Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
Preparing food for a day at the beach can be a fun and fulfilling experience. Charlie decided to make sandwiches for his family to snack on when they get hungry. In this case, each sandwich contains 3 slices of turkey and 3 slices of ham.
The first step in making the sandwiches is to gather all the necessary ingredients. Charlie will need bread, turkey slices, ham slices, and any other desired condiments such as mayonnaise, mustard, lettuce, or tomato. He can choose any type of bread, but a sturdy bread such as a ciabatta, sourdough, or French bread would be ideal for a day at the beach.
To assemble the sandwiches, Charlie can follow these simple steps:
1. Lay out the bread slices. Charlie can choose to use one slice of bread per sandwich or two slices for a heartier sandwich.
2. Add a layer of mayonnaise or mustard if desired. Charlie can choose to spread the condiment on one or both slices of bread.
3. Add a layer of lettuce or tomato if desired. This can add some crunch and freshness to the sandwich.
4. Add 3 slices of turkey on one slice of bread, making sure they are evenly distributed. Charlie can choose to overlap the slices or lay them flat.
5. Add 3 slices of ham on top of the turkey slices, again making sure they are evenly distributed.
6. Top the sandwich with the other slice of bread, condiment-side down.
7. If desired, cut the sandwich in half or quarters for easy sharing and eating.
Charlie can repeat these steps for as many sandwiches as needed for his family. He can also customize the sandwiches by adding or subtracting ingredients, such as cheese, bacon, avocado, or pickles.
In terms of nutritional value, the sandwiches provide a good source of protein from the turkey and ham. The bread provides carbohydrates for energy, while the lettuce and tomato provide vitamins and minerals. The mayonnaise or mustard provides some fat and flavor, but can be skipped if desired.
Overall, making sandwiches for a day at the beach is a simple and convenient way to provide nourishing and satisfying food for the family. By following these steps, Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
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Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich how does he adjust the situation ?
3. A man earns # 140 000 per annum. He is allowed a tax free pay of # 30 000. If he pays 25 kobo in the naira as tax on his taxable income, how much has he left as disposable income?
4. A discount of 15% is allowed on an article. If a customer received N600.00, find the actual amount paid on the article.
the man has #112,500 left as disposable income after paying taxes.
the actual amount paid on the article after the 15% discount is N600.00.
How to calculate the disposable income?To calculate the disposable income of the man, we first need to determine his taxable income.
Taxable income = Annual income - Tax-free pay
Taxable income = #140,000 - #30,000 = #110,000
Next, we need to calculate the tax he has to pay on his taxable income.
Tax = Tax rate x Taxable income
Note that the tax rate is given in kobo, so we need to convert it to naira.
1 naira = 100 kobo, so 25 kobo = 0.25 naira
Tax = 0.25 x #110,000 = #27,500
Finally, we can calculate the disposable income by subtracting the tax from the annual income.
Disposable income = Annual income - Tax
Disposable income = #140,000 - #27,500 = #112,500
Therefore, the man has #112,500 left as disposable income after paying taxes.
4.If the discount allowed on an article is 15%, it means that the customer will pay only 85% of the original price of the article after the discount is applied.
Let the original price of the article be P.
Then, the amount paid by the customer after the 15% discount is 85% of the original price:
Amount paid = 0.85P
We know that the customer received N600.00.
So, we can set up an equation:
0.85P = N600.00
Solving for P, we get:
P = N600.00 / 0.85
P = N705.88 (rounded to two decimal places)
Therefore, the actual amount paid on the article after the 15% discount is N600.00.
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a football stadium has a length of 125m and 85m. if a boundary wall is to be raised, how long should it be
The length of the boundary wall that needs to be raised to enclose the entire football stadium is 420 + 40 = 460 meters.
how to determine the length of the boundary wall ?To determine the length of the boundary wall that needs to be raised, we need to know which part of the stadium the wall will enclose.
If the wall is to be raised along the length of the stadium (i.e., the longer side), then the length of the wall will be equal to the length of the stadium, which is 125 meters.
If the wall is to be raised along the width of the stadium (i.e., the shorter side), then the length of the wall will be equal to the width of the stadium, which is 85 meters.
If the wall is to enclose the entire stadium, then we need to find the perimeter of the stadium and add the length of the wall that will enclose the remaining side.
Perimeter of the stadium = 2 x (length + width)
Perimeter of the stadium = 2 x (125 + 85) = 420 meters
To enclose the remaining side, we need to add a wall of length 125 - 85 = 40 meters.
Therefore, the length of the boundary wall that needs to be raised to enclose the entire football stadium is 420 + 40 = 460 meters.
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my neighborhood is full of one-way streets. to drive from my house to the grocery store, i have to go 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east. each block is of a mile. how much shorter would my trip be if i could fly like a bird?
if you could fly like a bird, your trip would be approximately 3.9 miles shorter than the route you currently have to take (9 - 5.1 = 3.9).
If you were able to fly like a bird, you could take a direct path from your house to the grocery store, which would be shorter than the route you currently have to take.
By looking at the given directions, we can see that you have to travel a total of 1+1+5+2=9 blocks, with each block being a mile long, so your total distance traveled is 9 miles.
If you could fly like a bird, you could take a straight-line path from your house to the grocery store, which would be the hypotenuse of a right triangle with sides of 1 block and 5 blocks. Using the Pythagorean theorem, we can calculate that the distance of the hypotenuse would be the square root of[tex](1^2 + 5^2)[/tex] = square root of 26, which is approximately 5.
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The surface of a cylinder is represented [tex]A = 2\pi r^{2} + 2\pi rh[/tex], where r is the radius of the cylinder and h is its height. Factor the right side of the formula.
Formula given for surface area of cylinder A=2πr² + 2πrh, where r is the radius and h is the height of the cylinder and its factorised form is A=2πr(r+h).
What is cylinder?
Cylinder is a three dimensional solid containing three faces, of which two are flat circles and third face is the curved face. The volume or space occupied by this solid is given by πr²h. And its curved surface area is given by 2πrh. The total surface area of this solidis the sum of areas of all three faces which is given by 2πr² + 2πrh.
Given that, surface area of cylinder is A=2πr² + 2πrh
To factorise any given expression or equation, we find the factors of the each terms.
1st term=2πr²
factors of 1st term= 2 × π × r × r
2nd term= 2πrh
factors of 2nd term= 2 × π × r × h
Next, find the common factors from these terms
common factors or highest common factors of 1st and 2nd term=2 × π × r
The highest common factors are written outside the brackets & the remaining terms inside the brackets.
A=2πr² + 2πrh
=2 × π × r (r + h)
=2 π r (r + h)
A=2 π r (r + h) is the factorised form of the surface area of cylinder.
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in a city on average there are 2 power failures per month. calculate the probability of 12 power failures occurring in a semester.
The probability of 12 power failures occurring in a semester is approximately 0.065 or 6.5%.
To calculate the probability of 12 power failures occurring in a semester, we need to use the Poisson distribution, which models the number of events that occur in a fixed interval of time or space.
The Poisson distribution is appropriate when the events occur randomly and independently, and the rate of occurrence is constant.
The Poisson distribution has a single parameter, lambda (λ), which represents the mean and variance of the distribution. In this case, λ = 2 power failures per month * 6 months in a semester = 12 power failures per semester.
Using the Poisson probability mass function, we can calculate the probability of exactly 12 power failures in a semester:
P(X = 12) = (e^(-λ) * λ^12) / 12!
= (e^(-12) * 12^12) / 12!
≈ 0.065
This means that in a large number of semesters, we would expect to observe 12 power failures in about 6.5% of them.
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Find the value of X.
The value of x as required to be determined in the task content is; 10.7°.
What is the value of x?It follows from the task content that the value of x is to be determined from the task content.
Since the given figure is such that the lines MN and MP are tangents to the circle; the assertion which holds is that <MLP and <MNP are supplementary angles.
On this note, it follows that;
73° + x° = 180°.
On this note;
x = 180 - 73
x = 107°.
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The distance between two tourist attractions on a map is
[tex]5 \frac{3}{4} [/tex]
inches. The map has a scale of 3 in : 2km. What is the actual distance between the two tourist attractions?
The map is scaled at 3 in. to 2 km. Therefore , 3 inches on the map correspond to 2 kilometres in actual distance between two tourist.
WHO DEFINES SCALE?A scale is a group of figures—numbers, amounts, etc.—used to gauge or contrast an object's level. A scale in maps refers to the relationship between an object's actual size and its size on a map, model, or diagram.
We can use the following ratio to determine the real separation between the two tourist attractions:
"2 kilometers / 3 inches= kilometers /× 5 3/4 inches"
where x is the actual separation between the two attractions for tourists.
To find x, we can cross-multiply:
`3× x = (5 + 3/4× 2`)
`3x = 11.5`
`x = 11.5 / 3`
`x = 3.83 km`
The actual distance between the two tourist destinations is 3.83 kilometers
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.
Solve for the unknown variable. Give all of the exact general solutions.
cosθ = sinθ
1 + sinθ = 2cos^2 (θ)
sin3θ = -1
Answer:
Solving for the unknown variable:
cosθ = sinθ
Dividing both sides by cosθ, we get:
tanθ = 1
Taking the inverse tangent of both sides, we get:
θ = π/4 + nπ, where n is an integer.
Therefore, the exact general solution is:
θ = π/4 + nπ, where n is an integer.
1 + sinθ = 2cos^2 (θ)
Using the identity cos^2 (θ) + sin^2 (θ) = 1, we can rewrite the equation as:
1 + sinθ = 2(1 - sin^2 (θ))
Expanding the right-hand side, we get:
1 + sinθ = 2 - 2sin^2 (θ)
Rearranging, we get:
2sin^2 (θ) + sinθ - 1 = 0
Using the quadratic formula, we get:
sinθ = (-1 ± √5)/4
Taking the inverse sine of both solutions, we get:
θ = arcsin [(-1 ± √5)/4] + 2nπ or π - arcsin [(-1 ± √5)/4] + 2nπ, where n is an integer.
Therefore, the exact general solution is:
θ = arcsin [(-1 ± √5)/4] + 2nπ or π - arcsin [(-1 ± √5)/4] + 2nπ, where n is an integer.
sin3θ = -1
Taking the inverse sine of both sides, we get:
3θ = (-1)^n (π/2) + 2nπ, where n is an integer.
Dividing both sides by 3, we get:
θ = (-1)^n (π/6) + (2nπ)/3, where n is an integer.
Therefore, the exact general solution is:
θ = (-1)^n (π/6) + (2nπ)/3, where n is an integer.
PLEASE PLEASE HELP HURRY!!!
Score for Question 2:___ of 2 points)
2. Determine the volume of the figure that has a radius of 2 feet. Round your answer to the nearest tenth of a
cubic foot.
Answer:
-3 ft
-2 ft
10 ft
Step-by-step explanation:
The volume of a cone is given by the formula (1/3)πr^2h, where r is the radius of the base and h is the height. So, the volume of the cone is:
V_cone = (1/3)π(2 ft)^2(3 ft)
V_cone = (4/3)π ft^3
The volume of a cylinder is given by the formula πr^2h, where r is the radius of the base and h is the height. So, the volume of the cylinder is:
V_cylinder = π(2 ft)^2(10 ft)
V_cylinder = 40π ft^3
To find the total volume, we add the volumes of the cone and cylinder:
V_total = V_cone + V_cylinder
V_total = (4/3)π + 40π
V_total = 133.2 ft^3
Rounding off the answer to the nearest tenth of a cubic foot, the total volume is approximately 133.2 ft^3.
Answer: 138.23 ft³
Step-by-step explanation:
V = V of Cylinder + V of Cone
V of Cylinder = πr^2h
V of Cylinder = (2)^2 x 10 x π
V of Cylinder = 40π
V of Cone = πr^2(h/3)
V of Cone = π x (2)^2 x 3/3
V of Cone = π x 4 x 1
V of Cone = 4π
Total V = 40π + 4π
Total V = 138.23 ft³
higher levels of confidence generally require: question 8 options: wider confidence intervals. narrower confidence intervals. a smaller standard error. unbiased estimates.
The correct answer is wider confidence intervals.
Why higher levels of confidence generally require wider confidence intervals?In statistics, a confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. The level of confidence is typically set at 90%, 95%, or 99%, and represents the percentage of intervals that would contain the true parameter if we were to repeat the sampling process many times.
Higher levels of confidence mean that we are more certain that the true parameter falls within the interval. However, achieving higher levels of confidence requires larger sample sizes or larger standard errors, which in turn leads to wider confidence intervals.
To understand this, consider the formula for a confidence interval:
CI = point estimate ± margin of error
The margin of error is a function of the sample size and the standard error. As the sample size increases or the standard error decreases, the margin of error decreases, which leads to a narrower confidence interval. Conversely, if we want to increase the level of confidence, we need to increase the margin of error, which requires either a larger sample size or a larger standard error, leading to wider confidence intervals.
Therefore, higher levels of confidence generally require wider confidence intervals, which means we are less precise in our estimate but more certain that the true parameter falls within the interval.
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the probability that a person will miss the bus is 0.4, find the probability that on two consecutive morning, he will miss the bus at least one morning
Answer:
To find the probability that on two consecutive mornings the person will miss the bus at least one morning, we can use the complement rule. The complement of missing the bus is catching the bus. Therefore, the probability of missing the bus on both mornings is (0.4) x (0.4) = 0.16. The probability of not missing the bus on both mornings is (1 - 0.4) x (1 - 0.4) = 0.36. To find the probability of missing the bus at least one morning, we can subtract the probability of not missing the bus on both mornings from 1: P(missing bus at least once) = 1 - P(not missing bus on both mornings) P(missing bus at least once) = 1 - 0.36 P(missing bus at least once) =
I NEED HELP ON THIS ASAP!!! IT'S DUE TONIGHT
Because the distances XY and X'Y' are different, we can conclude that the rotation is incorrect (it shouldn't affect the lengths of the sides).
How to determine if the rotation is correct or not?Let's look at the original triangle, we can see that the distance between the vertices X (2, 5) and Y (10, 9) is:
Distance = √( (2 - 10)² + (5 - 9)²)
Distance = 8.94
The distance between the corresponding vertices in the second triangle X' (0, 1) and Y' (3, 9) is:
D = √( (0 - 3)² + (1 - 9)²) = 8.54
So that distance changed, which means that the shape of the triangle is now different, so the rotation is not done correctly.
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PLease help me answer this question urgently
Answer:
64 units^2
Step-by-step explanation:
The area of a triangle is:
A = 1/2×base×height
For the base, any side can be the base and the corresponding height to go with it has to be perpendicular.
For this question, the left side, 16, will be the base. And the height will be 8.
Area = 1/2bh
= 1/2•16•8
= 64
complete the table below
The complete table is :
10 40 12.4 150 360
200 800 248 320 768
What is table?In mathematics, a table is a way of organizing and presenting data in rows and columns.
The data is usually numerical or categorical, and the table allows us to compare and analyze the data in a structured way.
Tables can be used to display the results of calculations, record experimental data, or summarize information from surveys or questionnaires.
10x = 40 ×200
10x = 8000
x = 8000/10
x = 800
800x = 40 × 248
x = 12.4
150x = 320 × 360
x = 768
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how do you write a linear equation?
The standard form for linear equations in two variables is Ax+By=C.
What is a system of linear equations?A group of two or more linear equations that you want to solve simultaneously is referred to as a system of linear equations. A combination of numbers that makes every equation true simultaneously is the solution to a system of linear equations.
Systems of linear equations can be solved using a variety of techniques, including substitution, elimination, and graphing.
For example, 2x+3y=5 is a linear equation in standard form.
Utilize it to determine the slope and y-intercept before writing the Slope-intercept form should be used to formulate the equation.
A linear equation can be used to represent a straight line on a graph.. There are several ways to write it, however one of the most used is the slope-intercept form:
y = mx + b
where m denotes the line's slope and b its y-intercept. The difference in y between any two points on a line, divided by the difference in x, is the slope of the line. The line's intersection with the y-axis is known as the y-intercept.
You need to know either two points on the line or the slope and one point on the line in order to form a linear equation. With this knowledge in hand, you may utilize it to determine the slope and y-intercept before writing the Slope-intercept form should be used to formulate the equation.
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How do you Writing Linear Equations Using the Slope and Intercept?
Follow this link to view Jamie’s work. Critique Jamie’s work by explaining the reasonableness of the scenario and the accuracy of the two parts of the graph he described . For any portion of Jamie’s response in which he has made an error, provide and explain an alternative response.
To enhance Jamie’s explanation, describe both sections of the piecewise function using linear equations. Include any limits to the domain.
Using the graph,
The 1st statement is true as we can see from the graph the runner starts at origin 0 and till it reaches the point (12,1) it grows steadily as the graph is steep and increasing as we move forward.
This 2nd statement is also true as we can see in the graph that the 2nd runner's graph is a lot steeper than the 1st runner & stops at a point (20,2).
Define graph?An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.
In the first statement:
It says that the runner begins the race & runs at a steady pace for 1 minute.
This statement is true as we can see from the graph the runner starts at origin 0 and till it reaches the point (12,1) it grows steadily as the graph is steep and increasing as we move forward.
Now in the 2nd statement it says, another runner runs from point (12,1) and runs at a steady but faster pace for 1 minute.
This statement is also true as we can see in the graph that the 2nd runner's graph is a lot steeper than the 1st runner.
So, the 2nd runner is going faster than the 1st and we can see that the 2nd runner stops at a point (20,2).
That shows the 2nd runner also ran for 1 minute.
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Meadow View State Park has a great nature program for students. The ranger has a deck of 50 flash cards of things that they can see while visiting the park. He shuffles the deck and holds up 14 randomly chosen flash cards to show the students before putting them back in the deck. Here are the types of cards he has shown so far:
tree, animal, tree, rock, insect, tree, rock, animal, animal, tree, rock, tree, insect, tree
Based on the data, estimate how many tree cards are in the deck.
Answer:21 tree cards
Step-by-step explanation:
A bag has 12 different-colored marbles: 4 green, 5 blue, 1 yellow, and 2 orange. You draw a marble from the bag. If you get an orange marble or yellow marble, you win a prize.
Simulations may be used to find experimental probability. A simulation is a representation or model used to show outcomes of multiple trials of an experiment. For example, you could model 50 coin flips by assigning a 1 to heads and a 2 to tails, then using a random number generator to generate 50 outputs of the numbers 1 and 2. You may also simulate draws of a number by using a spinner, where the numbers on the spinner directly represent the numbers to be randomly drawn.
Use the game you chose in Part 1 to complete these tasks and answer these questions:
a. For the game you chose in Part 1, create a simulation to determine the experimental probability of winning the game. Your simulation should use tools that are not the same as those used in the game. Do not use a bag of marbles for the first game, a spinner for the second game, or cards for the third game. After you have chosen your tools, do at least 50 trials of your simulation. Record the trial results using a frequency table.
b. Describe how the simulation is used to calculate the experimental probability of winning the game.
c. Use the results of the simulation to calculate the experimental probability of winning. Show your work and provide the formula/ratio used.
d. What was the most likely outcome in the simulation? What was the least likely outcome? Why?
Thus, the theoretical probability (winning the game) when given that when orange marble or yellow marble appears is 1/4.
Explain about the term probability:The concept of probability can be applied to either individual events or relationships between them, including intersection and union, in the field of accounting. Any event's probability value could be between 0 and 1 (or 0% and 100%).
The probability value represents the likelihood that a specific event or outcome will occur given a list of all conceivable events or outcomes. It is possible to express the probability value as a fraction or percentage. Also, depending on how an event is related to other events, the probability of an occurrence may be described in terms both independent or conditional probability.Given data:
Total marbles in bag = 12.4 green, 5 blue, 1 yellow, and 2 orange.probability = favourable outcome / total outcome
probability (winning the game) --> only when orange marble or yellow marble appears.
Thus,
Total favourable outcome = 1 yellow + 2 orange = 3.
probability (winning the game) = 3/12 = 1/4
Thus, the theoretical probability (winning the game) when given that when orange marble or yellow marble appears is 1/4.
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Correct question:
A bag has 12 different-colored marbles: 4 green, 5 blue, 1 yellow, and 2 orange. You draw a marble from the bag. If you get an orange marble or yellow marble, you win a prize.
What is the theoretical probability of winning the game?
Find the equation of the line that passes through the point (8,-7) and is perpendicular to the line y = 1/2x-2
The equation of the line is
(Use integers or fractions for any numbers in the equation. Simplify your answer.)
Answer:
[tex]y=-2x+9[/tex]
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other, so the line we need to find has a slope of [tex]-2[/tex].
Using point-slope form,
[tex]y+7=-2(x-8) \\ \\ y+7=-2x+16 \\ \\ y=-2x+9[/tex]
Mrs Sweet has 8 different milk chocolates and 9 different plain chocolates.
-
Her daughter chooses one of the milk chocolates.
Her son then chooses one of the plain chocolates.
Mrs Sweet then chooses one of the remaining chocolates.
Work out how many different combinations of three chocolates they can choose.
There are 1008 different combinations of three chocolates that they can choose.
What is a combination?
Combination is a way of selecting objects from a larger set, where the order of the selected objects does not matter.
There are three separate choices to be made, so we need to multiply the number of choices for each step.
First, the daughter chooses one of the 8 milk chocolates. She has 8 options.
Next, the son chooses one of the 9 plain chocolates. He has 9 options.
Finally, Mrs. Sweet chooses one of the remaining 14 chocolates (8 milk and 9 plain chocolates have already been chosen). She has 14 options.
To find the total number of combinations, we multiply the number of choices for each step:
8 x 9 x 14 = 1008
Therefore, there are 1008 different combinations of three chocolates that they can choose.
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Pls solve this and explain or show work pls
A step has a height of 5 inches. A ramp starts 4 feet away from the base of the step, making a 5.9° angle with the ground. What can
you say about the angle the ramp would make with the ground if the ramp starts farther away from the step?
the ramp gets further away from the step, the angle it has with the ground decreases.
θ = [tex]tan^{-1}[/tex](0.515 / (48 + x))
How to find the angle that the ramp would make with the ground?Assuming that the ramp remains the same height as the step, we can use trigonometry to find the angle that the ramp would make with the ground if it starts farther away from the step.
First, let's convert the distance from feet to inches, since the height of the step is given in inches: 4 feet = 48 inches.
Next, we can use the tangent function to find the angle theta:
tan(θ) = opposite / adjacent
where opposite is the height of the step (5 inches) and adjacent is the horizontal distance from the base of the step to the point where the ramp meets the ground (48 inches * tan(5.9°) = 5.514 inches).
So, tan(θ) = 5 / 5.514, which gives us θ = 41.2°.
Now, let's say the ramp starts at a distance x from the base of the step. We can use the same formula, but with a different value for adjacent:
tan(θ) = 5 / (48 + x) * tan(5.9°)
We can simplify this expression by substituting the value of tan(5.9°) as approximately 0.1032:
tan(θ) = 0.515 / (48 + x)
Solving for theta, we get:
θ = [tex]tan^{-1}[/tex](0.515 / (48 + x))
As a result, we can see that the denominator of the fraction within the arctan function gets larger as x increases (i.e., the ramp starts further from the step), resulting in a smaller fraction and, consequently, a smaller angle theta. To put it another way, as the ramp gets further away from the step, the angle it has with the ground decreases.
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what is the mean mode and median of 5,5,5,6,9
Answer:
Mode: 5
Mean: 6
Median: 5
Step-by-step explanation:
- The mean is the sum of the data divided by the number of data points.
- The mode is the data point that appears most frequently.
- The median is the middle value in the sorted data set.
Help PLSSSSSSS I'm bad at math ;-;
Elizabeth's statement is incorrect because she didn't divide the inequality by 6 to isolate x.
How can the inequality be true ?To find the correct values of x that make the inequality true, we can solve the inequality:
6x < 42
Divide both sides by 6:
x < 7
Now, we can describe in words all values of x that make the inequality true:
Any value of x less than 7 makes the inequality 6x < 42 true.
For example, x = 5
6 x 5 < 42
30 < 42
This is therefore true.
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Find the lateral area of the pyramid
Answer:
The lateral surface area of the given square-based pyramid is 74 in².
Step-by-step explanation:
The lateral surface area of a three-dimensional object is the total surface area excluding the area of the base(s), so the total area of the "sides".
Therefore, the lateral surface area of a square-based pyramid is the sum of the area of the four triangular sides.
The area of a triangle is half the product of its base and height.
Therefore, the formula for the lateral surface area (L.S.A.) of a square-based pyramid is:
[tex]\boxed{\begin{minipage}{6 cm}\underline{L.S.A. of a square-based pyramid}\\\\$\sf L.S.A.= 2 \cdot s \cdot \ell$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the base length. \\ \phantom{ww}$\bullet$ $\ell$ is the slant height.\\\end{minipage}}[/tex]
From inspection of the given diagram:
[tex]\ell = \sf 7.4\;in[/tex][tex]s=\sf 5\;in[/tex]Substitute the given values into the formula to calculate the L.S.A. of the given square-based pyramid:
[tex]\begin{aligned}\implies \sf L.S.A.&=\sf 2 \cdot 5 \; in \cdot 7.4 \; in\\&=\sf 10 \; in \cdot 7.4 \; in\\&=\sf 74 \; in^2\end{aligned}[/tex]
Therefore, the lateral surface area is 74 in².
The lateral area of the pyramid is approximately 74square inches.
What defines a pyramid's horizontal side?
The triangular faces of the pyramid that converge at the apex are known as the lateral faces. These are the four triangles that encircle the square base in the provided net. As a result, the entire area of the four triangles makes up the pyramid's lateral surface area.
According to the given information:To find the lateral area of a pyramid, we need to find the sum of the areas of all the triangular faces except for the base. The lateral area formula for a pyramid is given by:Lateral area = 0.5 × Perimeter of base × Slant height where the slant height is the height of each triangular face.
First, let's find the perimeter of the base. Since the base is a square with a side length of 5.1 inches, its perimeter is:
Perimeter of base = 4 × Side length = 4 × 5.1 in = 20.4
In Next,
let's find the slant height. We can use the Pythagorean theorem to find the slant height of each triangular face.
The slant height is the hypotenuse of a right triangle with one leg equal to half the base length (since the base is a square) and the other leg equal to the height of the pyramid.
Half the base length = 5.1 in / 2 = 2.55
In Using the Pythagorean theorem, we get:Slant height = √(2.55² + 7²) ≈ 7.45 In Finally,
we can use the lateral area formula to find the lateral area of the pyramid:
Lateral area = 0.5 × Perimeter of base × Slant height= 0.5 × 20.4 in × 7.45 in≈ 76.02 in²
Therefore, the lateral area of the pyramid is approximately 76.02 square inches. Which is near to 74
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a population consists of 13 items. what is the number of different simple random samples of size 3 that can be selected from this population?
Step-by-step explanation:
to select 3 out of 13.
no repetition, and the sequence of the selected items does not matter.
that means combinations :
C(13, 3) = 13! / (3! × (13 - 3)!) = 13! /(3! × 10!) =
= 13×12×11 / (3×2) = 13×2×11 = 286
there can be 286 different random samples of size 3.
The answer is 286.
The number of different simple random samples of size 3 that can be selected from a population consisting of 13 items is 286.Explanation:Simple random sampling is a statistical technique used in research. In this sampling method, a subset of a population is selected randomly, with each member of the population having an equal chance of being selected. There are different types of random sampling methods, such as systematic sampling, stratified sampling, cluster sampling, etc.The number of different simple random samples of size k that can be selected from a population of size N is given by the formula N!/k!(N-k)!, where ! denotes factorial. Here, the population consists of 13 items, and we need to find the number of different simple random samples of size 3 that can be selected from this population.So, the required number of different simple random samples of size 3 that can be selected from this population is 13!/3!(13-3)! = 286.
Therefore, the number of different simple random samples of size 3 that can be selected from a population consisting of 13 items is 286.
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help asap assignment closes soon!
Answer:
Step-by-step explanation:
Given: d= 12 and h= 14
formula for the volume of a cone:
V= (1/3) · π · r² · h
V= volume
r= radius
h= height
to find the radius of the cone, we will use this formula r = 1/2 · d
r = 1/2 · 12
r = 6
Now that we know the value of the radius we can now plug it in in our formula.
V= (1/3) · π · 6² · 14
V= 1π · 6² · 14 / 3
V= 1π · 2²· 3² · 14 / 3
V= 2² · 14 · 3π
V= 2² · 14 · 3π
V= 2² · 42π
V= 4 · 42π
V= 168π
V=527.79
Hope this helps =D
Roven bought 1/3kg of surkey ham. Chisa bought 2/9kg less barkey
ham thon Raven, How many kilograms of turkey hom did they
buy together!
Raven bought 1/3 kg of turkey ham, and Chisa bought 2/9 kg less. The total amount of turkey ham they bought together is 1/3 + 1/9 = 3/9 + 1/9 = 4/9 kg. Together, they bought a total of 4/9 kg of turkey ham.
What is fraction?A fraction is a mathematical symbol that represents a portion of a whole or a component of a number. It is made up of two numbers divided by a horizontal line, with the number above the line (numerator) indicating the portion under consideration and the number below the line (denominator) indicating the entire or the total number of equal parts in the whole.
How many kilograms of turkey ham did they buy together?From the given information, we know that Raven bought 1/3 kg of turkey ham, and Chisa bought 2/9 kg less than Raven. This means that Chisa bought:
1/3 kg - 2/9 kg = 3/9 kg - 2/9 kg = 1/9 kg
Now we can find the total amount of turkey ham they bought together by adding Raven's purchase and Chisa's purchase:
1/3 kg + 1/9 kg = 3/9 kg + 1/9 kg = 4/9 kg
Therefore, Raven and Chisa bought a total of 4/9 kg of turkey ham together.
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When Ram was 16 years old, he deposited a certain sum of money in a bank at the rate of 10% p. a. Compounded annually. After his balance became 121 /700 times of the initial principal, he deposited 1/70 of the existing balance in the same account. After 1 year to this deposition, the bank changed it's policy to give interest at 20%p.a. simple interest. At the age of 24 years, Ram planned to start a business so, he withdrew all the money from his account. He found that the withdrawn amount was Rs. 359 less than thrice of the initial principal. Then,
1) Find the sum deposited by Ram at the age of 16 years.
2)The amount withdrawn from the bank was not enough so, he borrowed a loan of Rs. 1,10,000 from the bank and agreed to pay within 4 years, at a rate of 15% pa. compounded annually. He paid the interest of the first year at the end of the 1st year. He cleared his debt by paying equal installments in next year 2 years and 1 year. Find the total interest paid by him to the bank.
3) For how many years, he should have waited -to start the business so that he need not borrow an entra loan?
Step-by-step explanation:
Let the principal deposited by Ram at the age of 16 be P.
After the balance became 121/700 times of the initial principal, we have:
(121/700)P = P(1 + 10/100)^n
where n is the number of years for which the amount is compounded annually.
Simplifying the above equation, we get:
n = log(121/700)/log(1.1)
After Ram deposited 1/70 of the existing balance, his new balance became:
(121/700)P + (1/70)[(121/700)P] = (121/700)P(1 + 1/10)
After 1 year of this deposit, the new balance became:
(121/700)P*(1 + 1/10)(1 + 20/100) = (121/700)P(11/10)*(6/5) = (363/350)P
Given that this amount is Rs. 359 less than thrice of the initial principal, we get:
(363/350)P = 3P - 359
=> P = Rs. 2450
Therefore, the sum deposited by Ram at the age of 16 years was Rs. 2450.
The loan amount borrowed by Ram from the bank is Rs. 1,10,000 at a rate of 15% p.a. compounded annually for 4 years. Let the interest paid by Ram at the end of the 1st year be I1.
The amount to be paid by Ram at the end of the 1st year = 1,10,000*(1 + 15/100) = Rs. 1,26,500
Out of this, Ram pays only the interest amount, i.e., I1.
The remaining amount to be paid by Ram after the 1st year = 1,26,500 - I1
This amount is to be paid in 3 years, at a rate of 15% p.a. compounded annually.
Let the equal installments to be paid by Ram for the next 3 years be X.
Therefore, we have:
X*(1 + 15/100)^3 + X*(1 + 15/100)^2 + X*(1 + 15/100) = 1,26,500 - I1
Solving the above equation, we get:
X = Rs. 36,285.47
Therefore, the total interest paid by Ram to the bank is:
I1 + 3X - 1,10,000 = I1 + 336,285.47 - 1,10,000 = Rs. 59,856.41
To avoid borrowing an extra loan, the withdrawn amount should be equal to or greater than the amount required to start the business.
The withdrawn amount is given by:
3P - 359 = 3*2450 - 359 = Rs. 6891
Therefore, Ram should have waited for the amount in his bank account to become Rs. 6891 or more, which would take n years, where:
(121/700)2450(1 + 10/100)^n >= 6891
Solving the above equation, we get:
n >= 4.52
Therefore, Ram should have waited for at least 5 years to start the business, to avoid borrowing an extra loan.
12 ft
65 ft
33 ft
11 ft
20) Choose the correct answer.
Gracie covered her square playroom with 130.4 ft² of flooring. Which measurement is closest
to the side length of the playroom measured in feet?
The area of a square can be calculated by squaring the length of one of its sides. So, we can find the length of the side of the playroom by taking the square root of 130.4:
√130.4 ≈ 11.4
Therefore, the measurement closest to the side length of the playroom in feet is 11 ft. Answer: 11 ft.