Answer:
Step-by-step explanation:
Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance of about 466.2 miles. A second flight option flies first to city C and then connects to A. The bearing from B to C is N28.9∘E, and the bearing from B to A is N59.8∘E. The bearing from A to B is S59.8∘W, and the bearing from A to C is N79.4∘W. How many more frequent flyer miles will Adam receive if he takes the connecting flight rather than the direct flight? Adam would receive more frequent flyer miles. (Round to one decimal place as needed.)
Since the calculated value is negative, it means that the direct flight is shorter than the connecting flight. Therefore, Adam would not receive additional frequent flyer miles by taking the connecting flight; in fact, he would cover approximately 150.8 fewer miles compared to the direct flight.
To find the additional frequent flyer miles Adam would receive by taking the connecting flight rather than the direct flight, we need to calculate the distance between city B and city C, and then subtract it from the direct flight distance between city B and city A.
Let's start by calculating the distance between city B and city C using the Law of Cosines:
\(c^2 = a^2 + b^2 - 2ab*cos(C)\)
where c is the distance between B and C, a is the distance between B and A, and b is the distance between A and C.
Using the given information, we have:
a = 466.2 miles
b = ?
C = N28.9°E (angle at B)
To find b, we can use the Law of Sines:
sin(B) / b = sin(C) / a
sin(B) = sin(180° - (C + A))
sin(B) = sin(180° - (28.9° + 59.8°))
sin(B) ≈ 0.4921
Now we can solve for b:
0.4921 / b = sin(28.9°) / 466.2
b ≈ (0.4921 * 466.2) / sin(28.9°)
b ≈ 315.4 miles
Now that we have the distance between B and C, we can calculate the additional frequent flyer miles:
Additional miles = Distance(B to C) - Distance(B to A)
Additional miles = 315.4 - 466.2
Additional miles ≈ -150.8 miles
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If a = b, then ac = bc. This is called the
Answer:
Transitive property of equality
Step-by-step explanation:
Solve the equation.
25-3(2w + 1) = 10w-3(10+w)
Bobby has $125 to spend. Used video games
are $15.50 each. Write an equation Bobby
could use to find out how many games he can
afford to buy? Use the variable x
Answer:
he can buy 8 video games
Step-by-step explanation:
125/15.50=8.06
hope this helps
pl make me brainliest
the radius of a circle is decreasing at the rate of -2cm/sec.how fast the area of a circle is decreasing when r =10. recall thatthe area is given by A= πr2.
on this problem do you have todifferentiate the formula A = πr2 then plugthe information in the equation?
The area of the circle is decreasing at a rate of -40π square cm/sec when radius is 10 cm.
To solve this problem, you need to differentiate the formula for the area of a circle, which is A = πr², with respect to time. Since the radius is changing with time, you'll need to apply the chain rule in calculus.
Given:
The rate of change of the radius: dr/dt = -2 cm/sec (negative because the radius is decreasing)
The initial radius: r = 10 cm
Differentiating area of circle w.r.t t
dA/dt = d/dt (πr²)
To differentiate, we'll use the chain rule.
dA/dt = d(πr²)/dr × dr/dt
dA/dt = 2πr × dr/dt
Substituting r = 10 cm and dr/dt = -2 cm/sec:
dA/dt = 2π(10) × (-2)
dA/dt = -40π
So, when the radius is 10 cm and decreasing at a rate of -2 cm/sec, the area of the circle is decreasing at a rate of -40π square cm/sec.
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It took Leo 3 hours to type a 4125-word essay. Sarah typed her 3800-word essay in 3 hours and 10 minutes. At these rates, how much longer would it take Sarah than Leo to type a 5500-word essay?
Answer:
Sarah would take 35 minutes longer than Leo to type 5500 word essay
Step-by-step explanation:
Let us solve the question
∵ It took Leo 3 hours to type a 4125-word essay
→ The rate is the number of words divided by the time
∴ Leo's rate = 4125 ÷ 3 = 1375 words/hour
∵ Sarah typed her 3800-word essay in 3 hours and 10 minutes
→ Change the 10 min to the hour by divide it by 60
∵ 3 hours 10 min = 3 + \(\frac{10}{60}\) = 3 + \(\frac{1}{6}\) = 3\(\frac{1}{6}\) hours
∴ Sarah's rate = 3800 ÷ 3\(\frac{1}{6}\) = 1200 words/hour
∵ Leo will type a 5500-word essay
→ Divide it by his rate to find the time taken
∴ Leo takes = 5500 ÷ 1375 = 4 hours
∵ Sarah will type a 5500-word essay
→ Divide it by her rate to find the time taken
∴ Sarah takes = 5500 ÷ 1200 = 4\(\frac{7}{12}\) hours
→ Find the difference between their times
∵ The difference = 4\(\frac{7}{12}\) - 4 = \(\frac{7}{12}\) hour
→ Multiply it by 60 to change to minutes
∴ The difference = \(\frac{7}{12}\) × 60 = 35 minutes
∴ Sarah would take 35 minutes longer than Leo to type 5500 word essay
Plz tell me the answer
Answer:
first is correct
second should be
4a² + 5a
Find the volume of this prism.
In
9 cm=height
6 cm
12 cm
The given values are:
9cm -height
6cm- base
12cm - length
Any prism volume is V = BH, where B is the base area and H is the prism height. To calculate the base area, divide it by B = 1/2 h(b1+b2) and multiply it by the prism height.
A rectangular prism is a cuboid.
V= LxBxH
V= 9x6x12= 648cm
A prism's volume is calculated by multiplying its height by its base's area. Prism volume (V) is equal to B h, where B is the base's area and h is the prism's height. Two solids have the same volume if they are the same height h and cross-sectional area B throughout.
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Probably the full question is:
Find the volume of this prism:
9cm -height
6cm- base
12cm - length
A lever is used to lift a load by applying an effort of 200 N. If load is 2o cm and effort is 80 cm far from the fulcrum, find the amount of load.
PLEASE HELP ASAP SOLVE WITH EXPLANATION PLEASEEE
Answer: 415 in
Step-by-step explanation:
Volume of a cone: 1/3 height multiplied by radius
radius = 6
height = 11
V=π r(squared) h/3 π · 6(squared) · 11/3 ≈ 414.69023
414.69023 = (rounded) 415in
what is the slope of the line in the graph?
○-4/3
○-3/4
○3/4
○4/3
Answer:
y=-3/4
Step-by-step explanation:
hsusussssusuasus
Find the calories in 25 potato chips if 10 potato chips contain 115 calories.
A. 140.5 calories
B. 287.5 calories
C. 230.0 calories
D. 250.0 calories
Answer:
b
Step-by-step explanation:
115 / 10 is 11.5
multiply 25 x 11.5
There are 287.5 calories in 25 potato chips. Therefore, option B is the correct answer.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, 10 potato chips contain 115 calories.
Number of calories in one potato chips = Total number of calories ÷ Number of calories
= 115/10
= 11.5 calories
Number of calories in 25 potato chips
= 25×11.5
= 287.5 calories
Therefore, the number of calories in 25 potato chips is 287.5 calories.
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a nurse is planning care for a client to prevent postoperative atelectasis. which of the following interventions should the nurse include in the plan of care except?
Answer:
You didn't provide any choices or options to pick from but here are the possible answers is:
- Encourage the use of the incentive spirometer every 2 hours
-Instruct to splint incision when coughing and deep breathing.
-Reposition the client every 2 hours
-Assist with early ambulation.
Step-by-step explanation:
Hope I could help!
In the plan of care to prevent postoperative atelectasis, interventions should not include the use of tobacco products or exposure to secondhand smoke.
The nurse should include several interventions in the plan of care to prevent postoperative atelectasis, but there are specific interventions that should not be included. Atelectasis is the partial or complete collapse of the lung, and preventing it is crucial after surgery. Here are some interventions that should be included:
Incentive Spirometry: The nurse should encourage the client to use an incentive spirometer to promote deep breathing and lung expansion.
Early Ambulation: Encouraging the client to get out of bed and walk as soon as possible after surgery helps improve lung function.
Pain Management: Adequate pain control measures should be in place to ensure the client can take deep breaths without discomfort.
Coughing and Deep Breathing Exercises: The nurse should teach and encourage the client to perform regular coughing and deep breathing exercises to clear the airways and prevent mucus buildup.
Positioning: Proper positioning, such as elevating the head of the bed, can aid lung expansion.
What should not be included in the plan of care is the use of tobacco products or exposure to secondhand smoke, as smoking and smoke exposure are detrimental to lung health and can worsen atelectasis. These should be strictly avoided to prevent postoperative complications.
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Write a nuclear equation to describe the neutron induced fission of 23994 pu to form 8936 kr and 14958 ce. determine how many neutrons are produced in the reaction.
The nuclear equation for the neutron-induced fission of 23994 Pu to form 8936 Kr and 14958 Ce is:
^239_94Pu + ^1_0n -> ^89_36Kr + ^149_58Ce + x^1_0n
In this equation, a neutron collides with a Pu-239 nucleus, causing it to undergo fission. This results in the formation of Kr-89 and Ce-149 isotopes, along with the release of additional neutrons (represented by x). The number of neutrons produced in the reaction can vary and depends on various factors, such as the energy of the incident neutron and the specific reaction conditions.
The neutron-induced fission reaction involves the collision of a single neutron with a Pu-239 nucleus (^23994Pu). As a result of the collision, the Pu-239 nucleus undergoes fission and splits into two smaller fragments, which are Kr-89 (^8936Kr) and Ce-149 (^14958Ce). The equation also includes the symbol x, representing the number of neutrons released in the reaction.
The exact number of neutrons produced in the reaction can vary. Fission reactions typically release multiple neutrons, which can go on to induce further fission in other nuclei, leading to a chain reaction. The number of neutrons produced depends on factors such as the energy of the incident neutron and the specific isotopes involved in the reaction.
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If you toss 2 dice, what is the probability you roll a 2 on one die and a 6 on the other?
hello
the probability of having a 2 on ine dice = 1/6
the probability of having a 6 on the other dice = 1/6
the probability of having a 2 on one dice and a 6 on the other dice = x
\(x=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}\)the probability of having a one dice of 2 and the other dice of 6 is equal to 1/36
A line segment whose endpoint are on the circle is called a __________ of a circle .
Chord
Radius
Tangent
Diameter
A line segment whose endpoint are on the circle is called a __________ of a circle.
Chord
Radius
Tangent
Diameter
Answer: Chord
HELP ASAP!! PLEASE!! Which ordered pair is not a solution to the equation y = 6.15 + x?
A) (2.41, 8.56). B) (6.09. 12.24). C) (9.72, 15.87). D) (12.42, 18.09)
Answer: D (12.42, 18.09)
Explanation:
For A, if you substitute them, 6.15+2.41(x because x always is first), you get 8.56 but y is 8.56. So therefore, A is wrong cause it is a solution but it asks us for an incorrect solution.
For B, if you substitute the numbers, 6.09+6.15 = 12.24 but y is 12.24 meaning 12.24 = 12.24 which is true. But the question asks us which is not true/a solution, so therefore, B is also wrong.
For C, if you substitute the numbers, you get 9.72+6.15 which is 15.87. Since y is 15.87, the substituted question is 15.87=15.87 which is true and therefore, C is also wrong since it is true but it is asking us for an incorrect solution.
We are then left with D, which is the correct option. I'm guessing you want an explanation for why it is correct. So if you substitute the numbers, you would get y = 12.42+6.15 and 12.42+6.15 is 18.57 but y is 18.09. So the equation is 18.09 = 18.57 which doesn't make sense and is false. Thus, D is the correct answer because it provides a set of numbers that is a false solution to the equation.
REMEMBER:
In an ordered pair, x is the first number while y is the second, so make sure you substitute correctly!
TENSIONS BETWEEN ENGLAND AND THE AMERICAN COLONIES WOULD RISE DUE TO THE HUGE COST OF WHICH WAR?
A. French and Indian War B. the War of the Roses C. the Mexican War
Answer:
I'm pretty sure the answer is A
Step-by-step explanation:
Hope this helps:).......if not then sorry for wasting your time and may God bless you<3
Please help me out!!! There’s 25 questions I can’t
Answer:
217.70 cubic units
Step-by-step explanation:
Volume of composite solid Cone:h= 5 units & r = 4 units
\(\sf \boxed{Volume \ of \ cone = \dfrac{1}{3} \pi r^2h}\)
\(\sf = \dfrac{1}{3}*3.14*4*4*5\\\\ = 83.73 \ cubic units\)
Hemisphere:r = 4 units
\(\sf \boxed{Volume \ of \ hemisphere = \dfrac{2}{3} \pi r^3}\)
\(\sf = \dfrac{2}{3}*3.14*4*4*4\\\\= 133.97 \ cubicunits\)
Volume of composite solid = 83.73 + 133.97
= 217.70 cubic units
In this question we are provided with the height and radius. We are asked to calculate the volume of a composite solid
First we will find the volume of a cone
We know,
\( \orange{\star \: \small\boxed{ \sf{ Volume_{(cone)} = \dfrac{1}{3}πr²h}}}\)
Where,
r stand for radiush stand for heightAssuming π as 3.14Substituting the values we get
\( \small\bf Volume_{(cone)} = \dfrac{1}{3} \times 3.14×4 × 4×5\)
\( \rightarrow \small\rm{ Volume_{(cone)} = \dfrac{1}{3}×251.2}\)
\( \small\sf{ Volume_{(cone)} = 83.73 \:cubic \: units }\)
Now we will calculate the volume of a hemisphere
We know,
\( \red{\star \: \small \boxed{\sf{ Volume_{(hemisphere)} = \dfrac{2}{3}πr³}}}\)
Substituting the values we get
\( \small\bf{ Volume_{(hemisphere)} = \dfrac{2}{3} \times 3.14 × 4 × 4 × 4}\)
\( \rightarrow\small\rm{ Volume_{(hemisphere)} = \dfrac{2}{3} \times 200.96}\)
\( \rightarrow\small\rm{Volume_{(hemisphere)} = 2 \times 66.98} \)
\( \small\sf{ Volume_{(hemisphere)} =133.97}\)
Now we will calculate the volume
Volume = 83.73 + 133.97 = 217.70 cubic units
A square garden has an area of 5 square feet. Without using a calculator, find the side length of the garden to the nearest tenth of a foot
Answer:
2.23
Step-by-step explanation:
tune able to find the area you should x one side by the other side to find the area 2.23 * 2.23 equals close to 5 square feet
Find the volume of this object.
Use 3 for T.
2 ft
12 ft
8 ft
8 ft
7 ft
Volume of a Cone
πr²h
3
Volume of a
Rectangular Prism
V = lwh
V≈ [?]in³
V=
The volume of the given composite shape formed with a combination of cone & rectangular prism in cubic feet is 880 cubic feet and approximately cubic inches is 1,520,640 in3.
What is volume?Various solid figures or shapes have various volumes. We have investigated a variety of three-dimensionally specified solids and shapes, such as cubes, cuboids, cylinders, cones, etc. A shape created from two or more basic shapes is referred to as a composite, compound, or complicated shape. Any three-dimensional shape, figure, or solid's volume is simply the quantity of space it occupies or contains. By finding the product of the dimensions we can calculate the volume of a solid or 3D figure. The measurement units are cubic units. These solids can be of various shapes like cube, cuboid also called rectangular prism, cone, cylinder, sphere , hemishphere, frustum, etc.
Volume of cone = \(\frac{\pi\ r^2h}{3}\)
Volume of cuboid=L.W.H
Given that the solid shape is made up of cone & cuboid(also called rectangular prism)
Volume of solid= volume of cone+volume of rectangular prism
Given dimensions:
Cone:radius(r) = 8 ft
height(h) = 12 ft
Cuboid: Length(L) = 8 ft
Width(W) = 7 ft
Height(H) = 2 ft
Given that π = 3
Volume of solid = \(\frac{\pi\ r^2h}{3}\) + L.W.H
= \(\frac{3(8^2)(12)}{3} +8(7)(2)\)
= 64(12) + 56(2)
= 768 + 112
= 880
Volume of solid=880 cubic feet.
We know that 1 foot = 12 inches, & 1 cu. ft = 12x12x12 cu. inches
on converting volume into inches we get:
Volume of solid = 880 x 12 x 12 x 12 cubic inches
= 1,520,640 cu. inches.
Volume of solid is 1,520,640 in3
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I have no clue how I’m supposed to do this…
Answer:
Step-by-step explanation:
We will need to rewrite the Pythagorean Theorem
A^2 + B^2 = C^2
Substitute. tIn this case:
18^2 + x^2 = 82^2
Subtract 18^2
x^2 = 82^2 - 18^2
In order to get x alone, take the root:
x = sqrt(82^2 - 18^2)
And solve:
x = 80
root a+b=7 and root b +a - 11 If a and b are real numbers that satisfy the equation above, what is the value of a and b respectively?
a = 4 and b = 5 are the answers to the system of equations.
Let's square both sides of the first equation to eliminate the square root:
√a + b = 7
(√a + b)² = 7²
a + 2√ab + b² = 49
a + b² = 49 - 2√ab ---(1)
Now, let's square both sides of the second equation:
√b + a = 11
(√b + a)² = 11²
b + 2√ab + a² = 121
a² + b + 2√ab = 121 ---(2)
We can use equation (1) to substitute for √ab in equation (2):
a + b² = 49 - 2√ab
√ab = (49 - a - b²)/2
Substituting for √ab in equation (2), we get:
a² + b + 2(49 - a - b²)/2 = 121
Simplifying and rearranging, we get:
a² - a + b² - b - 36 = 0
(a - 1/2)² + (b - 1/2)² = 37.25
This is the equation of a circle centered at (1/2, 1/2) with a radius √37.25. We need to find the points where this circle intersects the line defined by equation (1).
Substituting b = 49 - a - 2√(a(49 - a))/2 into equation (1), we get:
a + (49 - a - 2√(a(49 - a)))² = 49 - 2√a(49 - a)
Simplifying and rearranging, we get:
4a³ - 294a² + 2421a - 5929 = 0
Using a numerical solver or the rational root theorem, we can find that one solution of this cubic equation is a = 4.
Substituting this value back into equation (1), we can solve for b:
4 + b² = 49 - 2√(4b)
b² + 2√(4b) - 45 = 0
Using the quadratic formula, we get:
b = 5
Therefore, the solutions of the system of equations are a = 4 and b = 5.
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Complete question:
√a+b=7 and √b +a = 11 If a and b are real numbers that satisfy the equation above, what is the value of a and b respectively?
A professor gives two types of quizzes, objective and recall. He is planning to give at least 15
quizzes this quarter. The student preparation time for an objective quiz is 15 minutes and for a
recall quiz 30 minutes. The professor would like a student to spend at least 5 hours (300 minutes)
preparing for these quizzes above and beyond the normal study time. The average score on an
objective quiz is 7, and on a recall type 5, and the professor would like the students to score at
least 85 points on all quizzes. It takes the professor one minute to grade an objective quiz, and 1.5
minutes to grade a recall type quiz. How many of each type should he give in order to minimize
his grading time?
Answer:
x₁ = 20 x₂ = 0
z (min) = 20
Step-by-step explanation:
According to the problem statement:
Let´s call
Objective quiz = x₁ Recall quiz = x₂
First constraint
Quantity of quizzes at least 15
x₁ + x₂ ≥ 15
Second constraint:
Preparation time at least 300 minutes, then
15*x₁ + 30*x₂ ≥ 300
Third constraint
Average score at least 85 points
7*x₁ + 5*x₂ ≥ 85
General constraint x₁ ≥ 0 x₂ ≥ 0
Objective function z is:
z = 1* x₁ + 1,5*x₂ to minimize
The model:
z = x₁ + 1,5x₂ to minimize
Subject to
x₁ + x₂ ≥ 15
15*x₁ + 30*x₂ ≥ 300
7*x₁ + 5*x₂ ≥ 85
Using Atozmax (online solver) we find
x₁ = 20 x₂ = 0
z (min) = 20
51. The optimistic time for completion of Activity " \( X \) " on a PERT chart was 6 hours, the most likely time was for this same activity was 9 hours and the pessimistic time was 12 hours. Using the
The expected time for completion of Activity "X" on a PERT chart is 9 hours.
PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.
Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:
Optimistic time (O) = 6 hours
Most likely time (M) = 9 hours
Pessimistic time (P) = 12 hours
Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9
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A statistics student gave a survey to students which asked how many first cousins they have. The data from the first nine responses are shown below.
6, 2, 7, 8, 8, 8, 5, 10, 10
The interquartile range for the data-set is given as follows:
3 first cousins.
How to obtain the interquartile range?The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.
The ordered data-set for this problem is given as follows:
2, 5, 6, 7, 8, 8, 8, 10, 10.
The cardinality of the data-set is given as follows:
n = 8, as the data-set has eight elements.
The quartiles for the data-set are given as follows:
First quartile: 2nd element, as 0.25 x 8 = 2 -> 5.Third quartile: 6th element, as 0.75 x 8 = 2 -> 8.Hence the interquartile range for the data-set is given as follows:
8 - 5 = 3 first cousins.
Missing InformationThe problem asks for the interquartile range of the data-set.
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In the given problem, find a similar relationship to the given relationship. Support the answer with an explanation.
Notice that the relation between the first two figures is that the outside figure becomes the inside figure, and the inside figure becomes the outside figure.
Therefore the triangle inside the square corresponds to the square inside the triangle.
Answer: Option A.
Wesley drives 12 miles to work every day. During his drive to work he sees 18 billboards. Which ratio shows miles driven to billboards seen by Wesley?
Answer:
2:3
Step-by-step explanation:
divide both by 6.
please help and thank you
Answer:
=
Step-by-step explanation:
Answer:
=
Step-by-step explanation:
the square root of 169 is 13
Can you help me please?
Answer:
its 34
Step-by-step explanation: