At : a.m. the angle of elevation of the sun for one city is . If the height of a monument is approximately , what is the length of the shadow it will cast at that time? Round to the nearest foot.
Answers
This question is incomplete, the complete question;
At 11:30 a.m. the angle of elevation of the sun for one city is 55.7°. If the height of a monument is approximately 555 ft, what is the length of the shadow it will cast at that time? Round to the nearest foot.
Answer:
the length of the shadow will be 379 ft
Step-by-step explanation:
Given the data in the question and as represented in the diagram below;
height of monument = 555 ft
angle of elevation = 55.7°
From the image below, this makes a right angled triangle
we know that the some of the interior angles of a triangle is 180
so
∠ABC + ∠BCA + ∠CAB = 180°
90° + 55.7° + ∠CAB = 180°
∠CAB = 180° - 145.7°
∠CAB = 34.3°
Now, using sine rule;
BC / sinA = AB / sinC
so we substitute
BC / sin( 34.3°) = 555 / sin( 55.7° )
BC / 0.563526 = 555 / 0.826098
we cross multiply
BC × 0.826098 = 0.563526 × 555
BC × 0.826098 = 312.75693
BC = 312.75693 / 0.826098
BC = 378.595 ≈ 379 ft
Therefore, the length of the shadow will be 379 ft
Related Questions
which equation is correctly rewritten to solve for x?
Answers
explanation
given the function f(x) = 2x^2 - 6x +4. calculate the following values
Answers
Answer:
x^1 = 1, x^2 =2
Step-by-step explanation:
its hard to explain but there's the answer
Consider a fishery in which harvesting is taking placeat a constant rateh. The population at the fisherywill be modeled by
dP/dt = kP- h
Required:
Find the general solution to this DE.
Answers
Answer:
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
Step-by-step explanation:
We are given the following differential equation:
[tex]\frac{dP}{dt} = kP - h[/tex]
Solving by separation of variables:
[tex]\frac{dP}{kP-h} = dt[/tex]
Integrating both sides:
[tex]\int \frac{dP}{kP-h} = \int dt[/tex]
On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then
[tex]\frac{1}{k} \ln{kP-h} = t + K[/tex]
In which K is the constant of integration.
[tex]\ln{kP-h} = kt + K[/tex]
[tex]e^{\ln{kP-h}} = e^{kt + K}[/tex]
[tex]kP - h = Ke^{kt}[/tex]
[tex]kP = Ke^{kt} + h[/tex]
[tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
The general solution to this differential equation is [tex]P(t) = \frac{Ke^{kt} + h}{k}[/tex]
How many vertices does a triangular prism have?
4 5 6 9
Answers
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Vertices are the vertex points. there are 4 vertices at the bottom and 2 vertices at the top which makes 6.
Hope this helps
Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n cubed minus n Over n squared + 5 n EndFraction?
Answers
Answer:
The answer is " The sequence converges to infinity. "
Step-by-step explanation:
Given:
[tex]\to a_n=\frac{n^3-n}{n^2+5n}[/tex]
[tex]\lim_{n \to \infty} a_n= \lim_{n \to \infty} \frac{n^3-n}{n^2+5n}[/tex]
[tex]= \lim_{n \to \infty} \frac{n(n^2-1)}{n(n+5)}\\\\= \lim_{n \to \infty} \frac{(n^2-1)}{(n+5)}\\\\= \lim_{n \to \infty} \frac{n(n-\frac{1}{n})}{n(1+\frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n-\frac{1}{n})}{(1+\frac{5}{n})}\\\\[/tex]
Denominator[tex]= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1[/tex]
Numerator [tex]=\lim_{n\to \infty}n-\frac{1}{n}=\infty[/tex]
[tex]\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty[/tex]
Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.
Carpeted Un-Carpeted
15.9 8.1 15 7.2 10.4 6.1
11.2 16 11.2 6.8 11.3 6.8
8.6 10 12.1 6.3
Requried:
State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.
Answers
Answer:
The null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:
H[tex]_{0}[/tex]: μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].
