The group wants to travel from its current location on the map to the South Pole, and then directly back to the base camp. How many miles will they have to travel? Explain your answer.
Answers
Using the Pythagorean Theorem, it is found that the group will have to travel 90 miles.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In this problem:
First, the group travels 5 x 5 = 25 miles to the south pole.Then, the distance to the camp is the hypotenuse of a right triangle with sides of 25 miles and of 12 x 5 = 60 miles, hence:[tex]d^2 = 25^2 + 60^2[/tex]
[tex]d = \sqrt{25^2 + 60^2}[/tex]
d = 65.
The total distance is given by:
Td = 25 + 65 = 90 miles.
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Related Questions
Tell whether the ordered pair is a solution of the linear system.
(4, -1)
x + 2y = 2
x - 2y = 6
Answers
Answer:
(4,-1) is a solution
Step-by-step explanation:
x + 2y = 2
x - 2y = 6
We want to see if (4,-1) is a solution to the system.
To do so we plug in x = 4 and y = -1 into both equations and if it is true then the ordered pair is a solution but if one of the equations isn't true then the solution isn't a solution
x + 2y = 2
==> plug in x = 4 and y = -1
4 + 2(-1) = 2
==> multiply 2 and -1
4 - 2 = 2
==> subtract 2 from 4
2 = 2
x - 2y = 6
==> plug in x = 4 and y = -1
4 - 2(-1) = 6
==> multiply -2 and -1
4 + 2 = 6
==> add 4 and 2
6 = 6
Both equations are true therefore (4,-1) is indeed a solution to the system
The cost, y, of red apples can be represented by the equation y = 2x, where x
is the number of pounds of red apples.
The graph shows the cost of green apples.
Which type of apple costs more per pound?
Cost of Green Apples
11
10
PLEASE HURRY I NEED IT IN 5 mins
Cost (5)
.
3
Weight (pounds)
A. Red apples
B. Red and green apples cost the same.
C. Green apples
Answers
Answer:
red apples
Step-by-step explanation:
1 lb of green apples is 1.5
1 lb of red apples is 2
Which polynomial matches the expression -x (x – 3)?
Answers
Answer:
=> -x² + 3x
Step-by-step explanation:
-x (x – 3)
=> -x² + 3x
Kim caught a fish that was 9/10 of a meter long. Doug caught a fish that was 2/3 as long as kim's fish
Answers
Kim caught a fish that was 9/10 of a meter long. Doug caught a fish that was 2/3 as long as Kim's fish. So, Doug caught a fish that was 3/5 meters long.
What is the fundamental principle of multiplication?
If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways
Kim caught a fish that was 9/10 of a meter long. Doug caught a fish that was 2/3 as long as Kim's fish.
Kim caught a fish of length = 9/10 m
Doug caught a fish of length = 2/3 as long as Kim's fish.
= 2/3 x 9/10
= 18 / 30
= 3/5
Thus, Doug caught a fish that was 3/5 meters long.
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In how many ways can she grab 3 Snickers, 2 Starbursts, and 2 Reese's?
Answers
(1) Basket (2) Hands (3) Cart. 3 ways i can think of
solve for x : -172 = -11x + 4
Answers
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Alright so:
-172 = -11x + 4
-4 - 4 (-4 on both sides)
so,
-176 = - 11x
divide by -11
so,
-11x ÷ - 11 = x
-176÷-11= 16
x=16
When finding an indefinite integral, your answer must include:.
Answers
Answer:
is the set of infinitely many primitives that a function can have. It is represented by ∫ f(x) dx. It reads: integral of x differential of x. ∫ is the integration sign.
What is the measure of WV
(Value of x is 19)
Answers
Please hurry... Have a blessed day!
