The following probabilities are found under the condition that a certain national survey of heads of households P(woman asked for a promotion) = 24%, P(woman received promotion, given she asked for one) = 45%, P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%
Now,
Regarding a national survey concerning the head od households, only 24% of women interviewed had requested for a promotion and of those women who had asked for a promotion, 45% received the raise.
Therefore,
(a) P(woman asked for a promotion) = 24%
(b) P(woman received promotion, given she asked for one) = 45%
(c) P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%
Probability refers to the percentage of an event taking place in a required time frame, in a specified place. It is considered a great aid in the fields of science and mathematics.
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URGENT - Will also give brainliest
Answer:
The area of the shaded sector is
(π/4)(6^2) = (π/4)(36) = 9π
Find the surface area of a square pyramid with side length 6 cm and slant height 7 cm.
The surface area of a square pyramid with a side length of 6cm and a slant height of 7cm is 110cm²
Given side length of the square pyramid (a) = 6cm
Given slant height of the square pyramid (l) = 7cm
The formula for finding the surface area of a square pyramid is = a²+2al
By substituting the given values in the above formula we can obtain the value of the surface area of the square pyramid.
So, Surface Area = a²+2al = (6)² + (2 x (6) x (7))
Surface Area = 36 + 84
Surface Area = 110cm²
From the above solution, we can conclude that the surface area of the given square pyramid of length 6cm, and slant height 7cm is 110cm².
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For a charity event, Jean biked at a fixed speed from Pine Bluff to Newberry. The graph shows the distance she rode along the y-axis and the amount of time it took along the x-axis.
The proportionality constant (y to x) is _____
.
Please help I really need this quick!!! NO SPAM!!!!
The calcuated value of the proportionality constant (y to x) is 15
Calculating the proportionality constantTo find the proportionality constant between the distance and time, we can use the formula:
proportionality constant = y/x
where y is the distance and x is the time.
From the graph, we know that when x = 1, y = 15. Therefore, the proportionality constant can be calculated as follows:
proportionality constant = y/x = 15/1 = 15
So, the proportionality constant between the distance and time is 15.
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please answer only if you know the answer.
The dimensions of the net for the cube lampshade which fits into the sheet of plastic with dimensions 20 cm by 15 cm indicates;
5. The area of each square of (5 cm)² on the sheet of plastic, indicates that the area of the net comprising of six squares is 150 cm²
6. The percentage of the plastic sheet wasted is 50%
What is a cubic shape?
A cubic shape is a shape that consists of six square faces, twelve edges and eight vertices. The area of each square face of side length s = Side length, s × Side length, s.
5. The surface area of the net in the figure can be calculated by finding the sum of the area of the squares within the area of the net.
The number of squares in the figure are 6 squares
The area of each square = (5 cm)²
The area of the sheet of plastic = 20 cm × 15 cm = 300 cm²
The area of the net containing six squares is therefore;
Area = 6 × (5 cm)² = 150 cm²
The surface area of the net is 150 cm²6. The amount of plastic sheet wasted can be obtained by finding the difference between the area of the plastic and the area of the net
Area of the sheet of plastic = 20 cm × 15 cm = 300 cm²
Area of the net = 150 cm²
Amount of the plastic sheet wasted = 300 cm² - 150 cm² = 150 cm²Therefore, the percentage of the plastic sheet wasted is (150/300) × 100 = 50%Learn more on the area of a net here: https://brainly.com/question/26581443
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Identify the function that possesses a period of 16 units, a midline at y=3, and a maximum at y=8.
The function that possesses a period of 16 units, a midline at y=3, and a maximum at y=8 is f(x) = 5 sin(π/8 x) + 3
Identifying the sine functionThe sine function with a period of 16 units, a midline at y=3, and a maximum at y=8 can be written in the form:
y = A sin(Bx) + C
where A is the amplitude, B is the frequency (related to the period), and C is the vertical shift (related to the midline).
The frequency is related to the period by the formula: B = 2π/period.
So, in this case,
B = 2π/16 = π/8.
So, we have
y = A sin(π/8x) + C
Using the list of options as a guide the sine function that satisfies these conditions is f(x) = 5 sin(π/8 x) + 3
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Use the quadratic formula to solve the equation.
What are the solutions to the equation 4x² + 3x + 1 = 0?
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
The total 460 cards are sold on Mothers day.