H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
Step-by-step explanation:
In the question, the given assertion is that carpeted rooms have more bacteria than uncarpeted rooms, i.e. μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
The assertion made in the question can either be the null hypothesis (H[tex]_{0}[/tex]) or the alternate hypothesis (H[tex]_{1}[/tex]). An equality must be present in the null hypothesis. The alternative hypothesis expresses the exact opposite of the null hypothesis if the claim is the null hypothesis.
Therefore, the null (H[tex]_{0}[/tex]) and alternative (H[tex]_{1}[/tex]) hypotheses can be stated as follows:
H[tex]_{0}[/tex]: μ[tex]_{1}[/tex] = μ[tex]_{2}[/tex].
H[tex]_{1}[/tex]: μ[tex]_{1}[/tex] > μ[tex]_{2}[/tex].
Eric wants to buy a new hat
which costs $17. He made
$5 by raking leaves and
$8 by washing cars.
How much more money does he need?
Answers
Answer:
the answer is 4
Step-by-step explanation:
you subtract 13 from 17 =4
Complete the function, count_bases(s). It takes as input a DNA sequence as a string, s. It should compute the number of occurrences of each base (i.e., 'A', 'C', 'G', and 'T') in s. It should then return these counts in a dictionary whose keys are the bases.
Answers
Answer:
The function is as follows:
def count_bases(DNA_str):
retDNA = {}
for i in DNA_str:
if i in retDNA:
retDNA[i]+=1
else:
retDNA[i] = 1
return retDNA
Step-by-step explanation:
This defines the function
def count_bases(DNA_str):
This initializes a dictionary
retDNA = {}
This iterates through the dictionary
for i in DNA_str:
If an item exists in the dictionary
if i in retDNA:
The count is updated by 1
retDNA[i]+=1
Otherwise
else:
The count is set to 1
retDNA[i] = 1
This returns the DAN
return retDNA
The amount of increase from the cost to the selling price is called the?
Answers
Answer:
profit
hope it is helpful to you
Step-by-step explanation:
Markup is the percentage amount by which the cost of a product is increased to arrive at the selling price.
the temperature at 6 pm in frost frozen antarctica was -37 if the tem dropped 8 1 /2 c uring the next hour what was the the temp at 7 pm
Answers
Answer:
-45 1/2
Step-by-step explanation:
ANSWER ASAPPP PLSSS. ILL MARK BRAINLIEST TOO
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
Answers
Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
Answer:
Part A
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
The average rate of growth over the 4 days is .21 cm per day
Step-by-step explanation:
f(n) = 10(1.02)^n
Part A
Let f(n) = 11.04
11.04 = 10 * 1.02 ^n
Divide each side by 10
11.04/10 = 1.02^n
1.104 = 1.02^n
Taking the log of each side
log 1.104 = log 1.02^n
We know log a^b = b log a
log 1.104 = n log 1.02
log 1.104 / log 1.02 = n
4.99630=n
Rounding n to 5
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
To find the average rate of change
f(5) - f(1)
-----------
5-1
f(5) = 11.04
f(1) = 10 *1.02 =10.2
11.04 - 10.2
-----------
5-1
.84
-----
4
.21 cm per day
The average rate of growth over the 4 days is .21 cm per day
As preparation for designing a new line of business wear, a clothing manufacturer asked a large sample of department store customers, "What is your favorite
color of dress shirt?" The ple chart below summarizes their responses.
(a) Which color was chosen by approximately one fourth of
the customers?
Answers
Answer:
white
Step-by-step explanation:
if you cut the shape in half both ways it makes white take up a fourth.
The points P and Q have coordinates (-1, 6) and (9, 0) respectively.
The line l is perpendicular to PQ and passes through the mid-point of PQ.
Find an equation for l, giving your answer in the form ax + by + c =0, where a, b and c are integers.
