The plan would be to send 2 group members back to base camp with enough food to sustain them for 5 days, while the remaining 3 members continue to receive 5,600 calories per day from the remaining food supply to complete the journey to the South Pole.
To create a plan for the rest of the trip, we need to consider the total number of days it will take for the group to return to base camp from their current location, and the number of group members who can be taken to the South Pole given the remaining food supply.
Given that the group is missing 28,000 calories, we can calculate the number of days of food that are missing by dividing 28,000 by the daily requirement of 5,600 calories per person. This gives us 5 days of missing food. Therefore, the group has enough food for 5 people to continue to receive 5,600 calories per day for 5 days, but not for all 5 members to continue for the entire trip.
To maximize the number of group members who can continue to the South Pole, we can send two members back to base camp immediately with enough food to sustain them for 5 days (2 people x 5 days x 5,600 calories/day = 56,000 calories). This will leave us with 3 group members who can continue to receive 5,600 calories per day for the remaining journey.
Assuming the trip back to base camp takes the same amount of time as the trip to the current location, we can estimate that the total trip duration will be around 20 days. Therefore, the remaining 3 group members will need a total of 20 days x 3 people x 5,600 calories per day = 336,000 calories.
Given the remaining food supply of 28,000 calories, we have a total of 364,000 calories available (28,000 missing calories + 336,000 required calories). Therefore, the 3 remaining group members can continue to receive their required daily calorie intake and complete the journey to the South Pole.
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The perimeter of a rectangle is
35
cm
35 cm35, start text, space, c, m, end text. The rectangle's area (in
sq. cm
sq. cmstart text, s, q, point, space, c, m, end text) as a function of its length (in
cm
cmstart text, c, m, end text) is graphed.
What is the approximate average rate at which the area decreases, as the rectangle's length goes from
13
cm
13 cm13, start text, space, c, m, end text to
16
cm
16 cm16, start text, space, c, m, end text?
The average rate of decrease of the area as the length goes from 13 cm to 16 cm is given as follows:
D) 11 and 1/3 cm² per cm.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
From the graph, the parameters are given as follows:
Length of 13 cm -> Area of 60 cm².Length of 16 cm -> Area of 24 cm².Hence the rate is approximated as follows:
r = (24 - 60)/(16 - 13)
r = -12 cm² per cm.
Which is closest to option D.
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I answered this on Khan Academy and my lawyer above me has the papers for the work.
See u in court...
Determine the number of triangular films that can be formed by using the measurements a = 17 cm,b = 23 cm, and m∠A = 40°. Solve each triangle. Round to the nearest tenth.
PLS HELP!!!!
The solution of the triangle have been shown below.
How do you solve the triangle?To solve a triangle means to find the values of all its angles and sides. The method for solving a triangle depends on the given information.
Given that;
a/Sin A = b/SinB
Sin B = bSin A/a
B = Sin-1(bSin A/a)
B = Sin-1 (23Sin 40/17)
B = 60.4 degrees
Then we have that
C = 180 - (40 + 60.4)
= 79.4 degrees
Then;
a/sinA = c/Sin C
c= aSin C/Sin A
c = 17 * Sin 79.4/Sin 40
c = 16.71/0.643
c = 25.9
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The point [ -√2/2, √2/2] is the point at which the terminal ray of angle 0 intersects the unit circle. What are the values for the cosine and cotangent functions for the angle 0
O cos0 = -√2/2, cot0=-1
O cos0=√2/2, cot0= 1
O cos0= √2/2, cot0= -1/2
O cos0= - √2/2, cot0= 1/2
PLEASE HURRY
The values for the cosine and cotangent functions for the angle x is
O cos0 = -√2/2, cot0 =-1
How to find the cosine and cotangent angleLet the angle be x
given that the point [ -√2/2, √2/2] is on the terminal ray of angle x
the x-coordinate of the point is -√2/2 and this is the cos hence
cos x = -√2/2.
To find the cotangent
the y coordinate is the sin therefore sin x = √2/2
tan x = sin x / cosx = (√2/2) / (-√2/2) = -1
and cotangent is the reciprocal of the tangent
cot x = 1 / tan x = -1/1 = -1.
cos x = -√2/2 and cot x = -1.
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group of students conduct an investigation to learn more about pea plants. Their data are summarized below. Plant Water per day (mL) Height after 2 weeks (cm) 1 20 11 2 50 18 3 100 24 4 20 16 Which is the independent variable in the investigation?
If Group of students conducted an investigation to learn about "pea-plants", then the "independent-variable" is "Water-per-day (mL)".
The "Independent-Variable" is defined as a variable which is controlled by the researcher.
In the investigation of the "pea-plants", the amount of water per day (mL) given to the plants is the independent variable because it is the variable that is intentionally varied by the students.
