The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 22°. If the vertical distance from the bottom to the top of the mountain is 689 feet and the gondola moves at a speed of 130 feet per minute, how long does the ride last?
Answers
[tex] \sin( \alpha ) = \: \frac{opp}{hyp} [/tex]
[tex] \sin(22) = \frac{689}{hyp} [/tex]
[tex]hyp \: = \frac{689}{ \sin(22) } [/tex]
[tex]speed = \frac{distance}{time} [/tex]
[tex]time = \frac{ \frac{689}{ \sin(22) } }{130} \: \: \:minutes[/tex]
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
Using SOH CAH TOA in right triangle,
[tex]sin 22=\frac{opposite}{hypotenuse}[/tex]
[tex]sin 22=\frac{689}{x}[/tex]
[tex]x=\frac{689}{sin 22}[/tex]
Plugging the value of sin 22
[tex]x=\frac{689}{0.3746}[/tex]
[tex]x=1839.29[/tex] feet
So the distance is 1839.29 feet.
[tex]time=\frac{distance}{speed}=\frac{1839.29}{130}[/tex]
time=14.15 minutes : Answer
Hope it will help :)
Related Questions
What is the place value of 5 in 5.36
Answers
Answer:
5
Step-by-step explanation:
the five is in the ones place so you count five ones and that equals 5
Good luck!
Answer:
ones
Step-by-step explanation:
look at the pic below
Can someone help me
Answers
Answer:
The call it the Donut Eatting Contest
Step-by-step explanation:
okay the first line on that line is 0 in a min then 1 in a min then 2 in a min then 3 in a min then 4 in a min cause she said how many donuts per min
then on each person that eat that many put a x obove the number
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!! I NEED AN ANSWER ASAP!!!!!!!!!!!! 30 POINTS FOR ANSWER:
Use the constant of proportionality to write a unit rate for the data in the table.
(I the constant is 45, so answer the question plz)
Write an equation to represent the relationship between time, t, and distance, d.
Answers
1t+45d
i think. could be wrong.
Therefore the equation should be
D=45t
Joey chestnut is trying to break his own world record for eating the most hot dogs and buns in 10 minutes. He needs to eat more than 72 hot dogs to break his record. After 1 minutes of competition, Joey has eaten 10 hot dogs. Joey wants to know the number of hot dogs per minute that he need to eat for the next 9 minutes to break his own record.
Answers
Answer:
Joey needs to eat 7 hot dogs per minute to break his own record in next 9 minutes.
Step-by-step explanation:
Joey needs more than 72 hot dogs in 10 minutes to break his own record.That means Joey needs to eat at least 73 hot dogs in 10 minutes.
After 1 minute Joey has eaten = 10 hot dogs.
In remaining 9 minutes balance hot dogs = 73-10 =63
Therefore per minute hot dogs to be eaten = 63/9 =7
So answer is 7 hot dogs per minute to be eaten.
Joey needs to eat 7.00 hot dogs per minute for the next 9 minutes to break his own record.
To break his record, Joey Chestnut needs to eat more than 72 hot dogs in 10 minutes. After the first minute, he has already eaten 10 hot dogs. So, he has 9 minutes left to eat the remaining hot dogs needed to break the record, which is 72 - 10 = 62 hot dogs.
To find out how many hot dogs per minute Joey needs to eat for the next 9 minutes, we divide the remaining number of hot dogs by the remaining time:
Hot dogs per minute = Remaining hot dogs / Remaining time
Hot dogs per minute = 62 hot dogs / 9 minutes
Hot dogs per minute ≈ 6.89 hot dogs per minute
Therefore, Joey needs to eat 7.00 hot dogs per minute for the next 9 minutes to break his own record.
It's important to note that Joey needs to eat more than this calculated rate per minute to ensure he breaks his record, as he cannot consume a fraction of a hot dog. So, he should aim to eat at least 7 hot dogs per minute to secure his victory.
PLEEAASSEE HELP!!!!!!!
Answers
Answer would be the third option.