Answers
Answer:
A
Step-by-step explanation:
divide all sides by four and you get first answer.
divide every side by 4, and you get the results
Evaluate a+4a+4a, plus, 4 when a=7a=7a, equals, 7
Answers
(But if not it’s 60)
Answer:
the answer is 11
Step-by-step explanation:
pls help complete the sequence
Answers
Step-by-step explanation:
1,2,4,8,16,32,64,128
Multiplying by 2
1,3,5,7,9,11
Adding 2
30, 25, 20, 15, 10, 5
Subtracting 5
Answer:
1,2,3"8"16,32"64"128
1"3"5,7"9"11
30"25""20"15,10,5
Step-by-step explanation:
by x2
My sister needs help again MATHHH
Answers
Answer:
31
Step-by-step explanation:
PEMDAS is Parentheses, Exponent, Multiplication, Addition, Subtraction
This is just the order you do the operations.
First, Parentheses.
Second, Exponents,
Third, Multiplication or Division
Last, Addition or Subtraction
So we have,
[6(20) + 3(15)] ÷ 5
We first look at Parentheses.
The first case is 6(20)
6(20) = 120
We have [120 + 3(15)]÷ 5
We solve 3(15) as its the next parentheses
3(15) = 45
We have [120 + 45] ÷ 5
Then we solve for [120 + 45] as it's in brackets.
[165] ÷ 5 = 31
The answer is 31.
Queetlon 10 or 15
People leaving the library were aaked how many books they checked out that
day The resulta are:
1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
Which histogram correctly ahows the data set?
Books Checked Out
0-5 6-11 12-1718-23
Number of booke
Books Checked Out
Answers
Answer:
[B]
Step-by-step explanation:
Given:
People leaving the library were asked how many books they checked out that day The result are: 1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
To Find:
Which histogram correctly shows the data set?
Solution:
Since it given from the histogram:
0-5, 6-11, 12 - 17,18-23
From the result :
1,2, 3, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20
Thus,
1,2,3,5 = 0-5
8,9,10,11 = 6-11
12,13,14,15,16 = 12-17
18,20 = 18-23
From this we can see that:
for
0 - 5 = 4
6 - 11 = 4
12 - 17 = 5
18 - 23 = 2
Hence, the answer is [B]
Kavinsky
Harper has a bag that contains apple chews, cherry chews, and lime chews. She
performs an experiment. Harper randomly removes a chew from the bag, records the
result, and returns the chew to the bag. Harper performs the experiment 38 times.
The results are shown below:
An apple chew was selected 22 times.
A cherry chew was
selected 6 times.
A lime chew was selected 10 times.
Based on these results, express the probability that the next chew Harper removes
from the bag will be lime chew as a percent to the nearest whole number.
Answers
The question says that out of the 38 chews taken out of the bag, 10 of them were lime chews. All we need to do to answer this question is to put that into a percentage. We can do this by doing 10/38 and then multiplying by 100. This will give 26.32%. Since we want this to the nearest whole number we will round to 26%.
Hope this helps
If f(1) = 1 and f(n) = 5f(n-1) + 4 then find the value of f(5).
Answers
Answer:
[tex]f(5)=1249[/tex]
Step-by-step explanation:
Given:
[tex]f(1)=1[/tex][tex]f(n) = 5f(n-1)+4[/tex][tex]\implies f(2) = 5f(1)+4=5(1)+4=9[/tex]
[tex]\implies f(3) = 5f(2)+4=5(9)+4=49[/tex]
[tex]\implies f(4) = 5f(3)+4=5(49)+4=249[/tex]
[tex]\implies f(5) = 5f(4)+4=5(249)+4=1249[/tex]
Richard and Cameron buy a carton containing 6 66 eggs. The back of the carton says, "The expected number of broken eggs per package is 0.12 0.120, point, 12." Richard says, "The probability that one of these cartons contains a broken egg is 0.12 0.120, point, 12, on average." Cameron says, "For every 100 100100 packages like this, we'd predict about 12 1212 broken eggs in total." Whose statement is correct based on the expected value?
Answers
Using the binomial distribution, it is found that Cameron's statement is correct based on the expected value.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np.
In this problem, we have that:
The probability of a package containing a broken egg is of p = 0.12.There is a sample of 100 packages, hence n = 100.Thus, the expected value is given by:
E(X) = np = 100 x 0.12 = 12.
Hence, Cameron's statement is correct.
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1. Let the sample space represent all the values from 1 to 10. Let A = {1, 2, 8} and B = {2, 7}. What is the P(A ∩ B)?
Answers
Answer:
It's {2} since it's the common between A and B
an equation for 72th term in 4,7,10,13
Answers
Answer:
[tex]\huge\boxed{\bf\:Equation: a_{72} = 4 + (72 - 1)3}[/tex]
[tex]\huge\boxed{\bf\:a_{72} = 217}[/tex]
Step-by-step explanation:
Let the series be: 4, 7, 10, 13,.....
Given,
First term (a) = 4Common difference (d) = [tex]a_{2} - a_{1} = 7 - 4 = \bf\:3[/tex]Number of terms (n) = 72[tex]72^{nd}[/tex] term of the series ([tex]a_{72}[/tex]) = ?We know that,
[tex]\bf\:a_{n} = a + (n - 1)d[/tex]
Equation for the [tex]72^{nd}[/tex] term of the series,
[tex]\boxed{\bf\:a_{72} = 4 + (72 - 1)3}[/tex]
By using this formula & substituting the values,
[tex]a_{72} = 4 + (72 - 1)3\\a_{72} = 4 + (71)3\\a_{72} = 4 + 213\\\boxed{\bf\:a_{72} = 217}[/tex]
•°• The [tex]72^{nd}[/tex] term of the series is 217.
[tex]\rule{150pt}{2pt}[/tex]
A company makes an ice-cream treat in the shape of a hemisphere on top of a cone, as shown below.
2 cm
10 cm
Answers
Answer:
56/3 pi cm^3
Step-by-step explanation:
1/2 volume of sphere = 1/2 4/3 pi r^3
volume of cone 1/3 pi r^2 h
r =2 h = 10
result : 56/3 pi cm^3
The volume of the ice cream is 58.64 cubic cm.
What is a three dimensional figure?A three dimensional figure has three dimensions as length, breadth and height. The volume of a three dimensional figure is the amount of the substance contained by it.
Given that,
The height of cone part of the ice cream is h = 10 cm.
The radius of the hemisphere is r = 2 cm.
As per the diagram given the radius of the hemisphere is equal to the radius of cone as 2 cm.
The volume of hemisphere is given as (2/3) × πr³.
And, the volume of cone is given as (1/3) × πr²h.
Now, the volume of the ice cream treat is equal to the sum of the volume of cone and hemisphere as,
V = (1/3) × π × r²h + (2/3) × π × r³
Substitute the values to get,
V = (1/3) × π × 2² × 10 + (2/3) × π × 2³
= (56/3) × π
= 58.64
Hence, the volume of the ice cream treat is 58.64 cubic cm.
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In a box there are 11 similar balls where 8 are red and the remaining are blue. if we draw one ball at random.then what is the probability to draw a blue ball?
Answers
Answer:
27%
Step-by-step explanation:
There are 11 balls in total. If 8 are red, (11-8) are blue =3
3/11 is the fraction of blue balls. Convert to percent =27%
Which of the following is an equivalent expression to the expression a1/3 / a1/4
A. A1/12
B. A7/12
C. 1/1/1/a12
D. 1/7/a12
Answers
Answer:
Option A :- [tex] \sf {a}^{\frac{1}{12}} [/tex]
Step-by-step explanation:
[tex] \hookrightarrow \sf \: \frac{ {a}^{ \frac{1}{3} } }{ {a}^{ \frac{1}{4} } } [/tex]
Simplify the expression
[tex] \hookrightarrow \sf \: {a}^{ \frac{1}{3} - \frac{1}{4} }[/tex]
Transform the Expression
[tex] \hookrightarrow \sf \: {a}^{ \frac{4 - 3}{12} }[/tex]
Calculate
[tex] \hookrightarrow \sf {a}^{\frac{1}{12}} [/tex]
A museum receives an average of 488 visitors per day. The museum 15 open every day. A. Estimate the number of visitors the museum receives during a month.
Answers
An estimate of the number of visitors that vist the museum during a month given the average number of visitors per day is 15,128.
What is multiplication?
Multiplication is an arthmetic operation that can be used to determine the product of a number. The sign used to denote multiplication is x.
How many visitors does the museum have in a month?
In order to determine this value, multiply the average daily visitors by the number of days in a month
488 x 30 = 15,128
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pls help me solve this answer its urgent
Answers
Answer:The equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
Step-by-step explanation:Lines that are perpendicular to each other have slopes that are negative reciprocal of each other.
For example, if a line has a slope of 2, the slope of a line that is perpendicular to it would be, -1/2 (negative reciprocal of 2).
Determine the slope of the given line whose equation is, y + 2 = 3/2(x + 4). Rewrite the equation in slope-intercept form [y = mx + b]:
y + 2 = 3/2x + 6
y = 3/2x + 6 - 2
y = 3/2x + 4
The slope is therefore 3/2.
Negative reciprocal of 3/2 is -2/3.
Examine each of the equations given and see which equation has a slope of -2/3.
A. y = -3/2x +4, the slope is -3/2.
B. y = -2/3x + 4, the slope is -2/3. (perpendicular)
C. y = 2/3x +4, the slope is 2/3.
D. y = 3/2x +4, the slope is 3/2.
E. y+1=-4/6(x+5), rewrite in slope-intercept form
y+1=-4/6x + 20/6
y + 1 = -2/3x + 10/3
The slope is -2/3. (perpendicular)
F. y+ 1 = 3/2(x + 5), the slope is 3/2.
Therefore, the equations representing the lines that are perpendicular to line m are:
B. y = -2/3x +4
E. y+1=-4/6(x+5)
If the quadratic equation x2 + 6x + 19 = 0 is rewritten in the form (x - p)2 = q ,
what is the value of p and q
Answers
Answer:
p = -3
q = -10
Step-by-step explanation:
[tex]x^{2}+6x+19=x^{2}+6x+9+10[/tex]
[tex]\text{we know that} \ x^{2}+6x+9=\left (x+3)^2\right\ \text{ because it is a special product}[/tex]
[tex]\text therefore \ ,\ x^{2}+6x+19=(x + 3)^2+10[/tex]
[tex]\text therefore \ ,\ x^{2}+6x+19=0 \ means\ (x + 3)^2= -10\ means\ (x -\ - 3)^2= -10[/tex]
-5=0.1x-8.5 what is the answer
Answers
Answer:
x = 35
Step-by-step explanation:
hope this helps
Answer: x = 35
Step-by-step explanation:
-5 = 0.1x - 8.5
Step 1: Rewrite the equation:
0.1x - 8.5 = -5
Step 2: Add 8.5 on both sides.
0.1x = 3.5
Step 3: Divide 0.1 on both sides.
x = 35
i really need help ASAP
Answers
Answer:
B
Step-by-step explanation:
2q+437= 931
subtract 437
2q= 494
divide by 2
q= 247
i need answer please
Answers
Answer:
∠ BED = 57°
Step-by-step explanation:
angles on the circumference subtended by the same arc are congruent,
∠ BCD and ∠ BED are both subtended by arc BD , then
∠ BED = ∠ BCD = 57°
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A test of 10 different types of candy are being tested. If a person is given 6 of the candies to taste how many combinations are possible?
Answers
A box contains ten cards labeled Q,R,S,T,U,V,W,X,Y, and Z. One card will be randomly chosen. What is the probability of choosing a letter from Q to T?
Write your answer as a fraction in simplest form.
Answers
Answer:
4/10 = 2/5 = 40%
Step-by-step explanation:
Q,R,S,T = 4
Q R S T U V W X Y Z =10
Which table represents a function?
X y
-4 6
0 8
4 12
X y
-4 3
-2 6
-2 9
X y
-3 7
-1 9
-3 -7
X y
1 2
1 6
2 10
Answers
Answer:
-2x+4>18.
Step-by-step explanation:
Solve and graph a one variable inequality. Solve the inequality and graph the solution on a number line.