These characteristics create a unique triangle.
Define congruent sidesCongruent sides are sides of a polygon (such as a triangle) that have the same length or measure. In other words, if two sides of a polygon are congruent, they are exactly the same length.
Given: Triangle has two acute angle (angle lass than 90)
third angle should be obtuse has a measure greater than 90 degrees.
To classify the triangle by its sides, we can look at the length of each side. Since there are no congruent sides, this triangle is a scalene triangle.
There is only one possible triangle that fits these characteristics - a scalene, obtuse-angled triangle with two acute angles and one obtuse angle, and no congruent sides.
Therefore, these characteristics create a unique triangle.
Image is attached below.
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Directions: Use the information in the charts to answer the questions. Show your
work and include equations to show how you solved each problem. Refer to the unit
glossary terms to remind yourself of the measurement conversions.
Beverages
at the Store
2 pints of
milk
2 quarts of
orange juice
16 cups of
chocolate
milk
32 ounces of
lemonade
1. Julius is buying beverages for brunch. He needs to buy a total of 5
gallons of beverages. He decides to buy two containers of each
beverage. How many gallons of beverages did he buy?
Therefore , the solution of the given problem of equation comes out to be Julius thus purchased a total of 2 gallons of beverages.
What is an equation?In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics associated with the x + 7 suggestions.
Here,
Julius needs to purchase a total of 5 gallons of beverages, therefore let's begin by converting the given measurements to gallons.
2 quarts of milk were given.
Orange juice, 2 quarts
16 cups of milk, chocolate
Lemonade, 32 ounces
The following conversion factors are available to us:
1 Pints = 1/8 gallon.
1/4 gallon = 1 quart.
1 cup = 1/16 gallon
1 ounce = 1/128 gallon.
2 pints of milk are equal to 1/8 gallon each pint, or
=> 2 pints * 1/8 gallon/pint = 1/4 gallon
2 quarts of orange juice converted to gallons:
=> 2 quarts * 1/4 gallon/quart = 1/2 gallon
16 cups of chocolate milk converted to gallons:
=> 16 cups * 1/16 gallon/cup = 1 gallon
How many litres of lemonade are in 32 ounces?
=> 32 ounces * 1/128 gallon/ounce = 1/4 gallon
Let's now calculate the total number of gallons of beverages Julius purchased:
=> 1/4 gallon (milk) + 1/2 gallon (orange juice) + 1 gallon (chocolate milk) + 1/4 gallon (lemonade) = 2 gallons
Julius thus purchased a total of 2 gallons of beverages.
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In the coordinate plane, a square has vertices (4, 3), (-3, 3), (-3, - 4). What is the location of the fourth vertex?
The two possible locations for the fourth vertex are (4, -4) and (-3, -1).
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
To find the location of the fourth vertex of the square, we need to use the fact that a square has four equal sides and four right angles.
The first two vertices given are (4, 3) and (-3, 3), which lie on a horizontal line segment of length 7.
The third vertex is (-3, -4), which is 7 units away from the first two vertices and lies on a vertical line segment.
Since the square has four equal sides, the distance between the third vertex and the fourth vertex must also be 7 units.
And since the square has four right angles, the fourth vertex must be located on a vertical line passing through the first two vertices or on a horizontal line passing through the third vertex.
So, there are two possible locations for the fourth vertex:
(4, -4): This point is located 7 units below the first vertex (4, 3) on the vertical line passing through it.
(-3, -1): This point is located 7 units to the right of the third vertex (-3, -4) on the horizontal line passing through it.
Therefore, the two possible locations for the fourth vertex are (4, -4) and (-3, -1).
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(01.08)
Let f(x) = 3x² + x - 3 and g(x) = x² - 5x +
1. Find f(x) - g(x).
Answer:
f(x) - g(x) = 2x² + 6x - 4
Step-by-step explanation:
f(x) - g(x)
= 3x² + x - 3 - (x² - 5x + 1) ← distribute parenthesis by - 1
= 3x² + x - 3 - x² + 5x - 1 ← collect like terms
= 2x² + 6x - 4
i need help pleaseeee!!!
a. The number of red roses left t hours after the store opens [tex]R(t) = 400/2^{t/2}[/tex]
b. The number of boxes of chocolate left t hours C(t) = 200 - 0.15t
c. One possible solution is t ≈ 7.546 hours after the store opens.
d. there are 194 boxes of chocolates left.
e. you need to arrive at the store no later than 7.504 hours after it opens.
How to find the number of red roses left ?a. The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.:
[tex]R(t) = 400/2^{t/2}[/tex]
b. Let C(t) be the quantity of boxes of chocolate left t hours after the store opens. At first, there are 200 boxes, of which 15% are purchased every hour. We can therefore write:
C(t) = 200 - 0.15t
c. We must solve the equation R(t) = C(t) in order to determine the time at which the number of boxes of chocolates and the number of roses are equal. We obtain: by substituting the formulas we discovered in parts a and b:
[tex]400/2^{t/2} = 200 - 0.15t[/tex]
Simplifying this equation, we get:
[tex]2^{t/2 + 1} + 0.15t - 400 = 0[/tex]
We can solve this equation numerically, using a calculator or a computer program. One possible solution is t ≈ 7.546 hours after the store opens.
d. At 12:30 in the early evening, which is 3.5 hours after the store opens, we can utilize the recipe we tracked down to some extent b to work out the quantity of boxes of chocolates left:
C(3.5) = 200 - 0.15(3.5) = 194.25
We ought to adjust this solution to appear to be legit with regards to the issue. Since we cannot have a fraction of a box, we can round to the nearest integer and state that there are 194 chocolate boxes remaining.
e. To buy 36 red roses, we need to solve the equation R(t) = 36. Substituting the formula we found in part a, we get:
[tex]400/2^{t/2}= 36[/tex]
Simplifying this equation, we get:
2^(t/2) ≈ 11.111
Taking the logarithm of both sides, we get:
t/2 ≈ log2(11.111)
t ≈ 2 log2(11.111)
Using a calculator, we get:
t ≈ 7.504 hours after the store opens.
Therefore, you must arrive at the store no later than 7.504 hours after it opens in order to purchase 36 red roses.
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A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 8 m and a diameter of 10 m. The container will be made from steel (including its top and bottom). Suppose the total cost of the steel will be $13,062.40. How much will the steel cost per square meter? Use 3.14 for it, and do not round your answer.
The per square meter cost of steel will be $32. The solution has been obtained by using the cylinder.
What is a cylinder?
The cylinder, one of the most basic curvilinear geometric shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.
We are given that the height of cylinder is 8 m and diameter is 10 m.
So, the radius is 5 m.
Now, using the surface area formula, we get
⇒ S = 2πrh + 2π[tex]r^{2}[/tex]
⇒ S = 2π * 5 * 8 + 2π * [tex]5^{2}[/tex]
⇒ S = 2 * 3.14 * 5 * 8 + 2 * 3.14 * 25
⇒ S = 251.2 + 157
⇒ S = 408.2 square meter
Now, it is given that the total cost of the steel will be $13,062.40.
So, per square meter cost will be:
⇒ Cost = [tex]\frac{13,062.40}{408.2\\}[/tex]
⇒ Cost = $32
Hence, the per square meter cost of steel for the cylinder will be $32.
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6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?
Answer:
40%
Step-by-step explanation:
2/5=x/100
cross multiply and you get 5x=200
by isolation the variable you will get x=40
therefore, 40% of Canadians read at least 10 books a year
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 17 , 22 36th term
Answer:
the 36th term is 187.
Step-by-step explanation:
To find the 36th term of a sequence, we need to know the rule that generates the sequence. Without that rule, we cannot find the 36th term.
However, if we assume that the sequence is an arithmetic sequence (meaning that there is a common difference between consecutive terms), we can use the given terms to find the common difference and then find the 36th term.
The common difference is found by subtracting the second term from the first term, or the third term from the second term.
Using the first and second terms, we get:
17 - 12 = 5
Using the second and third terms, we get:
22 - 17 = 5
Since both calculations give the same result, we can be confident that the common difference is 5.
Therefore, to find the 36th term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Using a1 = 12, d = 5, and n = 36, we get:
a36 = 12 + (36 - 1)5
a36 = 12 + 175
a36 = 187
So, if the sequence is an arithmetic sequence with a common difference of 5, then the 36th term is 187.
3√b in exponential form
A rectangular solid has edges that are 10, 8, and 3 units long.
1. Draw the solid, showing the 10 x 8 face as the base. Find:
a. The lateral area
b. The total area
c. The volume
2. Repeat Exercise 1, but show the 10 x 3 face as the base.
a.
b.
c.
We are adjusting the original rectangular solid and here is what we have:
1. Rectangular solid showing 10x8 face as the base(a) The lateral area is the sum of the areas of the four sides, which are all rectangles. The two sides with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two sides with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the lateral area is:
2(24) + 2(30) = 48 + 60 = 108 square units
(b) The total area is the sum of the areas of all six faces. The two faces with dimensions 10 x 8 have an area of 10 x 8 = 80 square units each, the two faces with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two faces with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the total area is:
2(80) + 2(24) + 2(30) = 160 + 48 + 60 = 268 square units
(c) The volume is the product of the length, width, and height of the rectangular solid. Therefore, the volume is:
10 x 8 x 3 = 240 cubic units
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Ricky would like to retire with an amount of 200,000 she found a bank that offers 9% interest compounded yearly and has an initial investment of 20,000.how much time will Ricky have to wait until she attains the 200,000 in this situation?
Ricky will have to wait for 26.78 years to have 200,000 in her account with this investment.
How do you calculate how long Ricky will wait for her investment to reach 200,000?In order to determine the time it takes for Ricky's initial investment to grow to the desired amount, we can use the compound interest formula: A = P(1 + r/n)^(nt)
Where:
A is the final amount in the account (in this case, 200,000)
P is the initial investment (in this case, 20,000)
r is the annual interest rate (in this case, 0.09 for 9%)
n is the number of times interest is compounded per year (in this case, 1 for yearly compounding)
t is the number of years
We are trying to solve for t, so we can rearrange the formula to:
t = ln(A/P) / (n * ln(1 + r/n))
Plugging in the values:
t = ln(200,000/20,000) / (1 * ln(1 + 0.09/1))
t = ln(10) / ln(1.09)
t ≈ 2.303 / 0.086
t ≈ 26.78
Ricky will have to wait approximately 26.78 years to have 200,000 in her account with this investment.
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1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
Answer:
Step-by-step explanation:
Answer:
You can make 12 possible sundaes with these toppings.
Step-by-step explanation:
Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:
1. Fudge & Chocolate Sprinkles
2. Fudge & Rainbow Sprinkles
3. Marshmallow & Chocolate Sprinkles
4. Marshmallow & Rainbow Sprinkles
-------------------------------------------------------------------------------------------------------------
4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.
Find m∠KRL.
help me on the question.
Angle KRL is equal to 34°. The main reason behind this is that KRL is vertically opposite to Angle QRP.
What are different types of rules applied in the above answer?KLR and LRM are complementary angles i.e.
KLR + LRM = 90
Similarly, HRQ and QRP are complementary angles i.e.
HRQ + QRP = 90
HRQ = 56 = LRM (vertically opposite angle)
KLR = KRM - LRM = 90 - 56 = 34
KLR = QRP = 34.
The two geometrical rules applied are,
(a) Vertically Opposite angles are always equal.
(b) Complementary angles are those angles which adds upto make 90 degree angle
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please help me answer this
The prompt that examines linear functions and ordered pairs are given below.
What is the explanation for the above response?1) Here are the ordered pairs for each point:
Point A: (4, 9)
Point B: (6, 3)
Point C: (1, 3)
Point D: (8, 7)
Point E: (8, 9)
See the attached graph.
2) Part A: The completed table and graph for Derek is given as attached.
Part B: Derek makes 10 bracelets in 5 hours.
3) The ordered pairs are given in the labelled graph accordingly.
4) Deanna's coordinates plane is labelled and attached accordingly. The correct answer is Option B (5,8)
5) The other ordered pairs that could be the vertext are Options A - E. See the attached image (Miguel's Squre
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HELP
Stained glass windows come in circles, semicircles, and quarter-circles. If Flo buys 2 circular windows, 5 semicircular windows, and 20 quarter-circular windows that all have a radius of 4 feet, what is the total area of the windows purchased by Flo? Round your final result to the nearest hundredth square foot.
Area of circle: _____
Area of semicircles: _____
Area of quarter-circles: _____
Total area of pattern: _____
Answers
Area of semicircles = 125.60
Area of quarter-circles=125.6
Area of circle=50.24
Total area of pattern=238.64
Area of quarter-circles = 251.20
Area of circle =100.48
Total area of pattern = 477.28
Area of semicircles=62.8
Rounding to the nearest hundredth, the total area is 238.64 square feet. Therefore, the correct answer is:
Area of circle: 50.24
Area of semicircles: 125.60
Area of quarter-circles: 251.20
Total area of pattern: 238.64
what is the total area of the windows purchased by Flo?The area of a circle with radius 4 feet is:
Area of circle = π × [tex]r^{2}[/tex] = 3.14 × [tex]4^{2}[/tex] = 50.24 square feet
The area of a semicircle with radius 4 feet is half the area of a circle with the same radius:
Area of semicircle = 0.5 × Area of circle = 0.5 × 50.24 = 25.12 square feet
The area of a quarter-circle with radius 4 feet is a quarter of the area of a circle with the same radius:
Area of quarter-circle = 0.25 × Area of circle = 0.25 × 50.24 = 12.56 square feet
Flo bought 2 circular windows with an area of 50.24 × 2 = 100.48 square feet.
She also bought 5 semicircular windows with an area of 25.12 × 5 = 125.60 square feet.
And she bought 20 quarter-circular windows with an area of 12.56 × 20 = 251.20 square feet.
The total area of the windows purchased by Flo is:
Total area = 100.48 + 125.60 + 251.20 = 477.28 square feet.
Rounding to the nearest hundredth, the total area is 238.64 square feet. Therefore, the correct answer is:
Area of circle: 50.24
Area of semicircles: 125.60
Area of quarter-circles: 251.20
Total area of pattern: 238.64
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Draw a bar model to represent the expression
t-2
One such tool that enables us to visualise the given math issue using various-sized rectangles or bars is the bar model.
What is bar model Representation?A bar model in mathematics is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes. To answer issues involving the four operations of addition, subtraction, multiplication, and division, bar models are most frequently utilised.
To help kids "see" mathematical structure, the bar model is utilised in teaching for mastery. It is not a method for solving issues, but rather a strategy to uncover the mathematical underpinnings of a problem and obtain knowledge and clarity to aid in its resolution.
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Image attached below,
3. How many ways can you line up 7 books on a shelf?
Answer:
There are 5040 different ways to arrange the 7 books on a shelf.------------------------------
Use the formula for permutations:
n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.The number of objects is n = 7 books.
Calculate the factorial:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040A convenience store collected data on its customers to determine the most popular items purchased. The manager of the convenience store created a table of the data they gathered.
Convenience Store Item Number of Purchases
Candy 75
Snacks 125
Automotive Supplies 100
Beverages 200
Which of the following circle graphs correctly represents the data in the table?
circle graph titled convenience store purchases, with four sections labeled candy 15 percent, snacks 20 percent, auto supplies 40 percent, and beverages 25 percent
circle graph titled convenience store purchases, with four sections labeled candy 30 percent, snacks 40 percent, auto supplies 20 percent, and beverages 10 percent
circle graph titled convenience store purchases, with four sections labeled snacks 20 percent, candy 40 percent, beverages 25 percent, and auto supplies 15 percent
circle graph titled convenience store purchases, with four sections labeled snacks 25 percent, candy 15 percent, beverages 40 percent, and auto supplies 20 percent
Candy accounts for 15% of the total purchases, snacks account for 25%, automotive supplies account for 20%, and beverages account for 40%.
Which of the following circle graphs correctly represents the data in the table?The correct circle graph representing the data in the table is:
circle graph titled convenience store purchases, with four sections labeled candy 15 percent, snacks 25 percent, auto supplies 20 percent, and beverages 40 percent.
This graph accurately represents the proportion of each item's purchases out of the total number of purchases. Candy accounts for 15% of the total purchases, snacks account for 25%, automotive supplies account for 20%, and beverages account for 40%.
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the equation of a parabola is f(x)=x^2-4x-5
the axis of symmetry is x = ?
the vertex of the parabola is (?,?)
