The distance the visitor should run to minimize the time it takes to reach the rock formation is 3/4 miles.
A unitary method is a mathematical technique used to solve problems involving proportional relationships between different quantities.
Let's use the unitary method to find the time it takes to complete the journey.
Time taken to run = Distance / Rate = x / 4
Time taken to swim = Distance / Rate = (3 - x) / 3
Total time taken = Time taken to run + Time taken to swim
= x / 4 + (3 - x) / 3
To minimize the total time taken, we need to find the value of x that minimizes the above expression. Let's differentiate it with respect to x and equate it to zero.
d/dx (x/4 + (3-x)/3) = 1/4 - 1/3 = -1/12
-1/12 = 0 (at minimum)
Solving for x, we get:
x = 3/4
The visitor should run westward along the shoreline until reaching the point 3/4 miles away from the tent, and then swim the remaining 2 1/4 miles to reach the rock formation.
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A water sample shows 0.03 grams of some trace element for every cubic centimeter
of water. Brianna uses a container in the shape of a right cylinder with a radius of 9.6
em and a height of 11.6 cm to collect a second sample, filling the container all the
way. Assuming the sample contains the same proportion of the trace element,
approximately how much trace element has Brianna collected? Round your answer to
the nearest tenth.
According to the solving volume of the cylinder where the Brianna has collected approximately 99.1 grams of trace element (rounded to one decimal place).
Define volume of cylinder?The cylinder has a circular base and is a three-dimensional shape. A group of circular discs placed on top of one another might be thought of as a cylinder. Consider a situation where we need to figure out how much sugar can fit inside a cylindrical box.
In other words, we want to figure out the volume or capacity of this box. A cylindrical box's capacity is essentially equal to the volume of the cylinder inside. As a result, the volume of a three-dimensional shape is determined by how much space it takes up.
The volume of the cylinder is given by the formula V = πr²h
where r is the radius and h is the height.
Substituting the given values,
we get V = π(9.6 cm)²(11.6 cm) = 3,301.57 cm³ (rounded to two decimal places).
Since the sample contains 0.03 grams of trace element for every cubic centimeter of water,
Brianna has collected approximately 0.03 × 3,301.57 = 99.05 grams of trace element (rounded to two decimal places).
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1. What is the vertex of the parabola?
Answer:
Step-by-step explanation: frost add the vertical and horizontal axis to find your nearest angle
the median and mean of : 24 , 44 , 10 , 22
Answer:
The mean is 25 and the median is 23
Th e surface area S, in square units, of a sphere with volume V, in cubic units, is given by the formula S 5 p 1 3(6V) 2 3. What is the surface area of a sphere with volume 4 3 mi3? Write your answer in terms of p 1 3. Show your work.
According to the question the surface area of the sphere with volume 4/3 mi^3 is: S = 4π^(1/3) square units.
Explain volume?The volume of a cube is measured in terms of the total amount of cube unit that something that fills. Simply put, volume is the entire amount of space that an object occupies. The formula a3, wherein there is the cube's edge, can be used to determine the cube's volume.
The formula given is:
[tex]S = \pi ^(1/3) * (6V)^(2/3)[/tex]
We are given that [tex]V = 4/3 mi^3[/tex]. Substituting this into the formula:
[tex]S = π^(1/3) * (6(4/3))^(2/3)\\S = π^(1/3) * (8)^(2/3)[/tex]
Now we need to evaluate [tex]8^{2/3}[/tex]. This means finding the number that, when raised to the power of 3, gives us 8. This is the cube root of 8, which is 2:
[tex]8^{2/3} = (2^3)^(2/3)= 2^(3*2/3)= 2^2 = 4[/tex]
Substituting this back into the formula:
[tex]S =\pi ^(1/3) * 4[/tex]
So the surface area of the sphere with volume [tex]4/3 mi^3[/tex]is:
[tex]S = 4\pi ^(1/3)[/tex]square units.
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!NEED HELP NOW!
Triangle ABC
maps to triangle XYZ
by a rotation of 90∘
counterclockwise about the origin followed by a reflection across the line y=x.
In triangle ABC,
m∠A=45∘,
m∠B=55∘,
and m∠C=80∘.
What is the measure of ∠Y?
i have tried 350, 76, 35,14, and none of them have been right
Answer:
Hopes this helps
Step-by-step explanation:
Therefore , the solution of the given problem of triangle comes out to be the angle Y has a value of roughly 76.4 degrees.
What precisely is a triangle?
Because a triangle has four or more extra parts, it is a polygon. Its form is a straightforward rectangle. A triangle is a rectangle with the edges A, B, and C. A singular plane but instead cube are produced by Euclidean geometry when the sides aren't truly collinear. A triangular is a shape if it has three sides and three angles. Angles are the points where a quadrilateral three sides meet. A triangle's sides add up to 180 degrees.
Here,
We can determine the images of locations A, B, and C using the following method:
=> A': (-yA, xA)
=> B': (-yB, xB)
=> C": (-yC', xC')
where C' is the rotated version of location C.
We can determine the side lengths of triangular ABC using the Law of Cosines:
Assume that
=> a = BC = 2R sin(A/2) = 2R sin(45/2) 1.441R,
=> b = AC = 2R sin(B/2) = 2R sin(55/2) 1.663R, and
=> c = AB = 2R sin(C/2) = 2R sin(80/2) 2.219R.
where R represents the triangular ABC's circumradius.
Now, by turning point C 90 degrees anticlockwise with respect to the origin, we can determine the coordinates of point C':
xC' = -yC
yC' = xC
Then, to obtain the picture of point C, we can reflect point C' across the line y = x:
xC"=yC' and yC"=xC'
Again employing the Law of Cosines, we can determine the triangular XYZ's side lengths:
=> x = YZ = 2R sin(A'/2) = 2R sin(35) ≈ 1.189R
=> y = XZ = 2R sin(B'/2) = 2R sin(45) ≈ 1.414R
=> z = XY = 2R sin(C'/2) = 2R sin(55) ≈ 1.630R
where the picture angles of angles A, B, and C are A', B', and C', respectively.
Last but not least, we can apply the Law of Cosines once more to determine the size of angle Y:
cos(Y) i= t (x2 + z2 - y2)/ (2xz)
cos(Y) = 0.224 Y = 76.4 °
As a result, the angle Y has a value of roughly 76.4 degree
Using v^2 - u^2 =2as, find " v " when s = 21, u = 4 and a = 2.
Answer:
v = 10
Step-by-step explanation:
[tex] \dashrightarrow \: { \sf{ {v}^{2} - {u}^{2} = 2as}} \: \: \: \\ \\ \dashrightarrow \: { \sf{ {v}^{2} = {u}^{2} + 2as }} \: \: \: \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {u}^{2} + 2as} }} \\ \\ \: \: \: \: \: \: \: { \colorbox{lightblue}{substitute \: variables}} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{ {4}^{2} + 2(2 \times 21) } }} \\ \\ \dashrightarrow \: { \sf{v = \sqrt{16 + 84} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\dashrightarrow \: { \sf{v = \sqrt{100} }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \dashrightarrow \: { \sf{v = 10}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
a senate subcommittee consists of ten democrats and seven republicans. in how many ways can a chairman, vice chairman, and secretary be chosen if the chairman must be a democrat and the vice chairman must be a republican?
There are 16 ways to choose a chairman, vice chairman, and secretary under these conditions
Since, the chairman must be a Democrat and the vice chairman must be a Republican, we have one choice for the chairman (out of the 10 Democrats) and one choice for the vice chairman (out of the 7 Republicans).
For the secretary, we have 16 people left to choose from (since we have already chosen the chairman and vice chairman), and it can be either a Democrat or a Republican.
Therefore, the number of ways to choose a chairman, vice chairman, and secretary is:
¹⁶C₁ = 16
So, there are 16 ways to choose a chairman, vice chairman, and secretary under these conditions
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a sphere has a radius of 2.7cm what is its volume to the nearest cubic centimeter
Answer:
around 82.45 cubic cm
Step-by-step explanation:
The formula for the volume of a sphere is (4/3) * pi * r^3.
Since the radius is 2.7, we can plug this into the formula to get (4/3) * pi * 19.683.
This simplifies to 26.244pi, which is around 82.45 cubic cm.
The owner of the Jazz has given out 10 signed basketballs at a pre-season event. Their goal is to give out 3 basketballs each week during the season. Function b gives the total number of basketballs as a function of the number of weeks since the pre-season event.
describe four right that individuals in relationships have when they stay together
if i'm given a list of values and asked to graph the average and standard deviation, what kind of graph should i use
To graph the average and standard deviation of a given list of values, you should use a bar graph or a histogram.
