Answers
The measure of the required angle is [tex]27^{0}[/tex].
What is the angle ?The angle is the magnitude or measure of the turn between two lines or planes intersecting each other. It is measured in degrees, radians, or gradians. Angles are used to measure shapes, directions, distances, and other aspects of geometry. Angles can be classified into two types: acute angles and obtuse angles.
In the given figure there are two triangles in the figure:
As we know sum of all the angles of triangle is [tex]180^{0}[/tex],
therefore in the first triangle third angle will be:
[tex]75^{0} + 35^{0} + third angle = 180^{0}[/tex]
∴ Third angle = [tex]180^{0} - 75^{0} - 35^{0} = 70^{0}[/tex]
Using the triangle property third angle of one triangle is equal to its opposite angle in another triangle, we can find the third angle of another triangle also:
[tex]83^{0} + 70^{0} + third angle = 180^{0}[/tex]
∴ Third angle = [tex]180^{0} - 153^{0} =27^{0}[/tex]
Therefore, the required angle is [tex]27^{0}[/tex].
To learn more about angles visit:
brainly.com/question/28293784
#SPJ1
Related Questions
A certain inect can beat it wing 240 time per econd. Write an equation in lope-intercept form that how the relationhip between flying time in econd and the number of time the inect beat it wing
Answers
The equation is in slope-intercept form is y = 240t + 0
How to write an equation in slope-intercept form?The equation of a line in slope-intercept form is given by:
y = mx + b
where m is the slope and b is y-intercept
Let's say the number of times the insect beats its wing in t seconds is represented by y. Then the relationship can be expressed as:
y = 240t
The slope (240) shows that for every 1 second increase in time, the number of wing beats increases by 240. The y-intercept (0) indicates that when t = 0, y=0, i.e. when the insect has not started flying, it has not beaten its wing yet.
Therefore, the equation is in slope-intercept form: y = 240t + 0
Learn more about equation in slope-intercept form on:
brainly.com/question/12626026
#SPJ1
To help determine the roots of x =tan(x), graph y = x and y = tan(x), and look at the intersection points of the two curves. (a) Find the smallest nonzero positive root of x = tan(x), with an accuracy of E=0.0001. Note: The desired root is greater than 1/2. (b) Solve x =tan(x) for the root that is closest to x = 100.
Answers
(a) the root of the equation is =4.4.(b) x=31pi for x=100 approx.
the root of an equation is said to be that value where the equation gets zero. And the intersection point of two equations is the same value of equations.
The roots of x =tan(x), graph y = x and y = tan(x), and look at the intersection points of the two curves.
a) Find the smallest nonzero positive root of x = tan(x),
after seeing the graph the root of the equation is =4.4.
(The desired root is greater than pi/2).
b) Solve x =tan(x) for the root that is closest to x = 100.
after examining the graph of the function we can see that 31pi for x=100 approximately.
learn more about graphs.
https://brainly.com/question/17267403
#SPJ4
using the 68-95-99.7 empirical rule-of-thumb, answer the following questions. no partial credit will be given for using any other method. a given exam has a normal distribution with a mean of 70 and a standard deviation of 10. a sample of size 25 is selected. what percentage of the time would you expect the mean of this sample size to fall between 68 and 72? %
Answers
The mean of the sample size of 25 would fall between 68 and 72 68% of the time.
68% Expect Mean IntervalUsing the 68-95-99.7 rule, if a variable is normally distributed with mean μ and standard deviation σ, then:
68% of the data falls within 1 standard deviation of the mean (μ - σ to μ + σ)95% of the data falls within 2 standard deviations of the mean (μ - 2σ to μ + 2σ)99.7% of the data falls within 3 standard deviations of the mean (μ - 3σ to μ + 3σ)Given that the mean of the exam scores is 70 and the standard deviation is 10, the range of 68% of the data falls between 60 and 80.So, 100% - 68% = 32% of the data falls outside this range.Since the interval we are interested in (68 to 72) falls within the 68% of the data that falls within 1 standard deviation of the mean, it means that 100% - 32% = 68% of the data falls within this interval.
Thus, the mean of this sample size of 25 would fall between 68 and 72 68% of the time.