If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:
(a) P(A')
(b) P(A∪B)
(c) P(A'∩B)
(d) P(A∩B')
(e) P[(A∪B)']
The probabilities are as follows:
(a) P(A')= 0.7
(b) P(A∪B) = 0.3
(c) P(A'∩B) = 0
(d) P(A∩B') = 0.1
(e) P[(A∪B)'] = 0.7
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7
(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3
(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0
(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1
(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7
Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.
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Michelle is building a car for the local soap box derby. The floor boards of her car need to be 2.2 meters long. If she has 13.2 meters of wood, how many floor boards can she make? 20 boardo
Michelle can make 6 floor boards for her car.
How many times does 2.2 meters fit into 13.2 meters?To determine how many floor boards Michelle can make, we need to divide the total length of wood she has (13.2 meters) by the length of each floor board (2.2 meters).
The number of floor which boards Michelle can make is:
= 13.2 meters / 2.2 meters/floor board
= 6 floor boards
Therefore, Michelle can make 6 floor boards for her car using the 13.2 meters of wood she has.
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2. The designers need to know the total surface area of the
entire robot in order to determine painting costs. If it costs
$0.02 per square centimeter, determine the cost to paint
each action figure.
12 cm
3. The designers also need to determine the total amount
of plastic to be used in the molds for each robot. If each cubic centimeter of
plastic costs $0.03, determine the total cost to mold each action figure.
4. The designers are discussing the best figure to use for the neck of the robot.
They have narrowed their decision to three options: a right circular cone with
a radius of 1 cm and a height of 2 cm, a square pyramid with base edge 2 cm
and a height of 2 cm, and a right hexagonal pyramid with base edges of 1 cm
and a height of 2 cm. Which figure will cost the least amount to produce?
Justify your answer.
Answer:
it's complex but i will justify wait me
Hurry help Greg plants a seed and as soon as the plant sprouts, he measures its height each day and records his data for two weeks. If the plant continues to grow the whole two weeks, what would a line graph of Greg's data look like?
It would be flat.
It would move downward.
It would go up and down.
It would move upward.
The line graph of Greg's data wood look like "It would move upward."
What is graph?A graph is a visual representation of data that shows the relationship between two or more variables. There are several types of graphs that can be used to display data
If Greg is measuring the height of the plant each day and the plant is continuing to grow for two weeks, then the line graph of his data would move upward. The graph would show an increasing trend as the plant grows taller each day. Therefore, the correct answer is "It would move upward."
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The test scores of students on a science test are normally distributed with an average score of 78 and a standard deviation of 4. Which statement is true? Responses About 16% of the students scored 74 or below. About 16 percent of the students scored 74 or below. About 32% of the students scored 82 or above. About 32 percent of the students scored 82 or above. About 50% of the students scored 74 or above. About 50 percent of the students scored 74 or above. About 68% of the students scored 82 or below.
The statement "About 16% of the students scored 74 or below" is true for the given normal distribution of test scores with an average of 78 and a standard deviation of 4.
What is standard deviation?Standard deviation is a measure of the amount of variation or dispersion of a set of values from their mean (average) value. It is calculated as the square root of the variance of a set of data. A smaller standard deviation indicates that the values are tightly clustered around the mean, while a larger standard deviation indicates that the values are more spread out.
In the given question,
About 16% of the students scored 74 or below is true. This is because of the empirical rule for normal distributions, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. So, if the average score is 78 and the standard deviation is 4, a score of 74 falls one standard deviation below the mean, which represents about 16% of the total data.
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Answer:
About 97.5% of the students scored 86 or below.
Step-by-step explanation:
NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6
. In an earlier study, the population proportion was estimated to be 0.33
.
How large a sample would be required in order to estimate the fraction of people who black out at 6
or more Gs at the 95%
confidence level with an error of at most 0.03
? Round your answer up to the next integer.
We need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.
How to determine how large a sample would be required in order to estimate the fraction of people who black out at 6or more Gs
We can use the formula for the sample size required to estimate a population proportion with a specified margin of error and confidence level:
n = (Z^2 * p * (1-p)) / E^2
where:
Z = the z-score corresponding to the desired confidence level (95% confidence level corresponds to a z-score of 1.96)
p = the estimated population proportion from the earlier study
E = the desired margin of error
Substituting the given values, we get:
n = (1.96^2 * 0.33 * (1-0.33)) / 0.03^2
n = 753.69
Rounding up to the next integer, we need a sample size of 754. Therefore, we need to select at least 754 people for the experiment to estimate the fraction of people who black out at G forces greater than 6 with an error of at most 0.03 and a 95% confidence level.
