The volume of the solid whose base is a circle with radius 25 and cross-sections perpendicular to the x-axis that are squares is 1562500π/3 cubic units.
Let's consider a cross-section of the solid at a distance x from the center of the circle. This cross-section is a square with side length equal to the diameter of the circle minus 2x. Since the diameter of the circle is 50, the side length of the square can be expressed as 50 - 2x.
The volume of the solid can be found by integrating the area of each cross-section over the interval [0, 25]. The area of each cross-section is simply the square of the side length, which can be expressed as (50 - 2x)².
So, the volume of the solid can be found by integrating (50 - 2x)² with respect to x over the interval [0, 25]:
V = ∫[0,25] (50 - 2x)² dx
This integral can be evaluated using integration by substitution, with u = 50 - 2x:
du/dx = -2
dx = -1/2 du
When x = 0, u = 50, and when x = 25, u = 0. So, the integral becomes:
V = ∫[50,0] u² (-1/2) du
V = (-1/2) ∫[50,0] u² du
V = (-1/6) [u³]50_0
V = (-1/6) [(50³) - (0³)]
V = 1562500π/3
Therefore, the volume of the solid whose base is a circle with radius 25 and cross-sections perpendicular to the x-axis that are squares is 1562500π/3 cubic units.
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A city is located at a height of 138m above sea level while a town is at a height of 51m below sea level represent the altitude of the town using a negative number. Hence, find the difference in altitude between the city and the town
Answer:
The difference between city and town is 189m.
Step-by-step explanation:
A city is 138m above sea level and town is 51m below see level.
When finding the differences, you have to take the highest value and subtract the lowest value :
\(138 - ( - 51) = 138 + 51 = 189m\)
Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in Sandy's experiment.
The points (1,5), (5,10), (7,8), and (8,1) are on the graph of the function p. Which expression belo gives the average rate of change of the function p on 5 less than or equal x less than or equal 8
Answer:
Step-by-step explanation:
Since it is x that is bound by 5≤x≤8, you should use the points (5,10) and (8,1), since a coordinate is written as (x,y).
Then, use the formula for slope, as the average rate of change means find the slope, \(\frac{y2-y1}{x2-x1}\)
thus, plug in
\(\frac{1-10}{8-5}\), and you get -9/3, or -3. :)
help i need the answer
Answer:
the first one
\(.5x+10\geq .25x+15\)
Step-by-step explanation:
They want to know how much I will take for the amount they have read to be the same. So that automatically crosses out the last one. They asking you to subtract anything so that crosses the third one out. The second option has the number of pages the both read first switched so that crosses that one out.
I hope this explanation was helpful.
Proving the Sum of the Interior Angle Measures of a Triangle Is 180°
The two column proof showing that m∠5 + m∠2 + m∠6 = 180° is as detailed below.
How to use two column proof?A two-column proof is defined as geometric proof that consists of a list of statements, and then the reasons that we know those statements are true.
Thus, the two column proof is;
Statement 1: y || z
Reason 1: Given
Statement 2: m∠1 + m∠2 + m∠3 = m∠LAM
Reason 2: Angle addition postulate
Statement 3: m∠1 + m∠2 + m∠3 = 180°
Reason 3: definition of straight angle
Statement 4: ∠1 ≅ ∠5
Reason 4: Alternate interior angles theorem
Statement 5: ∠3 ≅ ∠6
Reason 5: Alternate interior angles theorem
Statement 6: m∠1 ≅ m∠5
Reason 6: Definition of ≅(congruency)
Statement 7: ∠3 ≅ ∠6
Reason 7: Definition of ≅(congruency)
Statement 8: m∠5 + m∠2 + m∠6 = 180°
Reason 8: substitution
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Answer:
check picture ..
edge 2023
Step-by-step explanation:
PLEASE ANWSER ASAP
Below, a two-way table is given
for student activities.
Sports Drama Work Total
7
3
13
2
5
5
Sophomore 20
Junior
20
Senior
25
Total
Find the probability the student is a sophomore,
given that they are in work.
P(sophomore | work) = P(sophomore and work) = [? ]%
P(work)
Round to the nearest whole percent.
The probability of P(sophomore | work) is 0.30.
Given that:
Sports Drama Work Total
Sophomore 20 7 3 30
Junior 20 13 2 35
Senior 25 5 5 35
Total 65 25 10 100
The probability is given as,
P = (Favorable event) / (Total event)
The probability of P(sophomore | work) is calculated as,
P = (3/100) / (10/100)
P = 3 / 10
P = 0.30
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WILL GIVE BRAINLIEST!!
A line has a slope of 1/3 and passes through the point (–9, –3). What is its equation in slope-intercept form?
Answer:
y = \(\frac{1}{3}\) x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = \(\frac{1}{3}\) , then
y = \(\frac{1}{3}\) x + c ← is the partial equation
to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation
- 3 = \(\frac{1}{3}\) (- 9) + c = - 3 + c ( add 3 to both sides )
0 = c
y = \(\frac{1}{3}\) x + 0 , that is
y = \(\frac{1}{3}\) x
a company purchases shipments of machine components and uses this acceptance sampling plan: randomly select and test 25 components and accept the whole batch if there are fewer than 3 defectives. if a particular shipment of thousands of components actually has a 7% rate of defects, what is the probability that this whole shipment will be accepted?
If particular shipment of thousands of components actually has a 7% rate of defects, there is a 54.29% probability that this whole shipment will be accepted.
According to the company's acceptance sampling plan, 25 components are randomly chosen and tested from a shipment before the entire batch is accepted if there are no more than three defects. The probability of choosing a defective component from a sample of 25 is computed as follows, assuming that the shipment genuinely has a 7% defect rate:
P(defective) = 0.07
P(non-defective) = 0.93
Using the binomial distribution, we can calculate the probability of having 0, 1, or 2 defectives in a sample of 25:
P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)
= (0.93)²⁵ + 25(0.07)(0.93)²⁵ + (0.07)²(0.93)²³
= 0.5429
This means that there is a 54.29% chance of having 2 or fewer defectives in a sample of 25. Since the whole shipment will be accepted if there are fewer than 3 defectives in the sample, this is the probability that the whole shipment will be accepted. Therefore, there is a 54.29% chance that the company will accept the shipment based on their acceptance sampling plan.
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Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.
Answer:
The amount she saves is 25% of her income
Step-by-step explanation:
She is paid $11 per hour
She works 9 hours per day
and for 24 days per month
So, she works 9(24) hours per month
= 216 hours per month
Now, she is paid $11 hourly, so for 216 hours,
she will have 11(216) = $2376
Total income = $2376 per month
Saving = $594 per month
As a percentage, we divide the savings by the total income,
savings/(total income) = 594/2376 = 1/4 = 0.25
Hence we get 25%
Given that ∠ADC≅∠BCD, AC⊥CD and BD⊥CD, which of the following proves that △ACD≅△BDC?
Answer:
1. ∠ADC≅∠BCD (Given)
2. AC¯¯¯¯¯⊥CD¯¯¯¯¯; BD¯¯¯¯¯⊥CD¯¯¯¯¯ (Given
)3. ∠ACD and ∠BDC are right angles(Def. of ⊥)
4. ∠ACD≅∠BDC (Rt. ∠≅Thm.)
5. CD¯¯¯¯¯≅CD¯¯¯¯¯ (Reflex. Prop. of ≅)
6. △ACD≅△BCD (ASA Steps 1, 5, 4)
△ACD and △BCD are Congruent triangles because Two angles are the same, as is a corresponding side.
What is of congruent triangle?Congruent triangles have comparable sides and angles that are equal. The symbol "≅" represents congruence.The three sides are all the same (SSS: side, side, side)Two angles are the same, as is a corresponding side (ASA: angle, side, angle)We know that two triangles are congruent if all of their sides are the same— thus side, side, side (SAS: side, angle, side). We also know they are congruent if we have a side, an angle between the sides, and another congruent side—so side, angle, side.1. ∠ADC≅∠BCD (Given)
2. AC⊥CD; BD⊥CD (Given
3. ∠ACD and ∠BDC are right angles(Def. of ⊥)
4. ∠ACD≅∠BDC (Rt. ∠≅Thm.)
5. CD≅CD (Reflex. Prop. of ≅)
6. △ACD≅△BCD
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In 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both vermont and hawaii. From the survey, vermont had 65. 3% who said yes and hawaii had 62. 2% who said yes. What is the value of the sample proportion of people from vermont who exercised for at least 30 minutes a day 3 days a week?.
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653, which is equivalent to 65.3%.
It is important to note that this value is based on a random sample of respondents and may not necessarily represent the true proportion of the entire population of Vermont who exercise regularly.
To find the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week, follow these steps:
1. Convert the given percentage (65.3%) to a decimal by dividing by 100: 65.3 / 100 = 0.653
2. Multiply the decimal by the number of participants in the random sample (100 respondents): 0.653 * 100 = 65.3
3. Round the result to the nearest whole number to find the number of participants who exercised: 65.3 ≈ 65
4. Divide the number of participants who exercised (65) by the total number of participants in the random sample (100): 65 / 100 = 0.65
This means that out of the 100 participants sampled from Vermont, 65.3 of them answered "yes" to the question of whether they had exercised for more than 30 minutes a day for three days out of the week.
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.65 or 65%.
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Which of the following is not a layer of the Earth?
Answer:
Nickel is not a layer of earth. It is a white metal that belongs to the group of transition metals and is said to be present in the core of the Earth. Sial- refers to the upper layer of the Earth's crust. This layer has an abundance of minerals having aluminum and silicates.
Answer:
I dont see the following but these are the layers of the Earth
Step-by-step explanation:
how do you get a car running?
Answer:
There should be a little keyhole behind the steering wheel put your key in it and turn it to the right
Evaluate the following expression.
1/8^2 I NEED HELPPPP!!!!!!!!
Answer:
1/64
Step-by-step explanation:
What is the contrapositive of "If our plane is not late, then we make our connecting flight.
Answer:
If we make our connecting flight then our plane is not late.
Step-by-step explanation:
The contrapositive occurs when the conclusion and the hypothesis change places. Let the hypothesis be represented by "p" and the conclusion be represented by "q".
hypothesis (p) [ conclusion (q)]
Now in the given statement: If (our plane is not late), then [we make our connecting flight].
statement If p then q
contrapositive If q then p
The required contrapositive statement is: "If we do not make our connecting flight, then our plane is late."
The contrapositive of the statement "If our plane is not late, then we make our connecting flight" is formed by negating the hypothesis (antecedent) and the conclusion (consequent) and then switching their positions. The contrapositive is logically equivalent to the original statement. Here's the contrapositive:
Original Statement: If our plane is not late, then we make our connecting flight.
Contrapositive: If we do not make our connecting flight, then our plane is late.
In the contrapositive, we negate the "our plane is not late" to "our plane is late" and negate "we make our connecting flight" to "we do not make our connecting flight." Then we switch their positions.
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what is 4x=8 proof reason
Answer:
x=2
Step-by-step explanation:
4x=8
/4 /4
divide both sides by 4
x=2
Answer:
x = 2
Step-by-step explanation:
divide both sides by 48÷4 = 2Please help me it’s due soon!
Answer:
Step-by-step explanation:
The standard equation for a parabola is \(y=x^2\)
The given equation is: y = 2(x+2)(x-2)
The given equation is factored out. Since it is factored, we can set each x expression to zero, to solve for the x intercepts.
x+2 = 0
-2 -2
x = -2
x-2 = 0
+2 +2
x = 2
We can therefore graph, (-2, 0) and (2, 0), because we know that it is the x intercepts of the given quadratic function.
to find the vertex, you will take both x intercepts, divide them by two, and that will get you the x cooridnate. Following that you can plug in that value as x into the equation solve for the y coordinate.
\(\frac{(-2 + 2)}{2} = 0\\\\x=0\\y = 2(x+2)(x-2)\\\\y = 2(0+2)(0-2)\\y=-8\\\\vertex = (0, -8)\)
finally graph that point and create the parabola shape. If you'd like to make your parabola more accurate, you can always make a t chart of x and y values. and plug in x values into the equation to find the other y values.
I've attached a graph of the given parabola.
is y=5^w an exponential function if so state the initial value and the base if not then which type of function is it
By using the property of exponential function, the results obtained are
Base of the function is 5.
Initial value of the function is close to zero.
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In \(2^4 = 2\times 2\times 2\times 2\)
Here, 2 is multiplied by itself 4 times.
If \(a^m = a \times a\times a....\times a\) (m times), a is the base and m is the index.
Here,
\(y = 5^w\) is an exponential function.
The base of the function is 5.
As \(x \rightarrow -\infty\), the function tends to 0
So the initial value of the function is close to zero.
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please help me I don't understand this at all
Step-by-step explanation:
180 degrees ok.
height of the goal is 90
2. Divide $7200 into four parts proportional
to 1:2:3:4. How much is each part?
Answer: 720, 1440, 2160, 2880
Step-by-step:
Create arbitrary variable a, such that 7200 = a + 2a + 3a + 4a.
Reduce to get 720 = a
and plug in a into the set {a, 2a, 3a, 4a} to get the answer
Opposites and absolute value mean the same thing.
True or false
Answer:
The absolute value of a number is the distance between the number and zero on a number line. In other words, a number and its opposite have the same absolute value.
Step-by-step explanation:
Lenovo uses the ZX-81 chip in some of its laptop computers. The prices for the chip during the last 4 months were as follows: Month January February March April Price Per Chip $1.80 $1.67 $1.70 $1.85 This exercise contains only parts a, b, and c. a) Using a 2-month moving average, calculate the forecast for March and April (round your responses to two decimal places). Month Forecast Mar $ $ b) Using a 3-month moving average, calculate the forecast for April. The forecast for April is $ (round your response to two decimal places). c) Calculate the mean absolute deviation based on a 2-month average. The mean absolute deviation based on 2-month moving average of March through April is $ (round your response to three decimal places) Calculate the mean absolute deviation based on a 3-month average The mean absolute deviation based on a 3-month moving average of April is $ (round your response to three decimal places). Based on the mean absolute deviation, the V has performed better. Enter your answer in each of the answer boxes.
The mean absolute deviation is calculated for both the 2-month and 3-month moving averages. The mean absolute deviation based on the 2-month average of March through April is $0.055, while the mean absolute deviation based on the 3-month average of April is $0.048. Based on the mean absolute deviation, the 3-month moving average performs better.
To calculate the forecast for March and April using a 2-month moving average, we take the average of the prices from January and February for the forecast of March, and the average of the prices from February and March for the forecast of April.
To calculate the forecast for April using a 3-month moving average, we take the average of the prices from February, March, and April.
The mean absolute deviation is calculated by taking the absolute difference between the forecasted prices and the actual prices for each month, and then calculating the average of these differences. This gives us a measure of the average deviation from the actual prices.
Based on the mean absolute deviation values, we can compare the performance of the 2-month and 3-month moving averages. A lower mean absolute deviation indicates better performance in terms of accuracy in predicting the chip prices.
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please solve a, c, d, e, and f i don’t understand this
a) n° + n°+ 42 = 180°
2n + 42 = 180
2n = 180 – 42
2n = 138
n = 138 /2
n° = 69°
_____o___o____
b) ( x+10) + x + ( x+5 ) = 180
x + 10 + x + x + 5 =180
3x + 15 =180
3x =180 – 15
3x = 165
x = 165 /3
x° = 55°
_____o___o___
c) 3q + q + q = 180
5q =180
q = 180/5
q=36°
___o___o____
d) m + 2m + ( m+10) = 180
m+2m+m+10=180
4m + 10=180
4m = 180 – 10
4m = 170
m=170 / 4
m = 42.5°
____o___o___
e) y + (y – 30 ) + 90° = 180°
y + y – 30 + 90 = 180
2y + 60 = 180
2y = 180 – 60
2y = 120
y = 120/2
y = 60°
____o___o____
f) ( t + 10.5 ) + 2t + 90 = 180
t + 10.5 + 2t +90=180
3t + 100.5 = 180
3t = 180 – 100.5
3t = 79.5
t = 79.5/3
t =26.5°
I hope I helped you^_^
PLEASE HELP ME PLEASE HELP HURRY
Answer:
Step-by-step explanation:
\(.\frac{5}2} w-11 > =31\)
or \(.\frac{5}{2} w +11 > =31\)
there can be another way to solve the situtation
The coordinates of the vertices of quadrilateral HIJK are H(1,4), I(3,2), J(-1,-4), and K(-3,-2). If quadrilateral HIJK is rotated 270 about the origin, what are the vertices of the resulting image, quadrilateral H’ I’ J’ K’
The vertices of the resulting image, quadrilateral H’ I’ J’ K’ include the following:
H' (4, -1).
I' (2, -3).
J' (-4, 1).
K' (-2, 3).
What is a rotation?In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).
By applying a rotation of 270° about the origin to quadrilateral HIJK, the location of its vertices is given by:
(x, y) → (y, -x)
Ordered pair H (1, 4) → Ordered pair H' (4, -(1)) = (4, -1).
Ordered pair I (3, 2) → Ordered pair I' (2, -(3)) = (2, -3).
Ordered pair J (-1, -4) → Ordered pair J' (-4, -(-1)) = (-4, 1).
Ordered pair K (-3, -2) → Ordered pair K' (-2, -(-3)) = (-2, 3).
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arrange 4/8 3/4 8/12 11/16 in ascending order
Answer:
8/12, 11/16, 3/4, 4/8
Step-by-step explanation:
hope this helps
please help me whats the answer for jim has 100 cards there is a whole number from 1 to 100 on each card no cards have the same number jim puts a star on every card has a multiple of 3 on it he puts a circle on every card that has a multiple of 7 on it what number are on the cards that have both a star and a circle on them the final line on your answer must list only these numbers
Answer:
4
Step-by-step explanation:
Multiples of 7 and 3 are 21, 42, 63, 84
Hope this helps.
Answer:
21, 42, 63, 84
Step-by-step explanation:
Cards with both star and circle are multiples of both 3 and 7, ie 3*7= 21
21, 21*2= 42, 21*3= 63, 21*4= 84
So 21, 42, 63 and 84 are the required numbers
convert each decimal to fraction in lowest term
1. 0.39 5. 0.45
2. 0.07 6. 0.81
3. 0.22 7. 0.777
4. 0.98 8.0.444
9.0.434343 10. 0.121212
Answer:
1. 3.9
2. 0.7
3. 2.2
4. 9.8
5. 4.5
6. 8.1
7. 7.7
8. 4.4
9. 4.3
10. 1.2
Step-by-step explanation:
Hope it helps
24.7% of the products in the local shop are specialty soaps. 76% of those soaps are made with fresh herbs. if there are 350 bars of specialty soap in the shop, approximately how many of them are not made with fresh herbs? round your answer up to nearest whole number
we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs? well, just 76% of those 350
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)
What is the distance between the following points?
Answer:
\(\sqrt{85}\) or 9.21954
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
\(d = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} - x_{1})^{2} }\)
d = distance
\((x_{1}, y_{1})\) = coordinates of the first point
\((x_{2}, y_{2})\) = coordinates of the second point