A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.
Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:
1. Enter the lengths of the sides of the right triangle into the calculator.
2. Select the angle for which you want to find the trigonometric ratios.
3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.
Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.
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A trigonometric ratios calculator is a tool that helps you find the sine, cosine, and tangent ratios in a right triangle. To use a trigonometric ratios calculator, you need to enter the lengths of the sides of the right triangle and the calculator will calculate the values of the sine, cosine, and tangent ratios for the angles in the triangle.
Here's how you can use a trigonometric ratios calculator to find the sine, cosine, and tangent ratios in a right triangle:
1. Enter the lengths of the sides of the right triangle into the calculator.
2. Select the angle for which you want to find the trigonometric ratios.
3. The calculator will display the values of the sine, cosine, and tangent ratios for the selected angle.
Note that the trigonometric ratios are defined only for right triangles, so it's important to make sure that the triangle you are working with is a right triangle before using a trigonometric ratios calculator.
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Kuta Software - Infinite Algebra 2
Right Triangle Trig. - Finding Missing sides and angles
Find the measure of each angle indicated.
1)
-
12
13
The measure of the indicated angle in each triangle is ∠U=80° and ∠Q =93°
The measure of each triangle's specified angle.
Comprehensive explanation:
Calculate the indicated angle's measurement.
Given: The additional two triangle angles.
Solution:
We are aware that a triangle's three angles add up to 180 degrees.
So,
The measure of the indicated angle in each triangle.
1st TRIANGLE
∠U+∠V+∠T =180°
∠U+63°37° =180°
∠U= 180°-100°
∠U=80°
2ND TRIANGLE
∠A+∠B+∠C=180°
46°+90°+∠C =180°
∠C=44°
The measure of the indicated angle in each triangle.
3rd TRIANGLE
∠R+∠P+∠Q= 180°
36°+51°+∠Q =180°
∠Q =93°
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select all of the following ways you can calculate percentages of normal populations between 2 values. a0z-tables b)exel c)slide rule d)some calculators e)mean tables
This set of ordered pairs defines a function.
{(-49,7), (-56,8), (-63,9), (-70,10)}
Which table represents the inverse of the function defined by the ordered pairs?
The inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)
What is an inverse function?An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of the function produces the output x. x. A function that has an inverse is called invertible, and the inverse is denoted by f⁻¹.
Given that, a set of ordered pairs defines a function.
{(-49,7), (-56,8), (-63,9), (-70,10)}
We need to find its inverse function,
Since, we know that,
The inverse of a function means that the input becomes the output of the function and the output becomes input.
When the function is given in the form of ordered pairs, the first element of each ordered pair represents the input and the second element represents the output.
Therefore,
The inverse will be:
{(7, -49), (8,-56), (9,-63), (10, -70)}
Hence, the inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)
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The population of a city grew from 23,000 in 2010 to 25,000 in 2015. What was the average rate of change during this time interval
The average rate of change for a city population of the city was growing steadily and can be used to predict future population growth.
The average rate of change for a city can be calculated by subtracting the initial population (23,000 in 2010) from the final population (25,000 in 2015) and then dividing that number by the total number of years (five). The equation for this calculation is:
(Final Population - Initial Population) / (Number of Years)
Using this equation, the average rate of change for the city is calculated as follows:
(25,000 - 23,000) / 5 = 2,000 / 5 = 400
Therefore, the average rate of change for the city between 2010 and 2015 was 400 people per year. This means that on average, the population of the city increased by 400 people each year during this time interval. This calculation shows that the population of the city was growing steadily and can be used to predict future population growth.
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Viola drives 2 kilometers up a hill that makes an angle of 9 with the horizontal. To the nearest tenth of a kilometer, what horizontal distance has she covered? Group of answer choices 12. 6 km 3. 2 km 2 km 0. 3 km
The horizontal distance jade she covered is approximately 2.0 km.
Let x be the horizontal distance,
Given,
Viola drives 2 kilometers up a hill that makes an angle of 9 with the horizontal.
Thus, the angle between the horizontal and the direction of his walking = 9°, and The angle between the horizontal and vertical = 90°
By making the diagram of the given situation,
The angle between vertical and the direction of his walking = 180°(9+90°)=180° - 99° = 81°
By the law of sine,
[tex]\frac{sin90}{2}=\frac{sin 81}{x}[/tex]
x*sin 90°=2*sin 81°
x= 1.97537668119 ≅ 2.0
Hence, the horizontal distance jade she covered is approximately 2.0 km.
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what's the difference between discrete math and continuous math like calculus?
Discrete mathematics is focused on discrete objects and the relationships between them, while calculus is focused on continuous change and motion.
Discrete mathematics and calculus are two branches of mathematics that deal with different types of mathematical objects and concepts. Discrete mathematics studies discrete objects, such as integers, graphs, and algorithms, while calculus deals with continuous and smooth objects and their derivatives and integrals.
Discrete mathematics provides the mathematical foundations for computer science, especially in areas such as algorithm design, data structures, and complexity theory.
In contrast, calculus is a branch of mathematics that focuses on continuous change, and provides a foundation for many other branches of mathematics and science, including physics, engineering, and economics.
In discrete mathematics, concepts are studied in a finite and countable manner, meaning that the objects and structures being studied can be counted and identified.
For example, in graph theory, discrete mathematical structures like vertices and edges are studied and their properties are analyzed. In discrete mathematics, the focus is on finding relationships between discrete objects and how they can be manipulated, such as in combinatorics and number theory.
On the other hand, calculus deals with the study of change and motion, specifically the rate at which objects change and the accumulation of these changes over time.
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solve for the given variable
3(m + 7) =
Answer: 3m + 21
Step-by-step explanation:
Jackie is looking on a map at the distance between her campsite and a trail which she plans to hike. The distance between the two points on the map is 1.8 centimeters. If the map uses a scale in which 1 centimeter represents 5 miles, find the actual distance in miles that Jackie’s campsite is from the trail.
The actual distance in miles between the campsite and the trail is 9 miles.
What is map?Map can be defined as a symbolic depiction emphasizing relationships between elements of some space such as objects and regions.
To convert from centimeters on the map to miles, we use the scale of 1 centimeter represents 5 miles.
So, 1.8 centimeters on the map represents 1.8 * 5 = 9 miles in real life.
Therefore, The actual distance in miles between the campsite and the trail is 9 miles.
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ANSWER QUESTION han or em Using the table of equalities, select the correct conversion factors that indicate the number of feet (ft) in one mile (mi). O O O O O Z dit or 082LA U.S. Metric-U.S. 2.54 cm - l in exact) Some Common Equalities Quantity Metric (SD) Length Im-1000 mm 1 cm - 10 mm 1 - 1000 ml 1 dl - 100 ml 1 ml - Icm Mass 1 kg - 1000 1 - 1000 mg Time 1h 60 min 1 min - 605 I ft 12 in 1 yd - 3 11 I mi - 520 ft Iqt4 cups 19 - 2p Igal - 4 1 lb 16 . Volume 1 km 0.621 mi 946 ml. It IL- 1.0691 popor der Ikg - 2.20 lb 4549 - I b I DON'T KNOW YET
The correct conversion factors to indicate the number of feet in one mile is: 1 mi = 5280 ft.
To convert miles to feet, we must use the equality: 1 mi = 5280 ft.
Using the table of equalities, we can see that 1 mi = 5280 ft, so the correct conversion factor to indicate the number of feet in one mile is 1 mi = 5280 ft.
To convert miles to feet, we use the conversion factor of 1 mile being equal to 5280 feet. This means that for every 1 mile, there are 5280 feet. To convert a specific number of miles to feet, we multiply the number of miles by the conversion factor of 5280 feet/mile. For example, if we want to convert 2 miles to feet, we multiply 2 by 5280 to get 10560 feet. Hence, 2 miles is equal to 10560 feet. This conversion factor can be used to convert any number of miles to feet, as long as we use it consistently and accurately.
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Suppose you wanted to estimate the proportion of people who feel that unemployment compensation should be expanded with 95% confidence to within ± 1. 5%. Calculate how large a sample you would need
To achieve a 95% confidence level and ±1.5% precision, you would need a sample size of approximately 3845 people.
To estimate the proportion of people who feel that unemployment compensation should be expanded with 95% confidence to within ±1.5%, you would need to determine the sample size necessary to achieve this level of precision.
The formula for sample size estimation in proportion estimation is given by:
[tex]n = (Z^2 * p * (1 - p)) / E^2[/tex]
Where:
Z is the Z-score for a confidence level of 95%, which is approximately 1.96.p is the estimated proportion of people who feel that unemployment compensation should be expanded. If no previous data is available, p can be assumed to be 0.5.E is the maximum error allowed in the estimate, which is 1.5% or 0.015.Substituting the values, we get:[tex]n = (1.96^2 * 0.5 * 0.5) / 0.015^2 = 3844.83[/tex]
Therefore, to achieve a 95% confidence level and ±1.5% precision, you would need a sample size of approximately 3845 people.
In conclusion, to estimate the proportion of people who feel that unemployment compensation should be expanded with 95% confidence to within ±1.5%, a sample size of approximately 3845 people is necessary. This calculation assumes that the estimated proportion of people in favor of expanding unemployment compensation is 0.5, and that the Z-score for a confidence level of 95% is 1.96.
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How do you convert from kJ to J?
A joule is one unit of energy, while a kilojoule is 1000 joules.
What is the kJ to J formula?KJ x 1,000 = J.
It would be simple to calculate if you had a calculator, but you can get the same answer by simply shifting the decimal point 3 places to the left and adding any necessary zeros.A megaJoule (MJ) is 1,000,000 Joules, whereas a kiloJoule (kJ) is 1000 Joules. The Watt, which is a measure of power, is a comparable unit (energy per unit time). Energy units can be created by multiplying power units by seconds (s), hours (h), or years (yr).A joule is one unit of energy, while a kilojoule is 1000 joules.To learn more about joule refer to:
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What is the geometric relation between the vectors v and w if vw =-||v|| ||w|| ?
The geometric relation between the vectors v and w are:
The vectors are in the same direction.
Now, According to the question:
Geometrical Interpretation of Scalar Product
From the scalar product formula, we have a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → ) , that is, the scalar product of vectors a and b is equal to the magnitude of vector a times the projection of a onto vector b.
Vectors describe movement with both direction and magnitude. They can be added or subtracted to produce resultant vectors. The scalar product can be used to find the angle between vectors.
Now, vw =-||v|| ||w||
a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → )
vw =-||v|| ||w|| cos θ = |v| proj →w(→v) proj w → ( v → )
Hence, The vectors are in the same direction.
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Hanz and Franz are in a shooting competition. The object of the match is to be the first to hit the bull's eye of a target 100 feet away. The two opponents alternate turns shooting, and each opponent has a 40% chance of hitting the bull's-eye on a given shot. If Hans graciously allows Franz to shoot first, what is the probability that Hans will win the competition and take no more than three shots?
Answer: The probability of Hans winning and taking no more than three shots can be calculated using the principle of total probability and the law of total probability.
Let's call the event of Hans winning and taking no more than three shots "A". Then, the probability of event A can be broken down into several cases:
Case 1: Hans wins in one shot: P(A|Hans wins in one shot) = P(Hans wins in one shot) = 0.4.
Case 2: Hans wins in two shots: P(A|Hans wins in two shots) = P(Franz misses in the first shot) * P(Hans wins in the second shot) = (1 - 0.4) * 0.4 = 0.24.
Case 3: Hans wins in three shots: P(A|Hans wins in three shots) = P(Franz misses in the first two shots) * P(Hans wins in the third shot) = (1 - 0.4)^2 * 0.4 = 0.144.
Finally, the probability of event A can be calculated using the law of total probability as follows:
P(A) = P(A|Hans wins in one shot) + P(A|Hans wins in two shots) + P(A|Hans wins in three shots) = 0.4 + 0.24 + 0.144 = 0.784.
So, the probability of Hans winning the competition and taking no more than three shots is 0.784.
Step-by-step explanation:
Which meaurement repreent the ide length of a right triangle?
Right Triangle
NOT a Right Triangle
6 cm, 8 cm, 10 cm
12 cm, 35 cm, 37 cm
4 cm, 6 cm, 10 cm
10 cm, 24 cm, 26 cm
6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.
Which dimension best describes a right triangle?A right triangle, like the triangle below, is one in which one of the angles measures 90 degrees (a right angle). In most cases, right angles are shown by drawing a square at the angle's vertex.