Learn more about 68% Expect Mean Interval here:
https://brainly.com/question/16160543
#SPJ4
Bear Mountain Summer Camp opened last year and had 650 campers. After doing some advertising in the off-season, the camp has enrolled 676 campers for this year, and enrollment is expected to continue increasing each year. Write an exponential equation in the form y = a(b) that can model the number of campers, y, x years after the camp opened. Use whole numbers, decimals, or simplified fractions for the values of a and b.
Answers
The number of campers is y = 650(676/650)^x
What is exponential equation ?
Exponential equations are equations in which variables occur as exponents.
An exponential equation in the form y = a(b)^x can be used to model the number of campers, y, x years after the camp opened. Let's use x = 0 for the first year the camp opened (last year) and x = 1 for this year.
Then, we have:
y = a(b)^0 = 650 (when x = 0)
y = a(b)^1 = 676 (when x = 1)
We can use these two points to solve for the values of a and b.
First, we'll use the first equation to solve for a:
a = 650
Next, we'll use the second equation to solve for b:
676 = 650(b)^1
676/650 = (b)^1
b = 676/650
So, the exponential equation in the form y = a(b)^x that can model the number of campers is:
y = 650(676/650)^x
Learn more about exponential equation here: brainly.com/question/29506679
#SPJ1
Specific names for each shape
Answers
Three edges and three vertices make up the three-sided polygon known as a triangle. The fact that a triangle's internal angles can be added up to equal 180 degrees is its most significant characteristic.
Explain about the triangle?Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Each side is different, and each angle is less than 90 degrees. Obtuse isosceles: two identical sides and identical angles, with one angle more than 90 degrees.
Shapes with three sides are called triangles. The various triangle varieties go under various names. The dimensions of a triangle's sides and angles determine its type (corners).
To learn more about triangle refer to:
https://brainly.com/question/17335144
#SPJ1
Find the specified lengths and measures.
Given: △ABC ≅ △DEF
Find: AB and m∠F
A
B
C
4
6
30°
50°
D
E
F
Answers
Answer:
In the given triangle △ABC, AB is equal to 4 and m∠F is equal to 30°. In the triangle △DEF, AB is equal to 6 and m∠F is equal to 50°.
If ¯x represents the mean of n observations x1, x2, ……xn, then value of ∑ni−1(xi−¯x) is:A) -1B) 0C) 1D) n - 1
Answers
If [tex]\overline{x}$[/tex] represents the mean of n observations x₁, x₂, ……xₙ, then the value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is 0.
Mean is the average value of the group of values. It shows the equal distribution of values for a given data set.
To calculate the arithmetic mean of a group of data, first, add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed, we obtain the following formula for the mean ([tex]\overline{x}[/tex]):
[tex]\overline{x}= $\sum {\frac{x}{n} $[/tex]
The formula of the mean ([tex]\overline{x}$[/tex]) is:
[tex]\overline{x} = $\sum_{i=0}^{n} {x_{i}$/n[/tex]
[tex]$\sum_{i=0}^{n} {x_{i} = \overline{x}n[/tex] Eqn(1)
Here, n is total number of observations.
The value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is calculated as follows:
[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = \sum_{i=0}^{n} x_{i} - \sum_{i=0}^{n}\overline{x}[/tex]
Now, from equation (1), we get
[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \sum_{i=0}^{n}\overline{x}[/tex]
[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}\sum_{i=0}^{n}1[/tex]
[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}n[/tex]
[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = 0[/tex]
Hence, the correct answer is B.
To know more about mean, here
https://brainly.com/question/29895356
#SPJ4
3) Which inequality represents the solution for n + 6 < 13?
a.) n < 19
b.) n > 19
c.)n <7
d.) n > 7
Ps the photo attached is part 2 of this question pls answer both
Answers
Answer:
see explanation
Step-by-step explanation:
solving the inequality
n + 6 < 13 ( subtract 6 from both sides )
n < 7
this means that any value less than, but not including, 7 is a solution
listing the values that are a solution from - 10 through to 10 , then list of solutions is
- 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6
The dimenion of a playground are repreented by a width of 9x1 and a length of 5x-2 feet. Write of expreion that repreent the area of the playground
Answers
The expression that represents the area of the playground is 45x² - 13x - 2 square feet.
The area of a rectangle is found by multiplying its length by its width. Here the length is given as 5x - 2 feet and width is given as 9x + 1 feet. So, the expression that represents the area of the playground is:
Area = Length * Width
= (5x - 2) * (9x + 1)
= 5x × 9x + 5x -2 × 9x - 2
= 45x² + 5x - 18x - 2
= 45x² - 13x - 2
Therefore, the expression that represents the area of the playground is 45x² - 13x - 2 square feet.
To know more on area
https://brainly.com/question/8663941
#SPJ4
Karen owns a seafood restaurant. She orders trout from an online retailer. Each pound of trout costs $28, and the company charges a $4 fee for shipping the order. However, if Karen orders 10 or more pounds, the trout costs only $22 per pound, but the shipping fee is $8. Which piecewise function models the cost of x pounds of trout?
Answers
Answer: the answer is A), normal is 28 + 4fee, but if she buys LOTS its 22 +8
contact me through discord Acathia#0103, its easier to help, I can help with multiple questions aswell
Step-by-step explanation:
bryant bought 24 hockey tickets for $83. adult tickets cost $5.50 and child tickets cost $2.00. how many child tickets did he buy?
Answers
There about 24 hockey tickets were bought by Bryant. Out of which 14 tickets were child tickets.
A mathematical claim containing two equal algebraic expressions is known as an algebraic equation.
Given that the cost of an adult ticket is $5.50, and a child ticket is $2.00. The total spent is $83, and the total number of tickets bought is 24.
Let us consider the number of adult tickets bought is x and the number of children tickets bought is y.
Then x+y=24. From this, x=24-y.
Also, the given situation is written in an expression as,
[tex]\begin{aligned}5.50x+2.00y&=83\\5.50(24-y)+2.00y&=83\\132-5.50y+2.00y&=83\\-3.5y&=-49\\y&=14\end{aligned}[/tex]
The required answer is 14.
To know more about algebraic equations:
https://brainly.com/question/29131718
#SPJ4
1) How much would you have to invest in an account earning 8% interest compounded continuously, for it to be worth one million dollars in 30 years?
Answers
The principal that would need to be invested to have an accrued amount of 1 million dollars after 30 years is $90,717.95.
What is the amount of principal to be invested?The formula compound interest where interest is compounded continuously is expressed as;
A = P × e^(rt)
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Accrued amount A = $1,000,000Time t = 30 yearsInterest rate r = 8% = 8/100 = 0.08Compounded consciouslyPrincipal P = ?Plug the given values into the above formula and solve for P.
A = P × e^(rt)
P = A / e^(rt)
P = $1,000,000 / e^( 0.08 × 30 )
P = $1,000,000 / e^( 2.4 )
P = $90,717.95
Therefore, the amount of principal is $90,717.95.
Learn more about compound interest here: brainly.com/question/27128740
#SPJ1
Please help me figure out what the last one is and how to get the answer
Tysm!
Answers
Answer:
see explanation
Step-by-step explanation:
for the given angles to form a triangle they must sum to 180°
given
31 [tex]\frac{3}{4}[/tex]° , 53 [tex]\frac{1}{2}[/tex]° , 94 [tex]\frac{3}{4}[/tex] ° ( changing to decimal form and adding )
= 31.75° + 53.5° + 94.75°
= 180°
Thus the 3 given angle measures can form a triangle.
Solve the given system of equations
2y = 6y = -15
Answers
The system of equation has no solution
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
2y = 6
y = -15
Since these are two different equations with the same variable, y, we can use substitution to find a solution.
Starting with the second equation, y = -15, we can substitute this value into the first equation:
2y = 6
2(-15) = 6
-30 = 6
This equation is false, meaning there is no solution for y that satisfies both equations.
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
-12=-(2x + 8) explanation
Answers
Answer:
24x+96
Step-by-step explanation:
so we could use Distributive property
which means -12time -2x+-12times-8
=24x+96
i hope is helpful
A gas company's delivery truck has a cylindrical tank that is 14 feet in diameter and 40 feet long.