Given that, Bob's gift shop sold a record number of cards for Mother's Day.
One salesman sold 46 cards, which was 10% of the cards sold for Mother's Day.
Let the number of cards sold on mothers day be x.
Here, 10% of x =46
10/100 ×x= 46
10x=4600
x=460
Therefore, total 460 cards are sold on Mothers day.
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Solve each one of the following equations and check your result. 4x+7=9
Solving the equation 4x + 7 = 9 will give value of x = 1/2
To solve we will use the equation
4x + 7 = 9
By subtracting 7 from both side we get
4x + 7 -7 = 9 -7
4x = 2
By diving 4 from both sides we get
4x/4 = 2/4
x = 1/2
To check we put the value of x in the equation we get
4(1/2) + 7 = 9
2 + 7 = 9
9 = 9
Hence the value of x is satisfying the equation
Therefore, the value of x is 1/2
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an accountant claims the the average amount of a tax refund is less than 250 dollars. if the account wants to conduct a hypothesis test, should they use a left-, right-, or two-tailed hypothesis test to analyze whether the average amount of a tax refund is less than 250 dollars? select the correct answer below: left-tailed test right-tailed test two-tailed test
The accountant should use a left-tailed hypothesis test to analyze whether the average amount of a tax refund is less than 250 dollars.
A left-tailed test is used when the null hypothesis states that the population mean is greater than or equal to a certain value, and the alternative hypothesis states that the population mean is less than that value. In this case, the null hypothesis would be that the average amount of a tax refund is greater than or equal to 250 dollars, and the alternative hypothesis would be that the average amount is less than 250 dollars.
what is average amount?
The average amount, also known as the mean, is a measure of central tendency that represents the sum of a set of values divided by the total number of values in the set. It gives an idea of the typical value or the central value of a dataset.
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a quality control inspector has drawn a sample of 17 light bulbs from a recent production lot. suppose 30% of the bulbs in the lot are defective. what is the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective? round your answer to four decimal places.
Answer: This is a binomial distribution problem with parameters n = 17 and p = 0.3, where n is the sample size and p is the probability of a defective bulb. We need to find the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective.
Let X be the number of defective bulbs in the sample. Then X has a binomial distribution with parameters n = 17 and p = 0.3, i.e., X ~ B(17, 0.3).
We want to find P(3 ≤ X ≤ 6). Using the binomial probability formula, we have:
P(3 ≤ X ≤ 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
= (17 choose 3)(0.3^3)(0.7^14) + (17 choose 4)(0.3^4)(0.7^13) + (17 choose 5)(0.3^5)(0.7^12) + (17 choose 6)(0.3^6)(0.7^11)
≈ 0.1566 (rounded to four decimal places)
Therefore, the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective is approximately 0.1566.
Step-by-step explanation:
i dont understand what this means if yall want to help
Answer: Just simply replace the letter with the number that it equals in the equation. Then solve the equation using PEMDAS order of operations, (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction).
Step-by-step explanation:
Which of the following is often provided by your employer at no cost?
O life insurance
O 403 (B)
O 401 (K)
O healthcare
O life insurance is often provided by your employer at no cost
Many employers often provide life insurance coverage at no cost as part of their employee benefits package.
O life insurance.
The other options, 403(B), 401(K), and healthcare, usually require employee contributions or have shared costs between the employer and the employee.
Employers may provide different benefits packages, and the specific benefits offered can vary from one employer to another.
However, it is common for employers to provide healthcare coverage at no cost to employees.
Life insurance, 403(B), and 401(K) plans may also be offered by some employers, but they may not always be provided at no cost to the employee.
It's essential to check with your employer's human resources department to determine which benefits are offered and whether there are any associated costs.
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Using the explicit formula find the 11th term of the sequence. -4, 8, -16, 32, ...
Answer:
4096.
Step-by-step explanation:
We need to check if it's a geometric or arithmetic sequence (looking for the common ratio, r). The sequence goes -4, 8, -16, 32, so we can multiply the previous number by -2 to get the next number, and so on and so forth. This makes it a geometric sequence.
The formula for finding the nth term of a geometric sequence is [tex]u_{n} = u_{1} r^{n-1}[/tex]. The term we are looking for is the 11th. Let's plug these values in now:
[tex]u_{n} = u_{1}r^{n-1}[/tex]
[tex]u_{11} = -4(-2)^{11-1}[/tex]
[tex]u_{11} = 4096[/tex]
Therefore the 11th term is 4096.
Giovanna deposited $1600 into two different savings account she deposited half of the money at first Oak and the other half at West United how much interest will she have earned from both accounts at the end of five years ?
Answer: $8000r
Step-by-step explanation:
Assuming that both savings accounts earn the same interest rate over the five-year period, Giovanna would have earned the same amount of interest on both accounts.
If she deposited half of the money, which is $1600/2 = $<<1600/2=800>>800, into each account, then the total amount of money she deposited into savings is $800 + $800 = $1600.
Let's say the interest rate on both accounts is r, expressed as a decimal. The amount of interest Giovanna earns on the Oak account after five years would be:
Interest on Oak account = $800 * r * 5
Similarly, the amount of interest she earns on the West United account after five years would be:
Interest on West United account = $800 * r * 5
The total amount of interest she earns from both accounts would be the sum of these two amounts:
Total interest = Interest on Oak account + Interest on West United account
= ($800 * r * 5) + ($800 * r * 5)
= $1600 * r * 5
= $8000r
So, the total amount of interest Giovanna will have earned from both accounts at the end of five years is $8000r. The actual value of r would depend on the interest rate offered by each savings account.
on average, what percentage of infants born to 45-year-old mothers have down syndrome? on average, what percentage of infants born to 45-year-old mothers have down syndrome? 1% 3% 8% 10% 30%
The number of infants born to 45-year-old mothers who have Down syndrome on average is approximately 1 in 30 or 3.33%. The Down disorder may be a hereditary clutter that happens when there's an additional duplicate of chromosome 21.
The chance of having a child with Down disorder increments with maternal age. Agreeing to the American College of Obstetricians and Gynecologists, at age 35, the hazard of having an infant with Down disorder is around 1 in 350, or 0.29%. By age 40, the hazard increments to around 1 in 100, or 1%. And by age 45, the chance is around 1 in 30 or 3.33%.
In any case, pre-birth testing can offer assistance distinguish the chance of Down disorder and other hereditary anomalies amid pregnancy. This will offer assistance to hopeful guardians to make educated choices approximately their pregnancy and their baby's wellbeing.
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While Brian traveled, the pilot taught him
O how to steer a Cessna 406
O how to fill the gas tank on the Cessna 406
O how to read the instrument panel on the Cessna 406
While Brian traveled, the pilot taught him A. how to steer a Cessna 406.
What is a Cessna 406?The Cessna 406 is a twin-engine aircraft that is commonly used for various purposes, such as air ambulance services, freight transport, and surveillance operations. Steering the aircraft is an essential skill that any pilot must learn in order to control the aircraft's direction of flight.
Learning how to steer a Cessna 406 would be an important skill for Brian to acquire if he was planning to become a pilot or work in the aviation industry.
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What is the area of this composite shape? Enter your answer in the box
The area of the given composite figure is 40 square inches.
What is a composite figure?
A composite figure and shape are the same thing. A composite figure is any object that may be disassembled into multiple fundamental shapes.
We are given a composite figure which can be broken into a triangle and a rectangle.
So,
⇒ Area of composite figure = Area of Rectangle + Area of triangle
⇒ Area of composite figure = (length * breadth) + ([tex]\frac{1}{2}[/tex] * base * height)
⇒ Area of composite figure = (5 * 7) + ([tex]\frac{1}{2}[/tex] * 5 * 2)
⇒ Area of composite figure = 35 + 5
⇒ Area of composite figure = 40 square inches
Hence, the area of the given composite figure is 40 square inches.
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In 2007, Jessica earned p dollars, where p > 100,000. She was paid monthly. Express the
amount her employer contributed to her Social Security tax in February algebraically.
The algebraic expression representing her employee's contribution to Social Security Tax is given as follows:
p > 516.67.
How to obtain the algebraic expression?The algebraic expression representing her employee's contribution to Social Security Tax is obtained applying the proportions in the context of the problem.
An year is composed by 12 months, hence the monthly salary is represented as follows:
p > 100000/12
p > 8,333.33.
The Social Security tax is of 6.20%, hence the expression is given as follows:
p > 8,333.33 x 0.062
p > 516.67.
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Which line best describes the narrative structure of "Cautionary Tale of Girls and Birds of Prey"?
1) alliteration and assonance that create a peaceful, dreamlike rhythm
2)exaggeration and hyperbole used to describe a girl’s irrational fear of a bird of prey
3)images that make the reader question whether the girl only imagined the hawk
4)two-line stanzas that slowly build suspense about the girl’s fear of the hawk
The answer is Option 4) two-line stanzas that slowly build suspense about the girl’s fear of the hawk.
What is a metaphor?In literature, metaphors are frequently used to evoke strong feelings and express nuanced concepts. Because they establish a clear connection between two objects, they can be more effective than similes, but they can also be trickier to understand because they depend on the reader's comprehension of the suggested meaning. On the other hand, similes are frequently used in everyday language and might have a clearer meaning.
The poem is divided into two-line stanzas, with each stanza offering a specific concept or illustration that helps to heighten the tension around the girl's hawk phobia. Up until the final stanza, where the story's climax is disclosed, each of the stanzas builds on the one before it, intensifying the situation and the girl's anxiety. The short, pointed lines that emphasise the bird's unexpected arrival and motions, as well as the poem's structure, all contribute to its tense, unsettling atmosphere.
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calculate a lower confidence bound using a confidence level of 99% for the percentage of all such homes that have electrical/environmental problems.
With a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.
To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have electrical/environmental problems, we need to have a sample of data on this issue. Let's assume that we have a random sample of 100 homes, and 20 of them were found to have electrical/environmental problems.
To calculate the lower confidence bound, we can use the formula:
Lower bound = p - zα/2 * sqrt(p * (1-p) / n)
where:
p = proportion of homes in the sample that have electrical/environmental problems = 20/100 = 0.2
zα/2 = z-score for the given confidence level of 99% = 2.576 (obtained from a standard normal distribution table or calculator)
n = sample size = 100
Plugging in these values, we get:
Lower bound = 0.2 - 2.576 * sqrt(0.2 * 0.8 / 100) = 0.083
Therefore, with a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.
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This means we can be 99% confident that the true percentage of all homes with electrical/environmental problems is
at least 17.5%.
To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have
electrical/environmental problems, you would need a sample of homes and the number of homes in the sample that
have such problems. Using this information, you could calculate the sample proportion (p-hat) of homes with
electrical/environmental problems.
Then, using a formula or calculator, you could find the lower confidence bound by subtracting the margin of error (ME)
from the sample proportion.
The margin of error can be calculated using the sample proportion, sample size, and the chosen confidence level (in
this case, 99%).
For example, if the sample proportion is 0.25 and the sample size is 100, the margin of error would be 0.075 and the
lower confidence bound would be 0.175 (0.25 - 0.075).
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Which term is a constant numerical value in w/4+12.5-7z????
help me i need help with what I’m doing!
Explanation:
The w/4 term is the same as (1/4)w or 0.25w since 1/4 = 0.25
Because a variable is attached to this term, it is not constant. The same can be said about the -7z term as well.
The 12.5 is constant. It never changes. It will always be 12.5 no matter what the other variable terms change to.
For example, if w = 12, then the term w/4 becomes 12/4 = 3. Or if w = 24, then w/4 = 24/4 = 6 is the new value. This shows that term changing depending on the input variable.
what is equivelent to −2y−8+4y khan academy
The equivalent expression is 2(y-4).
What is an expression?
A statement with more than two variables or integers can be written as an expression using addition, subtraction, multiplication, and division operations.
What is equivalent?Even though they have different looks, expressions that are equivalent do the same action. Two algebraic expressions that are equivalent have the same value when the variable is entered with the same value.
We have,
-2y - 8 + 4y
-2y and 4y are like terms.
So,
Add the like terms.
2y - 8
Taking out 2 commons.
2(y - 4)
Now,
We can not further simplify the expression.
Thus,
The equivalent expression is 2(y - 4).
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SOMEONE ANSWER MY MATH QUESTIONS ON MY PROFILE (IF CORRECT YOU GET BRAILST)
Jessica needs an additional material of 511.875 cm^3 to make the second prism.
How to calculate the amount neededJessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5.
The volume of the first prism is 35 cm^3. Since the second prism is a dilation of the first prism with a scale factor of 2.5, its volume will be (2.5)^3 = 15.625 times greater than that of the first prism. Therefore, the volume of the second prism will be 35 x 15.625 = 546.875 cm^3.
To make the second prism, Jessica needs an additional material of 546.875 - 35 = 511.875 cm^3.
So Jessica needs an additional material of 511.875 cm^3 to make the second prism.
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Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5
How much more material does Jessica need in order to make the second prism?
can someone do this i don’t understand
A good way to solve for lines and segments will be to know the equations and properties of the shapes that we are provided with.
How to solve for lines and segmentsTo get the answers for the lines and segment, you can begin by applying the following steps:
Identify the given information: Determine what information is provided about the line or segment. For example, you may be given the coordinates of two points on the line or segment, or the slope and y-intercept of a line.Find the equation: Use the information provided to find the equation of the line or segment. For a line, the general equation is y = mx + b, where m is the slope and b is the y-intercept. For a segment, you may need to use the distance formula or midpoint formula to find the endpoints, and then find the equation of the line that passes through those points.Check for intersections: If you need to find the intersection of two lines or segments, set their equations equal to each other and solve for the variables. If the lines or segments do not intersect, they are parallel or skew.Find lengths and angles: Once you have the equations and intersection points, you can use geometry and trigonometry to find lengths and angles of the lines and segments.Learn more about lines and segments here:
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My rabbit Nibbles lives in a moveable pen and helps to keep the grass short. The pen is rectangular and measures 3m by 2m, as shown in the diagram, where the arrow indicates North. On successive days, the pen is moved 1m East, 2m South, 1m West and 2m North.
What is the total area, in square metres, of the region of grass which Nibbles can nibble?
Answer:
We can break down the total area of grass that Nibbles can nibble into two parts: the original rectangular pen, and the additional grass that Nibbles can reach as the pen is moved.
The area of the original rectangular pen is:
A1 = length x width = 3m x 2m = 6 square meters
To calculate the area of the additional grass, we can visualize the movements of the pen. The pen moves 1 meter to the east, 2 meters to the south, 1 meter to the west, and 2 meters to the north. This creates an irregular pentagon shape, as shown in the diagram below:
```
+-------+
| |
| |
E |
+----+---+ |
| S|
| |
| |
| |
| |
| |
+-----------+
W
```
To calculate the area of this irregular pentagon, we can divide it into two triangles and one rectangle:
- The east and west sides of the pen form a rectangle with dimensions 1m x 2m, for an area of 2 square meters.
- The south side of the pen creates a right triangle with legs of 2m and 1m, for an area of (1/2) x base x height = 1 square meter.
- The north side of the pen creates a right triangle with legs of 2m and 1m, for an area of (1/2) x base x height = 1 square meter.
Therefore, the total area of grass that Nibbles can nibble is:
A = A1 + 2 + 1 + 1 = 10 square meters.
So the answer is 10 square meters.
a right circular cylinder is inscribed in a sphere of radius r. find the largest possible surface area of such a cylinder
For a inscribed right circular cylinder in sphere of radius r, largest possible surface area of such a cylinder is equals to the [tex]= πr²( 1 + \sqrt{5}) [/tex].
The maximum or minimum value of a continuous function can be determined by derivatives of the function. If y= f(x) is a continuous function, Then slope of function at extreme points( maximum or minimum) is zero, [tex]\frac{dy}{dx} =0[/tex]. Let's consider r be the radius of the sphere and is a constant. Let R and h be the radius and height of the cylinder that can be inscribed in a sphere of radius r as shown in the above figure. By Pythogoras Theorem, base radius of cylinder as,[tex]R =\sqrt{ r²-\frac{h²}{4}}[/tex]
Surface area of cylinder, S = 2πRh + 2πR²
=> [tex]S= 2πh\sqrt{ r²- \frac{h²}{4}} + 2π(r²- \frac{h²}{4}) \\ [/tex]. We need to calculate height of cylinder such that surface area is maximum. For surface area to be maximum, [tex] \frac{dS}{dh} =0[/tex]
