Two hikers start a trip from a camp walking 15 miles due east. They turn north and walk 17 miles to a large pond. How far is the pond from base camp to the nearest tenth of a miles.
Answers
Answer:
22.7 miles
Step-by-step explanation:
The hikers start walking 15 miles due east and then they turn north and walk 17 miles to a large pond.
The shape of their journey can be represented as a right angled triangle, shown below.
To find the distance between the pond and the base camp, we need to find the hypotenuse of the triangle.
We can do this by using Pythagoras theorem:
[tex]hyp^2 = a^2 + b^2[/tex]
where a and b are the other two sides of the triangle. Therefore:
[tex]hyp^2 = 15^2 + 17^2\\\\hyp^2 = 514\\\\hyp = \sqrt{5`4} \\\\hyp = 22.7 miles[/tex]
The pond is 22.7 miles far from the base camp.
Related Questions
answer question please
Answers
Answer:
a) 4.18330013267
b) 7.65643191324
Step-by-step explanation:
Use the calculator to find out the values.
√17.5
=4.18330013267
2.3²+√5.6
5.29+2.36643191324
=7.65643191324
Answer:
a 4.1833
b 7.656
hope its helpful
Sergio wants to glue a ribbon around the top of a cube box with a volume of V. Which expression gives the length of the ribbon?
Answers
Answer:
Length of ribbon = 4 × ∛(V)
Step-by-step explanation:
The question is incomplete without the options of the expression to choose from.
Find attached the diagram used in solving the question.
Volume of a cube = side × side × side
Let side = s
Volume of a cube = side³ = s³
Volume of cube box = V
V = s³
s = ∛(V)
The shape of the top of a cube box is a square.
Length of the ribbon to be used to glue round the top of a cube box = Perimeter of a square
Perimeter of a square = length + length + length + length = 4× length
Length = side
Perimeter of a square = 4×s
Perimeter of a square = 4 × ∛(V)
Length of ribbon = 4 × ∛(V)
Assume that y varies directly with x . Ify = 18when x = 6 , findywhen x = 5 . Write and solve a direct variation equation to find the answer. y =
Answers
Answer:
y = 15
Step-by-step explanation:
It's given in this question that y varies directly with x.
That means, y ∝ x
⇒ y = kx (where k is the proportionality constant)
If y = 18 when x = 6,
⇒ 18 = 6k
⇒ k = 3
Therefore, relation between x and y is,
y = 3x
From this relation, if x = 5
y = 3×5
y = 15
Therefore, for x = 15 value of y will be 15.
Given f(x) = -x – 4, find f(4).
Answers
Step-by-step explanation:
f(4) = -4 -4
= -8
......
.......
Here are two similar cones. The area of the base of the small cone is equal to 36 t cm2. The radius and apothem of the large cone are 9 cm and 15 cm respectively. What is the volume of the small cone? *
( IF YOU CAN DO ALL OF THE STEPS THAT WILL BE VERY HELPFUL)
thx
Answers
V=1/3(pi)(9)^2(15)
V=1/3(3.14)(81)(15)
Then multiply all numbers in parentheses:
3815.1/3=1271.7 cm^3
Hope this Helps!
ASAP 7 POINTS + LINK TO A 50 POINT QUESTION
Which of the following will always represent a function?
1: a table of pairs of numbers
2: an equation in the form y = mx + b
3: a list of ordered pairs
4: a list of numbers
Link to 50 point question: https://brainly.com/question/16753532
Answers
Answer: 2: an equation in the form y = mx + b
1. An x/y table may have two entries with the same x; not a function in that case.
2. That's a line with a slope; for each x there's a single y, definitely a function
3. Ordered pairs -- like the table, the same x with different ys is possible, which wouldn't be a function.
4. List of numbers -- a list isn't a function, at least not without more context
Frank works in the supply room of a law firm. At the beginning of the month, he had 21 boxes of pens with 13 pens in each box. At the end of the month, there were 45 pens left. How many pens did he give out over the month?
Answers
273 - 45 =228
He gave away 228 pens
A printer takes 30 minutes to print a banner and a poster. I will take 50 minutes to print a banner and three posters. How long does it take to print a banner?
Answers
Answer:
It takes the printer 20 minutes to print a banner
Step-by-step explanation:
Notice that there are two unknowns in this problem: the time to print a poster and the time to print a banner. Let's assign the letter "b" to the time it takes to print a banner, and "p' the time it takes to print a poster.