Area of a triangle is half of the base times the height. A=(b·h)/2
In the third option the height is 8 ft. and base is 6 ft. which when multiplied together gets you 48. Half of that is 24.
Hanukkah is an eight day Jewish cele bration which is observed in November or December, as determined by the Hebrew calendar. One of the symbols of Hanukkah is the menorah, a candle holder which holds nine candles. According to thed code of Jewish law, menorah can be a maximum of 20 cubits high. A cubit Is a traditional measurement equal to 18 inches. In feet, what is the maximum height of a menorah, according to the code of Jewish law?
Answers
Answer:
30 feet
Step-by-step explanation:
Interesting question.
1 cubit = 18 inches20 cubits = x1/20 = 18/x Cross multiplyx = 20 * 18x = 360 inches.The maximum height is 360 inches.
1 foot = 12 inchesx feet = 360 inches Cross multiply12x = 360 * 112x/12 = 360/12x = 30The maximum height reached was 30 feet.
Berto invested in a precious mineral. The value of the mineral tends to increase by about 11% per year. He invests $40,000 in 2015.
How much more will his investment be worth in 2020?
Enter your answer in the box.
Round to the nearest whole dollar.
Answers
Answer:
$27402.
Step-by-step explanation:
We have been given that Berto invested in a precious mineral. The value of the mineral tends to increase by about 11% per year. He invests $40,000 in 2015.
Let us write a function using our given information for the value of minerals.
We are told that the value of minerals increase by 11% every year, so our function will be an exponential function.
Since an exponential function is in form: [tex]y=a*b^x[/tex]; for growth b=(1+r), where r is rate of growth in decimal form.
a= Initial value.
Let us convert our given rate in decimal form.
[tex]11 percent= \frac{11}{100}=0.11[/tex]
Let G(t) be the growth of minerals t years after 2015.
Upon substituting our given values we will get our function as: [tex]G(t)=40,000*(1+0.11)^t[/tex]
[tex]G(t)=40,000*(1.11)^t[/tex]
To find the value of Berto's investment in year 2020 by substituting t=5 in our function as 2020-2015=5.
[tex]G(2020)=40,000*(1.11)^5[/tex]
[tex]G(2020)=40,000*1.6850581551[/tex]
[tex]G(2020)=67402.326204\approx 67402[/tex]
Therefore, the value of his investment in 2020 will be $67402.
Let us find the difference of values of minerals between 2020 and 2015.
67402-40000=27402
Therefore, Berto's investment will be worth $27402 in 2020.
Answer:
Step-by-step explanation:
20742
The rectangle below has an area of x^2-6x-7x 2 ?6x?7 square meters and a width of x-7x?7 meters. What expression represents the length of the rectangle?
Answers
Answer:
[tex]x+1[/tex] meters.
Step-by-step explanation:
Let L be the length of rectangle.
We have been given that the rectangle has an area of [tex]x^{2}-6x-7[/tex] square meters and a width of [tex]x-7[/tex] meters.
Since we know that area of rectangle is the product of its length and width.
[tex]\text{Area of rectangle}=\text{Width* Length}[/tex]
[tex]\text{ Length}=\frac{\text{Area of rectangle}}{\text{Width}}[/tex]
To find the length of our given rectangle we will divide area of rectangle by width of our rectangle.
[tex]L=\frac{x^2-6x-7}{x-7}[/tex]
Let us factor out our numerator by splitting the middle term.
[tex]L=\frac{x^2-7x+x-7}{x-7}[/tex]
[tex]L=\frac{x(x-7)+1(x-7)}{x-7}[/tex]
[tex]L=\frac{(x-7)(x+1)}{x-7}[/tex]
Upon cancelling out x-7 from numerator and denominator we will get,
[tex]L=(x+1)[/tex]
Therefore, the length of our rectangle will be [tex]x+1[/tex] meters.