[tex]2πh \frac{1}{2\sqrt{ r² - \frac{h²}{4}}}( \frac{ - 2h}{4} ) + 2π\sqrt{ r² - \frac{h²}{4}} + 2π \frac{(-2 )h}{4} = 0 \\ [/tex]
=>[tex] \frac{- h²}{4\sqrt{ r² - \frac{h²}{4}} } + \sqrt{ r² - \frac{h²}{4}} - \frac{h}{2} = 0[/tex]
=> [tex]- h² + 4 ( r² - \frac{h²}{4} ) - 2h\sqrt{ r² - \frac{h²}{4}} = 0 \\ [/tex]
[tex]- 2h² + 4r² - 2h\sqrt{ r² - \frac{h²}{4}} = 0[/tex]
=>[tex]- 2h²+ 4r² = 2h\sqrt{r²- \frac{h²}{4}}[/tex]
Squaring on both sides, [tex]4h^{4} + 16r⁴ - 16r²h² = 4h² ( r² - \frac{h²}{4}) = 0 \\ [/tex]
[tex]h^{4} + 4r⁴ - 4r²h² = h² r² - \frac{h⁴}{4} = 0 \\ [/tex]
=> [tex]5h^{4} + 4r⁴ - 5r²h² = 0 [/tex]
which is Quadratic equation with h² variable, so using quadratic formula for determining the values of h², [tex]=4r^{2} ( \frac{5 ± \sqrt{5}}{10})[/tex]. Since we need largest possible surface area, we will consider, [tex]h² = 4r²( \frac{ 5 - \sqrt{5}}{10})[/tex]
=> [tex]r² - \frac{h²}{4} = r²( \frac{ 5 + \sqrt{5}}{10})[/tex]
Substituting the values in the surface area equation, [tex]S= 2πh\sqrt{ r² - \frac{h²}{4}} + 2π(r² - \frac{h²}{4}) \\ [/tex]
[tex]= 4πr²(\sqrt{ \frac{5 - \sqrt{5}}{10}})(\sqrt{ \frac{ 5 + \sqrt{5}}{10}} )+ 2πr²( \frac{ 5 + \sqrt{5}}{10}) \\ [/tex]
[tex]= 2πr²( \frac{ 4\sqrt{5}}{10} + \frac{ 5 + \sqrt{5}}{10} ) \\ [/tex]
=> [tex]= πr²( 1 + \sqrt{5}) [/tex]
Hence, required area is [tex]= πr²( 1 + \sqrt{5}) [/tex].
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Based on the graphs of the two functions, which statement is true?
Answer:f(4)=g(4)
Step-by-step explanation:We see that when x= 4, we see that f(4) intersects g(4)
Writing What is the volume of the sphere? Use 3.14 for . Use pencil and paper. Describe how the volume of the sphere changes if the radius is increased by 1. radius is 19 in
Comparing the two volumes, we can see that the volume of the sphere decreased when the radius was increased by 1 inch. This is because the volume of a sphere increases with the cube of its radius, so small changes in the radius can result in significant changes in the volume.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the volume of a sphere, we use the formula:
V = (4/3)πr³
where "r" is the radius of the sphere and "π" is approximately 3.14.
If the radius of the sphere is 19 inches, we can substitute this value into the formula to find its volume:
V = (4/3)π(19)³
V = (4/3)π(6859)
V = 36,236.71 cubic inches (rounded to two decimal places)
Therefore, the volume of the sphere with a radius of 19 inches is approximately 36,236.71 cubic inches.
If the radius is increased by 1 inch to 20 inches, we can find the new volume of the sphere using the same formula:
V = (4/3)π(20)³
V = (4/3)π(8000)
V = 33,510.32 cubic inches (rounded to two decimal places)
Hence, Comparing the two volumes, we can see that the volume of the sphere decreased when the radius was increased by 1 inch. This is because the volume of a sphere increases with the cube of its radius, so small changes in the radius can result in significant changes in the volume.
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3-3 The slope of a simple fable roof may be defined as:A. The rise of the roof times the run of the roof.B. The rise of the roof divided by the run of the roof.C. The rise of the roof divided by 1/2 the run.D. The run of the roof times the rise squared.
The slope of a simple gable roof can be defined using the terms rise and run.
The correct definition is:
B. The slope of a simple gable roof is the rise of the roof divided by the run of the roof.
To calculate the slope, follow these steps:
Measure the rise of the roof (the vertical distance between the highest and lowest points).
Measure the run of the roof (the horizontal distance between the edge of the roof and the point directly below the highest point).
Divide the rise by the run to find the slope.
Remember, the slope is a ratio representing the steepness of the roof, and it is important for proper drainage and structural stability.
Option B. The slope of a simple gable roof is the rise of the roof divided by the run of the roof.
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What is the height of the tree?
Answer:
Step-by-step explanation:
The height of a tree would be the height of its root node, or equivalently, the depth of its deepest node.