Answers
Answer:
[tex]3y - 5x +11=0[/tex]
Step-by-step explanation:
Given
[tex]P(x_1,y_1) = (-1,6)[/tex]
[tex]Q(x_2,y_2) = (9,0)[/tex]
Required
The equation of l
First, calculate the slope (m) of PQ
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{0-6}{9--1}[/tex]
[tex]m = \frac{-6}{10}[/tex]
[tex]m = \frac{-3}{5}[/tex]
Since l is perpendicular to PQ, the slope of l is:
[tex]m_2 = -\frac{1}{m}[/tex]
[tex]m_2= -\frac{1}{-3/5}[/tex]
[tex]m_2 = \frac{5}{3}[/tex]
Next, calculate the midpoint of PQ
[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]
[tex]M = \frac{1}{2}(-1+9,6+0)[/tex]
[tex]M = \frac{1}{2}(8,6)[/tex]
[tex]M = (4,3)[/tex]
The equation of l is:
[tex]y = m(x -x_1) + y_1[/tex]
[tex]y = \frac{5}{3}(x -4) +3[/tex]
Multiply through by 3
[tex]3y = 5(x -4) +9[/tex]
Open bracket
[tex]3y = 5x -20 +9[/tex]
[tex]3y = 5x -11[/tex]
Rewrite as:
[tex]3y - 5x +11=0[/tex]
if the volume of a Sphere is 36 pie cm³. then find its radius
I will give brainliest
Answers
Answer: r = 3
Step-by-step explanation:
V=(4/3)πr^3 (this is the formula to identify a volume of the sphere. Since we know that V = 36π, add it into the following formula like so:
36π = (4/3)πr^3; from here we can cancel out the π
36 = (4/3)r^3; multiply both sides by 3/4
27 = r^3;
the final answer is r = 3.
There are 12 squares and 9 circles . What is the simplest ratio of circles to total shapes?
Answers
:) sorry i put the wrong answer before bc i thought i knew it but it was the wrong one and i dont know how to delete the answer sorrryyyyyyyyyyyyyyyy
In the population of young children eligible to participate in a study of whether or not their calcium intake is adequate, 52% are 5 to 10 years of age and 48% are 11 to 13 years of age. For those who are 5 to 10 years of age, 18% have inadequate calcium intake. For those who are 11 to 13 years of age, 57% have inadequate calcium intake.
Required:
a. Use letters to define the events of interest in this exercise.
b. Convert the percents given to probabilities of the events you have defined.
Answers
Answer:
(a) A = 5 to 10 years old
B = 11 to 13 years old
C = adequate calcium intake
I = inadequate calcium intake.
(b) P(A) = 0.52, P(B) = 0.48, P(I|A) = 0.18, P(I|B) = 0.57.
Step-by-step explanation:
Complete question
Please find the attached image
(a) A = 5 to 10 years old
B = 11 to 13 years old
C = adequate calcium intake
I = inadequate calcium intake.
b) P(A) = 0.52, P(B) = 0.48, P(I|A) = 0.18, P(I|B) = 0.57.
Can someone answer with steps and explanation? Thanks.
Answers
Answer:[tex]\color{yellow}{}[/tex]
∆ABC
∆DEF
∆ABC
<C
<D
<X
BE>
CF>
AD>
34>
x9×>
A=3.7
Gemma, a scuba diver, begins a dive on the side of a boat 4 feet above sea level. She descends 28 feet. Which integer represents Gemma’s position with respect to sea level?
–32
Answers
Answer:
-24 feet
Step-by-step explanation:
Boat is 4 feet above sea level => +4 feet
She descends 28 feet => -28 feet
Position = +4-28 = -24 feet
Therefore,
Gemma is 24 feet below the sea level
Answer:
-24 feet
Step-by-step explanation:
Because she is 4 feet above sea level, she can descend 4 feet to be at sea level. Now she only has to descend 24 feet below sea level, which is -24 feet.
what type of data states that every value in the set is a number
Answers
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Step-by-step explanation:
QUALITATIVE DATA-type of data states that every value in the set is a number.
Answer:
QUALITATIVE DATA-type of data states that every value in the set is a number.
What is the domain of the square root function graphed below?
Answers
Answer:
Set the expression inside the square root greater than or equal to zero. We do this because only nonnegative numbers have a real square root, in other words, we can not take the square root of a negative number and get a real number, which means we have to use numbers that are greater than or equal to zero.
