Answer:U₁ = 2
.
Step-by-step explanation:
Un+1 = 2U₁ + 6 (Equation 1)
Uo = 10
We want to find U₁. We can start by using Equation 1 with n = 1 to get:
U2 = 2U₁ + 6
We can then use the value of Uo = 10 to find U₂ as follows:
U₂ = 2U₁ + 6
U₂ = 2U₁ + 2(3)
U₂ = 2(U₁ + 3)
We can then use the value of U₂ to find U₃:
U₃ = 2U₂ + 6
U₃ = 2(2U₁ + 2(3)) + 6
U₃ = 4U₁ + 12 + 6
U₃ = 4U₁ + 18
We can keep using this process to find Un in terms of U₁, until we reach the value of n we need. For example, we can find U₄ as follows:
U₄ = 2U₃ + 6
U₄ = 2(4U₁ + 18) + 6
U₄ = 8U₁ + 36
So we have:
Uo = 10
U₂ = 2(U₁ + 3)
U₃ = 4U₁ + 18
U₄ = 8U₁ + 36
and so on.
To find U₁, we need to use the equation for U₂:
U₂ = 2(U₁ + 3)
Substituting U₂ = 10 (from the given value of Uo), we get:
10 = 2(U₁ + 3)
Simplifying, we get:
5 = U₁ + 3
Subtracting 3 from both sides, we get:
U₁ = 2
Therefore, U₁ = 2.
James is participating in a 6-mile walk to raise money for a charity. He has received $600 in fixed pledges and raises $15 extra for every mile he walks. Use a point-slope equation to find the amount he will raise if he completes the walk.
Answer: Use a point-slope equation to find the amount he will raise if he completes the walk.
Step-by-step explanation:
We can start by using the point-slope equation:
y - y1 = m(x - x1)
where y is the amount James raises, x is the number of miles he walks, m is the rate at which he raises money per mile, and (x1, y1) is a point on the line.
We know that James raises $15 extra for every mile he walks, so m = 15. We also know that he has received $600 in fixed pledges, which is the amount he would raise if he walked 0 miles. So (0, 600) is a point on the line.
Using this information, we can write the point-slope equation:
y - 600 = 15(x - 0)
Simplifying, we get:
y = 15x + 600
This equation tells us the amount James will raise, y, for any number of miles he walks, x. For example, if he completes the 6-mile walk, we can plug in x = 6 to find:
y = 15(6) + 600 = 690
Therefore, if James completes the walk, he will raise $690.
{Hope This Helps! :)}
Mr Tobias is buying new tires for his bike. He wants to make sure the new tires will fit on his bike but the only measurement he has is the the radius of 13inches what is the circumference of the new tires
The circumference of the new tires is 81.64 inches
From the question, we have the following parameters that can be used in our computation:
Radius, r = 13 inches
The circumference of the new tires is calculated as
C = 2πr
Substitute the known values in the above equation, so, we have the following representation
C = 2 * 3.14 * 13
Evaluate
C = 81.64
Hence. the circumference of the new tires is 81.64 inches
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According to a paint specialist one needs at least two coats of paint prudence therefore decided that she will paint three coats just to be sure that all areas are covered . Remember that the area that need to be covered is 14.42.how many litres of paint will be needed if one litre of paint covers 8m
Prudence needs to purchase 6 litres of paint to cover the area with three coats.
Step 1: Calculate the total area to be covered with paint
Since Prudence wants to apply three coats of paint, we need to multiply the area by the number of coats.
Area per coat = 14.42 m²
Total area = 14.42 m² x 3 coats = 43.26 m²
Step 2: Determine the number of litres needed
One litre of paint covers 8 m². To find the number of litres needed for the total area, we need to divide the total area by the coverage of one litre.
Litres needed = Total area / Coverage per litre
Litres needed = 43.26 m² / 8 m²/litre = 5.4075 litres
Step 3: Round up to the nearest whole litre
Since we can't buy a fraction of a litre, we need to round up to the nearest whole litre.
Paint needed = 6 litres
So, Prudence needs to purchase 6 litres of paint to cover the area with three coats.