In 1992, Jason bought a gallon of gas for $1.20. Yesterday, he bought a gallon of gas for $2.24. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
Answers
Answer: 86.7%
Step-by-step explanation:
[tex]\dfrac{New - Original}{Original}[/tex]
[tex]\dfrac{\$2.24 - \$1.20}{\$1.20}[/tex]
= [tex]\dfrac{\$1.04}{\$1.20}[/tex]
= 0.867
= 86.7%
Parabola Skate Rental rents skate boards for $4.50 per hour with a rental fee of $35. Arc of Hawk Skate Rental rents skate boards for $5.25 per hour with a rental fee of $25. Rate of change
Answers
Answer: [tex]\bold{13\dfrac{1}{3}\ \text{hours}}[/tex]
Step-by-step explanation:
Parabola Skate Rental: 4.50x + 35
Arc Hawk Skate Rental: 5.25x + 25
If you want to know when their cost will be the same, set the equations equal to each other.
5.25x + 25 = 4.50x + 35
0.75x + 25 = 35 subtracted 4.50x from both sides
0.75x = 10 subtracted 25 from both sides
[tex]x=\dfrac{1000}{75}[/tex] divided both sides by 0.75
x = [tex]13\dfrac{1}{3}[/tex] simplified the fraction
−4x+3y=−2
y=x−1
i need x and y
Answers
Answer:
Rewrite equations:
y=x−1;−4x+3y=−2
Step: Solvey=x−1for y:
y=x−1
Step: Substitutex−1foryin−4x+3y=−2:
−4x+3y=−2
−4x+3(x−1)=−2
−x−3=−2(Simplify both sides of the equation)
−x−3+3=−2+3(Add 3 to both sides)
−x=1
−x
−1
=
1
−1
(Divide both sides by -1)
x=−1
Step: Substitute−1forxiny=x−1:
y=x−1
y=−1−1
y=−2(Simplify both sides of the equation)
Answer:
x=−1 and y=−2
6÷2(1+2)
I WILL GIVE 15 PTS TO CORRECT PERSON
Answers
Answer:
9
Step-by-step explanation:
Make sure to use PEMDAS.
[tex]6/2(1+2)\\\text{Simplify.}\\3(3)\\\text{Simplify.}\\9[/tex]
Simplify the expression where possible.
(r ^-3 s^2 t) ^4
Answers
[tex]Use\\\\(ab)^n=a^nb^n\\\\ (a^n)^m=a^{n\cdot m}\\-------------------\\\\\left(r^{-3}s^2t\right)^4=\left(r^{-3}\right)^4\left(s^2\right)^4(t)^4=r^{(-3)(4)}s^{(2)(4)}t^4\\\\=\boxed{r^{-12}s^8t^4}\to\boxed{\dfrac{s^8t^4}{r^{12}}}[/tex]
To simplify the expression (r⁻³ s² t)⁴, the power of a power rule is used to obtain the result r⁻¹² s⁸ t⁴.
To simplify the expression (r⁻³ s² t)⁴, we apply the power of a power rule, which states that (ab)c = ab*c. Using this rule, we raise each factor within the parentheses to the fourth power:
r⁻³ raised to the 4th power is r⁻¹²s² raised to the 4th power is s⁸t raised to the 4th power is t⁴Therefore, the simplified expression is r⁻¹² s⁸ t⁴.
What are the zeros of the quadratic function? f(z)=3z^2−11z−4 Enter your answers, as simplified fractions if necessary, in the boxes.
Answers
Answer:
z=4 and z=-1/3 are the zero's
Step-by-step explanation:
To find the zeros of the quadratic function, we need to set it equal to zero.
f(z)=3z^2−11z−4
0 =3z^2−11z−4
Now we need to factor the function
0 = (z - 4) (3 z + 1)
Then using the zero product property set each factor to zero
0 = z-4 0 = 3z+1
Now solve
0+4 = z-4+4 0 -1 = 3z+1-1
4 =z -1 = 3z
-1/3 = 3z/3
-1/3 =z
Answer:
z=4 and z=-1/3
Step-by-step explanation:
Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1 key chain. She wants to use at least 5 times as many key chains as thumb drives. She has 25 thumb drives and 200 key chains.
Let x represent the number of key chains. Let y represent the number of thumb drives.
Which inequalities are among the constraints for this situation?
Select each correct answer.
x+y≥50
x≥5y
x≤5y
x+5y≤50
y≤25
Answers
Answer:I Believe the Correct answers are:
x+5y ≤ 50
and
x+y≥50
Answer:
y ≤ 25
x ≥ 5y
x + y ≥ 50
Step-by-step explanation:
Vint is testing ceiling fans in a factory. For one of the tests, he switches the fan on, and after it attains a maximum speed of 500 rotations per minute (rpm), he switches the fan back off, recording the amount of time it takes for the fan to completely stop spinning. The given equation models Vint's test, where x represents time in seconds and y represents the speed in rotations per minute. The equation has been graphed as shown.
Assuming that the test was complete when the fan stopped spinning completely, how long was the test?
A. 100 seconds
B. 10 seconds
C. 20 seconds
D. 500 seconds
Answers
Answer:
C. 20 seconds
Step-by-step explanation:
We want to know when y=0.
We are finding the x intercepts.
The first y is when it started and the second y=0 is when it stops.
Looking at the graph y=0 at x=0 and y=0 at x=20
The fan started at time 0 and stopped at 20 seconds.
The difference is the length of the test.
20-0 = 20
20 seconds
Answer:
20 seconds
Step-by-step explanation:
Given :
[tex]y=-5x^2+100x[/tex]
Where x represents time in seconds and y represents the speed in rotations per minute.
To Find : Assuming that the test was complete when the fan stopped spinning completely, how long was the test?
Solution:
Since we are supposed to find how long will it take to stop the fan completely
We assumed that test was complete when the fan stopped spinning completely
i.e. y = Speed = 0
So, Substitute y = 0 in the equation [tex]y=-5x^2+100x[/tex]
⇒[tex]0=-5x^2+100x[/tex]
⇒[tex]5x^2=100x[/tex]
⇒[tex]5x=100[/tex]
⇒[tex]x=\frac{100}{5}[/tex]
⇒[tex]x=20[/tex]
Thus it took 20 seconds to stop the fan
Hence the test was 20 seconds long.
Ryan has three sticks of lengths 6 inches, 10 inches, and 8 inches. He wants to join the three sticks to form a right triangular base for a model. Discuss whether these sticks form a right triangle. EXPLAIN
Answers
Answer:
yes
Step-by-step explanation:
for the sticks to form a right triangle, the 3 sticks' lengths must comply w the Pythagoras theorem: hypothesis^2 = first side^2 + second side^2
hypothesis is the longest length so its 10
10^2 = 100 = 36 + 64 = 6^2 + 8^2
so the 3 sticks will form a right triangle
Answer:
6^2+8^2=10^2 so yes
Step-by-step explanation:
In order to test a triangle with lengths 6, 8 and 10 inches is right-angle or not, the Pythagoras equation should be used: a^2+b^2=c^2.
As 6^2+8^2=10^2 so yes, the three sticks will form a right-angle triangle.
Sweet T saved 20% of the total cost of the Green-Eyed Fleas new album let there be fleas on earth.If the regular price is $30,how much did sweet T save
Answers
30×(1-20 percent)=24
or 30×(1+20percent)=36
There are about 1.6 km in every mile. Write an expression to represent the approximate number of kilometers in M miles. Then use the expression to find the approximate number of kilometers in 5 miles
Answers
Answer: 1.6M kilometers, 8 kilometers
Step-by-step explanation:
Kilometers per mile times miles gives kilometers.
(1.6 kilometers / mile) × M miles = 1.6M kilometers
5×1.6 is 8
7 3/5 - 4 4/5 because I don’t know what to do with my life anymore :,)
Answers
Answer:
14/5 or 2 4/5
Step-by-step explanation:
7 3/5 = 38/5
4 4/5 = 24/5
38/5 - 24/5 = 14/5 = 2 4/5
the units of volume are always A. cubic units B. square units C. units
Answers
Answer:
Cubic Units
Step-by-step explanation:
Self explanatory
Answer:
the units of volume are always cubic units
Find x.