Step 2: Solve the equation found in step 1. Remember that when you are solving equations involving inequalities, if you multiply or divide by a negative number, you must reverse the direction of the inequality symbol.
Step 3: Write the answer using interval notation.
If point (x, y) is rotated 90 degrees about the origin, the resulting point is (-y, -x).
True or false?
Answers
Answer:
False
Step-by-step explanation:
Take the point (2, 3) = (x, y)
Rotated 90º clockwise (3, -2) = (y, -x)
Rotated 90º counter clockwise (-3, 2) = (-y, x)
Neither rotation becomes (-3, -2)
You put $600 in a savings account. The account earns 6% simple interest per year.
a. What is the interest earned after 10 years?
b. What is the balance after 10 years?
Answers
what is the area of a rectangular driveway measuring 20 feet long and 15 feet wide?
Answers
Answer:
300 square feet
Step-by-step explanation:
Area is found by multiplying the length and width of a surface
for what value of x does 4x=(1/8)^x+6?
Answer please help
A. -15
B. -3
C. 3
D. 15
Answers
Im sorry but what I got was x=1.5 I don't know if this helps or not.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per
year, compounded monthly. Give your answer accurate to 2 decimal places.
Preview
years.
Answers
Answer:
The time required is of 17.53 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.
This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]
[tex](1.0033)^{12t} = 2[/tex]
[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]
[tex]12t\log{1.0033} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]
[tex]t = 17.53[/tex]
The time required is of 17.53 years.
Learning Task 1: Conduct a survey of the favorite fruit of your classmates and/or friends 10 boys and 10 girls by
sending them messages on messenger or SMS. Use the table to record the data.
Favorite Fruit of My Classmate and Friends
Tally
Fruits
Boys
Girls
1. pineapples
2. ripe mangoes
3. rambutan
4. lansones
5. buko
Answer the following questions:
1. What is the set of data all about?
2. Which fruit is the favorite among the girls Boys
3. What is the least favorite fruit among the girls Boys
4. What is the top choice fruit of both girls and boys
5. What is the least favorite fruit of both boys and girls
Answers
Answer:
1 Its all about there favorite fruits
2 the favorite fruits of the girls are buko less than the boys.
3 the least fruit favorite fruits is pineapple among the girls boys.
4 the top choice of the fruit is the lansones both girls and boys.
5 the rambutan is the least favorite both of them
Step-by-step explanation:
Hope its help po pa brainlest
Answer:
girl
-apple
-masanas
boy
-lansones
-rambotan
sorry yan lang alam ko
Find the area of the figure below (Do Not put the units in your answer)
Answers
Answer:
54
Step-by-step explanation:
Area of rhombus= (12×9) ÷2
5+9+9 divided by 3= ?
Answers
Which of the following best describes the equation below? y = x + 8 OA. function only B. both a relation and a function Oc. neither a relation nor a function OD. relation only?
Answers
9514 1404 393
Answer:
B. both a relation and a function
Step-by-step explanation:
Every linear equation with defined slope is both a relation and a function.
__
Only a vertical line of the form x=constant is linear equation that is a relation, but not a function.
What proportion of families own as opposed to rent their home? To find out, an urban planner selected a random
sample of 400 families in a large city to participate in a survey about homeownership. Of the 362 families that
responded to the survey, 42% reported that they own their home. Which of the following statements about the
survey results is true?
O A suitable estimate of all families who own their home is 42%.
The survey suffers from voluntary response bias and may not accurately represent the population.
O Only 362 responses cannot provide a suitable estimate of families who own their home.
O The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Mark this and return
Save and Exit
fyext
Submit
Answers
Answer:
A suitable estimate of all families who own their home is 42%.
Step-by-step explanation:
42% reported that they own their home.
This means that the sample proportion is of 42%. So that an estimate for the percentage of all families who own their home is of 42%., and that the first option is correct.
Answer:
The correct answer is: The survey suffers from undercoverage and may not provide a suitable estimate of homeownership.
Step-by-step explanation:
I just took the review test. The person above me is wrong