Use the space in your supplement to draw the tank, if that would help. Use 3.14 as an approximation of
π
. Round to the nearest tenth if needed.
How much gas can fit in the tank?
Answers
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
Volume of Cylinders:Cylinder volume: Considering that;
14 feet is the cylindrical tank's diameter.
The cylindrical tank is 40 feet long.
Find:
how much gas is in the tank.
Computation:
14 feet is the cylindrical tank's diameter.
Tank's cylinder's radius is 14/2, or 7 feet.
Volume of the tank: x amount of gas inside it
Volume of gas in the tank equals πr²h.
Portion of gas in the tank = (3.14)(7)²(40)
Fuel level in tank equals (3.14)(49) (40)
6154.4 feet³ of gas have been filled into the tank.
(Hope this helped!)
100 points
answer ?
( L to G )
Answers
Answer:
It's already in order
[tex]\frac{3}{4}[/tex] × [tex]\frac{4}{9}[/tex], [tex]\frac{7}{7}[/tex] × [tex]\frac{4}{9}[/tex] , [tex]1\frac{2}{3}[/tex] × [tex]\frac{4}{9}[/tex], [tex]2[/tex] × [tex]\frac{4}{9}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] × [tex]\frac{4}{9}[/tex]
[tex]=\frac{1}{3}[/tex]
[tex]\frac{7}{7}[/tex] × [tex]\frac{4}{9}[/tex]
[tex]=\frac{4}{9}[/tex]
[tex]1\frac{2}{3}[/tex] × [tex]\frac{4}{9}[/tex]
[tex]=\frac{20}{27}[/tex]
[tex]2[/tex] × [tex]\frac{4}{9}[/tex]
[tex]=\frac{8}{9}[/tex]
Change them all to the same common denominator of 27
[tex]\frac{9}{27}, \frac{12}{27}, \frac{20}{27}, \frac{24}{27}[/tex]
I need help with this question please and thank you .
Answers
Answer:
below
Step-by-step explanation:
Use right triangle Pythagorean theorem
L^2 = 8^2 + 4^2
L^2 = 80
L = sqrt (80) units <====exact
approx is sqrt(80) =~8.94 units
Find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 4 to 1. Round your answers to the nearest tenth. (i rlly need help)
Answers
The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
AP to PB is in the ratio of 4 to 1. Then the coordinate of the point P is given as,
x = (4 × 8 + 1 × 1) / (4 + 1)
x = (32 + 1) / 5
x = 33 / 5
x = 6.6
y = (4 × 4 + 1 × 3) / (4 + 1)
y = (16 + 3) / 5
y = 19 / 5
y = 3.8
The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).
More about the section of the line link is given below.
https://brainly.com/question/6582647
#SPJ1
solve the following differential equation using laplace transforms. assume zero initial conditions. () 2 () 4 ()
Answers
The solution to the differential equation y'' + 4y' + 2y = 4 with zero initial conditions is y(t) = 2e^-2t.
CORRECTION: Given the differential equation: y'' + 4y' + 2y = 4
To solve this differential equation using Laplace transforms, we first need to take the Laplace transform of both sides. The Laplace transform of the derivative of y is given by:
L{y'} = sY(s) - y(0) = sY(s) (assuming zero initial conditions)
L{y''} = s^2Y(s) - sy(0) - y'(0) = s^2Y(s) (assuming zero initial conditions)
Now, substituting these Laplace transforms in the given differential equation, we have:
s^2Y(s) + 4sY(s) + 2Y(s) = 4/s
Solving for Y(s), we get:
Y(s) = (4/s) / (s^2 + 4s + 2) = 2 / (s + 2)^2
Finally, taking the inverse Laplace transform of Y(s), we get:
y(t) = L^-1{Y(s)} = 2e^-2t
Therefore, the solution to the differential equation y'' + 4y' + 2y = 4 with zero initial conditions is y(t) = 2e^-2t.
To learn more about Laplace transform,
Visit; brainly.com/question/14487937
#SPJ4
A large university accepts 50% of the students who apply. Of the students the university accepts, 40% actually enroll. If 30,000 students apply, how many actually enroll?
Answers
The number of students actually enrolled is 6000.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a large university accepts 50% of the students who apply. Of the students the university accepts, 40% actually enroll. If 30,000.
The number of students will be calculated as:-
Number = ( 30000 x 0.5 x 0. 4 )
Number = 6000
Therefore, the number of students will be 6000.
To know more about an expression follow
https://brainly.com/question/21242786
#SPJ1
4. Genry worked for 6 consecutive days and earned an average wage of $144 per day as a freelance handyman. During the first 3 days, Genry averaged $132 per day. His average earned per day for the next 2 days was $163. How much did he earn on the last day?
Answers
Answer:
142
Step-by-step explanation:
6 day av 144 / day so total =144*6
first 3 day av 132 so total =132*3
next 2 days av 163 so total =163*2
144*6= 132*3+163*2+final day
so final day = 142
The perimeter of a rectangle is 96 cm. if the ratio of the length to width is 7 : 5, find the dimensions of the rectangle
Answers
Salut/Hello!
Answer: w = 20 cm and l = 28 cm
Step-by-step explanation:
l - length
w - width
P - perimeter
/ - fraction line
=> - results
we know that P = 2 x (l + w)
we also know that our ratio is l/w = 7/5
l/w = 7/5 => l = 7/5 x w
so now we can go back to the perimeter and replace l
96 = 2 x (7/5 x w + w)
96 = 2 x (7/5 x w/1 + w) Why w/1? - We can't multiply unless w is also in a fraction, so we put it as w/1
96 = 2 x (7w/5 + w)
96 = 2 x (7w/5 + w/1) and we amplify w/1 with 5
96 = 2 x (7w/5 + 5w/5)
96 = 2 x 12w/5
48 = 12w/5
48/1 = 12w/5
48 x 5 = 12w
240 = 12w
w = 20 cm
with that we can find l
96 = 2 x (l + 20)
48 = l + 20
l = 48 - 20
l = 28 cm
I hope it was helpful! :]
The Hillsboro Inlet Lighthouse lights up how much more area than the Jupiter Inlet Lighthouse? Round your answer to the nearest tenth.
The difference in area is about _
square miles.
Answers
The difference in area is of about 1445.1 square miles.
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr²
The radius is the distance of the center of the circle to any point on the circumference of the circle.
For the circle with a radius of 18 miles, the area is given as follows:
A = π x 18² = 1017.9 square miles.
For the circle with a radius of 28 miles, the area is given as follows:
A = π x 28² = 2463 square miles.
Hence the difference is of:
2463 - 1017.9 = 1445.1 square miles.
More can be learned about the area of a circle at https://brainly.com/question/15673093
#SPJ1
The circumference of a circle is 98.596 millimeters. What is the radius of the circle? Use 3.14 for π.
197.2 mm
49.3 mm
31.4 mm
15.7 mm
Answers
Answer: D) 15.7
Step-by-step explanation:
Start with the formula C=2 πr
Then solve for r r=C2π = 98.62·π = 15.69(7)204
The radius of the circle is 15.7 mm.
What is Circumference?The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
We have,
The circumference of Circle = 2πr
Also, The circumference of a circle is 98.596 millimeters.
So, circumference of Circle = 2πr
98.596 = 2πr
98.596 = 6.28r
r= 98. 596 / 6.28
r = 15.7 mm
Thus, the radius is 15.7 mm.
Learn more about Circumference here:
https://brainly.com/question/28757341
#SPJ2
what happens to the rnase a in sample 3 that does not occur in sample 2?
Answers
Sample 3's mercaptoethanol and urea mixture breaks sulphide bonds, resulting in the loss of tertiary structure and activity, whereas in sample 2, urea is introduced. This chemical denaturing agent aims to break up peptide connections, which would then affect the structure and function of the protein.
An experiment data is given below:
This experiment describes how protein denaturing chemicals affect a protein's ability to function.
Sample 1 preserves protein structure and function because it just contains buffer and no denaturing agent.
Enzymatic activity then results in high fluorescence as a result of this.
In sample 2, urea is added, a chemical denaturing agent that seeks to dismantle peptide bonds, disrupting protein structure and activity.