The students are manipulating the amount of water given to each plant to observe the effect it has on the height of the plant after two weeks.
By controlling the amount of water given to each plant, the students can determine whether there is a relationship between water intake and plant growth.
Therefore, water given to plants per-day will be the "independent-variable".
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The given question is incomplete, the complete question is
Group of students conduct an investigation to learn more about pea plants. Their data are summarized below.
Plant Water per day (mL) Height after 2 weeks (cm)
1 20 11
2 50 18
3 100 24
4 20 16
Which is the independent variable in the investigation?
In each figure, all b. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain
your answer.
미미미
a. Yes; it is one reflection after another with respect to the two parallel lines.
b. No; it is a reflection followed by a translation.
c. No; it is a reflection followed by a rotation.
d.
No; it is one reflection after another with respect to the two parallel lines.
Answer:
a
Step-by-step explanation:
Find the measure of each angle indicated.
Z
?
A
B
56°
98
O 82°
O 103°
O 121°
42°
C
Answer:
The correct answer is 98°.
Answer: 82
Step-by-step explanation: all the angles of the triangle have to add up to 180 you all up the other angles and you get 98. 98= angle A your trying to find the outside angle we know that a line equals 180 degrees therefore we subtract that angle from 180 and get 82 which is your answer
I need help on 11-12 please i need this done asap! Can someone help me out
For what value of A is the function, (x), continuous at x=0?
(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = 3
(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = -1
(iii) h(0) = 1/7
The value of λ must be 7, for h(x) to be continuous at x = 0.
The given function is,
h(x) = 1/7, when x = 0
= 1 - 2 cos 2x, when x < π/2
= 1 + 2 cos 2x, when x > π/2
= x cos x/sin λx, when x < 0
Now,
(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3
(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1
(iii) h(0) = 1/7
Since the function is continuous at x = 0, so
[tex]\lim_{x \to 0}[/tex] h(x) = h(0)
[tex]\lim_{x \to 0}[/tex] x cos x/sin λx = 1/7
[tex]\lim_{x \to 0}[/tex] cos x.[tex]\lim_{x \to 0}[/tex] 1/λ(sinλx/λx) = 1/7
1/λ = 1/7
λ = 7
Hence the value of λ must be 7.
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brainiest !!!!!!!! this needs to be done asappp
The coordinates best represent the vertex of the graph is given by (1, -2).
Hence the correct option is (D).
Graph is a pictorial representation of a curve or a function or a relation.
From the given graph we can see that the curve is an upward parabola which has vertex at a point other than origin.
We can see that where the vertex is formed the value along X axis is 1 and the value along Y axis is -2 (towards down).
So the vertex of the given graph is at (1, -2).
Hence the correct option will be (D).
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if a1= 9 and =-3a n-1 then find the value of a5
If a₁ = 9 and sequence aₙ = -3aₙ₋₁ , then the value of a₅ is approximately equal to 729.
To find the value of a₅, we need to use the recursive formula provided, which relates each term in the sequence to the previous one. The formula given is a bit unusual, as it defines each term in terms of the negative three times the previous term. However, we can use this information to work out the value of a₅.
Starting with a₁ = 9, we can use the recursive formula to find the next few terms of the sequence:
a₂ = -3a₁ = -3(9) = -27
a₃ = -3a₂ = -3(-27) = 81
a₄ = -3a₃ = -3(81) = -243
a₅ = -3a₄ = -3(-243) = 729
Therefore, the value of a₅ is 729. We can check that this is correct by verifying that it satisfies the given recursive formula:
a₄ = -3a₃ = -3(81) = -243
a₅ = -3a₄ = -3(-243) = 729
This confirms that our solution is correct.
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Select all numbers that are irrational.
Answer:
The irrational numbers are:
368.5468432...
14.19274128...
√.156
CAN SOMEONE HELP WITH THIS QUESTION?
Part(A),
The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and right endpoints is approximately 0.231 square units.
Part(B),
The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.
To estimate the area under the graph of f(x) = 1/(x²+1) over the interval [3, 5] using four rectangles and right endpoints, we can use the following formula:
[tex]R_n = \dfrac{(b-a)}{n} \times [f(x_1) + f(x_2) + ... + f(x_n)],[/tex]
where a = 3, b = 5, n = 4, and xi = a + i(b-a)/n for i = 0, 1, 2, ..., n.
Using this formula with the right endpoints, we get:
[tex]R_4 = \dfrac{(5-3)}{4 }\times [f(3.5) + f(4) + f(4.5) + f(5)][/tex]
R₄ = (1/2) x [0.361 + 0.250 + 0.178 + 0.132]
R₄ = 0.231
Hence, the estimated area under the f(x) graph utilizing four rectangles and the right endpoints over the range [3, 5] is about 0.231 square units.
To repeat the approximation using left endpoints, we can use the following formula:
[tex]L_n = \dfrac{(b-a)}{n} \times [f(x_0) + f(x_1) + ... + f(x_{n-1)],[/tex]
where [tex]x_i = a + i\dfrac{(b-a)}{n}[/tex] for i = 0, 1, 2, ..., n-1.
Using this formula with left endpoints, we get:
[tex]L_4 = \dfrac{(5-3)}{4} \times [f(3) + f(3.5) + f(4) + f(4.5)][/tex]
L₄ = (1/2) x [0.250 + 0.361 + 0.250 + 0.178]
L₄ = 0.2405
Therefore, the estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.
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Amber baked 120 cookies to give to five friends she wants to put the same number of cookies in each bag which of the following can she use to find out how many cookies to put in each bag
Answer:
she can divide the amount of cookies to friends
Step-by-step explanation:
120/5= 24
One meter of shielded microphone cable weighs 75/1,000 kilogram. What is the length of cable in coil that weigh 5 1/2 kilogram
The length of cable in the coil that weighs 5 1/2 kilograms is 1/2 meter.
Let x be the length of cable in meters that weighs 5 1/2 kilograms.
Then, we can write:
1 meter / (75/1000) kilograms = x meters / 5.5 kilograms
Simplifying the left side, we get:
1 meter / (75/1000) kilograms = 1000 / 75 meters/kilogram
= 40/3 meters/kilogram
Substituting this into our proportion, we get:
40/3 meters/kilogram * x meters = 5.5 kilograms
Multiplying both sides by 3/40, we get:
x meters = (5.5 kilograms) * (3/40) * (40/3 meters/kilogram)
= 1/2 meter
The length is 1/2 meter
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Write the slope of tangent and normal to the curve y=f(X) at (x1,y1).
The slope of the tangent line is:
a = (df(x1)/dx)
The slope of the normal one is:
a' = -1/(df(x1)/dx)
How to find the slope of the tangent line?For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.
So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:
df(x1)/dx
And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:
a*(df(x1)/dx) = -1
a = -1/(df(x1)/dx)
Where df/dx reffers to the derivative of f(x).
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a number from 1 to 8 is chosen at random. What is the probability that the number chosen is not even
Answer:
The probability that the number chosen is not even = 4/8
Expand and evaluate the series.
∑6n=13n
{
,
,
,
,
,
}
S6=
Answer:
The series ∑6n=1 3n is a sum of the first 6 terms of the sequence 3n, which starts with n = 1 and increases by 3 for each successive term. Therefore, the first 6 terms of the sequence are:
3(1), 3(2), 3(3), 3(4), 3(5), 3(6)
which simplify to:
3, 6, 9, 12, 15, 18
The sum of these terms is:
∑6n=1 3n = 3 + 6 + 9 + 12 + 15 + 18 = 63
Therefore, S6, the sum of the first 6 terms of the series, is 63.
What is a formula for the nth term of the given sequence?
12,6,3...
Answer:
The given sequence is decreasing by a factor of 2 each time, so each term is half of the previous term.
We can write the nth term of the sequence as:
a_n = a_1 * (1/2)^(n-1)
where a_1 is the first term of the sequence (12 in this case) and n is the position of the term we want to find.
For example, to find the 4th term of the sequence, we would have:
a_4 = 12 * (1/2)^(4-1)
= 12 * (1/2)^3
= 12 * 1/8
= 1.5
Therefore, the formula for the nth term of the sequence 12, 6, 3, ... is:
a_n = 12 * (1/2)^(n-1)
You would like to estimate the prevalence of a disease. You randomly sample 10 people from the population of interest and 4 of them have the condition. Using a Beta prior with αα and ββ both being 1010, what is the posterior mean prevalence closest to?
The required posterior mean prevalence is closest to 0.47.
We can use Bayes' theorem to find the posterior distribution of the prevalence parameter, given the data and the Beta prior:
posterior ∝ likelihood x prior
where the likelihood is given by the binomial distribution:
likelihood = P(observing 4 cases out of 10 | prevalence)
and the prior is a Beta distribution with parameters α = β = 10:
prior = Beta(α=10, β=10)
We can calculate the posterior distribution by multiplying the likelihood and prior, and then normalizing:
posterior = Beta(α=14, β=16)
where the posterior Beta distribution has parameters α=14 (10 + 4) and β=16 (10 + 10 - 4).
The posterior mean of a Beta distribution with parameters α and β is:
posterior mean = α / (α + β)
Plugging in the values of α and β from the posterior distribution, we get:
posterior mean = 14 / (14 + 16) = 0.467
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9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?
Using the expression 5x/12 = 20, the amount that A originally had was $48.
We have,
Let x be the amount of money that A originally had.
Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.
The amount received by B is 1/2 of the remaining amount,
which is (x - x/6)/2 = 5x/12.
We know that 5x/12 = 20,
Solving for x.
5x/12 = 20
5x = 240
x = 48
Therefore,
The amount that A originally had was $48.
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How to solve pre algebra?
Answer:
Pre-algebra is a fundamental branch of mathematics that deals with basic arithmetic operations, such as addition, subtraction, multiplication, and division, and introduces concepts like variables, equations, and inequalities. Here are some general steps to solve pre-algebra problems:
1. Identify the problem: Read the problem carefully and identify what it is asking you to do. Identify the key information and any variables that are given.
2. Translate the problem: Translate the problem into an equation or inequality, using variables to represent unknown quantities.
3. Solve the equation or inequality: Use algebraic manipulation to solve for the variable. Follow the order of operations and simplify the expression as much as possible.
4. Check your answer: Verify that your solution is correct by plugging it back into the original equation or inequality and making sure that it satisfies the conditions of the problem.
It's important to practice pre-algebra problems regularly to develop your problem-solving skills. You can find practice problems and tutorials online or in textbooks, and you can work with a tutor or teacher to get additional help. Remember to stay patient, focused, and positive, and don't be afraid to ask for help if you need it.
139(x-28)
Please help would save a girls lifeee fr fr
Answer:
69
Step-by-step explanation:
(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)
x - 28 = 41
x = 69
An artist is stained glass window that is 3 and 1/2 ft x 2 and 3/4 ft. The artist designed to use squares of colored glass that measures 1/4 ft by 1/4 foot. How many colored squids did the artists use?
Answer:
The artist used 1680 colored squares of glass.
Tommy's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 18 regular sodas and 82 diet sodas. What percentage of the sodas served were regular?
The percentage of the sodas that was served which were regular would be = 18%
How to calculate the percentage of sodas served?The quantity of regular sodas served = 18
The quantity of diet soda served = 82
The total number of soda served = 18+82 = 100
Therefore the percentage of soda that were regular would be;
= 18/100 × 100/1
= 18%
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If 34 x 27 = 918, which of the following is true?
918 ÷ (-34) = 27
-918 ÷ 34 = -27
-918 ÷ 27 = 34
918 ÷ 27 = -34
Help me ASAPP Please :
The simplification of the fractions given above through multiplication would be;
1.) 9 11/12
2.) 11 19/40
How to simplify a given fraction through multiplication?For question 1.)
2 5/6 × 3 2/4
Change the mixed fraction to single fraction;
= 17/6 × 14/4
= 17/6 × 7/2
= 119/12
= 9 11/12
For question 2.)
5 2/5 × 2 1/8
= 27/5 × 17/8
= 459/40
= 11 19/40
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two 6 sided dice are rolled. What is the probability of rolling a number that is not an odd number?
Answer:1/4, 25%
Step-by-step explanation:
even number: 2,4,6
odd umber 1,3,5
even number probability when 1 dice is rolled: 3/6 = 1/2
2 dice is rolled: 1/2*1.2 = 1/4 = 25%
In a class of 50 students, they had a chance to read novel,comics and textbook 21 read novel,24 read comics and 18 read textbook 3 read only novel 9 read only comics and 2 read only textbook 5 read all the 3. illustrate your information on a venn diagram. use your diagram to find the number of students who read a. comics and novel only b. textbook and novel only c. none of the 3
Answer:
Here is a Venn diagram that illustrates the information:
```
___________
| |
| N |
|_____ ____|
|\ || /|
| \ || / |
| \ || / |
| \ || / |
| C \||/ T |
|_____\v/____|
A
```
In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.
Using the Venn diagram, we can find the number of students who read:
a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.
b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.
c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.
Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.
Jodi’s car used 12 gallons of gas to travel 456 miles. How many miles did her car travel per gallon of gas? Show work
Answer:
To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:
miles per gallon = distance traveled / amount of gas used
distance traveled = 456 miles
amount of gas used = 12 gallons
miles per gallon = 456 miles / 12 gallons
miles per gallon = 38 miles/gallon
Therefore, Jodi's car traveled 38 miles per gallon of gas.
Answer:
38 miles
Step-by-step explanation:
Set up your division: 456 / 12
456 divided by 12 is 38
So, Jodi's car travels at 38 miles per gallon of gas.
Solve for AB in simplified, rationalized form:
20/√2 20√2/2 40/√2 10√2
Answer:
AB = (20/√2)(√2/√2) = 10√2