So we can write the following two equations involving the total amount of time that takes to print in the two cases:
[tex]b+p=30\\b+3p=50[/tex]
We can solve for the unknown "p" by subtracting term by term in the equation set above:
[tex]b+3p=50\\b+p=30\\\\b-b+3p-p=50-30\\2p=20\\p=10[/tex]
So it takes 10 minutes to print each poster, we can find the time it takes to print the banner by using the value we just found in one of the equations:
[tex]b+p=30\\b+10=30\\b=20[/tex]
So, it takes 20 minutes to print a banner.
Maria has twenty-one coins in her piggy bank,all which are either dimes or quarters. Maria has $4.20 totally . Write the system of equations that model the situation
Answers
Answer:
x+y= 21
0.10x+0.25y= 4.20
Step-by-step explanation:
You can write a system of equations that model the situation in which one equation would determine the number of coins by adding up all the coins she has and the other one would indicate the total amount Maria has by adding up the results of multiplying the value of each type of coin for the quantity:
x+y= 21
0.10x+0.25y= 4.20
x= amount of dimes
y= amount of quarters
Triangle MNP is similar to triangle QRS. Which sides have the same slope?
Answers
Answer:
The corresponding sides have the same slope so the answer is QR and MN, SR and PN and MP and QS. Hope this helps!
What is the length of CD? In this diagram,
ABC ~ EDC.
Answers
Hey there!
Answer:
CD = 3.
Step-by-step explanation:
Since the triangles are similar, we can set up a ratio to determine the other side-lengths:
[tex]\frac{12-x}{18} =\frac{x}{6}[/tex]
Cross multiply:
[tex]6(12-x) = 18x[/tex]
Distribute the '6':
[tex]72-6x = 18x[/tex]
Combine like terms and simplify:
[tex]72 = 24x[/tex]
[tex]x = 3[/tex]
Therefore, the length of CD is 3.
two similar figures have an area of 25 in^2 and 4 in^2, what is the ratio of the corresponding sides?
Answers
Answer:
5/2
Step-by-step explanation:
ratio of sides=(√25)/(√4)=5/2
There are 4 students at the Math Club picnic. If 2 students are drinking punch
and 2 are drinking lemonade, what fraction are drinking punch?
Simplify your answer as much as you can
Answers
Answer: 1/2
If 2 students are drinking punch
and 2 are drinking lemonade that would mean it would be 2/4
but if you were to simplify by dividing both by 2
it would be 1/2.
what is 5.9736/7.349 reduced to simplest form
Answers
Answer:
I think that the answer would be, 0.813
Step-by-step explanation:
5.8736
7.349
equals 0.812845
If you round it you get 0.813
Find the number of ways a math test can be made with a 20 question test bank and a 15 question test
Answers
Answer: we can make 15,504 different math tests
Step-by-step explanation:
Ok, we have a bank with 20 questions (Q1, Q2........ , Q20)
and we want to make a test with 15 of those 20 questions.
As the order of the questions does not matter in the thest ( is the same if the order is Q1, Q2, ...., Q15 than if the order is Q15, Q14, ....., Q1 )
So we only want the number of combinations.
When we have N elements and we want to create groups of K elements, the total number of combinations is:
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here N = 20 and K = 15
[tex]C = \frac{20!}{5!*15!} = \frac{20*19*18*17*16}{5*4*3*2*1} = 15,504[/tex]
So we can make 15,504 different math tests
Allie need 4 2/3 yards of lace to finish sewing the edges of a blanket. she only has 3/4 of that amount. how much lace does alice have?
Answers
3 1/2 yards
Step-by-step explanation:
She needs 4 2/3 or 14/3 yards
She has 3/4 of that. / of is a sign of multiplication
3/4 of 14/3
3/4 * 14/3
42/12. Simplify
14 / 4. So she has 14/4 or 3 1/2 yards
What are the solutions to the quadratic equation 4x^2 = 64?
A. x = −16 and x = 16
B. x = −8 and x = 8
C. x = −4 and x = 4
D. x = −2 and x = 2
Answers
Answer:
C
Step-by-step explanation:
Given
4x² = 64 ( divide both sides by 4 )
x² = 16 ( take the square root of both sides )
x = ± [tex]\sqrt{16}[/tex] = ± 4
Solutions are x = - 4 and x = 4 → C
24 is 15% of what number
Answers
Answer:
160
Step-by-step explanation:
Is means equals and of means multiply
24 = 15% * N where N is the unknown number
Change to decimal form
24 = .15 N
Divide each side by .15
24/.15 = .15N/.15
160 = N
Answer:
160 because 15% of 160 is 24 meaning 24 is 15% of 160
Step-by-step explanation:
15 POINTS AND WILL MARK BRAINLIEST Help?? Pleasee
Answers
The experimental probability is calculated based on the results of the experiment; since the name Ted was chosen 26 times out of 123, the experimental probability is [tex]\boxed{\frac{26}{123}}.[/tex]
Typically, the theoretical probability assumes that events are chosen randomly; since the name Ted is one of the 6 in the hat, the theoretical probability is [tex]\boxed{\frac{1}{6}}.[/tex]
If we increased the number of names in the hat, we would expect both the experimental and theoretical probability to decrease, since there are now more names to choose from. Similarly, if we decreased the number of names in the hat, the experimental and theoretical probability would increase.
The hypotenuse of right triangle ABC is represented by segment AB, as shown on the graph.
On a coordinate plane, line A B has points (negative 3, negative 4) and (5, 3).
At which point could point C be located?
(–3, 3)
(–3, 2)
(5, –5)
(5, –3)
Answers
Answer:
(-3,3)
Step-by-step explanation:
just took the test on edg.
Answer:(–3, 3)
Step-by-step explanation:
what is the inequality shown
Answers
Answer:
-1
Step-by-step explanation:
Because the nembers before 0 are negitave and the ones after it are positive the equation to find the answer is (-3)(+2) and if you don't know how you add the two like: -3 +2
- negative
+ positive (which also goes for adding 2)
The inequality is shown in that number line 3 ≥ x > 2
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
In order to express inequalities on a number line, we mark a straight line and indicate the endpoints with either an open circle or a closed circle.
An open circle indicates that it does not include the value.
A closed circle indicates that the value is included.
These numbers solution set consists of all real numbers between -3 and 2.
Since 2 has an open circle, it excludes '2,' but it does include everything higher, up to and including -3, which has a closed circle.
Thus, we can represent this using the inequality 3 ≥ x > 2.
Learn more about the number line here:
brainly.com/question/17617832
#SPJ2
Select the values that correctly complete the problem. a = b = c = d = e =
Answers
Answer:
a=2, b=4, c=3
d=2, e=3
Step-by-step explanation:
[tex]\frac{1}{2} :\frac{3}{4} = \frac{1}{2} *\frac{4}{3} =\frac{1}{a} *\frac{b}{c} \\\\\frac{1}{2} *\frac{4}{3} =\frac{2}{3} =\frac{d}{e}[/tex]
a=2, b=4, c=3
d=2, e=3
Answer: a=2, b=4, c=3
d=2, e=3
Step-by-step explanation:
use factoring to solve this x^2-4x-12=0
Answers
Answer:
x= 6 x= -2
Step-by-step explanation:
x^2-4x-12=0
What 2 numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) = 0
Using the zero product property
x-6 =0 x+2 =0
x= 6 x= -2
A rectangular tank 50 cm long, 20 cm wide, and 33 cm high is filled with water to a depth of 12cm. How many more liters of water need to be added to fill the tank?
Answers
Answer:
21 litres
Step-by-step explanation:
1 litre = 1000 cubic cm
The rectangular tank is 50 cm long, 20 cm wide, and 33 cm high.
The tank is in the shape of a rectangular prism.
The volume of a rectangular prism is:
V = l * w * h
where l = length
w = width
h = height
Therefor, its volume is:
V = 50 * 20 * 33 = 33000 cubic cm = 33 litres
The tank is filled to a depth of 12 cm.
The volume of water in the tank is:
V = 50 * 20 * 12 = 12000 cubic cm = 12 litres
Therefore, the number of litres left to fill the tank is:
33 - 12 = 21 litres
The liters of water needed to fill the tank is 21 liters.
Determining the volume of the rectangular tankThe first step is to determine the volume of the tank. The tank has the shape of a cuboid. Thus, the formula for the volume of a cuboid would be used to determine the volume of the tank.
Volume of the tank = length x width x height
50 x 20 x 33 = 33,000
Determination of water needed to fill the tank.1 liter = 1000 cm
33,000 / 1000 = 33
The tank is already filled with 12 liters of water.
Water needed = 33 - 12 = 21 liters
To learn more about volume of a cuboid, please check: https://brainly.com/question/46030
Please help. Thank you!
Answers
Answer:
25 sin 42 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opposite/ hypotenuse
sin 42 = x / 25
Multiply each side by 25
25 sin 42 = x/25 *25
25 sin 42 =x
Answer:
A
Step-by-step explanation:
WILL GIVE BRAINLIEST! Alice, Bob, and Carrie can all choose a number from 1 to 10 (inclusive).
(a) Find the number of ways they can choose their numbers if all three numbers are different.
(b) Find the number of ways they can choose their numbers if they have to choose exactly two different numbers among all three people. (For example, Alice and Bob both pick 1, and Carrie picks 2.)
