South Pole Edition
Your Outdoor Adventures class is providing guidance to a group that is on an expedition to the South Pole. There are 5 people on the expedition.
Due to the extreme climate and conditions, each person in the group needs to consume 6000 calories per day. The table shows the three foods that will make up their total daily calories, along with the number of calories per unit and the daily needs by percentage.
(chart is in the photo i provided)
The map shows the current location of the group, as well as the location of the South Pole and the base camp. Each unit on the grid represents 5 miles. In the question that follow, you will determine whether the group has enough food to reach the South Pole and return to base camp.
Question:
The group thought there was enough food for all 5 group members to complete the trip, with each person getting the required 6000 calories per day. They discover that 2 of the crates they brought are missing.
Each crate contains
•80 biscuits
•50 packages of pemmican
•10 packages of butter and cocoa
Use the map, create a plan for the rest of the trip that includes taking as many group members as possible to the South Pole, while sending the rest of the group members directly back to base camp. Remember that each person must have 6000 calories of food per day until he or she gets back to base camp.
Answers
The group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.
How did we arrive at this assertion?According to the given chart, calculate that each crate contains a total of 48000 calories. Therefore, two missing crates result in a total loss of 96000 calories (48000 x 2).
Determining whether the group has enough food to reach the South Pole and return to base camp, calculate the total number of calories required for the entire trip. Supposing a round trip of 10 days to the South Pole and back, the total number of calories required would be:
Total Calories = (6000 calories/person x 5 people x 10 days) x 2 (round trip)
Total Calories = 600,000 calories
To cover for the lost calories, the group would need to sacrifice one member's trip to the South Pole and send them directly back to base camp. This would leave four members to continue to the South Pole, where they would have to ration their food carefully to make sure they have enough for the entire trip.
Below is a plan to ensure enough food:
Day 1-2:
All five members travel together to position (2,1) and set up camp.Each member would consume 6000 calories per day.Total calories consumed: 5 people x 6000 calories x 2 days = 60,000 caloriesDay 3-5:
Four members (let's call them A, B, C, and D) continue to the South Pole while one member (let's call them E) returns to base camp.E would need 6000 calories per day to return to base camp.Total calories consumed by E: 1 person x 6000 calories x 3 days = 18,000 caloriesA, B, C, and D would have to consume 15000 calories per day (60000 calories ÷ 4 people ÷ 2 days) to make up for the lost calories.Total calories consumed by A, B, C, and D: 4 people x 15000 calories x 3 days = 180,000 caloriesDay 6-7:
A, B, C, and D reach the South Pole and set up camp.They would need 6000 calories per day for 2 days.Total calories consumed: 4 people x 6000 calories x 2 days = 48,000 caloriesDay 8-10:
A, B, C, and D return to position (2,1) and pick up E on the way.They would need 6000 calories per day for 3 days.Total calories consumed: 5 people x 6000 calories x 3 days = 90,000 caloriesAdd up all the total calories consumed:
60,000 + 18,000 + 180,000 + 48,000 + 90,000 = 396,000 calories
This is less than the total calories required, which was 600,000 calories. Therefore, the group does not have enough food to complete the trip with all five members. By sacrificing one member's trip to the South Pole and carefully rationing the food, the group can ensure that each person has enough food to complete the trip safely.
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Related Questions
9. If a resident who has only completed high school is chosen at random, what is the probability that they are under age 50? Round your answer to the nearest thousandth.
10. If a resident who is aged 20-29 is chosen at random, what is the probability that they have completed only high school or just some college? Round your answer to the nearest thousandth.
Answers
To answer these questions, I would need more information about the population being referred to. Specifically, I would need to know the number of residents who have only completed high school and are under age 50, as well as the total number of residents who have only completed high school. I would also need to know the number of residents aged 20-29 who have completed only high school or just some college, as well as the total number of residents aged 20-29.
Do you have this information available?
PLEASE HURRY
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Sunny Town is symmetric
Mean, because Sunny Town is skewed
Median, because Beach Town is skewed
Mean, because Beach Town is symmetric
Answers
Answer:
Median, because Sunny Town is symmetric.
Please help, thanks!
Answers
Answer:
D=2, 3, 5, 6, 7, 8, 9,
Step-by-step explanation:
btw can i js get 1 brainly?
{2,3,5,6,7,8,9}
The union of two sets A and B is defined as the set of all the elements that lie in set A and set B or both the elements in A and B altogether.
Please help hurry! will give brainliest
Answers
Answer: 15/38 or 0.39473684210526315789473684210526
Step-by-step explanation:
Sorry if I'm wrong but I hope this helps! :)
What is the name of the following triangle?
Answers
Answer: Obtuse triangle? The line marked with O and E is more than 90 degrees
Step-by-step explanation:
In the figure, A MNP-AXYZ. Find the value of x.
X
P
+F
M
18
N
Z
27
G 12
Answers
The solution is: the values of x and y is 32° and 51° respectively.
Using the triangle theorem, the values of x and y is 32° and 51° respectively
From △MNP
∠M + ∠N + ∠P = 180° (Sum of interior angles in a triangle)
N = 180 - (142 + 24)
N = 180 - 168
N = 14°
Equate the expression :
2x - 50 = 14
2x = 14 + 50
2x = 64
x = 64 / 2
x = 32°
From ; 2x - y = 13 _____(1)
Substitute x = 32 into the expression ;
2(32) - y = 13
64 - y = 13
64 - 13 = y
51° = y
Therefore, the values of x and y is 32° and 51° respectively.
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complete question:
Find the value of x and y. Triangle MNP = triangle TUS
3. Find the distance from point A
B(-2, 1) D (0.0) A (2.4) C(2,-1)
Answers
The distance between point A (2, 4) and point B (-2, 1) is equal to 5 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-2 - 2)² + (1 - 4)²]
Distance = √[(-4)² + (-3)²]
Distance = √[16 + 9]
Distance = √25
Distance = 5 units.
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Complete Question:
3. Find the distance from point A to B.
A (2, 4) B (-2, 1) C(2, -1) D (0, 0)
What two names can be used to describe this triangle?
Use the drop-down menus to classify the triangle based on its side lengths and
angle measures
Answers
The Triangle is Equilateral and Equiangular.
We will use theses property of Equilateral Triangle as
All three sides of an equilateral triangle have the same length.Each interior angle of an equilateral triangle measures 60 degreesWe have a Triangle.
The Triangle all three angles measured 60 degree each.
and, We know the equilateral Triangle all angles measures 60 degree.
Now, from the figure all the three sides of triangle are equal.
and, we know Equilateral triangle have the three sides equal
Thus, the Triangle is Equilateral and Equiangular.
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A sample is taken from all teen drivers at a high school. They are given a
survey that includes the question, "Do you ever engage in the illegal activity of
texting while driving?" What is this an example of?
OA. Nonselection bias
OB. Nonresponse bias
C. Selection bias
OD. Response bias
Answers
The given scenario, where a sample of teen drivers at a high school is surveyed about their engagement in the illegal activity of texting while driving, is an example of Selection bias. Option C
How to determine what type of exampleSelection bias occurs when the process of selecting participants for a study or survey is not random or representative of the entire population.
In this case, the sample consists only of teen drivers at a high school, which may not accurately represent all teen drivers in the broader population. The sample is limited to a specific group, which can introduce bias and affect the generalizability of the results to the wider population of teen drivers.
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Is the figure shown in the coordinate plane a parallelogram? Why or why not? Use the given coordinates to justify your answer.
Answers
The given image is a parallelogram, because the two lines are Parallel to each other implying that they will never cross each other
What is the coordinate plane?Based on the question above, the coordinates of the figure are:
O = (0,0)
P = (a, b)
S = (a + c, b)
T = (c,0)
Note that the vertices O and T and they can be seen on the same horizontal level, due to the fact that they have the same y-coordinate and can be used also for vertices P and S
The length of the sides by distance formula will be:
PS = c
OT = c
So this implies that the opposite sides are parallel and congruent. Therefore, the image is a parallelogram
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Help pls on test (i need answer quick)
Answers
Answer: Thats a Trapezoid
Step-by-step explanation:
A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.
At Mr. Heritage and Mr. Fraser's old school they are working on making a new sandbox for the kindergarten kids to play in. One design is a 3 m x 3 m x 30 cm. A second design is 3.25 m x 3.25 m x 25 cm. For each design, calculate the area of materials needed to build it (think about the shape, AND what it will look like-sketching it is a good idea AND make the problem real- what would a sandbox LOOK like...), and the volume of sand it will hold. Which design would you recommend?
Find 2 solutions
Answers
Factoring in the dimensions , Design 1 would be the best recommendation because it requires less material and can hold a slightly larger volume of sand in comparison to Design 2.
How do we calculate?For Design 1:
Dimensions: 3 m x 3 m x 30 cm
We find the total area:
Two faces measures 3 m x 3 m = 9 m² each for the bottom and top
Two faces measures 3 m x 30 cm = 0.9 m² each for back and front
Two faces measures 3 m x 30 cm = 0.9 m² each
Therefore the total area of materials needed for Design 1 is found as
= 9 m² + 9 m² + 0.9 m² + 0.9 m² + 0.9 m² + 0.9 m² = 21.6 m²
Design 2:
Dimensions: 3.25 m x 3.25 m x 25 cm
In the same way, we find the area of materials needed for Design 2:
Total area of materials needed for Design 2 = 10.5625 m² + 10.5625 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² + 0.8125 m² = 24.375 m²
Design 1 volume is :
Volume = Length x Width x Height
Volume of sand for Design 1 = 3 m x 3 m x 0.3 m = 2.7 m³
Design 2 volume is :
Volume of sand for Design 2 = 3.25 m x 3.25 m x 0.25 m = 2.40625 m³
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In certain deep parts of oceans, the pressure of sea water,P, in pounds per square foot, at a depth of d feet below the surface, is given by the following equation P=14+ 4d/9
If a scientific team uses special equipment to measure the pressure under water and find it to be 306 pounds per square foot, at what depth is the team making their measurements?
Answers
It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.
The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.
Substituting P = 306 in the equation, we get:
306 = 14 + 4d/9
Multiplying both sides by 9, we get:
2754 = 126 + 4d
Subtracting 126 from both sides, we get:
2628 = 4d
Dividing both sides by 4, we get:
d = 657 feet
The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.
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Find the direction angle of w = 8j
Round your answer to the nearest tenth of a degree
Answers
Rounding to the nearest tenth of a degree, the direction angle of w = 8j is 90.0 degrees.
To find the direction angle of a vector, we can use the formula:
θ = arctan(y/x)
In this case, the vector w is given as w = 0 + 8j, which means its x-component is 0 and its y-component is 8.
Plugging the values into the formula, we get:
θ = arctan(8/0)
However, the division by zero is undefined, indicating that the x-component of the vector is zero, and thus the vector lies along the y-axis.
When a vector lies along the y-axis, its direction angle is either 90 degrees or -90 degrees.
In this case, since the vector is pointing upwards (in the positive y-direction), the direction angle is 90 degrees.
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I need help to answer this math question.
Answers
Scale drawings are valuable tools in various fields such as architecture, engineering, and design, allowing professionals to visualize and communicate ideas accurately. By employing scale factors and maintaining proportions, these drawings provide a reliable representation of real-world objects and spaces.
A scale drawing is a representation of an object or space that is proportional to the actual size or dimensions of the original. It involves using a scale factor, which is a ratio that compares the measurements on the drawing to the measurements of the real object or space. The scale factor determines how much the drawing is enlarged or reduced in relation to the actual size.
When creating a scale drawing, it is important to maintain the same proportion as the original object. Proportion refers to the relationship between the different parts of an object or space, ensuring that the relative sizes are accurate. This ensures that the scaled drawing provides an accurate representation of the original, even if it is smaller or larger in size.
The scale factor is typically expressed as a ratio or a fraction, such as 1:100 or 1/4. This ratio indicates how many times larger or smaller the drawing is compared to the actual object. For example, if the scale factor is 1:10, every unit on the drawing would represent ten units in reality. This allows for accurate measurements of length, as well as area.
Length is an essential aspect of scale drawings. By using the scale factor, the length of lines or dimensions on the drawing can be determined to reflect the corresponding measurements in the real object. For instance, if a line on the scale drawing represents 5 centimeters, and the scale factor is 1:10, the actual length of the line would be 50 centimeters.
In addition to length, scale drawings can also accurately represent areas. The scale factor can be used to determine the relationship between the areas on the drawing and the actual areas of the object or space. By applying the scale factor to the dimensions, the areas can be scaled up or down accordingly, maintaining the proportionality of the original.
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Pedro look out a 4-year loan for $32,500 to help pay his college tuition. He has to pay 4% simple interest on the loan. How much interest will Pedro have to pay?
Answers
The interest Pedro will have to pay is $5200
Calculating how much interest will Pedro have to pay?From the question, we have the following parameters that can be used in our computation:
Principal = $32.500
Rate = 4% simple interest
Time = 4 years
The formula of simple iinterest is
I = Principal * Rate * Time
substitute the known values in the above equation, so, we have the following representation
I = 32500 * 4% * 4
Evaluate
I = 5200
Hence, Pedro have to pay $5200 as interest
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Please help! What is the surface area of the cylinder with height 4 m and radius 8 m? Round your answer to the nearest thousandth.
Make sure to round please.
Answers
The surface area of the cylinder is 948m²
What is surface area of cylinder?The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;
SA = 2πr(r+h)
Where r is the radius of the base and h is the height of the cylinder.
r =8m
h = 4m
SA = 2 × 3.14 × 8 (8+4)
SA = 78.96 × 12
SA = 947.52 m²
to the nearest whole number
SA = 948 m²
therefore the surface area of the cylinder is 948 m²
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4x(3+6) devided by 2
Answers
After considering the given data we conclude that the value generated after performing divison of the given expression is 18x, under the condition that we follow the principles of divison.
Let us proceed by evaluating the given expression by applying division
4x(3+6) divided by 2
= 4x9/2
= 36x/2
= 18x
Division is considered one of the four basic mathematical operations, then the other three are addition, subtraction, and multiplication.
In short , division is referring to the breaking down of a given bigger number or expression into simpler yet smaller forms to meet the criteria of performing a function.
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find the area of the figure 8m, 5m 5m, 15m, 18m A= [?] m^2
Answers
Answer:
302 m²
Step-by-step explanation:
You want the area of the figure composed of a triangle and rectangle.
AreaThe formulas for the areas of the parts are given in the problem statement.
TriangleThe base length of the triangle is (18 m - 5m - 5 m) = 8 m. Then its area is ...
A = 1/2bh
A = 1/2(8 m)(8 m) = 32 m²
RectangleThe area of the rectangle is ...
A = LW
A = (18 m)(15 m) = 270 m²
FigureThe area of the figure is the sum of the areas of its parts:
A = (triangle area) + (rectangle area)
A = 32 m² +270 m² = 302 m²
The area of the figure is 302 m².
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A veterinarian visits an aninal shelter with 147 dogs. 42 are randomly selected for a study. Of tjose selected 14 have a disease. What is the best estimate for the number of dogs that suffer from tge disease? 49, 41,52 or 38?
Answers
Answer:
The answer is 49
Step-by-step explanation:
We can use proportions to estimate the number of dogs in the entire population that have the disease, based on the sample of dogs with the disease.
We know that 42 dogs were selected for the study, and 14 of them had the disease. This means that the proportion of dogs in the sample with the disease is:
14/42 = 0.3333
We can use this proportion to estimate the number of dogs in the entire population that have the disease, by multiplying it by the total number of dogs:
0.3333 * 147 = 49
Therefore, the best estimate for the number of dogs that suffer from the disease is 49.
Solve for x. Assume that lines which appear tangent are tangent.
Answers
The value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3
What is angle subtended by an arcThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
arc TV = 2(m∠TUV)
54x - 2 = 2(80)
54x - 2 = 160
54x = 160 + 2 {collect like terms}
54x = 162
x = 162/54 {divide through by 3}
x = 3
Therefore, the value of x for the angle m∠TUV subtended by the arc TV at the circumference is equal to 3.
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Answer the question by comparing the equation,
f
(
x
)
=
2
cos
(
2
π
6
(
x
+
4
)
)
+
3
to the equation,
f
(
x
)
=
acos
(
2
π
b
(
x
+
c
)
)
+
d
.
What is the period of the function?
Answers
The calculated value of the period of the function is 6
Calculating the period of the function?From the question, we have the following parameters that can be used in our computation:
The equation, f(x) = 2cos(2π/6(x + 4)) +3
A sinusoidal function is represented as
f(x) = acos(2π/b(x + c)) + d
Where the period is B
When the equations are compared, we have
2π/b = 2π/6
This gives
b = 6
Hence, the period of the function is 6
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Complete question
Answer the question by comparing the equation,f(x)=2cos(2π6(x+4))+3 to the equation,f(x)=acos(2πb(x+c))+d.What is the period of the function?
Dependent and Independent Variables
Can you think of a relationship between two quantities in your life? How could you apply your knowledge of dependent and independent variables to the scenario?
Answers
Answer:
Dependent and Independent could be used like a ride on a bike, or even traveling to a friend's house. The dependent variable depends on the independent variable, so let's say I biked at a speed of 7 min per hour and I traveled 42 miles. The independent variable is minutes, because distance depends on time.
Step-by-step explanation:
You roll two fair dice. Find the theoretical probability that the sum of
the outcomes is 2 or 5
Answers
[tex]|\Omega|=6^2=36\\A=\{(1,1),(1,4),(4,1),(2,3),(3,2)\}\\|A|=5\\\\P(A)=\dfrac{5}{36}\approx13.9\%[/tex]
This sentence includes a participial phrase. True or false.
The picture frame held a picture of our family on vacation.
True
False
Answers
The sentence given in the question does not include a participial phrase. Hence, correct option is False
The sentence "The picture frame held a picture of our family on vacation" does not include a participial phrase.
A participial phrase is a phrase that acts as an adjective. In this sentence, the phrase "on vacation" is an adjective phrase that describes the noun "family." However, it is not a participial phrase because it is not formed from a verb.
A participle is a verb form that can be used as an adjective. In this sentence, the verb "hold" is not used as an adjective.
Therefore, the phrase "on vacation" is not a participial phrase.
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Please help!!
Enter the correct answer in the box.
Function g is the result of these transformations on the parent sine function:
• vertical stretch by a factor of 3
• horizontal shift left
units
• vertical shift down 4 units
Substitute the values of A, C, and D to complete the equation modeling function g.
Answers
Answer:
By substituting the values of A, C, and D the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4
Step-by-step explanation:
From the given information, we have;The vertical stretch of the sine function = 3 × The parent function∴ A = 3Given that the horizontal shift left = π/2 units, (from an online source with similar question)The vertical shift down = 4 unitsThe given function, g is g(x) = A·sin(x + C) + DWhere;A = The amplitude = The maximum displacement from the rest or equilibrium position = 3C = The horizontal shift = -π/2 (The negative sign is for the shifting to the left)D = The vertical shift = -4 (The negative sign is for a shift in the downward direction)Therefore, the equation modelling the function is;g(x) = 3·sin(x - π/2) - 4
Factor completely 2x² - 18x + 36.
O 2(x − 6)(x − 3)
O 2(x − 6)(x + 3)
O2(x − 3)(x + 6)
O2(x + 3)(x + 6)
Answers
Answer: 2(x − 6)(x − 3) is the answer
Step-by-step explanation:
Dan will spin this wheel once. What are all the possible outcomes of the experiment? Separate each answer with a comma followed by a space (1 point)
Answers
There are 10 possible results when Dan spins the wheel of destiny with the numbers 2, 4, 6, 8, 10, 12, 14, 16, and 20.
Every possible result is represented by a different number, and Dan has an equal probability of choosing any of them.
The wheel serves as a tool for randomization, adding a degree of ambiguity and unpredictability to the experiment. There are 20 possible outcomes total, with increments of 2 between the lowest and highest numbers.
Thus, these results stand in for various values that Dan might get from spinning the wheel. We may analyse the likelihood and probable range of results for this particular experiment by taking into account all the conceivable possibilities.
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I need an answer ASAP!!!
And also possibly an explanation on how to solve, I really don't understand this.
Answers
4x/3 +x/6=6 can u pls help
Answers
Answer:
Step-by-step explanation:
4x/3 + x/6 =6
get a common denominator first
8x/6 + x/6 =6
then add
9x/6 = 6
multiply by six
9x = 36
divide by 9
x= 4