Step-by-step explanation:
the angle of elevation of the sun is θ is related to the given sides of the right triangle (assuming the ground is horizontal and the flag pole is vertical) by tangent.
the shadow is adjacent to the angle while the flagpole is opposite to it.
so to find the angle of elevation:
arctan(20/8.9)
= 66.01 degrees
comment if you have any doubt or need further help.
Angle be alpha
[tex]\\ \rm\Rrightarrow tan\alpha=\dfrac{P}{B}[/tex]
[tex]\\ \rm\Rrightarrow tan\alpha=\dfrac{20}{8.9}[/tex]
[tex]\\ \rm\Rrightarrow tan\alpha=2.25[/tex]
[tex]\\ \rm\Rrightarrow \alpha=tan^{-1}(2.25}[/tex]
[tex]\\ \rm\Rrightarrow \alpha=66.04°[/tex]
Julia has 2 chemistry books and 3 math books. In her rush to get to class, she grabs two books without stopping to look. What is the probability that she pulls out a math book and a chemistry book?
Answer:
P(M &C) = 0.24
Step-by-step explanation:
Chemistry book will be denoted by C
Mathematics book will be denoted by M
5C2 = 10
There are 10 possible ways in which she can choose two books from the 5 books.
The probability of choosing a chemistry book:
P(C) = 2/5
The probability of choosing a mathematics book:
P(M) = 3/5
Probability of choosing a chemistry book and a mathematics book:
P(M &C) = (2/5) × (3/5)
P(M &C) = 0.24 or 24%
The probability that she pulls out a math book and a chemistry book will be 0.24.
What is mean by Probability?The term probability refers to the likelihood of an event occurring
Given that;
Julia has 2 chemistry books and 3 math books.
Now,
Since, Julia has 2 chemistry books and 3 math books.
Hence, Total number of books = 2 + 3 = 5
So, The probability to choosing a chemistry book = 2/5
And, The probability to choosing a math book = 3/5
Thus, The probability that she pulls out a math book and a chemistry book is,
⇒ 2/5 × 3/5
⇒ 6/25
⇒ 0.24
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What whole number should replace C so that the
three values are in ascending order?
27%, С/10, 0.36
Answer:
3
Step-by-step explanation:
3/10 = .3
if 8 pieces is 180 calories how many calories would one piece be?
Answer:
22.5
Step-by-step explanation:
8 pieces is 180 calories to find the calorie of one piece :
180/8 to get 22.5
Given h of x equals 3 times the square root of x plus 2 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, –2).
The function h(x) is decreasing on the interval (2, ∞).
The function h(x) is decreasing on the interval (–∞, 2).
The function h(x) is increasing on the interval (–2, ∞).
Answer:
The function h(x) is increasing on the interval (-2, ∞)
Step-by-step explanation:
Given function: [tex]h(x)=3 \sqrt{x+2}[/tex]
We cannot square root a negative number, therefore the domain (x-values) is restricted:
[tex]x+2\geq 0 \implies x\geq -2[/tex]
Therefore, [tex]h(x)\geq 0[/tex]
⇒ The function h(x) is increasing on the interval (-2, ∞)
Answer:
FLVS ANSWER D- The function h(x) is increasing on the interval (–2, ∞).
Step-by-step explanation:
you dont need one
v(x)=x^2-25
————-
2x^2+13x+15
Describe the domain in complete sentences.
Write the domain in inequality notation.
Answer:
-∞ < x < -5 ∪ -5 < x < -3/2 ∪ -3/2 < x < ∞
Step-by-step explanation:
The domain of any polynomial is "all real numbers." The domain of any rational function excludes any values of the variable that result in the denominator being 0. The function is "undefined" there.
__
[tex]v(x)=\dfrac{x^2-25}{2x^2+13x+15}=\dfrac{(x+5)(x-5)}{(x+5)(2x+3)}\qquad x\notin \{-5,-\dfrac{3}{2}\}[/tex]
The values x=-5 and x=-3/2 make the denominator of v(x) become 0, so those values are excluded from the domain of v(x). The function is "undefined" when its denominator is zero.
-∞ < x < -5 ∪ -5 < x < -3/2 ∪ -3/2 < x < ∞
_____
Additional comment
The numerator and denominator factors (x+5) cancel each other, so there is no vertical asymptote at x=-5. Rather, the function has a "hole" there, where it is undefined. The limit as the function approaches x=-5 from either direction is v(x) = 10/7.