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IF YOU SOLVE THIS CORRECTLY WITH EXPLANATION U WILL GET BRAINILEST
-2r(8r+5)
Answer:
-16r^2 - 10r
Step-by-step explanation:
all you got to do is distribute
The ratio of the number of dolls jacky had to the number of dolls petter had was 5:2 but after jacky gave peter 15 dolls they have the equal amount of fools how many holes did they have in all
The total number of dolls they had in the beginning was 35, and after Jacky gave Peter 15 dolls, they each had 25 dolls. So, they had a total of 50 dolls in all.
Let the initial number of dolls Jacky had be 5x, and the initial number of dolls Peter had be 2x. So, the total number of dolls they had in the beginning was 5x + 2x = 7x.
After Jacky gave Peter 15 dolls, Peter had (2x + 15) dolls, and Jacky had (5x - 15) dolls. As they had an equal number of dolls after this, we get the equation:
5x - 15 = 2x + 15
Simplifying this, we get:
3x = 30
x = 10
So, the initial number of dolls Jacky had was 5x = 50, and the initial number of dolls Peter had was 2x = 20. Therefore, the total number of dolls they had in the beginning was 50 + 20 = 70.
After Jacky gave Peter 15 dolls, they each had 25 dolls, and the total number of dolls they had in all was 25 + 25 = 50.
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What is the area, in square centimeters, of the shape below?
3-5 cm;
6.2 cm
Answer:
Area = 10.85 square centimeters
Step-by-step explanation:
The formula for area of triangle is
A = 1/2bh, where
A is the area in square units,b is the base,and h is the heightWe see from the diagram that the base is 6.2 cm and the height is 3.5 cm. Thus, we can plug these numbers in for b and h in the base formula to find the area, A:
A = 1/2(6.2)(3.5)
A = 1/2(21.70)
A = 10.85 square centimeters
A child swims a child’s swimming pool is shaped like a cylinder with a diameter of 8 feet and a height of 1.5 feet .it is being filled with water at the rate of 8 gallon per minute.about how many hours will it take to fill a pool if 1 cubic foot is about 7.5 gallon ? Round to the nearest tenth
0.4 hours it take to fill a pool if 1 cubic foot is about 7.5 gallon
The radius of the cylinder is half of the diameter, so r = 8/2 = 4 feet.
The volume of the cylinder is given by:
V = πr²h
V = π(4²)(1.5)
V = 24π cubic feet
We know that 1 cubic foot is about 7.5 gallons, so the pool has a capacity of:
24π x 7.5 = 180.96 gallons
At a filling rate of 8 gallons per minute, the time it takes to fill the pool can be found by dividing the pool's capacity by the filling rate:
180.96 / 8 = 22.6 minutes
Converting minutes to hours:
22.6 / 60 = 0.4 hours
Hence, 0.4 hours it take to fill a pool if 1 cubic foot is about 7.5 gallon
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in circle d, ∠edh ≅ ∠edg. what is the measure of ? 114° 123° 228° 246°
If ∠EDH is congruent (∅≅) to ∠EDG in circle D, it means that the two angles have the same measure. Therefore, the measure of ∠EDH is equal to the measure of ∠EDG.
Since no specific angle measurement is provided in the question, I cannot determine the exact measure from the given options (114°, 123°, 228°, 246°). However, if ∠EDH ≅ ∠EDG, then they must have the same measure, which is unknown in this context.
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(Parallel and Perpendicular Lines) Which of the following equations represents a
line that is perpendicular to the line that passes through the points (-8,-8)(-6, 0)?
y=1/4x+2
y = -4x + 2
y = 4x+2
y=-1/4x+2
The equation of line for the give condition is,
⇒ y = - 1/4x - 10
Since, The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
The line passes through the points (-8,-8) and (-6, 0).