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The diameter of a circle is 5 centimeters. What’s the radius? Give the exact answer in simplest form
Answer:
2.5cm
Step-by-step explanation:
you half the diameter to get the radius
What’s 9 more then the quotient of 2 and x
Answer:
9+2/x or 2/x+9
Step-by-step explanation:
Answer:
I think it will be 2/x+9
Step-by-step explanation:
Could i get help on this pla
Using the formula for the area of a rectangle, the area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x
Calculating the area of the cellphoneFrom the question, we are to calculate the area of the cellphone shown in the diagram
From the given information,
We have a diagram that shows a cellphone which is rectangular in shape.
Thus,
We will use the formula for finding the area of a rectangle to calculate the area of the cellphone.
Area of a rectangle = Length * Width
From the given information,
Length of the cellphone = 6x²y⁶
Width of the cellphone = 3x⁻³y²
Thus,
Area of the cellphone = 6x²y⁶ × 3x⁻³y²
Area of the cellphone = 6 × 3 × x² × x⁻³ × y⁶ × y²
Area of the cellphone = 18 × x⁻¹ × y⁸
Area of the cellphone = 18x⁻¹y⁸ OR 18y⁸/x
Hence,
The area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x
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(6x^2+10x-7) + (-x^2-8x)
For the given expression, the addition of coefficients is [tex]5x^2 + 2x - 7[/tex].
What are coefficients?In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In other words, it is the number that is being multiplied by the variable.
What is addition?Addition is a basic mathematical operation that combines two or more numbers or quantities to produce a sum. It is denoted by the plus sign (+). When two or more numbers are added, the result is called the sum or total.
According to given information:First, we need to combine like terms by adding the coefficients of terms with the same variable(s) raised to the same power.
[tex](6x^2 + 10x - 7) + (-x^2 - 8x)[/tex]
[tex]= 6x^2 + (-x^2) + 10x + (-8x) - 7[/tex] (grouping like terms together)
[tex]= (6x^2 - x^2) + (10x - 8x) - 7[/tex] (rearranging terms)
[tex]= 5x^2 + 2x - 7[/tex] (combining the coefficients)
Therefore, the final answer for the addition of coefficients is [tex]5x^2 + 2x - 7.[/tex]
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A savings account earns an interest rate of 1.625 % compounded quarterly for an account with an initial deposit of $ 2 , 225 . How much money will be in the account after 6 years? Round your answer to the nearest hundredth.
The balance in the account after 6 years is $2,466.69.
What is compound interest?
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
We can use the formula for compound interest to find the balance in the savings account after 6 years:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where:
A is the balance in the account after t years
P is the initial deposit, which is $2,225
r is the annual interest rate, which is 1.625%
n is the number of times the interest is compounded per year, which is 4 (since it's compounded quarterly)
t is the number of years, which is 6
Plugging in these values, we get:
[tex]A = 2,225(1 + 0.01625/4)^{(4*6)}\\A = 2,225(1.0040625)^{24}[/tex]
A = 2,225(1.108227)
A = 2,466.69
Hence, the balance in the account after 6 years is $2,466.69.
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Determine which relation is a function.
A: {(–3, 2), (–1, 3), (–1, 2), (0, 4), (1, 1)}
B: {(–3, 2), (–2, 3), (–1, 1), (0, 4), (0, 1)}
C: {(–3, 3), (–2, 3), (–1, 1), (0, 4), (0, 1)}
D: {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}
The relation that is a function is D: {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}.
What is a relation?A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, for a relation to be a function, each input can only be related to one output.
In relation D, each input (x-value) has a unique output (y-value), meaning that each x-value is only paired with one y-value. In contrast, relations A, B, and C have repeated x-values with different y-values, which means that they are not functions.
In relation A, the input -1 is paired with two different outputs (2 and 3). In relation B, both inputs 0 and -1 are each paired with two different outputs. In relation C, both inputs 0 and -3 are each paired with two different outputs. Therefore, only relation D satisfies the definition of a function.
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