For a right triangle, where c is the hypotenuse and a and b are the smaller sides, the Pythagorean Theorem gives us a2 + b2 = c2.
The hypotenuse is usually the longest. Any triple would still represent the sides of a right triangle if we multiplied it by a constant. Therefore, the sides of a right triangle would be 6, 8, and 10.
a2 + b2 = c2.
= 6^2 + 8^2 = 10^2
36 + 64 = 100.
so,
6 cm, 8 cm, 10 cm meaurement repreent the ide length of a right triangle.
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find the equation of the tangent line to the graph of the function f(x)=x 1x−4 at the point (0,−14)
The equation of the tangent line to the graph of the function f(x)=x 1x−4 at the point (0,−14) is 4x + y +14 = 0.
To find the tangent equation we need slope and intercept for the equation.
To find slope we need to differentiate the given function as the differentiation at a given point gives us the slope :
firstly differentiate the given function :
f(x)=x(x−4)
= x^2 - 4x
f'(x) = 2x - 4
f'(x) at (0,-14) = 2(0) - 4
= -4
Hence , the slope is -4
Use the formula to find the equation of the tangent line that passes through a point (x1, y1) with the slope m, that is, y-y1=m(x-x1).
y-y1=m(x-x1) at a point (0,−14)
y - (-14) = -4 (x-0)
y+14 = -4x
therefore, 4x + y +14 = 0 is the required equation of the tangent.
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Anu brought an air cooler, its water tank is in the shape of a cuboid and can take 40 liters of water. Its dimensions are 50 cm x 20 cm. What will be the height of the water tank?.
The height of the water tank given the volume, length and width is 40 cm
What is the height of the water tank?Volume of the water tank= 40 liters
Length of the water tank= 50 cm
Width of the water tank= 20 cm
Height of the water tank= x
convert liters to centimeters
1 liter= 1000 cm
40 liters= 40,000 cm
Volume of the water tank= length × width × height
40,000 = 50 × 20 × x
40,000 = 1000x
divide both sides by 1000
x = 40,000 / 1000
x = 40 cm
Therefore, the height of the water tank is 40 cm
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Binomial Distribution Algebra 2B
Roughly 75% of students take the bus to school. If you were to ask 9 students in your class, what is the probability that at most 8 of them take the bus to school?
The probability that at most 8 of 9 students take the bus to school is approximately 0.9538.
To find the probability of at most 8 students taking the bus, we can use the cumulative distribution function (CDF) of the binomial distribution.
The CDF gives the probability of getting a certain number or fewer of successes in a fixed number of trials, where each trial has a fixed probability of success.
The CDF of a binomial distribution with parameters n (number of trials) = 9 and p (probability of success) = 0.75 is given by:
F(k) = Σ(i = 0 to k) (9 choose i) * (0.75)^i * (0.25)^(9-i)
where (9 choose i) is the binomial coefficient, which gives the number of ways to choose i successes from n trials.
Thus, to find the probability of at most 8 students taking the bus, we compute the CDF at k = 8:
F(8) = Σ(i = 0 to 8) (9 choose i) * (0.75)^i * (0.25)^(9-i)
Using a binomial calculator or programming language, we can find the value of F(8) which is approximately 0.9538.
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Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a poisson distribution with parameter m 5 20 (suggested in the article "dynamic ride sharing: theory and practice," j. Of transp. Engr. , 1997: 308–312). What is the probability that the number of drivers will
Poisson distribution is a discrete probability distribution that describes the number of events that occur randomly in a fixed interval of time or space.
a. The probability that the number of drivers will be at most 10 is calculated as the cumulative distribution function of Poisson distribution at 10, which is
[tex]P(X \leq 10) = \sum_{i}=0^{10 }e^{-\mu} *\frac{\mu^{i }}{i!}[/tex]
where i ranges from 0 to 10.
b. The probability that the number of drivers will exceed 20 is calculated as
[tex]P(X > 20) = 1 - P(X \leq 20) = 1 - \sum_i=0^{20} e^{(-\mu)} *\frac{ \mu^i }{i!}[/tex]
where i ranges from 0 to 20.
c. The probability that the number of drivers will be between 10 and 20, inclusive is calculated as
[tex]P(10 \leq X \leq 20) = \sum_i=10^{20} e^{(-\mu)} *\frac{\mu^i}{i! }[/tex]
where i ranges from 10 to 20. The probability that the number of drivers will be strictly between 10 and 20 is calculated as
[tex]P(10 < X < 20) = \sum_i=10^{19} e^{(-\mu)} * \frac{\mu^i }{i!}[/tex]
where i range from 10 to 19.
d. The standard deviation of Poisson distribution with parameter μ = 20 is [tex]\sqrt{(\mu)} = \sqrt{(20)} = 2\sqrt5[/tex]
The probability that the number of drivers will be within 2 standard deviations of the mean value is calculated as
[tex]P(\mu - 2 * \sqrt{(\mu)}\leq X\leq \mu + 2 * \sqrt{(\mu)}) = \sum_i=16^{24} e^{(-\mu)} * \frac{\mu^i}{i!}[/tex]
where i ranges from 16 to 24.
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The complete question is :
Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ =20 (suggested in the article “Dynamic Ride Sharing: Theory and Practice,” J. of Transp. Engr., 1997: 308–312). What is the probability that the number of drivers will
a. Be at most 10?
b. Exceed 20?
c. Be between 10 and 20, inclusive? Be strictly between 10 and 20?
d. Be within 2 standard deviations of the mean value?
A greenhouse owner wants to test the effectiveness of a new fertilizer on African violets. She has 60 violet seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants, and decides to use a simple random sample to select them. Which of the following statements is true?
A)She needs to select the 10 biggest plants to test the new fertilizer.
B)She needs to select the 10 smallest plants to test the new fertilizer.
C)She needs to number each plant 1–60 and randomly select 10 plants.
D)She needs to put the plants in 6 groups of 10 and randomly select 1 of the groups.
The required answer is she needs to number each plant from 1 to 60 and randomly select 10 plant. The correct option is C
What is probability?Probability can be defined as a number that reflects the chance or likelihood that a particular event will occur.
As she has 60 seeds, firstly she must number each plant in order or randomly see the height, After that he can peek at random 10 plants to test the fertilizer.
The required answer is she needs to number each plant from 1 to 60 and randomly select 10 plant.
A greenhouse owner wants to test. She has 60 violet seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants and decides to use a random number table to select a simple random sample. Which of the following correctly labels the population of violets Is to be determined.
The correct option is C
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a new cell phone design from samsung has demonstrated a constant failure rate of 0.06 fpmh. assuming customers will use their devices 5 hours per day, every day, what will the probability of failure after one year of use?
The probability of failure after 1 year of use will be approximately 109/1,000,000 = 0.000109 or 0.0109%.
The failure rate (fpmh) is the number of failures per million hours. If a device is used for 5 hours per day, every day, it will be used for 365 days * 5 hours/day = 1,825 hours in a year.
The probability of failure after 1 year of use can be calculated as:
Failure rate * total hours used = 0.06 fpmh * 1,825 hours = 0.06 * 1,825 failures = 109.35 failures
So, there will be approximately 109 failures after 1 year of use. Since the failure rate is per million hours, and there were 1,825 hours of use, the probability of failure after 1 year of use will be approximately 109/1,000,000 = 0.000109 or 0.0109%.
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a sector of a circle is enclosed by two 12.0-inch radii and a 9.0-inch arc. its perimeter is therefore 33.0 inches. what is the area of this sector, to the nearest tenth of a square inch? what is the central angle of the sector, to the nearest tenth of a degree?
The central angle of the sector to the nearest tenth of a square inch is 473.2 sq.
To find the area of the sector, we can use the formula:
Area = (θ/360) * π * r²
where θ is the central angle of the sector in degrees, and r is the radius. To find the central angle, we can use the formula:
Arc length = (θ/360) * 2 * π * r
So,
Arc length = (θ/360) * 2 * π * 12 = 9
θ/360 * 2 * π * 12 = 9
θ/360 = 9 / (2 * π * 12)
θ = (9 / (2 * π * 12)) * 360
Approximating π as 3.14, we get:
θ = (9 / (2 * 3.14 * 12)) * 360 = 75.39
To the nearest tenth of a degree, this is 75.4 degrees.
Next, we can use the first formula to find the area:
Area = (75.4 / 360) * 3.14 * 12² = 473.2 sq in
To the nearest tenth of a square inch, this is 473.2 sq in.
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The central angle of the sector to the nearest tenth of a square inch is 473.2 sq.
To find the area of the sector, we can use the formula:
Area = (θ/360) * π * r²
where θ is the central angle of the sector in degrees, and r is the radius. To find the central angle, we can use the formula:
Arc length = (θ/360) * 2 * π * r
So,
Arc length = (θ/360) * 2 * π * 12 = 9
θ/360 * 2 * π * 12 = 9
θ/360 = 9 / (2 * π * 12)
θ = (9 / (2 * π * 12)) * 360
Approximating π as 3.14, we get:
θ = (9 / (2 * 3.14 * 12)) * 360 = 75.39
To the nearest tenth of a degree, this is 75.4 degrees.
Next, we can use the first formula to find the area:
Area = (75.4 / 360) * 3.14 * 12² = 473.2 sq in
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Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of lemonade they sell. Write an equation that shows how their total earnings, y, depend on the number of cups sold, x.
Answer:
y = 2x
Step-by-step explanation:
We know
They earn $2 for each cup of lemonade they sell. So, the equation is
y = 2x
14/32 Marks
Round the following numbers to 1 significant figure:
a) 25637
b) £2.51
c)
9877m
The following values, when rounded to one significant figure in accordance with the stated statement, are 3*10⁴, 3, and 1*10⁴ m.
Give an example of a notable figure?True figures are the number of digits that increase a value's accuracy, often a measurement. Starting with the first semi-digit, we count actual numbers. All the decimal places to the right of the next non-zero digit after the calculation are significant. The number 0.0079800, for instance, includes five significant digits. If a measurement includes the noughts to the side of the last non-zero digit, they are all significant.
As stated in the preceding sentence:
a). 25637 ≈ 3*10⁴
b). 2.51 ≈ 3
c). 9877m ≈ 10000m = 1*10⁴m
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the isosceles trapezoid is part of an isosceles triangle with a 42 vertex angle. what is the measure of an acute base angle of the trapezoid? of an obtuse base angle? the diagram is not to scale
The measure of the acute base angle is 69°
The measure of the obtuse base angle is 111°
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Isosceles triangles mean two sides are equal and the angles opposite to the equal sides are also equal.
Now,
Isosceles trapezoid
Vertex angle = 42
This means,
The other two angles will be the same.
x + x + 42 = 180
2x = 180 - 42
2x = 138
x = 69
Now,
The opposite angles of an isosceles trapezoid are supplementary.
So,
Obtuse base angle + Acute base angle = 180
Obtuse base angle + 69 = 180
Obtuse base angle = 180 - 69 = 111
Thus,
Acute base angle = 69°
Obtuse base angle = 111°
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Katie invested a total of $6000, part at 2% simple interest and part at 3% simple interest. At the end of 1 year, the investments had earned $152 interest. How much was invested at each rate?
The investment in 2% rate of interest was $2800 and the investment in 3% rate of interest was $3200.
Let the amount invested in 2% interest rate be x. So, the remaining invested amount = (6000 - x). The simple interest will be calculated by the formula -
S.I. = P×R×T/100, where S.I. is simple interest, P is principal, R is rate of interest and T is time.
Also, the sum of interest in each is $152. So, finding the individual interest first.
SI = x × 2 × 1/100
SI = 2x/100
SI = (6000 - x) × 3 × 1/100
SI = (18000 - 3x)/100
Finding the value of x.
2x/100 + (18000 - 3x)/100 = 152
Multiplying the equation with 100
2x + 18000 - 3x = 15200
3x - 2x = 18000 - 15200
x = 2800
Investment in 3% rate = 6000 - 2800
Investment in 3% rate = $3200
Thus, the investment was $2800 and $3200.
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Determine the independent and dependent variable from the following situation. Quincy was given 3 video games for his new game system. Every month he saves enough to get 2 more video games.
what is the dependent variable and what is the independent variable.
The dependent variable is the number of games and the independent variable is the number of months.
How to identify the independent and dependent variables?We know that Quincy was given 3 video games for his new game system and every month he saves enough to get 2 more video games.