Now, The slope of line is,
m = = (y₂ - y₁) / (x₂ - x₁)
m = (0 - (-8)) / (-6 - (-8))
m = 8 / 2
m = 4
Hence, Slope of perpendicular line is,
m₁ = - 1/4
So, The equation of line with slope - 1/4 is,
⇒ y - (- 8) = - 1/4 (x - (- 8))
⇒ y + 8 = - 1/4 (x + 8)
⇒ y + 8 = - 1/4x - 2
⇒ y = - 1/4x - 10
Thus, The equation of line is,
⇒ y = - 1/4x - 10
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Onitsha is 450km due south of Kafanchan. Ibadan is due west of Onitsha and on a bearing 225° from Kafanchan. Find the distance between: (1) Ibadan and Onitsha (2) Ibadan and Kafanchan
The distance between Ibadan and Onitsha is 450km
The distance between Ibadan and Kafanchan is 636. 4km
How to determine the valueTo determine the distance, we have that;
The distance of Onitsha from Kafanchan is 450km
The distance between Ibadan and Onitsha is x
The distance between Ibadan and Kafanchan is y
Note that the third quadrant is 270 degrees
Then, the value of the angle = 270 - 225 = 45 degrees
Then, using the tangent identity, we have that;
tan 45 = x/450
cross multiply the values
x = 450km
Also, using the sine identity
sin 45 = 450/y
cross multiply the values
y = 636. 4 km
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a political candidate, bill mcwaffle, is personally indifferent on the issue of the legalization of gambling in his state and to this point has not taken a public stand. the election is fast approaching, and he has decided that he will adopt a public stand supporting gambling legalization, only if at least 65 percent of his constituents support it. otherwise, he will not for fear of alienating the voters who are against it. a random sample of 200 voters shows that 68 favor legalization and 132 oppose it. if he wants to be 99 percent confident not to alienate the ant-gambling voters, what should he do?
Based on the sample data and the hypothesis test, Bill McWaffle should not take a public position on the issue of gambling legalization.
Using the normal approximation, we can calculate the test statistic, which follows a standard normal distribution under the null hypothesis. The test statistic is given by:
Z = (p - p₀) / √(p₀(1 - p₀) / n),
where p₀ represents the proportion specified under the null hypothesis, which is 0.65 in this case.
Substituting the values into the formula, we have:
Z = (0.34 - 0.65) / √(0.65(1 - 0.65) / 200) ≈ -9.91.
Looking up the z-value in a standard normal distribution table or using statistical software, we find that the critical value for a one-sided 99 percent confidence level is approximately 2.33.
Since the test statistic (Z = -9.91) is much smaller (in absolute value) than the critical value (2.33), we have strong evidence to reject the null hypothesis. This means that the proportion of constituents in favor of legalization is significantly less than 65 percent.
This decision ensures that he does not risk alienating a large segment of voters, as the data does not provide sufficient evidence to support a clear majority opinion of at least 65 percent in favor of legalization.
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The city is building a new roundabout in order to correct a traffic flow issue at some of its intersections. Due to safety regulations, the inner circle must have a diameter of 8 ft. When construction is complete, they plan to cover this area with grass. How much sod (grass) do they need to cover the inner circle of the roundabout?
Use 3.14 for π.
(If you manage to answer this in 3 sentences you get a virtual high five here's some sentence starters if needed, The formula for the area of a circle is ____________.The area of the roundabout about is _________ ft².This is how I found the area of the circle ________
The city will need around 50.24 square feet of sod (grass) to cover the Inner circle of the roundabout. The formula for the area of a circle is A = πr² .The area of the roundabout about is 50.24 ft².This is how I found the area of the circle of the roundabout.
The area of a circle can be found using the formula A = πr², where A is the area and r is the radius. In this case, since the diameter of the inner circle is 8 ft, the radius is half of that, which is 4 ft. Thus, the area of the roundabout is A = π(4)² = 16π square feet. Using 3.14 for π, we can estimate the area to be approximately 50.24 square feet. Therefore, the city will need around 50.24 square feet of sod (grass) to cover the inner circle of the roundabout.
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Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = 5/2sqrt(x)+ 2 sec^2 x
The most general antiderivative of f(x) = (5/2)sqrt(x) + 2sec^2(x) is:
F(x) = (5/3)x^(3/2) + 2tan(x) + C
To find the most general antiderivative of the function f(x) = (5/2)sqrt(x) + 2sec^2(x), we can integrate each term separately.
The antiderivative of (5/2)sqrt(x) can be found using the power rule of integration. We add 1 to the exponent (1/2) and divide by the new exponent:
∫(5/2)sqrt(x) dx = (5/2) * (2/3)x^(3/2) + C = (5/3)x^(3/2) + C
The antiderivative of 2sec^2(x) can be found using the integral of the secant squared function, which is the tangent function:
∫2sec^2(x) dx = 2tan(x) + C
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HELP!! Solve this logarithmic equation for the value of the variable. Be sure to check for extraneous solutions. Thanks!!
The solution to the equation log₄(x) + log₄(x + 6) = 2 is x = 2.
Using the property logₐ(b) + logₐ(c) = logₐ(cb), we can rewrite the equation as:
log₄(x(x + 6)) = 2
Next, we can use the property logₐ(b) = c is equivalent to [tex]a^c=b[/tex], to rewrite the equation in exponential form:
4² = x(x + 6)
16 = x² + 6x
x² + 6x - 16 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
In this case, we'll use factoring:
(x + 8)(x - 2) = 0
Setting each factor equal to zero:
x + 8 = 0 --> x = -8
x - 2 = 0 --> x = 2
Therefore, the solution to the equation log₄(x) + log₄(x + 6) = 2 is x = 2.
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Which fraction is less than 1/2, not equal to 3/10, greater than 0. 1 and not equal to 1/5
0. 3, 7/10, 1/2, 0,8
0. 6, 2/5, 0. 2, 1/10
The fraction that satisfies the given conditions is 2/5.
We are looking for a fraction that meets the following criteria:
1. Less than 1/2
2. Not equal to 3/10
3. Greater than 0
4. Not equal to 1/5
Let's analyze the options:
1. 0.3: This decimal is less than 1/2 and greater than 0, but it is equal to 3/10, so it does not satisfy the second condition.
2. 7/10: This fraction is greater than 1/2, so it does not satisfy the first condition.
3. 1/2: This fraction is equal to 1/2, so it does not satisfy the first condition.
4. 0.8: This decimal is greater than 1/2, so it does not satisfy the first condition.
5. 6: This whole number is greater than 1/2, so it does not satisfy the first condition.
6. 2/5: This fraction is less than 1/2, greater than 0, and it is different from both 3/10 and 1/5. Hence, it satisfies all the given conditions.
Therefore, the fraction 2/5 is the correct answer that meets all the specified criteria.
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do infinite sequences and/or infinite series consistently imply convergence or divergence; why or why not?
No, infinite sequences and infinite series do not consistently imply convergence or divergence.
Whether a sequence or series converges or diverges depends on the specific terms and the nature of the sequence or series.
For example, the sequence 1, 1/2, 1/3, 1/4, ... approaches zero and converges, while the sequence 1, 2, 3, 4, ... increases without bound and diverges. Similarly, the series 1/2 + 1/4 + 1/8 + ... is an example of a convergent series, while the series 1 + 2 + 3 + ... is an example of a divergent series.
Therefore, it is important to analyze the specific terms of a sequence or series and use appropriate tests to determine whether it converges or diverges.
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In this rectangle, the base is 1 cm more than the height. The area of the rectangle is 100 cm². Using a trial and improvement method, find the value of h, correct to 1 decimal place. You must show all of your working
Let's assume the height of the rectangle is h cm. According to the problem, the base is 1 cm more than the height, so the base would be (h + 1) cm. The formula for the area of a rectangle is given by A = length × width.
Given that the area is 100 cm², we can write the equation as follows:
100 = h × (h + 1)
To solve this equation using a trial and improvement method, we can start by assuming a value for h and check if it satisfies the equation. Let's try h = 9:
100 = 9 × (9 + 1)
100 = 9 × 10
100 = 90
Since 90 is not equal to 100, we can try a different value. Let's try h = 10:
100 = 10 × (10 + 1)
100 = 10 × 11
100 = 110
Again, 110 is not equal to 100. We can continue this process until we find a value of h that satisfies the equation. Let's try h = 9.5:
100 = 9.5 × (9.5 + 1)
100 = 9.5 × 10.5
100 = 99.75
Now, 99.75 is close to 100 but not exactly. Let's try h = 9.6:
100 = 9.6 × (9.6 + 1)
100 = 9.6 × 10.6
100 = 101.76
101.76 is greater than 100, so we can conclude that the value of h is closer to 9.5 than 9.6. Therefore, the value of h, correct to 1 decimal place, is approximately 9.5 cm.