1. Calculate the average (mean) of the given list of values.
2. Calculate the standard deviation of the given list of values.
3. Create a bar graph or histogram with two bars.
4. Label the first bar as "Average" and set its height to the calculated average value.
5. Label the second bar as "Standard Deviation" and set its height to the calculated standard deviation value.
This graph will visually represent the average and standard deviation of the given list of values.
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I need some help please
Answer:
Step-by-step explanation:
Mr. Hesch has 4 stations set up in his classroom. Each station is labeled with a color: blue, purple, green, or yellow. As each student enters the classroom, they spin the spinner to decide at which station they will start. What is the probability a student spins purple?
The probability of spinning purple on the spinner is 1/4 or 25%.
What is permutation and combination?Calculating the variety of ways to select or arrange a collection of items is a key component of the probability theory concepts of permutation and combination. The key distinction between combination and permutation is whether or not order matters. Contrarily, combination refers to the variety of ways to choose a smaller subset of items from a larger collection, where the order of the items is irrelevant. For instance, there are three potential two-letter combinations if you have the letters A, B, and C: AB, AC, and BC.
Given there are 4 stations, thus he spinner is equally likely to land on any of the four colors.
The probability of spinning purple is 1/4 or 25%.
Hence, the probability of spinning purple on the spinner is 1/4 or 25%.
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In T-ball, batters hit a ball that is placed on a T-shaped stand. Batter A hits the ball by swinging the bat from a resting position on his shoulder. Batter B hits the ball with the bat directly behind it. In one or two sentences, create and justify a claim about which batter will likely hit the ball the greater distance.
It is likely that Batter A, who swings the bat from a resting position on his shoulder, will hit the ball a greater distance than Batter B, who hits the ball with the bat directly behind it. This is because Batter A is able to generate more power and momentum with his swing, whereas Batter B's swing may be more limited in its range of motion and force.
Alan has 1/3 of a pizza left. He wants to share the pizza equally among himself and three friends.
How much of the pizza will each person receive?
PLEASE PROVIDE MY ANSWER QUICKLY
Answer:0.08
Step-by-step explanation:If you divide the (1/3)/4 that will get you 0.08
A random sample of 100 customers at a local ice cream shop were asked what their favorite topping was. The following data was collected from the customers.
Topping Sprinkles Nuts Hot Fudge Chocolate Chips
Number of Customers 12 17 44 27
Which of the following graphs correctly displays the data?
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled Sprinkles going to a value of 12, the second bar labeled Nuts going to a value of 17, the third bar labeled Hot Fudge going to a value of 44, and the fourth bar labeled Chocolate Chips going to a value of 27 correctly displays the data.
One angle of an isosceles triangle measures 130°. What measures are possible for the other two angles? Choose all that apply.
75 65 25 50
Answer:
25
Step-by-step explanation:
Isosceles triangle has two congruent angles.
∠ + ∠ + 130 = 180
2∠ = 50
∠ = 25
Answer:
25°
Step-by-step explanation:
In an isosceles triangle, 2 angles are equal.
The sum total of all angles in a triangle = 180
Assume unknown angle as x.
As 1 angle is already given, the equation is
130 + x + x = 180
130 + 2x = 180
2x = 50
x = 25°
What is the correct fraction/percentage?
The probability that a student chosen at random will play the bass is 12/43.
What is probability?
Probability is a branch of mathematics that deals with the study of random events or experiments. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. An event with a probability of 0 means it is impossible, while an event with a probability of 1 means it is certain to occur. Probabilities between 0 and 1 indicate the degree of uncertainty of the event occurring.
To find the probability that a student chosen at random will play the bass, we need to find the total number of students who play the bass and divide it by the total number of students in the middle school School of Rock.
The total number of students who play the bass is the sum of the number of seventh-grade students who play bass and the number of eighth-grade students who play bass:
Total number of bass players = 14 + 10 = 24
The total number of students in the middle school School of Rock is the sum of the number of seventh-grade students and the number of eighth-grade students:
Total number of students = 12 + 14 + 9 + 5 + 10 + 36 = 86
Therefore, the probability that a student chosen at random will play the bass is:
P(bass) = Total number of bass players / Total number of students = 24/86
To simplify this fraction, we can divide both the numerator and denominator by 2:
P(bass) = (24/2) / (86/2) = 12/43
Therefore, the probability that a student chosen at random will play the bass is 12/43.