A) 2√5
B) 3√5
C) 6
Answers
Look at the picture.
ΔABC and ΔDAC are similar. Therefore the sides of the triangles are in proportion:
[tex]\dfrac{AC}{BC}=\dfrac{DC}{AC}[/tex]
AC = x
BC = 5 + 4 = 9
DC = 4
Substitute:
[tex]\dfrac{x}{9}=\dfrac{4}{x}[/tex] cross multiply
[tex]x^2=(9)(4)\\\\x^2=36\to x=\sqrt{36}\\\\\boxed{x=6\to C)}[/tex]
Which of the following values of x makes the rational expression below undefined?
Problem : 16-x/7+x
A. 7
B. -7
C. 16
D. -16
Answers
When the denominator equals zero, that makes it undefined
Answer: The correct option is (B) -7.
Step-by-step explanation: We are given to select the correct values of x that make the following rational expression undefined :
[tex]E=\dfrac{16-x}{7+x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
a rational expression is undefined at the points where the denominator becomes zero.
Therefore, the expression (i) will become undefined when
[tex]7+x=0\\\\\Rightarrow x=-7.[/tex]
Thus, the required value of x where the given expression is undefined is -7.
Option (B) is CORRECT.
*Help ASAP Please! Studying for finals and I'm stuck on this question!*
7. The two small triangles in the following are similar. Find the value of x to the nearest thousandth. (See attached image.)
A) x=32, y=25.6
B) x=12, y=15
C) x=9.6, y=12
D) x=15, y=12
E) None of the above.
Answers
So to find x you must first find y which can be done simply by using the pythagorean theorem. This theorem is defined as the sum of the squared legs is equal to the sum of the hypotenuse or x^2 + y^2 = z^2
If we substitute in the known values 16^2 + y^2 = 20^2 and solve for y we get that y = sqrt(20^2 - 16^2), this then simplifies to y = 12
Finding x is much more annoying, the easiest way I can immediately see is to find the upper angles by doing sin(16/20) and then 90 - sin(16/20) since the complementary angle is the one you want. I don't have a calculator or a trig table with me right now but I will tell you that x will be equal to 12 ÷ the inverse cosine of the angle (90degrees - sin(16/20)).
I am pretty sure the answer is D though because we know for sure y = 12 and x has to be greater than y because the hypotenuse must be larger than both legs. It could be E but you won't know unless you do the math for x. So it is either D or E but I would be surprised if a Professor made you do all of the work just to say it doesn't work...
Jim wants to buy strawberries and raspberries for the company party. Strawberries cost $1.80 per pound and raspberries cost $1.95 per pound. If he only has $15 to spend on berries, which inequality represents the situation where he buys x pounds of strawberries and y pounds of raspberries?
A) 1.80x + 1.95y ≤ 15
B) 1.80x + 1.95y ≥ 15
C) 1.95x + 1.80y ≤ 15
D) 1.95x + 1.80y ≥ 15
Answers
Answer: The answer is A.
Step-by-step explanation: You cant go over the $15 limit and in answer A, the sign shows that 1.80x + 1.95y is less than or equal to 15.
the answer to this question is A
Seattle, WA and San Francisco, CA lie on the same longitudinal line. San Francisco is at 38° latitude and Seattle is at 47° latitude. If the earth is a sphere of radius 4000 miles, use arc length to find the distance between the cities. [Use π = 3.14, and round to the nearest mile.]
A) 628 miles
B) 725 miles
C) 786 miles
D) 841 miles
Answers
Step 1.
Calculate measure of angle α:
[tex]47^o-38^o=9^o[/tex]
Step 2.
Calculate what fraction of the angle 360° is the angle α:
[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]
Step 3.
Calculate the circumference of the Earth (circle):
[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]
Step 4.
The length of arc is equal 1/40 of the circumference:
[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]
[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]
Answer: A) 628 miles
The question uses geometry and the concept of arc length to ask the distance between Seattle and San Francisco on the Earth's surface. The distance between the two cities is calculated to be 628 miles.
Explanation:This is a mathematics problem using geometry, specifically related to the calculation of the arc length. The difference in latitudes between Seattle and San Francisco gives us the angle measurement on the sphere's surface. The difference is 47° - 38° = 9°. Since 9° is 1/40th of a full circle (360°), the arc is 1/40th of the total circumference.
So, to find the distance between the two cities, we calculate 1/40th of the circumference of the Earth (which is 2πr) by using the given radius of the Earth (4,000 miles). The calculation is 1/40 * 2 * 3.14 * 4000 = 628 miles. So, The distance between Seattle and San Francisco via the arc length on the sphere's surface is approximately 628 miles.
Therefore, the correct answer is A) 628 miles.
Learn more about Arc Length here:https://brainly.com/question/37703789
#SPJ11
A _______ is invested by managers in a diversity of stocks, bonds, and other securities.
Answers
Answer:
Mutual Fund
Step-by-step explanation:
A mutual fund is invested by managers in diversity of stocks, bonds and other securities. Mutual fund is an investments that help you grow your money to bigger value. Your money will be used to invest in some companies, products and services to be able to gain more.
It is an investment programmed funded by share holders that trades in diversified holdings and is professionally managed. It pols money from many investors to purchase securities. These investors could be institutional or retail in nature.
Which expression is equivalent to the square root of -80?
Answers
Answer:
sqrt(-80) = 4sqrt(5)i
Step-by-step explanation:
Likely a list of answers should be provided. There are all kinds of possible answers (well 2 perhaps).
Begin by factoring 80 into prime factors.
80: 2*2*2*2*5
For ever pair of 2s, one can be taken outside the square root sign. The other one just disappears.
sqrt(80) = sqrt(2 * 2 * 2 * 2 * 5)
For every pair 2 is taken out of the root sign and the other forgotten
sqrt(2 * 2 * 2 * 2 * 5) = 2 * 2 * sqrt(5) = 4 sqrt(5)
The sqrt(-80) = 4sqrt(5)*sqrt(-1)
There is no real number that can be written as the sqrt(-1). So a number has been defined into existence. sqrt(-1) = i It's a definition, not a real number.
So the end result is sqrt(-80) = 4sqrt(5)i
Julia's frogs are 2 5 of the number of Rimma's frogs. If Rimma gives 1 2 of her frogs to Julia, what will be the ratio of Julia's frogs to Rimma's frogs?
Answers
Answer:
The required ratio is: 9:5
Step-by-step explanation:
Let the number of frog's Rimma has be x
Then Julia's will be [tex]\frac{2x}{5}[/tex]
Now, Rimma give 1/2 of her frog to Julia means now, Rimma will have [tex]x-\frac{1}{2}[/tex] frog
Then Julia's frog will be [tex]\frac{2x}{5}+\frac{1}{2}[/tex]
Now, Rimma will have [tex]x-\frac{x}{2}=\frac{x}{2}[/tex]
And Julia will have [tex]\frac{2x}{5}+\frac{x}{2}=\frac{4x+5}{10}=\frac{9x}{10}[/tex]
Hence, the ratio of Julia's frog to Rimma's frog is [tex]\frac{\frac{9x}{10}}{\frac{x}{2}}[/tex]
[tex]Ratio=\frac{9x\cdot 2}{10\cdot x}[/tex]
[tex]\Rightarrow Ratio=\frac{9}{5}[/tex]
The required ratio is: 9:5
Kellan's lemonade recipe uses 4 scoops of lemonade powder for every 2.5 cuos of water. Kellans uses 18 scoops of lemonade powder to make a batch of lemonade. How much water should he use?
Answers
4/2.5=1.6
1.6*18=28.8