9. Frigid Boards purchases one of its snowboards for $395 less a retail trade discount of 15% and a loyalty discount of 4%. Its markup on selling price percentage on all snowboards is 21%. At the end of the season, any leftover snowboards are marked down by 10%. What is the sale price for the snowboard?
The sale price for the snowboard after the trade and loyalty discount of 15% and 4% will be 351.01 dollars.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Frigid Boards purchases one of its snowboards for $395 less a retail trade discount of 15% and a loyalty discount of 4%. Then the price of the snowboards will be
⇒ $ 395 × 0.85 × 0.96
⇒ $ 322.32
Its markup on selling price percentage on all snowboards is 21%, then we have
⇒ $ 322.32 × 1.21
⇒ $ 390.01
At the end of the season, any leftover snowboards are marked down by 10%, then we have
⇒ $ 390.01 × 0.90
⇒ $ 351.01
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Find the value of y for the given value of x.
y=2−9x;x=2/3
Answer:
-4
Step-by-step explanation:
y=2-9×(2/3)=2-6= -4
If the annual interest rate 4%, how long does it tke for you investment of $10,000 to grow to $15,000
If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years. Hope this helps ! Have a good day! :)
Evaluate −6a^3+8a^2+8a+1, when a=5.
Answer:
-509
Step-by-step explanation:
1. Subsitute 5 for a in the expression. -6(5)^3+8(5)^2+8(5)+1
2. -6(125)+8(25)+40+1
3. -750+200+41
4. -509
I NEED HELP ASAP!!!!!!!!
QUESTION BELOW
Answer:
Step-by-step explanation:
if sin = 3/5, than cos =
Answer:
cos θ = 4/5
Explanation given below in the image,
I hope my answer helps you.
Brennan has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.15 times as many villagers as he had in the one before. The game gave Brennan 5 villagers to start with. Explain to Brennan how to create an equation to predict the number of villagers in any specific town. Then show how to use your equation to solve for the number of villagers he can create to live in the 15th town.
Answer:
Use the geometric sequence formula since you are multiplying each town's villagers by the amount your teacher gave you.
Step-by-step explanation:
Plug in the parts of the formula from the numbers given in the question, then you can calculate the number of villagers needed for the 15th town.
Answer:
35.375 Villagers Live in the 15th village
Step-by-step explanation:
Brennan can use the Geometric Sequence formula to predict the number of villagers in the 15th town.
(work attached)
Find the volume please help I don't understand.
By dividing the figure into a rectangular prism and a pyramid, we will see that the total volume is 2,400 ft^3
How to find the volume?
We can divide the given figure into two simpler ones.
A rectangular prism of 20 ft by 10 ft by 10 ft, whose volume is the product of these dimensions:
V = 20ft*10ft*10ft = 2,000 ft^3
And a pyramid of 4 sides, with a height of 6ft and a base of 20ft by 10ft, and we know that the volume of the pyramid is one-third of the product between the base and the height.
V' = (1/3)*6ft*(20ft*10ft) = 400ft^3
Then the total volume of the given figure is:
volume = V + V' = 2,000ft^3 + 400ft^3 = 2,400 ft^3
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A restaurant has a soup-and-salad lunch with the choices listed in the table below. A soup and a salad are selected at random.
What is the probability that tomato soup and a garden salad are selected?
A 1/6
B 1/5
C 1/3
D 5/6
Answer:
I think it is B) 1/5, but I am not sure.
Felix's kitchen table is round and has a radius of 3 feet. What is the tabletop's area?
use 3.14
Answer:
28.26 ft squared
Step-by-step explanation:
Area is pi*r^2
3.14*(3)^2
3.14*9
28.26
Solve the system of equations using substitution.
y = 2x + 3
y = 3x + 1
a. (-2,-1)
b. (-2,-5)
c. (2,7)
d. (-1,-2)
Answer:
C. (2,7)
Step-by-step explanation:
2x+3 = 3x+1
x=2
y= 2×2+3
y=7
Function g is represented by the table. x -1 0 1 2 3 4 g(x) 24 6 0 -2 Which statement correctly compares the two functions? A. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. C. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞.
The statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Function g is represented by the table.
x -1 0 1 2 3 4 g(x) 24 6 0 -2The line plotted with these data is shown below where y represent the g(x).