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Question
Solve the equation. Check your solutions.
∣x−7∣=∣2x−8∣
Answer:
x = 1, x = 5
Step-by-step explanation:
You want the solutions to the absolute value equation ...
|x -7| = |2x -8|
Piecewise equationEach of the absolute value functions is equivalent to a piecewise-defined function. The boundary for the pieces is the turning point of the absolute value function, where its argument is zero.
The turning points are ...
x -7 = 0 ⇒ x = 7
2x -8 = 0 ⇒ x = 8/2 = 4
This means the equivalent piecewise equation will have 3 pieces. We know the absolute value function is defined as ...
[tex]|x|=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x\ge0\end{cases}[/tex]
If we write the equation in the form |x -7| - |2x -8| = 0, we have ...
[tex]0=\begin{cases}-(x-7)-(-(2x-8))&\text{for }x < 4\\-(x-7)-(2x-8)&\text{for }4\le x < 7\\(x-7)-(2x-8)&\text{for }7\le x\end{cases}[/tex]
x < 4The equation simplifies to ...
-x +7 +2x -8 = 0
x -1 = 0 . . . . collect terms
x = 1 . . . . . . a value in the domain. This is one solution.
4 ≤ x < 7The equation simplifies to ...
-x +7 -2x +8 = 0
15 = 3x . . . . . . . . . . add 3x
5 = x . . . . . . . . a value in the domain. This is another solution
7 ≤ xThe equation simplifies to
x -7 -2x +8 = 0
-x +1 = 0
x = 1 . . . . . . . . . not in the domain 7 ≤ x, so not a solution
The solutions are x = 1 and x = 5.
__
Check
|1 -7| = |2·1 -8| ⇒ |-6| = |-6| . . . . true
|5 -7| = |2·5 -8| ⇒ |-2| = |2| . . . . true
Both solutions check in the original equation.
You are playing a board game. The board game uses a "spinner" that has the numbers 1 through 7 inclusive (ie: you flick the needle on the spinner and it indicates a random number, 1 through 7). It also uses a single 6-sided die. On any given turn, what are the odds that you will spin a 3? Ignore the die roll. Put your answer in the form of a decimal (ex: a 30% chance would be written 0. 3)
The odds of spinning a 3 on any given turn is 1 out of 7 or 14%. This can be expressed as a decimal by dividing 14 by 100, which yields probability of 0.14.
To calculate this, we divide the number of favorable outcomes (1) by the total number of possible outcomes (7). This is the same as the probability of spinning a 3 on a given turn, which can be expressed as a decimal, fraction, or percentage.The odds of spinning a 3 on any given turn is 1 out of 7 or 14%. This can be expressed as a decimal by dividing 14 by 100, which yields 0.14. To calculate this, we divide the number of favorable outcomes (1) by the total number of possible outcomes (7). This is the same as the probability of spinning a 3 on a given turn, which can be expressed as a decimal, fraction, or percentage.
P(Spin a 3) = favorable outcomes/ total outcomes
= 1/7
= 0.14
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a telephone call center uses two customer service representatives (csrs) during the 8:30 a.m. to 9:00 a.m. time period. the standard service rate is 2.0 minutes per telephone call per csr. assuming a target labor utilization rate of 70 percent, how many calls can these two csrs handle during this half-hour period? round your answer to the nearest whole number.
A telephone call center uses two customer service representatives (csrs) during the 8:30 a.m. to 9:00 a.m. time period. the standard service rate is 2.0 minutes per telephone call per csr. assuming a target labor utilization rate of 70 percent, Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.
Given a telephone call center uses two customer service representatives (CSRs)
during the 8:30 a.m. to 9:00 a.m. time period, and the standard service rate is 2.0 minutes per telephone call per CSR. Assuming a target labor utilization rate of 70%,
we have to determine the number of calls these two CSRs can handle during this half-hour period.
The formula to calculate the number of calls that can be handled during this half-hour period is:
Number of calls = (number of servers x utilization rate x service time) / arrival rate
= (2 x 0.70 x 2) / 1
= 2.8 calls (rounded to the nearest whole number)
Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.
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please help!! 20 points for those who help
Graph the line with an x-intercept of 3 and a y-intercept of -2.
Plot two points to graph the line.
the square root of 0.2468
Answer:
2468
Step-by-step explanation:
Scarlett needs to buy a bathroom mirror that is 5 feet wide and 7 feet long. If the mirror sells for $3.00 per square foot, what will the total cost of the mirror be?
Answer:
$105.00
Step-by-step explanation:
To find the total cost of the mirror, we need to first calculate its area. The area of the mirror can be found by multiplying its length by its width.
So, the area of the mirror would be:
Area = Length x Width
Area = 7 feet x 5 feet
Area = 35 square feet
Now that we know the area of the mirror, we can calculate the total cost by multiplying the area by the price per square foot:
Total Cost = Area x Price per square foot
Total Cost = 35 square feet x $3.00 per square foot
Total Cost = $105.00
Therefore, the total cost of the mirror would be $105.00.
Answer:105$
Step-by-step explanation: all you need to do is 5x7=35
35 is the amount of square feet the square has. Then you do 35 x 3.00=
105$
a cone is cut into two pieces: a smaller cone and a frustrum
Answer:
incomplete question, could u provide the whole question please?
4. The local grocery store wants to stock another brand of cereal that has 20% less grams of carbohydrates per serving than Tasty Oats 75% more grams of protein per serving than Cornbits. A serving size of 100 grams • How many grams per serving are not carbohydrates or protein in the new cereal? Show how you determined your answer.
The amount of grams per serving that are not carbohydrates or protein in the new cereal is 24.05 grams.
What is the amount of grams?In the preceding question, we were told that the amount of carbohydrates in both Cornbits and Tasty Oats is 700% of the amount of protein. The amount of protein is 12 grams. So, we can conclude that the amount of carbohydrates is 700% 0f 12 grams which equal 84 grams. Also, we know that there are 5 grams of protein in 45 grams of Cornbits cereal.
Now 20% less grams of carbohydrates gives us 0.8 × 84 = 67.2
while 75% more grams of protein per serving than Cornbits gives us 175% × 5 = 8.75
The number of grams per serving that are not carbohydrates or protein in the new cereal will be:
100 - 67.2 - 8.75 = 24.05.
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How to solve a system of equations by graphing
According to the solution we have come to find that, Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
What is graph?In mathematics, a graph is a collection of vertices or nodes and edges, where each edge connects a pair of nodes.
To solve a system of equations by graphing, follow these steps:
Write the two equations in the form y = mx + b, where m is the slope and b is the y-intercept.
Plot the y-intercept of each equation on the y-axis.
Use the slope of each equation to find one or two more points on the line, and plot these points.
Draw a line through the plotted points for each equation.
Look for the point where the two lines intersect. This point represents the solution to the system of equations.
Check the solution by plugging in the coordinates of the intersection point into both equations. If the coordinates satisfy both equations, then the point is the correct solution.
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What is the value of 4 in the hundreds place
Answer:
The Place Value of '4' will be 400 if we keep it in the Hundreds place
The Face Value of '4' will remain the same
6. Workers A and B, doing the same job, show the following results over a long period: A B mean time of completing job (in hours) 5 4 standard deviation (in hours) 1. 5 1. 5 a) Who appears to be more consistent in performance? b) Who is more efficient from an overall point of view?
Worker B appears to be more consistent in performance, while Worker B is more efficient from an overall point of view.
To determine who appears to be more consistent in performance, we need to compare the standard deviations of A and B. Both A and B have a standard deviation of 1.5 hours, which means that they have the same level of consistency in their performance.
To determine who is more efficient from an overall point of view, we need to compare the mean times of A and B. Worker B has a mean time of 4 hours, which is less than the mean time of Worker A (5 hours). This means that Worker B is more efficient than Worker A in completing the job from an overall point of view.
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Round 453, 605 to the nearest 10,000
Answer:450,000
Step-by-step explanation:It becomes 450,000 thousand because anything under 5 in the ten thousands place becomes a zero and anything in front of it which is the 4 will stay the same.
Cuanto es 13131312316273612618273681723617312863217682116+2364235425427542654273654236452547
Answer:
1.31313123x10^{46}
Step-by-step explanation: