a) If the slant range of the plane in the image is 14.5 km, and the ground range is 10.15 km, find the altitude of the plane to the nearest meter. Show your work and explain your thinking.
b) If this plane loses power and descends suddenly at a rate of 750 meters per minute, how much time will the pilot have before he has to land?
Answers
a) The altitude of the plane is approximately 8.4 kilometers.
b) The pilot has approximately 11.2 minutes before he has to land.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental theorem in mathematics that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the lengths of the other two sides (the legs).
In mathematical terms, if we have a right triangle with legs a and b and hypotenuse c, the Pythagorean theorem can be written as:
[tex]a^2 + b^2 = c^2[/tex]
This theorem is named after the ancient Greek mathematician Pythagoras, who was the first to prove it. The Pythagorean theorem has numerous applications in geometry, trigonometry, physics, and engineering, among other fields.
The Pythagorean theorem can also be used to determine whether a triangle is a right triangle or not. If the lengths of the three sides of a triangle satisfy the equation [tex]a^2 + b^2 = c^2,[/tex] then the triangle is a right triangle with sides a and b and hypotenuse c.
a) In the given image, we can see that the slant range, ground range, and altitude form a right triangle. We can use the Pythagorean theorem to find the altitude of the plane.
Pythagorean theorem: In a right triangle, the square of the hypotenuse (slant range in this case) is equal to the sum of the squares of the other two sides (ground range and altitude in this case).
Therefore, we can write:
[tex]Slant range^2 = Ground range^2 + Altitude^2[/tex]
Substituting the given values, we get:
[tex]14.5^2 = 10.15^2 + Altitude^2[/tex]
Simplifying and solving for altitude, we get:
Altitude ≈ 8.4 km (rounded to the nearest meter)
Therefore, the altitude of the plane is approximately 8.4 kilometers.
b) If the plane descends suddenly at a rate of 750 meters per minute, we can use the altitude of the plane (calculated in part a)) to find the time the pilot has before landing.
Time = Altitude/Descent rate
Substituting the values, we get:
Time = [tex]\frac{8.4 }{0.75}[/tex] ≈ 11.2 minutes
Therefore, the pilot has approximately 11.2 minutes before he has to land.
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Related Questions
Steve and Silva are both members of a population, and a simple random
sample is being conducted. If the chance of Steve being selected is 1
what is the chance of Silva being selected?
98,000'
OA.
B.
O C.
O D.
1
98
1
9800
1
980
98,000
Answers
According to the probability, the answer is option D: 1/98,000.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The chance of Steve being selected is 1. This means that out of 1 individual, Steve is selected. The probability of Steve being selected is 1/1 or 1. Since the sample is a simple random sample, each individual in the population has an equal chance of being selected. If there are a total of 98,000 individuals in the population, then the probability of Silva being selected is 1 out of 98,000, or 1/98,000.
Therefore, the answer is option D: 1/98,000.
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I think of a number, treble it and take 6 from my answer.
If the result is 18, find the number.
Answers
Answer:
number is 8
Step-by-step explanation:
let the number be n then trebling it ( multiplying it by 3 ) is 3n, then subtracting 6 from this is 3n - 6 , so
3n - 6 = 18 ( add 6 to both sides )
3n = 24 ( divide both sides by 3 )
n = 8
that is the number thought of is 8
The family likes peaches and other fruits. The local farmer’s market is selling fresh peaches at a discounted price. If the farmer’s market sold 35% of its produce and has 260 peaches remaining, how many peaches did it originally have on hand? Show all your work and explain how you used equivalent ratios to solve the problem.
Answers
The farmer's market originally had 400 peaches on hand.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and radicals.
Let's use x to represent the original number of peaches the farmer's market had on hand.
We know that the farmer's market sold 35% of its produce, which means it sold 0.35x peaches. The remaining number of peaches can be calculated by subtracting the number of peaches sold from the original number of peaches:
remaining peaches = x - 0.35x
We also know that there are 260 peaches remaining, so we can set up an equation:
260 = x - 0.35x
Simplifying this equation, we can combine like terms:
260 = 0.65x
To solve for x, we need to isolate the variable by dividing both sides by 0.65:
x = 260 / 0.65
x = 400
Therefore, the farmer's market originally had 400 peaches on hand.
To explain how we used equivalent ratios, we used the fact that the farmer's market sold 35% of its produce. This can be represented as a ratio of 35/100 or 0.35. We then used this ratio to find the number of peaches sold, which is 0.35x. We also used the fact that the remaining peaches are the original peaches minus the peaches sold, or x - 0.35x. Finally, we set up an equation using the remaining peaches and solved for x to find the original number of peaches.
Hence, the farmer's market originally had 400 peaches on hand.
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RIDDLE: Why was the Mathematician Late for Work?
Directions: Find the slope between each pair of points Show all work on a separate sheet of paper. After completing each set, find matching answers. One will have a letter and the other a number. Write the letter in the matching numbered box at the bottom of the page.
SET 2
T. (7, 5) and (10, 9) ______________ 16. (-5, -2) and (9, 2) ______________
B. (-8, 2) and (-5, -4) ______________ 8. (-10, -6) and (2, -8) ______________
H. (2, -2) and (-4, -1) ______________ 3. (-2, 1) and (-8, -7) ______________
S. (-4, 9) and (-11, 7) ______________ 5. (-4, -2) and (-3, 3) ______________
O. (5, -1) and (4, -6) ______________ 14. (-2, -4) and (-7, 6) ______________
SET 3
K. (1, -3) and (2, -3) ______________ 9. (8, -1) and (6, -4) ______________
R. (3, 0) and (-3, 5) ______________ 1. (-11, -6) and (-8, -5) ______________
E. (12, 4) and (8, -2) ______________ 15. (-5, 4) and (-5, 3) ______________
U. (7, -3) and (7, -9) ______________ 12. (-2, -3) and (-5, 9) ______________
O. (3, 1) and (2, 5) ______________ 6. (-3, 8) and (7, 8) ______________
H. (-1, -6) and (-7, -8) ______________ 10. (-5, 3) and (7, -7) ______________
TAKE YOUR TIME!!! THIS IS 60 POINTS!
Answers
Set 2:
T. Slope = (9-5)/(10-7) = 4/3 __16. Slope = (2-(-2))/(9-(-5)) = 4/14
B. Slope = (-4-2)/(-5-(-8)) = -6/3 __ 8. Slope = (-8-(-6))/(2-(-10)) = -2/12
H. Slope = (-1-(-2))/(-4-2) = -3/-6 __ 3. Slope = (-7-1)/(-8-(-2)) = -8/6
S. Slope = (7-9)/(-11-(-4)) = -2/-7 __ 5. Slope = (3-(-2))/(-3-(-4)) = 5/1
O. Slope = (-6-(-1))/(4-5) = -5/-1 __ 14. Slope = (6-(-4))/(-7-(-2)) = 10/-5
Set 3:
K. Slope = (-3-(-3))/(2-1) = 0/1 __ 9. Slope = (-4-(-1))/(6-8) = -3/-2
R. Slope = (5-0)/(-3-3) = 5/-6 __ 1. Slope = (-5-(-6))/(-8-(-11)) = 1/3
E. Slope = (-2-4)/(8-12) = -6/-4 __ 15. Slope = (3-4)/(-5-(-5)) = -1/0
U. Slope = (-9-(-3))/(7-7) = -6/0 __ 12. Slope = (9-(-3))/(-5-(-2)) = 12/3
O. Slope = (5-1)/(2-3) = 4/-1 ____ 6. Slope = (8-8)/(7-(-3)) = 0/10
H. Slope = (-8-(-6))/(-7-(-1)) = -2/-6 _ 10. (-5, 3) and (7, -7) Slope = (-7-3)/(7-(-5)) = -10/12
What are sets?A set is a collection of distinct objects, usually numbers, that are grouped together in a manner that follows specific rules. Sets can be used to determine if an element belongs to the set or not, and can also be used to perform operations such as unions and intersections. Sets are an important tool in mathematics, and they can help simplify complex problems.
The Mathematician had to calculate the slope between two points for each of the sets given. To calculate the slope, the Mathematician had to subtract the y-values of the two points and divide by the difference between the x-values of the two points. The Mathematician then had to match the answers to the corresponding letter or number and write the letter in the matching numbered box at the bottom of the page. By doing this, the Mathematician was able to solve the riddle and arrive at work on time.
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Suppose your boss proposes an alternative form of payment. For the first day of each month, you’ll earn a penny. Thereafter, each workday your wages will double what they were the day before. If there are 20 workdays in a month, how much would you make for the month?
Answers
We will make ₹1,048,575 for the month. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?The four basic operations, often referred to as "arithmetic operations", are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.
We are given that for the first day of each month, a penny is earned. Thereafter, each workday wages will double what they were the day before.
Now, since there are 20 workdays in a month so, the total amount earned is as follows:
⇒ 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1,024 + 2,048 + 4,096 + 8,192 + 16,384 + 32,768 + 65,536 + 131,072 + 262,144 + 524,288
⇒ ₹ 1,048,575
Hence, we will make ₹ 1,048,575 for the month.
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could you help with the question pls?
Answers
By using distributive property, an estimate for sin((π/6 + ε)(1 - ε)) is approximately 0.5108.
What is sinx ?
sinx is a trigonometric function that represents the ratio of the length of the side opposite to an angle x in a right-angled triangle to the length of the hypotenuse of the triangle. In other words, it is the sine of the angle x.
The sine function is typically denoted as sin(x), where x is the measure of an angle in radians. It is defined as follows:
sin(x) = opposite side / hypotenuse
According to the question:
We can use the small angle approximation sin(x) ≈ x for small angles x to estimate[tex]sin((\pi /6 + \epsilon)(1 - \epsilon))[/tex], where ε = 0.01.
First, we can expand the expression using the distributive property:
[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) = sin(\pi /6 - \epsilon^2 +\epsilon /6)[/tex]
Since ε is small, we can use the small angle approximation to estimate the value of sin(ε/6):
[tex]sin(\epsilon /6) =\epsilon/6[/tex]
Next, we can use the fact that [tex]sin(\pi /6) = 1/2[/tex] to estimate [tex]sin(\pi /6 - \epsilon ^2)[/tex] :
[tex]sin(\pi /6 - \epsilon ^2) ≈ sin(\pi /6) = 1/2[/tex]
Substituting these approximations into the original expression, we get:
[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) =sin(\pi /6 - \epsilon^{2} + \epsilon/6) =sin(\pi /6) + sin(\epsilon/6) - sin(\epsilon^{2} )sin((\pi /6 + \epsilon)(1 - \epsilon)) = 1/2 + \epsilon/6 - sin(\epsilon^{2} )[/tex]
Finally, we can use the fact that sin(x) is approximately equal to x for small values of x to approximate [tex]sin(\epsilon^{2} ) as \epsilon^{2}[/tex]:
[tex]sin(\epsilon^2) = \epsilon^2[/tex]
Substituting this approximation into the previous expression, we get:
[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) ≈ 1/2 + \epsilon/6 - \epsilon^2[/tex]
Now, we can substitute the value of ε = 0.01 into this expression to get an estimate:
[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) ≈ 1/2 + 0.01/6 - 0.01^2[/tex]
[tex]sin((\pi /6 + \epsilon)(1 - \epsilon)) =0.5108[/tex]
Therefore, an estimate for sin((π/6 + ε)(1 - ε)) is approximately 0.5108.
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Macroeconomics
The regular price for a set of four tires is $250, but Erin finds a store that has the tires she needs on sale for $175?
Which graph correctly illustrates this scenario?
Answers
The graph for the given question is mentioned below.
What is graph?A graph is a visual representation of data or information that is used to display and communicate relationships between variables or categories. Graphs can take many forms, including line graphs, bar graphs, pie charts, and scatter plots, among others. They are commonly used in fields such as science, economics, and statistics.
As the price of a set of four tires has decreased from $250 to $175, we can illustrate this scenario using a demand and supply graph with quantity on the horizontal and size on the vertical axis.
The graph should show a leftward shift of the demand curve, indicating that consumers are willing to buy more tires at a lower price. The supply curve remains constant, indicating that the supplier is willing to sell the same quantity of tires at a lower price. Therefore, the correct graph should be:
| P
250 | \
| \ Supply
| \
| \
175 | \
| \
| \ Demand (after discount)
| \
Q
where P is the price, Q is the quantity, and the demand curve has shifted to the right.
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What is the area of this composite figure round to the nearest hundredth
Answers
The area of the composite figure is 14.71 square units
What is the area of the composite figure?The area of the composite figure is found by calculating the sum of the areas of the various parts.
The area of the figure = area of sector + area of triangle + area of trapezium
Area of sector = 135/360 * π * 2²
Area of sector = 4.71 square units
Area of triangle = ¹/₂ * 2 * 1
Area of triangle = 1 square unit
Area of trapezium = ¹/₂ (3 + 6) * 2
Area of trapezium = 9 square units
Therefore, area of composite figure = (4.71 + 1 + 9) square units
The area of the composite figure = 14.71 square units
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Algebra question, multiple choice, photo attached
Answers
The graph of the linear inequality y ≥ 2·x - 1 is the region on or above the graph of the line y = 2·x - 1
Option A is correct;
(A) On or above
What is an inequality?An inequality is a comparison that expresses an unequal relationship between two expressions.
An example of an inequality is; V < W, R > Q, X ≥ W, etc
The region of the graph of a linear inequality is indicated by shading above the line when the inequality is >, and below the line when the inequality symbol is <
The specified linear inequality can be presented as follows;
y ≥ 2·x - 1
Therefore, w get;
The values of y are larger than 2·x - 1
The shaded region is the region on or above the graph of the line y = 2·x - 1
The correct option is therefore; (A) On or above the line y = 2·x - 1
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Summarize in your own words a quantity in the life-science that is modelled by a function of time. For your function, if you knew some values of its derivative, what would those values be telling you about your model? Be specific (don’t just say “rate-of-change”).
Answers
One example of a quantity in the life sciences that is modeled by a function of time is the population size of a species.
How can this be modeled?This can be modeled using a differential equation, where the rate of change of the population size is proportional to the current population size.
If we knew the values of the derivative of this function (i.e., the first derivative), we would be able to make inferences about the growth or decline of the population.
A positive derivative value would indicate that the population is growing, while a negative derivative value would indicate that the population is declining. The magnitude of the derivative would also give us information about the rate of growth or decline of the population. If the derivative is large, the population is changing quickly, while a small derivative indicates slower change.
If we had information about the second derivative of the function (i.e., the rate of change of the derivative), we would be able to make further inferences about the behavior of the population.
A positive second derivative value would indicate that the population is accelerating in its growth, while a negative second derivative value would indicate that the population is decelerating in its growth. This information could be useful in predicting future trends in population size and in making decisions about conservation efforts or resource management.
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What is the solution to the equation log2 (5x - 2) = -2?
Answers
Step-by-step explanation:
We can solve for x using the properties of logarithms as follows:
log2 (5x - 2) = -2
2^(-2) = 5x - 2 (using the definition of logarithms)
1/4 = 5x - 2 (simplifying 2^(-2))
5x = 2 + 1/4 = 9/4
x = 9/20
Therefore, the solution to the equation log2 (5x - 2) = -2 is x = 9/20.
Tell how many polygons can be formed by each set of points
Answers
The number of polygons that can be formed are
(0, 1) and (2, 3): Zero polygon(4, 5), (6, 7), and (8, 9): One polygon (triangle)(3, 5) and the x-axis: One polygon (triangle)How to determine the number of polygonsPoints (0, 1) and (2, 3)
The set of points (0, 1) and (2, 3) cannot form a polygon as they are collinear (i.e., lie on the same straight line) and do not enclose an area.
Points (4, 5), (6, 7), and (8, 9)
These are three different points.
Because a triangle has three sides, one triangle can be formed by the set of points (4,5), (6,7), and (8,9). i.e. One polygon
Points (3, 5) and the x-axis.
One polygon can be formed by the set of points (3,5) and the x-axis: a triangle with vertices at (3,5), (0,0), and (6,0).
How to determine the areas and the perimetersPolygon (4)
This is a rectangle with the dimension:
6 units by 5 units
So, we have
Perimeter = 2 * (6 + 5) = 22 units
Area = 6 * 5 = 30 squared units
Polygon (5)
This is a composite figure with the following dimensions:
Square of 4 units
Rectangle: 6 units by 2 units
So, we have
Perimeter = 4 * 4 + 2 * (6 + 2) = 32 units
Area = 4 * 4 + 6 * 2 = 28 squared units
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I need help! Please include an explanation.
Answers
The location of A ' given the rotation about the origin and the xy coordinate plane is D. In Quadrant IV.
How to find the location ?To rotate a point 180° about the origin, we switch the signs of both coordinates. For instance, if you have ( x, y ) rotated, then it becomes ( - x , - y ).
So, if A is located at (-4, 3), then A' is located at (4, -3).
The point A' is located in Quadrant IV, because it has a positive x-coordinate and a negative y-coordinate, which is the characteristic of points in this quadrant.
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What is the answer to this photo
Answers
The required number of tubs are 17.55 tubs.
How to find number of tubs?To solve the problem, we need to find the total amount of ice cream used in ounces and then convert it to pounds to find the number of tubs used.
Number of scoops for regular cones = 2 scoops/cone
Number of scoops for large cones = 3 scoops/cone
Total number of scoops of ice cream used for regular cones = 2 scoops/cone x 234 cones = 468 scoops
Total number of scoops of ice cream used for large cones = 3 scoops/cone x 156 cones = 468 scoops
Total number of scoops of ice cream used = 468 scoops + 468 scoops = 936 scoops
Total amount of ice cream used in ounces = 936 scoops x 3 ounces/scoop = 2808 ounces
Total amount of ice cream used in pounds = 2808 ounces / 16 ounces/pound = 175.5 pounds
Number of tubs of ice cream used = 175.5 pounds / 10 pounds/tub = 17.55 tubs
Rounding up to the nearest whole number, we get:
Answer: (C) 17.55 tubs.
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Julia needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on
sale contains 6 glasses, use the drop-down menu below to write an inequality
representing s, the number of sets of glasses Julia should buy
Answers
Answer:
Julia should buy at least 5 sets of glasses.
Step-by-step explanation:
The inequality will be
286 +6s ≥ 316
Solve for s to get s ≥ 5
What are the possible values for
From the diagram you know that the triangles have two pairs of congruent corresponding sides, that LM< _, and that m
Please imma give brainlest
Help
Answers
The converse of the [tex]H[/tex]inge theorem indicates that the angle subtended by the segment [tex]\overline{LM}[/tex], (∠K) which is less than the length of the segment [tex]\overline{OP}[/tex], will be less than the measure of the angle subtended by the segment [tex]\overline{OP}[/tex], which is 90°
The possible values for angle ∠K is; m∠K < 90°What is the H-i-n-g-e Theorem?The h-i-n-g-e theorem, which is also known as the open mouth theorem states that two triangles that have a pair of corresponding congruent sides and which have different measure of the included angle between the sides, then the third side of the triangle with the larger included angle will be longer.
The h-i-n-g-e theorem can be deduced from the triangle inequality theorem.
The corresponding congruent sides in the two triangles are;
[tex]\overline{KL}[/tex] is congruent to [tex]\overline{ON}[/tex], [tex]\overline{KM}[/tex] is congruent to [tex]\overline{NP}[/tex]
[tex]\overline{LM}[/tex] = 7 is less than [tex]\overline{OP}[/tex] = 9
Therefore;
[tex]\overline{LM}[/tex] < [tex]\overline{OP}[/tex]
m∠N = 90°, therefore, the converse of the h-i-n-g-e theorem, indicates that the angle subtended by the segment [tex]\overline{LM}[/tex] is less than the angle subtended by the angle [tex]\overline{OP}[/tex], which is 90°
The angle ∠K is less than the angle ∠N
m∠K < m∠N = 90°
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Which solid figures do NOT have a vertex or vertices? (Check all that apply.)
cylinders
cones
prisms
pyramids
Answers
Answer: Cylinders and Cones don't have a vertex or vertices.
Step-by-step explanation: I had the same question and got it right.
Have a good day! <3
39.6% of consumers believe that cash will be obsolete in the next 20 years. Assume that 6 consumers are randomly selected. Find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years.
Answers
The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.
The binomial probability:The binomial probability formula is used to calculate the probability of getting exactly k successes in n independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is denoted as p. The formula is:
[tex]P(X=k) = C(n,k)\times p^k\times(1-p)^{(n-k)[/tex]Here we have
39.6% of consumers believe that cash will be obsolete in the next 20 years.
Let p be the probability that a consumer believes that cash will be obsolete
=> p = 39.6% or 0.396.
Then, the probability that a consumer does not believe that cash will be obsolete is q = 1 - p = 0.604.
We need to find the probability that less than 3 of the selected consumers believe that cash will be obsolete.
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
Using the binomial probability formula, we have:
[tex]P(X = k) = C(n,k) \times p^k\times q^{(n-k)[/tex]
=> P(X = 0) = C(6, 0) × (0.396)⁰ × (0.604)⁶ = 0.048
=> P(X = 1) = C(6, 1) × (0.396)¹ × (0.604)⁵ = 0.18
=> P(X = 1) = C(6, 2) × (0.396)² × (0.604)⁴ = 0.3
P(X < 3) = 0.048 + 0.18 + 0.3 = 0.528
Therefore,
The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years IS 0.528.
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I need help please!!! It for geometry
Answers
Answer:
Below
Step-by-step explanation:
The diagonals WY and XZ are equal for a rectangle
14x+10 = 11x+ 22
3x = 12
x = 4
then use this value to calculate the length
WY = 14 x + 10
= 14 (4) + 10 = 66 units
What is the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labeled 1-10?
Answers
The probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.
What is meant by probability?An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur.
In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.
It is said that there are 10 balls in a bag, labelled 1-10.
Now,
The number of ways the ball labelled 1 is picked is 1
The number of ways the ball labelled 2 is picked is 2
So the number of ways a ball labelled certain number is picked is 1.
Now there is no replacement.
So the total number of balls decreases by 1 when 1 ball is taken.
Then,
The probability of choosing the ball numbered 1 = 1/10
The probability of choosing 2 = 1/9
The probability of choosing 3 = 1/8
.
.
.
the probability of choosing 10 = 1
Total probability of choosing the balls in consecutive order = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.
Therefore the probability of someone pulling 1-10 in consecutive order from a bad that contains 10 balls labelled 1-10 is 1/3628800.
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Solve for x given the info.
Ignore the pencil mark
Answers
Answer x is 7
Step-by-step explanation:
The three angles are 104degrees, (9x-25) and unknown
The pictures shows that the two sides are equal therefore the two opposite angles are equal
104 + (9x-25) +(9x-25) =180
RE write
104 +2(9x-25) =180
Subract 104 from both sides
2(9x-25) = 180-104
2(9x-25) = 76
Divide both sides by 2
9x - 25 = 38
Add 25 to both sides
9x = 63
Divide both sides by 9
X =7
The angle is 9x-25 = 38
he three data sets have the same mean and range, but is the variation the same? Prove your answer by computing the standard deviation. Assume the data were obtained from samples. (a) 4, 5, 11, 13, 13, 14 (b) 5, 7, 10, 10, 13, 15 (c) 3, 10, 11, 11, 12, 13
Answers
The standard deviations of the data are different.
Standard deviation:
The formula used to calculate the standard deviation of data is given by
Standard deviation = √[ ∑(x[tex]_{i}[/tex] - x)² /n ]x - mean of the data and n = number of observations
Here we have
(a) 4, 5, 11, 13, 13, 14
Mean of the data = [4 + 5 + 11 + 13 + 13 + 14 ]/6 = 60/6 = 10
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 96
=> √[ ∑(x[tex]_{i}[/tex] - x)²/n ] = √[ 96/ 6 ] = 4
(b) 5, 7, 10, 10, 13, 15
Since the mean of the data is equal for all
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 68
=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 68/ 6 ] = 3.36
(c) 3, 10, 11, 11, 12, 13
On calculating deviations
=> ∑(x[tex]_{i}[/tex] - x)² = 64
=> √[ ∑(x[tex]_{i}[/tex] - x)² /n ] = √[ 64/ 6 ] = 3.26
Therefore,
The standard deviations of the data are different.
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A school needs to go buy new notebooks and desk computers for it s computer lap the notebook cost $250 each, and the desktop computers cost $175
Answers
Answer:
I'm sorry, it seems like you didn't complete the question. Can you please provide me with the rest of the question so I can assist you?
Una fabrica ganaba $80 por hora hombre de mano de obra cuando se abrió Cada año, la fabrica obtiene un 5% adicional por hora hombre
Answers
As a result, after five years, the business makes $102.10 per hour of work performed by men.
What are a company's earnings?The gains that a company makes are its earnings. They are obtained by deducting revenue from cost of products sold, running costs, and taxes. The creation and ongoing running of a company are primarily motivated by the desire to generate profits. Dividend payments to stockholders can then be made with the earnings.
If the factory earned $80 per man-hour of labor when it opened, and each year earns an additional 5% per man-hour, we can calculate the earnings for any given year using the formula:
E = $80 × (1 + r)ⁿ
where E is the earnings per man-hour, r is the annual rate of increase (5% = 0.05), and n is the number of years since the factory opened.
For example, if we want to find the earnings per man-hour after 3 years, we would plug in n=3:
E = $80 × (1 + 0.05)³
E = $80 × 1.157625
E = $92.61
Therefore, after 3 years, the factory earns $92.61 per man-hour of labor.
Similarly, if we want to find the earnings per man-hour after 5 years, we would plug in n=5:
E = $80 × (1 + 0.05)⁵
E = $80 × 1.276282
E = $102.10
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The correct question is:
A factory earned $80 per man-hour of labor when it opened Each year, the factory earns an additional 5% per man-hour
A group of students is painting a background piece for the school play. What is the area of the part that is painted blue?
Answers
The area of the part that is painted blue is 679 ft.
What are the basic arithmetic operations?
The four basic arithmetic operations are addition, subtraction, multiplication, and division.
Arithmetic operations are the building blocks for all mathematical processes and methods. (Yeah, they’re kind of a big deal!) These types of operations are part of the “arithmetic” branch of math.
Arithmetic operations strip math down to the basics that we use every day, whether we realize it or not. Those basics are addition, subtraction, multiplication, and division.
The area
= 20×30+(1/2)×20×(40-30) -3x5 - 2×3
= boot 10x10- 15-6
= 700-21
= 679
Hence, The area of the part that is painted blue is 679 ft.
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Critique Reasoning Mario says that he drew two tangents to a circle
that meet at a point outside the circle. He also says that the two points
where the two tangents meet the circle separate the circle into two
semicircles. Is it possible for Mario to have drawn this figure? Explain.
Answers
No, it is not possible for Mario to have drawn this figure.
What are the properties of the circle?The circumference, which is the distance around the object, the diameter, which is the length of a circle measured from one end to the other and passing through its center, and the radius, which is equal to half of the diameter, are the three key characteristics.
If two tangents to a circle meet at a point outside the circle, they must be parallel to each other.
If the two points where the two tangents meet the circle separate the circle into two semicircles, then the center of the circle must lie on the line containing the two points.
However, since the tangents are parallel, they do not intersect the line containing the two points, and therefore, the center of the circle cannot lie on this line.
This contradicts the definition of a circle, which states that the center of a circle is equidistant from all points on the circle.
Therefore, Mario's reasoning is flawed, and it is not possible for him to have drawn this figure.
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Determine whether -(p « › q) and p «> -q are logically equivalent.
Answers
No, -(p « › q) and p «> -q are not logically equivalent.
What is logical equivalence?When two logical assertions have the same truth value for all conceivable truth value assignments to their constituent propositions, the two statements are said to be logically equivalent. In other words, two assertions are comparable logically if and only if all feasible permutations of the truth values of their component propositions are equal.
First, let's rewrite the statements using the standard logical operators of negation, conjunction, and implication:
-(p « › q) is equivalent to ¬(p ∧ ¬q)
p «> -q is equivalent to ¬p → ¬¬q, which simplifies to p → q
Now, we can construct a truth table with columns for p, q, ¬(p ∧ ¬q), and p → q:
p | q | ¬(p ∧ ¬q) | p → q
--|----------|------------------|-----
T T F T
T F T F
F T T T
F F T T
We can see that the truth values of the two statements are not always the same.
For example, when p is true and q is false, ¬(p ∧ ¬q) is true and p → q is false.
Therefore, -(p « › q) and p «> -q are not logically equivalent.
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Please Help!
Solve each inequality:
1) P=a+b+2c
2) y=2ab-C
Answers
We can write the expression for {P} as -
P = a + b + 4ab - 2y
What is inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size
Given are the expressions as -
P = a + b + 2c
y = 2ab - C
We can write -
C = 2ab - y
Putting the values in the equation -
P = a + b + 2c
P = a + b + 2(2ab - y)
P = a + b + 4ab - 2y
Therefore, we can write the expression for {P} as -
P = a + b + 4ab - 2y
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An isosceles triangle has a perimeter of 19 inches. A leg is 2 inches longer than the base. How long is the
base?
Answers
Answer:
Base = 5inches
Step-by-step explanation:
2(x+2) + x
2x+4+x
3x+4=19
3x=15
x=5
Answer:x5
Step-by-step explanation:
mean is 75 beats per min . s/d is 12.5 if 16 female adults randomly selected find the probability that they have pulse rates with mean less than 78 beats per min
Answers
The value of probability that they have pulse rates with mean less than 78 beats per min is,
⇒ 0.5948
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Given that;
Mean is 75 beats per min.
And, Standard deviation is, 12.5
Hence, We get;
z = (78 - 75) / 12.5
z = 3/12.5
z = 0.24
Hence, The probability is, 0.5948
Thus, The value of probability that they have pulse rates with mean less than 78 beats per min is,
⇒ 0.5948
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