Answer:
The correct volume of the largest sphere that fits inside the silo is 14,137.2 ft³
Step-by-step explanation:
Since the sphere must feet inside the silo it's diameter must be at most 30 feet, therefore it's radius is 15 feet. To calculate the volume of the sphere we can use the appropriate formula:
Volume = (4/3)*pi*r³
Volume = (4/3)*3.14*(15)³
Volume = 14137.2 ft³
The correct volume of the largest sphere that fits inside the silo is 14,137.2 ft³. The nearest option would be B.
Final answer:
The volume of the largest sphere that can fit into the cylindrical feed silo is calculated using the formula for the volume of a sphere, resulting in 47,712 ft³, which corresponds to option D.
Explanation:
The question asks for the volume of the largest sphere that can fit into a cylindrical feed silo with a diameter of 45 feet and a height of 30 feet. To find the volume of the sphere, we need to consider the diameter of the cylinder because the diameter of the silo will be the same as the diameter of the sphere that can fit inside it. Hence, the radius of the sphere (and cylinder) is half of the diameter, which is 22.5 feet. The formula for the volume of a sphere is V = (4/3)πr³. Substituting the radius into the formula gives us V = (4/3)π(22.5)³ = 47,712 ft³.
Jasmine invests $1500 in an account that earns an interest rate of 4% compounded
continuously. How much money will she have in 4 years? (round to the hundredth place)
Answer:
After 4 years she will have $1760.67 in her account.
Step-by-step explanation:
Jasmine invested initial amount = $1500
Rate of interest = 4% compounded continuously
Duration of investment = 4 years
Formula to calculate the final amount when compounded continuously is,
[tex]P(t)=Ie^{rt}[/tex]
where I = Initial amount
r = rate of interest
t = duration of investment
P(t) = Final amount
[tex]P(4)=1500e^{0.04(4)}[/tex]
= [tex]1500e^{0.16}[/tex]
= 1760.266
≈ $1760.27
Therefore, after 4 years she will have $1760.67 in her account.
Final answer:
To calculate the amount of money Jasmine will have in 4 years with a 4% continuous interest rate, use the formula A = P * e^(rt), where A is the final amount, P is the principal, e is Euler's number, r is the interest rate, and t is the time in years. Evaluating the expression, the result is approximately $1657.29.
Explanation:
To calculate the amount of money Jasmine will have in 4 years, we can use the formula for compound interest. The formula is: A = P * e^(rt), where A is the final amount, P is the principal (initial investment), e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years. In this case, Jasmine invests $1500 at an interest rate of 4% compounded continuously, so we have A = 1500 * e^(0.04*4). Evaluating this expression, we find that Jasmine will have approximately $1657.29 in 4 years.
If you were on the moon, your weight would only be 0.17 of your weight on Earth. If you weigh 195.75 pounds on Earth, how much would you weigh on the moon?
Answer:
32.49
Step-by-step explanation:
The weight of the person on the moon is 33.2775 pounds.
Given that, if you were on the moon, your weight would only be 0.17 of your weight on Earth.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, weight on earth is 195.75 pounds
Now, weight on the moon
= 0.17×195.75
= 33.2775 pounds
Hence, the weight of the person on the moon is 33.2775 pounds.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ5
What is Pythagorean Therom and how is it used?
Answer:
The Pythagorean Theorem in a^2 + b ^2 = c^2
It is used to solve for one side of a right triangle (any triangle where one angle is 90 degrees). Most of the times it is used to solve for the hypotenuse, which is represented by c. A and B represent the other sides of the triangle.
The Pythagorean Theorem also states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.
In other words, for the triangle shown below, a² + b² = c².
In the image below, I have drawn a triangle on my whiteboard.
In the triangle that is shown below, the legs, a and b, are the perpendicular sides of the right triangle and the hypotenuse, c, is the side opposite the right angle.
This only applies to right triangles!
You can use this theorem to find out if a triangle is an acute triangle, a right triangle, or even an obtuse triangle.
Find the solution set of the inequality −4x+35>2
Answer:
x < 37/4
Step-by-step explanation:
−4x+35>2
Subtract 35 from each side
−4x+35-35>2-35
-4x > -37
Divide each side by -4. remembering to flip the inequality
-4x/-4 < -37/-4
x < 37/4
What is 7-5 pls help
Answer: The answer is 2 :)
Step-by-step explanation:
Answer:
778
Step-by-step explanation:
Four rulers and three pencils cost £2.15
Three rulers and four pencils cost £2.05
Work out the cost of a ruler and the cost of a pencil.
Answer:
is it 10 cents lesser
Step-by-step explanation:
The diameter of a circle is 16 meters. What is the angle measure of an arc bounding a sector with an area eight pi square meters? (give the exact answer in simplest form)
Answer: 45°
Step-by-step explanation:
Diameter= 16m
Radius= 16/2 = 8m
The area of the circle= πr^2
= π8^2
= 64π square metres.
An area of 8π square metres is also 1/8 of the total area, therefore the arc must be 1/8 of the circumference.
The circumference = 2πr = 16π,
This gives us an arc length of 2π metres.
But since we are looking for the the angle.
In degrees: 360/8 = 45°
The angle of the sector is 45 degrees.
To understand the calculations, check below
Sector of circle:The radius of circle is [tex]\frac{16}{2} =8cm[/tex]
The area of circle is,
[tex]Area=\pi*8^{2} \\\\Area=64 \pi[/tex]
Area of sector [tex]=8\pi[/tex]
Angle of sector,
[tex]=\frac{8\pi}{64\pi} *360\\\\=\frac{360}{8}=45 degrees[/tex]
The angle of sector is 45 degrees.
Learn more about the sector angle here:
https://brainly.com/question/22972014
what is the area of a regular octagon with apothem 2.5 centimeters?
This is for geometry.
Mutiply that by the sides
Which types of graphs are most appropriate for displaying categorical data? Check all of the boxes that apply. bar graphs histograms pie charts or circle graphs stem-and-leaf plots
Answer: Bar graphs, pie charts or circle graphs
Step-by-step explanation: for it right
Pie charts or circle graphs and bar charts are the most appropriate displaying for categorical variables.
What is a graph?A graph is used to provide a pictorial representation or diagram so as to represents data in an orderly way. Examples of graphs are histogram, box plot, pie chart, dot plot.
Pie charts or circle graphs and bar charts are the most appropriate displaying for categorical variables.
Find out more on graph at: brainly.com/question/14323743
What is the area of the right triangle
Answer:
3.75
Step-by-step explanation:
2.5*1.5=3.75
- Alisha had 3/4 yards of ribbon. She wanted to use it to decorate
three picture frames. If she uses one-third of the ribbon on each
frame, how many yards of ribbon will she use for one frame?
Answer:
1/4 yards
Step-by-step explanation:
3/4 is the total. Divide the total by 3 to get the answer.
Which of the following graphs has a slope of
-5 and a y-intercept of 4?
Answer: B.
Step-by-step explanation:
I hope this helps!
Suggest a universal set for the sets given below:
{ odd number less than 8 }, {prime number less than 8} and {even number between 3 and 8}
Step-by-step explanation:
A = ( 1 3 5 7) B = (2 3 5 7) C = (4 6)
U = ( 1 2 3 4 5 6 7)
anyone know this ?! help pls asap
(-7)² ➡️ 49
(⅔)² ➡️ ⁴/6
- /100 ➡️ -10
/.81 ➡️ .9
Explain the difference between the superlative and comparative degree.
Answer:
The superlative degree compares more than two things to show which has the least or greatest degree of the quality.comparative degree is used when just comparing two things.
Step-by-step explanation:
Final answer:
The comparative degree is used to compare two items, while the superlative degree is used to compare three or more. Comparatives typically end in -er, while superlatives end in -est, except in cases of adjectives with more syllables where 'more' and 'most' are used respectively. Absolute adjectives generally do not have comparative or superlative forms.
Explanation:
Difference Between the Comparative and Superlative Degree
The comparative and superlative degrees are used to make comparisons between nouns based on some attributes described by adjectives or adverbs. The comparative degree is used when comparing two items, while the superlative degree is used when comparing three or more items. Comparative adjectives often end in -er, and superlative adjectives often end in -est. For example, the adjective 'hot' becomes 'hotter' in the comparative form and 'hottest' in the superlative form.
For adjectives of three or more syllables, and some two-syllable adjectives, the comparative is formed by adding the word 'more' before the adjective, and the superlative is formed with 'most'. For instance, 'famous' becomes 'more famous' and 'most famous' in comparative and superlative forms respectively. Some adjectives and adverbs are irregular and do not follow these standard patterns of formation. Furthermore, adjectives that describe absolute qualities, such as 'dead' or 'pregnant', typically do not have comparative or superlative forms.
It is important to never use both types of comparison for the same adjective, as in 'most hardest'. The correct form would be 'hardest', without the 'most'. Also, it's useful to know that adjectives imply a scale of degrees, and comparative forms indicate one item's position on that scale in relation to another, while superlatives indicate the extreme ends of that scale.
Find the midpoint of A and B where A has coordinates (2,4) and B has coordinates (-3,-9)
Which statements about the ellipse are true? Check all that apply.
The center is located at (2, –1).
The major axis is 8 units long.
The minor axis is 3 units long.
The vertices are 4 units above and below the center.
The foci are √ 7 units above and below the center.
The foci are located along a horizontal line.
Answer:
1,2,4,5
Step-by-step explanation:
Answer:
1, 2, 4, and 5
Step-by-step explanation:
just did the work
A random survey shows that 14 out of 21 students plan to vote for Jacob for class president. Which is the best prediction of the total number of votes Jacob will receive if 180 students vote?
A.35
B.90
C.120
D.173
Answer:
C. 120 Votes
Step-by-step explanation:
14/21 will get you 66.6. Taking that number and multiplying it by the 180 total students will end you with 120 which is your answer.
Which answer represents the range of the logarithmic function given below? f(x) = log0.3 x
Domain of the function F(x) = log 0.3 x is :
All Real Numbers greater than zero.
So the right answer is :
D. All real numbers
Answer:All real numbers
Step-by-step explanation:
A
P
E
X
What is the value of p in the equation of 2(3p -4) = 10
Answer:
p=3
Step-by-step explanation:
2(3p -4) = 10
6p-8=10 (distribute the 2)
6p=18 (add 8 to both sides)
p=3 (divide 3 from both sides)
Answer:
p = 3
Step-by-step explanation:
2 • (3p - 4) - 10 = 0
The weather report stated there is a chance of 2/3 rain on Friday. It is more likely to rain on Saturday than on Friday, but not certain. What is a possible probability of rain on Saturday?
3/4 chance of rain for saturday
Answer:
3/4 chance of rain for saturday
Step-by-step explanation:
If you help me get this right i will mark u as most brilliance!
Answer:
f(0) = -2
f(4) = -14
f(-1) = 1
Step-by-step explanation:
f(x) = -3x-2
f(0) means let x=0
f(0) = -3(0) -2
= 0-2
= -2
f(4) means let x =4
f(4) = -3(4) -2
= -12 -2
= -14
f(-1) means let x =-1
f(-1) = -3(-1) -2
= 3 -2
= 1
Answer:
f(0) = -2
f(4) = -14
f(-1) = 1
Step-by-step explanation:
To find each answer, you substitute the number in the parentheses for x.
-3(-0) - 2 = -2
-3(4) - 2 = -14
-3(-1) - 2 = 1
Can some one help me please with this questions
20 x + 15 = 10
20 x = - 5
x = -5/20 = -1/4
Answer: -1/4
5x - 5 = 15
5x = 20
x = 20/5 = 4
Answer: 4
n + 14 = 72
Answer: 14 + n = 72, first choice
sin^2x + sin x = 0
Find all solutions to the equation
What is the area of the shaded region?
21 m
23 m
10 m
34 m
Answer:
572
Step-by-step explanation:
Answer:
572 m
Step-by-step explanation:
step 1: find area of big box
23 m x 34 m = 782 m
step 2: find area of small box
21 m x 10 m = 210 m
step 3: subtract small box area from big box area to get shaded region
782 m - 210 m = 572 m
I need some help with middle school math
Answer:
1/8
Step-by-step explain i think it;s your answer
Answer:
24
Step-by-step explanation:
What is the measure of θ in radians?
In the diagram, θ is a central angle.
Answer:
5
Step-by-step explanation:
Arc length = r × theta
15 = 3 × theta
theta = 15/3
theta = 5 radians
5
Answer:
Step-by-step explanation:
h(t)= -16t^2 + 87t. find the average rate of change of the height of the ball from 2 to 4.5 seconds
Answer:
-17 ft/s
Step-by-step explanation:
The average rate of change is the difference in height on the interval, divided by the difference in time.
m = (h(4.5) -h(2))/(4.5 -2) . . . . . . . . definition of rate of change on [2, 4.5]
h(4.5) = (-16·4.5 +87)(4.5) = 67.5
h(2) = (-16·2 +87)(2) = 110
Then ...
m = (67.5 -110)/(2.5) = -17
The average rate of change on the interval from 2 to 4.5 seconds is -17 ft/s.
_____
Check
The slope of the curve is given by its derivative:
h'(t) = -32t +87
The midpoint of the interval is (2+4.5)/2 = 3.25.
The slope at the midpoint is ...
h'(3.25) = -32(3.25) +87 = -17 . . . . average rate of change on [2, 4.5]
For a quadratic function. the average rate of change on an interval is the slope of the function at the midpoint of the interval. This calculation confirms that.
Final answer:
The average rate of change of the height of a ball described by the function h(t) = -16t^2 + 87t from 2 to 4.5 seconds is calculated using the difference in height values at these points divided by the difference in time, resulting in -17 feet/second.
Explanation:
The student asks to find the average rate of change of the height of a ball, given the function h(t) = -16t2 + 87t, from t = 2 seconds to t = 4.5 seconds. To find the average rate of change, we will use the following formula:
Average Rate of Change = (h(t2) - h(t1)) / (t2 - t1)
First, we calculate h(2) and h(4.5):
h(2) = -16(2)2 + 87(2) = -64 + 174 = 110
h(4.5) = -16(4.5)2 + 87(4.5) = -324 + 391.5 = 67.5
Plugging these values into the formula:
Average Rate of Change = (67.5 - 110) / (4.5 - 2) = -42.5 / 2.5 = -17
The average rate of change of the height of the ball from 2 to 4.5 seconds is -17 feet/second.
Which value of x is the solution of: 5x - 1 = 2x + 20?
A) 19/7
B) 19/3
C) 3
D) 4
Answer:the correct answer is 7
Step-by-step explanation:
what does this graph represent....LINEAR FUNCTION, EXPONENTIAL FUNCTION, OR (neither)
Answer:
LINEAR function constant slope = 2
Step-by-step explanation:
We see points (-3, -11), (-2, -9), (-1, -7), (1, -3) , (2, -1)
slope: m = (-9 - -11)/(-2 - -3) = 2/1
m = (-7 - -9)/(-1 - -2) = 2/1
m = (-3 - - 7)/(1 - -1) = 4/2 = 2
m = (-1 - -3)/(2 - 1) = 2/1 = 2