Then the two variables are the number of months and the number of games.
We know that he starts with 3 games and each month he adds 2 more, then we can write the relation:
y = 3 + 2*x
Where y is the number of games and x the number of months.
Then the independent variable is the number of months, and the dependent variable (which depends on the other one) is the number of games.
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A sphere of radius 4 in. Is placed inside a rectangular prism with length 9 in. , width 8 in. , and height 10 in. What is the approximate volume of the prism not occupied by the sphere?.
The volume of the prism not occupied by the sphere is 704.69 cubic in.
Given that, the radius of the sphere=4 in. and the dimensions of a rectangular prism length=9 in. width=8 in. and height 10 in.
We need to find what is the volume of the prism not occupied by the sphere.
The formula to find the volume of the rectangular prism is Volume=Length×Width×Height.
The formula to find the volume of the sphere is Volume=4/3 πr³.
Now, the volume of the rectangular prism=9×8×10=720 cubic in.
The volume of the sphere=4/3×3.14×4³
V=15.31 cubic in.
Then, the volume of the prism not occupied by the sphere=The volume of the rectangular prism-The volume of the sphere
The volume of prism=720-15.31=704.69 cubic in.
Therefore, the volume of the prism not occupied by the sphere is 704.69 cubic in.
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The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 3 comma 4, negative 1 comma 1, 0 comma negative 2, 2 comma 0, and 4 comma negative 1.
WILL GIVE BRAINLIEST, PLEASE HELP
What is the domain of the relation?
{−3, −2, −1, 0, 1, 2, 4}
{−3, 0, 1, 4}
{−2, −1, 0, 1, 4}
{−3, −1, 0, 2, 4}
The domain of the function f(x) = {- 3, - 1, 0 2, 4}.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
Given, The graph represents a relation where x represents the independent variable and y represents the dependent variable.
The ordered pairs are given by, (- 3, 4), (- 1, 1), (0, - 2), (2, 0), and (4, - 1).
We know the domain of the function are all the x coordinates.
Therefore, The domain of the function f(x) = {- 3, - 1, 0 2, 4}.
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Can someone please help me here? Thank you!
Peter is a product manager earning a semi-monthly salary of P5,500. He is given commission of 2. 5% on his own sales and an override of 0. 5% on his men's sales. His men are entitled to a 3. 75% commission on their own sales and basic semi-monthly salary of P4,000. Peter and his men are given
transportation allowance of P2,000 per month. Compute the gross earnings of Peter and each of his men.
Peter's gross semi-monthly earnings are P7,717.5 and each of his men's gross semi-monthly earnings are P6,150.
To calculate Peter's gross earnings,
We need to find the commission he earns on his own sales and the override commission he earns on his men's sales.
Peter's Commission on his own sales:
2.5% of P5,500 = P137.5
Peter's Override Commission on his men's sales:
0.5% of (number of men * P4,000) = 0.5% of (number of men * 4000)
Let's assume he has 4 men.
Then the total override commission would be:
0.5% * 4 * 4000 = P80
So Peter's gross semi-monthly earnings would be:
P5,500 + P137.5 + P80 + P2,000 = P7,717.5
To calculate the gross earnings of each of Peter's men, we need to find their basic semi-monthly salary, their commission on their own sales, and their transportation allowance.
Each man's basic semi-monthly salary: P4,000
Each man's Commission on their own sales will be:
3.75% * P4,000 = P150
So each man's gross semi-monthly earnings would be:
P4,000 + P150 + P2,000 = P6,150
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The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in². The slant height of the pyramid is 6 in.
What is the surface area of the pyramid?
The total surface area of the triangular pyramid is 170.4 inches².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
A triangular pyramid has a triangular base and three triangular faces.
Given that, base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in².
Area of the base = 62.4 inches²
Slant height = 6 inches
Length of edge of each of the three triangular faces = 12 inches
Area of a triangular face = [tex]\frac{1}{2}[/tex] × 12 × 6 = 36 inches²
Area of three triangular faces = 3 × 36 inches² = 108 inches²
Total surface area = 108 inches² + 62.4 inches² = 170.4 inches²
Hence 170.4 inches² is the total surface area of the pyramid.
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