome in Yakima, Washington, rises to its maximum height of 92 ft. The angle of elevation from justins parking spot at a Yakama sun kings home to the top of the dome is 11. To the nearest fooot how far from the center court is Justin Parked?
Answer:
473 feet.
Step-by-step explanation:
Let's look at the image below. We have that the angle of elevation from Justin parking spot is 11º and the height of the building is 92 feet and we need to know how far from the building is Justin parked, in other words, we need to find x in the image.
We can see that to find x we can use a trigonometric function (in this case is tan since we have the Opposite side (92 feet) and we need the Adjacent side (x)
Thus we have:
[tex]Tan11= \frac{92}{x} \\0.1943=\frac{92}{x}\\ x=\frac{92}{0.1943}\\ x=473.49\\x=473[/tex]
Thus, Justin is parked 473 feet away from the center court.