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Find the product of the binomials.
(3x+4)²
O 9x² + 24x + 16
O 9x² + 16x + 12
O 9x² + 12x + 16
O 9x² +16
Jose is going to use a random number generator
500
500500 times. Each time he uses it, he will get a
1
,
2
,
3
,
1,2,3,1, comma, 2, comma, 3, comma or
4
44. Complete the following statement with the best prediction. Jose will get something other than a
2
22
Jose will get something other than a 2. If Jose uses the random number generator 500 times, we can predict that he will get a result other than a 2 approximately 375 times (75% of 500).
It is highly likely that Jose will get something other than a 2 at least once during the 500500 times he uses the random number generator. This is because the generator produces 1, 2, 3, 1, comma, 2, comma, 3, comma, or 4 with equal probability, and there are 4 possible outcomes. Therefore, the probability of getting a 2 is only 1/4 or 25%. This means that there is a 75% chance of getting something other than a 2.
To further support this prediction, we can use the law of large numbers, which states that as the number of trials increases, the experimental probability of an event will converge to the theoretical probability. In this case, as Jose uses the random number generator more and more times, the percentage of times he gets a 2 should get closer and closer to 25%. Therefore, it is highly likely that Jose will get something other than a 2 at least once during the 500500 times he uses the generator.
In order to provide you with an accurate answer, let's rephrase the question with the relevant information:
Jose is going to use a random number generator 500 times. Each time he uses it, he will get a 1, 2, 3, or 4. Complete the following statement with the best prediction: Jose will get something other than a 2.
Since the random number generator can produce four possible outcomes (1, 2, 3, and 4), each outcome has a 25% chance of occurring.
Therefore, the probability of getting something other than a 2 is 75% (25% for each of the other three outcomes). If Jose uses the random number generator 500 times, we can predict that he will get a result other than a 2 approximately 375 times (75% of 500).
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an appraisal that is based on facts and is likely to be numerical is a(n) ________ appraisal.
An appraisal that is based on facts and is likely to be numerical is a quantitative appraisal. Quantitative appraisals involve the use of data and statistics to determine the value of a property or asset.
This type of appraisal is commonly used in the real estate industry to determine the market value of a property by comparing it to similar properties in the area. Quantitative appraisals typically involve the use of various methods such as the cost approach, sales comparison approach, and income approach to determine the value of a property. These methods rely on quantitative data such as the property's size, location, condition, and income potential. In contrast, a qualitative appraisal is based on subjective criteria such as the overall condition and aesthetic appeal of a property. Overall, quantitative appraisals are considered to be more objective and reliable since they are based on measurable and verifiable data.
An appraisal that is based on facts and is likely to be numerical is an objective appraisal.
An objective appraisal is a type of evaluation that relies on factual information, data, and measurable criteria. In contrast to subjective appraisals, which are based on personal opinions, feelings, and preferences, objective appraisals aim to minimize bias and ensure a fair and accurate assessment.
Objective appraisals can be used in various settings, including performance evaluations in the workplace, academic assessments, and property valuations. In each case, the focus is on using quantifiable measures and clear, predetermined criteria to make an evaluation.
For instance, in a work performance evaluation, an objective appraisal might consider metrics such as sales figures, customer satisfaction ratings, or project completion rates. These numerical values can provide a clearer picture of an employee's performance, compared to subjective assessments, which may be influenced by personal relationships or other factors unrelated to actual performance.
Similarly, in an academic setting, objective appraisals can include standardized test scores, number of assignments completed, or attendance records. This data-driven approach helps to create a more equitable assessment of a student's abilities and achievements.
In summary, an objective appraisal is an evaluation method that relies on factual information and numerical data to minimize bias and provide an accurate and fair assessment. This type of appraisal can be applied in various settings, including performance evaluations, academic assessments, and property valuations.