Answers
Answer:
(a) 720
(b) 180
Step-by-step explanation:
We are given 10 numbers (1,2,3,4,.....,10).
(a) 3 unique numbers are to be chosen by Alice, Bob and Carrie.
Number of ways to choose the 1st number = 10
Number of ways to choose the 2nd number = 9 (1 number chosen earlier can't be chosen again)
Number of ways to choose the 3rd number = 8 (2 numbers chosen earlier can't be chosen again)
Total number of ways of choosing 3 unique numbers = [tex]10 \times 9 \times 8 \Rightarrow 720[/tex]
(b)
Number of ways of choosing 1st number = 10 (no restrictions)
Number of ways of choosing 2nd number = 9 (1 number chosen earlier can't be chosen again)
Now, restriction on the 3rd number to be chosen is that one of the two already chosen number should be chosen again.
So, number of ways to choose 3rd number = 2
the number of ways they can choose their numbers if they have to choose exactly two different numbers among all three people =
[tex]10 \times 9 \times 2 \Rightarrow 180[/tex]
Hence, the answers are:
(a) 720
(b) 180
The members of a men’s club have a choice of wearing black or red vests to their club meetings. A study done over a period of many years determined that the percentage of black vests worn is 70%. If there are 10 men at a club meeting on a given night, what is the probability, to the nearest thousandth, that at least 8 of the vests worn will be black?
Answers
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of the members of a men’s club that wear black vests to their club meetings. This is a binomial distribution since the outcomes are two ways. It is either they wear black or red. The probability of success, p = 70/100 = 0.7
The probability of failure, q would be 1 - p = 1 - 0.7 = 0.3
a) Number of samples, n = 10
We want to determine P(x ≤ 8)
From the binomial distribution calculator,
P(x ≤ 8) = 0.851
Answer:
The probability that at least 8 of the vest worn will be black is 0.75490
Step-by-step explanation:
The parameters given are;
The percentage of black vest worn = 70%, p₀ = 0.7
Number of men in sample, n = 10
Required number of men who wore black = 8
Proportion of sample [tex]\hat p[/tex] = 8/10 = 0.8
The z score of a proportion is given by the relation;
[tex]z = \dfrac{\hat p - p_0}{\sqrt{\dfrac{p_0(1 - p_0)}{n} } }[/tex]
Plugging in the vales, we have;
[tex]z = \dfrac{0.8 - 0.7}{\sqrt{\dfrac{0.7(1 - 0.7)}{10} } } = 0.69[/tex]
From the z table we have probability = p(z < 0.69) = 0.75490
The probability that at least 8 of the vest worn will be black = 0.75490.
Band rues charges $950 to play all night.
DJ phoria charges $350 plus $5 for each ticket sold.
Write a linear equation for the cost of the DJ where y = the total cost and x = the number of tickets sold. The equation for the Band is y = 950.
Graph each equation on the same coordinate plane and find the number of tickets for which the cost of the band and the DJ would be equal. Make sure to name and number the axes of your graph. Also, solve the system of equations analytically, showing all work.
Answers
Answer:
120 Tickets
Step-by-step explanation:
Band rues charges $950 to play all night.
Total Cost, y=$950DJ phoria charges $350 plus $5 for each ticket sold.
Total Cost, y=$(350+5x), x = the number of tickets sold.(a)The graph is attached.
From the point of intersection of the two lines, the number of tickets for which the cost of the band and the DJ would be equal is 120 tickets.
(b)
Given the two linear equations
y=950
y=350+5x
Therefore:
950=350+5x
950-350=5x
5x=600
x=120
Therefore, the number of tickets at which the cost of the band and the DJ would be equal is 120, just as obtained above.
What is the slope of the line represented by the equation y=-
5x?
0-5
or w/N wind
5
Answers
Answer:
the slope would be -5
Step-by-step explanation:
in linear equations, the slope of the line is the coefficient of x
so in this case, it is -5
Chen buys 4 tickets to a soccer game. The total cost before taxes is $80. Which equation would you use to determine the price, p, of the ticket? A 4p=80 B 80p=4 C 4+p=80 D p/4=80
Answers
Answer:
A. 4p=80
Step-by-step explanation:
Total Cost of 4 tickets=$80
Price=p
Quantity=4
Total cost=price×quantity
80=p×4
80=4p
80=4p is the equation that can be used to determine price
From the equation
80=4p
Divide both sides by 4
80/4=4p/4
20=p
Price is $20 per ticket
Answer:
4p = 80
Step-by-step explanation:
Total cost before tax = $80
Number of tickets purchased = 4
Price 'p' of each ticket
p = total price of ticket / number of tickets purchased
p = 80 / 4
Multiplying both sides by 4
4p = 80
