A meter stick casts a shadow 2.4 m long at the same time a flagpole casts a shadow 9.7 m long. How tall is the flagpole
Answers
We an draw tow similar triangle between the length of the shadows and the height of the stick and the pole.
Since meter stick has a length of 1 meter, the height of our smaller triangle is 1 meter. Let [tex]h[/tex] be height of of the pole. Since both triangles are similiar we can establish a proportion between their corresponding sides and solve for [tex]h[/tex]:
[tex] \frac{h}{1} = \frac{9.7}{2.4} [/tex]
[tex]h=\frac{9.7}{2.4}[/tex]
[tex]h=4.04[/tex]
We can conclude that the pole is 4.04 meters tall.
Related Questions
Name the algebraic property that is being shown in the example: 4(x+3) = 4x + 12
Answers
Jeremy is making a trail mix containing raisins and peanuts. Raisins cost $1.50 per pound. Peanuts cost $2.50 per pound. Jeremy spends $10.50 to make 5 pounds of trail mix. He uses the table below to organize this information. Which equation can Jeremy use to determine the amount of raisins in the trail mix?
a.r + 1.50 = 1.5r
b. r + (5 – r) = 5
c. 1.5r + 2.5(5 – r) = 10.50
d. 1.5r + 2.5(5 – r) = 5
Answers
Answer:
Option C.
Step-by-step explanation:
Let Jeremy mixes "r" pounds of raisins to make a trail mix.
As the total weight of trial is = 5 pounds
So weight of peanuts in the trail mix will be = (5 - r )
Now cost per pound of raisins = $1.50
so cost of r pounds of raisins = $1.50(r)
Cost of the peanuts = $2.50 per pound
so cost of (5 - r) pounds peanuts = $2.50(5 - r)
Jeremy spends total amount = $10.50
So expression will be
Cost of Raisins + cost of peanuts = cost of trail.
1.5r + 2.5(5 - r) = 10.50
Option C. is the answer.
Eric goes for a walk every night after work. A map of the route has a scale of 1:20,000, in cm.
If Eric walked 1.2 kilometers on Monday night, how many cm is the route on the map?
Answers
1.2 km = 120 000 cm.
If the map is made on a scale of 1: 20,000, in cm
So we have to divide 120,000 / 20,000 to know how many centimeters that distance on the map is represented.
Finally the answer is 6 centimeters. That is, 1.2 km equals 6 centimeters on the map
What must you do if you multiply one number in a ratio by n?
Answers
From what I know, when you multiply one number in a ratio, you must also multiply the other number by the same number. This allows for the ratio to stay the same, thus keeping it correct. If both terms were not multiplied by n, the ratio would no longer be the correct ratio.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Help I don’t know the answer to this question
Answers
y intercept, same thing, where x is equal to 0 and it's on the y axis
like the x-intercept would be: (-7,0)
y-intercept: (0,2)
What fraction is equivalent to the repeating decimal 0.18
Answers
Therefore the answer is 2/11!!
Hope this helps!!! :)
P.S. You can check it if you wish by dividing 2 by 11!
x=0.18181818...
The next step is a bit of a trick where we multiply by a power of 10 such that what remains to the right of the decimal is the repeating fraction itself, i.e.
100x=18.1818181818...=18+0.18181818...
which can be re-written
100x=18+x
taking x to the left-hand side we get
99x=18
and finally
x=18/99=2/11
Hope this helps!
A small refrigerator is a cube with a side length of 14 inches. Use the formula S = 6s2 to find the surface area of the cube.
Answers
Surface area = 6 (14)² = 1176 in²
Answer: 1176 in²
Nora created a flag that was shaped by the triangle below.
'\
' \
5in. ' \
' \
'-----------
12in
What is the measure of the third side of the triangle?
A.13in
B.14in
C.17in
D.16in
Answers
A saving account pays 3.6% per annum simple interest Heidi puts £400 into the account, how much will she have in the account after 5 years?
Answers
0.036(400)+400
Because it is 5 years:
5(0.036(400))+400
0.18(400)+400
We can make it simpler:
1.18(400)
Multiply
472
SHE WILL HAVE £472
Using the simple interest formula, Heidi will gain £72 in interest on her initial £400 deposit over 5 years at an interest rate of 3.6%. Therefore, she will have a total of £472 in her account at the end of 5 years.
Explanation:The subject of this question is simple interest calculation which is a topic in Mathematics. It's all about calculating the final amount Heidi will have in her account after 5 years, with a simple interest rate of 3.6% on her initial deposit of £400.
Given the simple interest formula, Interest = Principal × Interest rate × Time, here, the principal is £400, the interest rate is 3.6% (which is 0.036 as a decimal), and time is 5 years.
Using the formula: Interest = £400 × 0.036 × 5 = £72
So, Heidi earns £72 in interest over 5 years.
To find out how much money she will have after 5 years, we will need to add the interest to the initial deposit: Amount = Principal + Interest which gives: Amount = £400 + £72 = £472
So after 5 years, Heidi will have £472 in her account.
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What is the true solution on 2 in e ^in 5x=2 in 15
Answers
In(e^x)=x
2(ln5x)=2ln15
In 5x=In 15
5x= 15
x= 3
genius
How to solve these kind of questions.
Answers
hope this helped
In a '20% off' sale, a coat was £220. Work out the original price.
Answers
0.8p = 220
p = 220/0.8 (This is because we are making p the subject of the formula)
p = 275 (If you are not allowed to use a calculator for this, then: 220/0.8 is the same as 2200/8 because we are just simply multiplying both the numerator and denominator by 10. This can be simply worked out by long division)
1) Set up a proportion:
80/100=220/x
2) Simplify:
4/5=220/x
3) Solve by cross-multiplying:
4x=1100
x=275
Original Price: 275
how many 1 cup servings can be poured from 1 gallon of milk?
Answers
how to graph (-3,4) ;m=6
Answers
We have the point (-3; -4) in the coordinate system.
From this point we go 1 unit to the right and 6 units to the up.
We get the second point.
Draw a straight line.
Look at the picture.
A hose fills a hot tub at a rate of 3.45 gallons per minute. How many hours will it take to fill a 280 -gallon hot tub?
Answers
Q = V / t
Where,
Q: flow
V: volume
t: time
Clearing the time we have:
t = V / Q
Substituting the values:
t = (280) / (3.45)
t = 81.16 minutes
In hours we have:
t = (81.16) * (1/60)
t = 1.35 hours
Answer:
it will take to fill to 280 -gallon hot tub about:
t = 1.35 hours
It will take approximately 1.35 hours to fill the 280-gallon hot tub.
We have,
A hose fills a hot tub at a rate of 3.45 gallons per minute.
This can be written as an expression:
3.45 gallons = 1 minute
Now,
Multiply 280/3.45 on both sides.
280/3.45 x 3.45 gallons = 280/3.45 minutes
280 gallons = 81.16 minutes
Now,
81.16 minutes can be converted into hours.
Divide 81.16 by 60.
So,
81.16/60 = 1.35 hours
Therefore,
It will take approximately 1.35 hours to fill the 280-gallon hot tub.
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Cereal companies often advertise with statements like "collect all 8 dinosaurs" or "one in each specially marked box." Assume that the company sells an equal number of boxes with each type of dinosaur. If you wanted to collect all eight dinosaurs, does this mean that you will only have to purchase eight boxes of cereal? This investigation will help you better understand how theoretical probability compares to experimental probability.
Here are your goals: Use a simulation to determine the experimental probability of a problem. Compare and contrast the theoretical probability with the experimental probability.
Answers
You have a 1/8 chance of getting the dinosaur you want from a box. That means obviously you are significantly more likely to get another less dinosaur. Which it likely won't have lasers and stuff. Which is always sad.
The theoretical probability is far less likely to actually happen than the experimental probability.
From 9:00 AM to 12:00 PM, Linda's stock portfolio increased in value from $2,500 to $6,400. If Linda's portfolio continues to grow at this rate, how much will it be worth at 2:30 PM?
Answers
$6,400-$2,500=$3,900
$3,900/3= $1,300 per hour
12:00pm - 2:30pm = 2.5 hours
$1,300 x 2.5= $3,250
$6,400 + $3250 = $9,650
NEED HELP!!!
Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?
A.) How qualified is the trainer at the computer lab?
B.) Where is the computer lab located in the school?
C.) What is the number of learning stations at the computer lab?
D.) How many class projects did you complete using the computer lab?
Answers
Answer with explanation:
To know the use of Computer Lab in the School
A Survey has been done.Out of the four Question asked,
The education of the trainer in the computer Lab does not come into consideration,to know the use of computer lab in the school, the use of computer lab can be known only by whether students are getting well versed with Computer and it's applications or not.
Number of Learning Stations in the computer lab, also can't tell the use of computer Lab in the school, because we have to check knowledge of the students about computers to know the better use of the Lab.
So, number of Class projects, or in my own words A test on computer awareness and It's software tools will be a better survey Question.
Option D is the question in the survey is a STATISTICAL QUESTION.
(D) How many class projects did you complete using the computer lab?
susan surveys 20 people in her math class to find out the most popular movie. 5 students say star wars if the are 200 students in the total 7th grade using a proportion find out how many students susan would expect to like Star Wars
Answers
x= # of people in 7th gr who like Star Wars
5 out of 20= x out of 200
5/20= x/200
cross multiply
(5*200)= (20*x)
1000= 20x
divide both sides by 20
50= x
ANSWER: 50 people in the 7th grade should like Star Wars.
Hope this helps! :)
Answer:
50 people
Step-by-step explanation:
please rate and thank
A simulated game of chess is programmed between two computers. The game is supposed to be biased in favor of player B winning 4 out of 5 times. Which is the most suspicious set of outcomes of 30 games played between the two computers?
AABABBBABBBBBBBBABBBABBBBBBBBA
ABBABBAABBBBBABBBBBBBBBBBBBABB
ABBABABABABBABABABABABABABABAA
ABBABBBABBBBBBBBABBBABBBBBBBBB
Answers
Answer:
ABBABABABABBABABABABABABABABAA
Step-by-step explanation:
Player B is supposed to be winning 4 out of 5 times. This means that Player A is supposed to win 1 out of 5 times.
This means out of 30 games, player A should win roughly 1/5(30) = 6 times.
In the first list, player A wins 7.
In the second list, player A wins 6.
In the third list, player A wins 15. This is much different.
In the fourth list, player A wins 5.
NEED HELP ASAP!!! Susan makes $5 per hour babysitting and $7 per hour as a life guard. Her goal is to make at least $140. which of the following represents three possible solutions to the problem?
Answers
Number of horus Lifeguard: y
Susan makes $5 per hour babysitting
Money she makes Babysitting: 5x
Susan makes $7 per hour as a life guard
Money she makes as a life guard: 7y
Total money she mahes: 5x+7y
Her goal is to make at least $140:
5x+7y>=140
Answer: First option
5x+7y>=140
spining a spinner that has 5 equal section marked 1 through 5 and landing on an evean number
Answers
Write an inequality involving the variable x that describes the set of numbers graphed.
Answers
The equation above can be used to calculate the volume V, of a pyramid with a height h and base with length l and width w. If the volume of a pyramid is 81inches^3, and l=w=3h, what is the length of the base of the pyramid in inches?
Answers
You know
V=81
l=3h
w=3h
h=3
l=9
w=9
So length is 9 inches
The formula for a pyramid = (1/3) L * W * h The base in this case is square.
Givens
L = W
W =W
L = 3H
H = L/3 = (1/3L)
V = 81 in^3
Solve
V = 1/3 L * W * H
V = 1/3 L * L * 1/3 L
81 = 1/9 L^3 Multiply through by 9
81 * 9 = L^3
729 = L^3 Take the cube root of both sides.
cube root (L^3) = cube root (729)
L = 9 in
what does it mean if the quotient times the divisor does not equal the dividend? What should you do?
Answers
Final answer:
When the quotient times the divisor does not equal the dividend, it means there is a remainder. Depending on the context of the problem, you can round down, express the remainder as a fraction or decimal, or choose another appropriate method.
Explanation:
When the quotient times the divisor does not equal the dividend, it means that the division did not result in an exact whole number. This is called a remainder. For example, if you divide 15 by 4, the quotient is 3 and the remainder is 3. So, 3 times 4 does not equal 15.
If you encounter this situation, you can do a few things. You can round the quotient down to the nearest whole number, or you can express the remainder as a fraction or decimal. It depends on the context of the problem and what is required.
For example, if you are dividing cookies among friends, you may want to express the remainder as a fraction, saying each friend gets 3 and a half cookies. But if you are calculating the number of whole boxes needed, you may round down to 3 boxes.
On a map with a scale of 2 cm = 1km, the distance from Beau's house to the beach is 4.6 centimeters. What is the actual distance?
Answers
GIVEN: 2 cm = 1 km
4.6/2 = 2.3 km
2.3
since 2 cm=1k you divide by 2
A company's profit is described by the equation P(x)=-5x^2+300x+15,000
Where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum profit?
A)$20
B)$30
C$50
D$60
Answers
The formula x = -b / (2a) will produce that x-coordinate:
-(300)
x = ------------ = 30
2(-5)
When x=30 units, y = profit = -5(30)^2 + 300(30) + 15000 = $19500 (answer)
The company charge for the product to generate a maximum profit is $30. Then the correct option is B.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A company's profit is described by the equation
[tex]\rm P(x)=-5x^2+300x+15000[/tex]
Where x is the price in dollars that the company charges for its product.
Differentiate the equation with respect to x.
[tex]\rm \dfrac{dP(x)}{dx}=-10x+300[/tex]
For the maximum price
[tex]\rm \dfrac{dP(x)}{dx} = 0\\[/tex]
Then we have
[tex]\begin{aligned} \rm -10x+300 &= 0\\\\\rm 10x &= 300\\\\\rm x &= 30 \end{aligned}[/tex]
Then the company charge for the product to generate the maximum profit is 30 dollars for each.
More about the differentiation link is given below.
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Solve 120000/1+48e^0.015t=24e^0.055t
Answers
Hideki throws a baseball ball upward with an initial velocity of 12 meters/sec. When he throws the ball, it is two meters above the ground. How long will it take the ball to hit the ground?
Answers
h (t) = (1/2) * (- 9.8) * t ^ 2 + 12 * t + 2
Rewriting we have:
h (t) = -4.9 * t ^ 2 + 12 * t + 2
When the ball hits the ground we have:
-4.9 * t ^ 2 + 12 * t + 2 = 0
Solving the polynomial we have:
t1 = -0.16
t2 = 2.61
We ignore the negative root because it is time.
Answer:
It will take the ball to hit the ground about:
t = 2.61 sec
Answer:
-4.9^2 + 12t + 2 = 0
Step-by-step explanation:
The vanishing point of the picture is represented by point B.
A) The measure of angle ABD is is 6.2 times greater than the measure of angle CBD. Find the measure of angle CBD.
B) Angle FBE and angle EBD are congruent. Find the measure of angle FBE.
Answers
∠ABD + ∠CBD = 180°
6.2(∠CBD) + ∠CBD = 180°
7.2(∠CBD) = 180°
∠CBD = 180°/7.2
∠CBD = 25°
B) Angles EBD and CBD are complementary, so you have ...
∠FBE = ∠EBD = 90° - ∠CBD
∠FBE = 90° - 25°
∠FBE = 65°
To solve this, we use the fact that angles around a point add up to 360 degrees and angles on a straight line add up to 180 degrees. This allows us to find angle CBD to be 50 degrees and angle FBE to be 130 degrees.
Explanation:The subject of this question is geometry, specifically it deals with the properties of angles around a point. In the first part of the question, we are told that angle ABD is 6.2 times greater than angle CBD and we are asked to find the measure of angle CBD. As the total angle around a point is 360 degrees, we can set up the equation ABD + CBD = 360. Given that ABD = 6.2 * CBD, we can replace ABD in our equation, resulting in 6.2* CBD + CBD = 360, solving this gives us CBD = 360/7.2 = 50 degrees.
In the second part of the question, we're told that angle FBE and angle EBD are congruent. This means they have the same measure. Since angle EBD is adjacent to angle CBD and they form a straight line together, their measures add to 180 degrees. Since we already found angle CBD to be 50 degrees, thus angle EBD (or FBE) is 180 - 50 = 130 degrees.
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