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A(n) _____ shows the object classes and relationships involved in a use case.
Select one:
a.
class diagram
b.
association diagram
c.
use case diagram
d.
modeling diagram
The correct answer is c.A(n) use case diagram shows the object classes and relationships involved in a use case.
A use case diagram is a visual representation that shows the object classes and relationships involved in a use case. It provides a high-level view of the system and illustrates how different actors interact with the system through various use cases. Use case diagrams depict the functionalities and interactions between actors and the system, helping to understand the system's behavior and requirements. They are widely used in software development and system analysis to capture and communicate the system's functionality in a clear and organized manner.
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Help me with this please
A common formula/theorem when working with right triangles is called the Pythagorean Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
---a and b are legs of the triangle
---c is the hypotenuse
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
c = 10
Answer: The length of the hypotenuse of the triangle is 10cm.
Hope this helps!
the scatterplot and regression line below show the average income, in dollars, in several major american cities plotted against the rent for a 2 22-bedroom apartment in those cities. the fitted line has a slope of 0.031 0.0310, point, 031. what is the best interpretation of this slope?
Main Answer:The best interpretation of the slope of 0.031.
Supporting Question and Answer:
What does the slope of 0.031 represent in the context of the scatterplot and regression line?
The slope of 0.031 represents the average increase in income, in dollars, for every unit increase in the rent for a 222 -bedroom apartment in the major American cities.
Body of the Solution:The best interpretation of the slope of 0.031 in this context would be as follows:
For every increase of 1 unit in the rent for a 222- bedroom apartment in the major American cities, the average income in dollars increases by approximately $0.031.
In other words, there is a positive correlation between the rent for a 222-bedroom apartment and the average income in these cities. As the rent increases, the average income tends to increase as well, although the relationship is not necessarily causative. The slope of 0.031 indicates the magnitude and direction of this relationship.
Final Answer:Therefore,the best interpretation of the slope of the fitted line, which is 0.031.
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The best interpretation of the slope of 0.031.
What does the slope of 0.031 represent in the context of the scatterplot and regression line?The slope of 0.031 represents the average increase in income, in dollars, for every unit increase in the rent for a 222 -bedroom apartment in the major American cities.
The best interpretation of the slope of 0.031 in this context would be as follows:
For every increase of 1 unit in the rent for a 222- bedroom apartment in the major American cities, the average income in dollars increases by approximately $0.031.
In other words, there is a positive correlation between the rent for a 222-bedroom apartment and the average income in these cities. As the rent increases, the average income tends to increase as well, although the relationship is not necessarily causative. The slope of 0.031 indicates the magnitude and direction of this relationship.
Therefore, the best interpretation of the slope of the fitted line, which is 0.031.
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Find the area of each shaded sector. Round to the hundredths place.
Answer:
265.46 and 50.14
Step-by-step explanation:
Area of entire circle = π r² = π (13)² = 169π
area of shaded semicircle = (169π) /2 = 265.46
angle PTQ = 180 - 73 - 73 = 34°
area of shaded sector (PQT) = (34/360) X 169π
= (2873/180) π (m²) = 50.14
A scale drawing uses a scale of 4cm for every 5m.
Write this as a ratio in its simplest form.
Answer:
1 : 125
Step-by-step explanation:
We know that,
1m → 100cm
Accordingly, first, let us convert 5m into centimeters by multiplying it by 100.
5m × 100 = 500cm
So,
4cm : 5m
4cm : 500cm
4 : 500
To write the ratio in its simplest form divide it by 4.
1 : 125
a 0.350 inch diameter rod of an aluminum alloy is pulled to failure in a tensile test. if the final diameter of the rod at the fractured surface is 0.250 inches, what is the percentage reduction in area of the sample due to the test?
By Simplifying the expression, [tex](π(0.175)^2 - π(0.125)^2)/π(0.175)^2 * 100.[/tex] we find the percentage reduction in the area of the sample due to the test.
To find the percentage reduction in area of the sample, we need to calculate the difference in cross-sectional areas before and after the tensile test.