In this line,
X-intercept approaches negative infinity (-∞) to positive infinity (∞).Y-intercept approaches -2.426 to 24.86.Thus, the statement which correctly compares the two functions is that they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
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evelyn invests $3200.00 in an account for 9 months at a 5% annual interest rate, what is evelyns total amount in her account at the end of the term?
Answer:
3320
Step-by-step explanation:
So, 9 months is 9/12 of a year which is 3/4.
Each month they get 5/12% of their total money, so 9x5/12=3.75%.
3320
The interest on an investment varies directly as the rate of interest. If the interest is $48 when the interest rate is 10%, find the interest when the rate is 4.3%
Answer:
48×4.3=184 and that is the easy way how to do it
Kurtis is watching a movie. The movie lasts 280 min. Kurtis has watched 30% of the movie so far. How many minutes of the movie has Kurtis watched? Show your Work.
Answer:
ok so this is just multiplycation
30% is also 0.3 so
280*0.3=84
84 minutes or
1 hour 24 minutes
Hope This Helps!!!
Answer: 23810645.03820431-24
Step-by-step explanation:
Used my brain :)
Given that Cos0=5/13,find a)Tan0,b)Sin0,c)Sec0,d)Co sec0,e)Cot0,
cos θ = Adjacent/ hypotenuse
cosθ= 5/13
a²+b²= c²
a² + 5² = 13²
a² = 13² - 5²
a² = 144
a=√144
a= 12
a is the opposite = 12
b is the Adjacent = 5
c is the hypotenuse = 13
a) tan θ= opposite/Adjacent
tan θ = 12/5
b) sin θ= opposite/ hypotenuse
sinθ= 12/13
C) sec θ= hypotenuse / Adjacent
sec θ= 13/5
d) cscθ= hypotenuse /opposite
cscθ= 13/12
e) cotθ=Adjacent/ opposite
cotθ= 5/12
Pls help I cant figure it out ;-;
Answer:
coke red
Step-by-step explanation:
correct me if im wrong
In this picture, m∠XOZ = 77° and m∠YOZ = 40°. If m∠XOY = (5x + 16)°, what is the value of x?
A. 20.2
B. 37
C. 4.2
D. 2.1
PLSSSS HELP!!
Step-by-step explanation:
ang xoz = ang yoz + 5x+16
77 = 44 + 5x+16
77 = 5x+60
5x= 17
x= 3.4
use the equation f(x)=0.003x²-0.083x+2.514. Predict the value for x+20 years.
When x=20 years,f(x)=?
Answer:
2.054
Step-by-step explanation:
put the value of x in f(x)
9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? (Hint : convert data in cm.)
Answer:
1 Shirt and 185cm remaining cloth
Step-by-step explanation:
2m and 15cm = 215cm
40m = 400cm
400/215=1.860465116
A shirt cant be in decimal so we remove the decimals, and take the as the answer. For the decimals, they are the remaining cloth.. to calculate the amount of remaining cloth we do:
1.860465116-1
=860465116
215*860465116=185cm
A storage compartment is shaped like this hexagonal prism. The prism has a base area of 7.35 cm². What is the volume of the compartment? Enter your answer as a decimal in the box.
What is the surface area of this figure?
Enter your answer in the box.
ft²
Which of the following sets of numbers could be the side lengths of a right triangle?
3, 4, and 7
9, 40, and 42
8, 15, and 16
20, 21, and 29
Answer:
9, 40, and 42
Step-by-step explanation:
Answer:
9, 40,and 42 is the answer
Step-by-step explanation:
x^2 + 10x + 21 = 0
Solve for x using "Completing the Square"
Answer:
[tex]x=-7,-3[/tex]
Step-by-step explanation:
Completing the square means you are changing the polynomial so that it is a perfect square trinomial. Since the middle term is 10, we need the last term to be 25 since 5+5=10, thus, 5*5=25:
[tex]x^2+10x+21=0\\x^2+10x+21+4=0+4\\x^2+10x+25=4\\(x+5)^2=4\\x+5=\pm2\\x=-7,-3[/tex]
As you can see, because we change [tex]x^2+10x+21[/tex] to [tex]x^2+10x+25[/tex] by adding 4 to both sides, we were able to reduce it to [tex](x+5)^2[/tex], a perfect square, and solve the rest of the problem.
please help me Find m< G
Answer:
70°
Step-by-step explanation:
All angles in a kite equal 360°.∠F≅∠H. 360-(90+90+110) will get you the answer.