The cross-sectional area of a rod can be calculated using the formula: [tex]A = πr^2[/tex], where r is the radius of the rod.
Given that the initial diameter of the rod is 0.350 inches, the initial radius (r1) is 0.350/2 = 0.175 inches. Therefore, the initial cross-sectional area (A1) is[tex]π(0.175)^2.[/tex]
Similarly, the final diameter of the rod is 0.250 inches, and the final radius (r2) is 0.250/2 = 0.125 inches. The final cross-sectional area (A2) is [tex]π(0.125)^2[/tex].
Now, we can calculate the percentage reduction in area using the formula: (A1 - A2)/A1 * 100.
Substituting the values, we have: [tex](π(0.175)^2 - π(0.125)^2)/π(0.175)^2 * 100.[/tex]
Therefore, by Simplifying the expression, we find the percentage reduction in the area of the sample due to the test.
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Jenny is making broccoli cheddar soup and her recipe calls for 2 1/4 cups of broccoli and 3/4 cup of cheddar. Select the equation that represents the amount of cheddar, c, needed per cup of broccoli, b. Assume the situation is proportional. Answer key
An equation that represents the amount of cheddar, c, needed per cup of broccoli, b is: D. c = 1/3(b).
What is a proportional relationship?In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
c = kb
Where:
k is the constant of proportionality.b represent the number of cup of broccoli.c represent the amount of cheddar.Next, we would determine the constant of proportionality (k) based on the data points provided as follows:
Constant of proportionality, k = c/b
Constant of proportionality, k = 3/4/(9/4)
Constant of proportionality, k = 3/4 × 4/9.
Constant of proportionality, k = 1/3
Therefore, the required equation is given by;
c = kb
c = 1/3(b)
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Pauls age is three times barts age in 14 years pauls age will be twice as barts age how old are both of them
Given Pauls age is three times barts age in 14 years pauls age will be twice as barts age, therefore, Bart is currently 14 years old, and Paul is currently 42 years old.
Let's assume that Bart's current age is x. Then, Paul's current age is 3x. In 14 years, Bart's age will be x + 14, and Paul's age will be 3x + 14. We know that Paul's age in 14 years will be twice Bart's age in 14 years. We can set up an equation to solve for x:
3x + 14 = 2(x + 14)
Simplifying this equation, we get:
3x + 14 = 2x + 28
x = 14
Therefore, Bart's current age is x = 14, and Paul's current age is 3x = 42.
To check our answer, we can verify that in 14 years, Paul's age will be twice Bart's age:
Paul's age in 14 years = 42 + 14 = 56
Bart's age in 14 years = 14 + 14 = 28
56 = 2(28)
Thus, our solution is correct. Bart is currently 14 years old, and Paul is currently 42 years old.
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If a = 8, b = 6, and h = 10. Then what is Tan (A)
The value of Tan( A) = 53.1°
What is trigonometric ratio?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
sin(tetha) = opp/hyp
cos( tetha) = adj/hyp
tan ( tetha) = opp/adj
The opposite to the angle A is a which is 8, the adjacent is 6 and hypotenuse 10
Tan(A) = 8/6
Tan(A) = 1.33
A = tan^-1 ( 1.33)
A = 53.1°
therefore the value of tan A is 53.1°
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what is the perimeter of an oval
The formula for the perimeter of an oval is given as
P = 2π√((a² + b²)/2)
Understanding Oval ShapeOval is a shape that is not entirely circle but spherical. It is usually called or also known as an ellipse.
The formula for finding the perimeter (circumference) of an ellipse is:
P = 2π√((a² + b²)/2)
where:
P is the perimeter (or circumference) of the oval
π is a mathematical constant approximately equal to 3.14159
a is the distance from the center of the ellipse to its furthest point in the horizontal direction (semi-major axis)
b is the distance from the center of the ellipse to its furthest point in the vertical direction (semi-minor axis).
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Answer:
Its the perimeter of an oval ö
Nah, im just joking, it's 2 times pie times the square root of((a² + b²)/2)
Step-by-step explanation:
Sorry I don't have some of the symbols
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