As a result, there are now less fluorescence products and less active enzyme products overall.
In sample 3, when mercaptoethanol and urea are mixed, sulphide bonds are broken and tertiary structure and activity are lost.
After dialysis, sample 4 had both urea and mercaptoethanol eliminated from it.
To learn more about urea and mercaptoethanol link is here
brainly.com/question/13285827
#SPJ4
what is the unsigned base 7 equivalent (with 3 digits after the radix point, truncated, e.g., 12.345) of the following unsigned decimal number?
Answers
The process of converting a decimal number to its base 7 equivalent is explained below.
The radix point is the point that separates the whole number part of a number from its fractional part in a numerical system.
The process of converting a decimal number to its base 7 equivalent starts by dividing the decimal number by 7. The remainder from this division will be the first digit after the radix point in the base 7 equivalent.
We continue this process by dividing the quotient obtained in the previous step by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits after the radix point in the base 7 equivalent, in the reverse order.
To get the integer part, we keep dividing the decimal number by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits in the integer part of the base 7 equivalent, in the reverse order.
To know more about radix point here.
https://brainly.com/question/26815200
#SPJ4
pls help asap :(!!!!!!!
Answers
The midpoints of the segment is (4, -3.5).
What is Section Formula?The coordinates of the point A(x, y) which divides the line segment joining the points P(a , b) and Q(c , d) internally in the ratio m : n are given by the formula: P ( x , y ) = ( a x n + c x m / (m+n) , bn + dn / (m+n))
Given:
Points (-4, -7) and (12, -6).
So, the ratio is line is m:n = 1:1
let (x, y) be the midpoint.
Now, using section formula
x = (-4 x 1 + 12 x 1)/ (1+1)
x= (-4 +12) /2
x= 8/2
x= 4
and, y = (-7 x 1 -6 x 1)/ 2
y = -7-6/2
y = -13/2
y = -3.5
Hence, the midpoints are (4, -3.5).
Learn more about section formula here:
https://brainly.com/question/30242630
#SPJ1
a cone-shaped pile of sawdust has a base diameter of 32 feet, and is 14 feet tall. find the volume of the sawdust pile.
Answers
The volume of the sawdust pile is 3754.667 cubic feet
A cone is a three-dimensional shape that has a circular base with tapers from the flat base into the vertex.
The formula for searching the volume of the cone can be described below :
V = [tex]\frac{1}{3}[/tex] π [tex]r^{2}[/tex] h
which
V = volume of the cone
r = radius of cone circular base
h = height of cone ( tall of the cone )
From the question, we have following information :\
1. Base diameter = 32 feet
Base radius = Base diameter / 2 = 32 feet / 2 = 16 feet
2. Tall / Height of the cone = 14 feet
Since the known parameter is enough to be put into the formula, we can simply subtitute the formula with known parameter
V = [tex]\frac{1}{3}[/tex] π [tex]r^{2}[/tex] h
= [tex]\frac{1}{3}[/tex] x π x [tex]16^{2}[/tex] x 14
= 3754.667 cubic feet
Hence the volume of the cone is 3754.667 cubic feet
Learn more about cone here
https://brainly.com/question/16394302
#SPJ4
A continuous random variable X has a PDF f(x) = ax + X^2 for 0<=x<=1. What is the probability that X is between 0.5 and 1?
A. 15/24
B.17/24
C. 19/24
D. 21/24
Answers
The probability that X is between 0.5 and 1 is (C) 19/24.
The probability that X is between 0.5 and 1 can be found by calculating the definite integral of the PDF f(x) over the interval [0.5, 1]:
P(0.5 <= X <= 1) = ∫f(x)dx from 0.5 to 1
Given the PDF f(x) = ax + X^2 for 0<=x<=1, we can evaluate this definite integral as:
P(0.5 <= X <= 1) = ∫(ax + X^2)dx from 0.5 to 1
= [ax^2/2 + x^3/3] from 0.5 to 1
= (1.5a + 1/3) - (0.5a + 0.125)
= (1 + 1/6) - (0.5 + 1/8)
= (2/3 - 3/8)
= 5/24
Since 5/24 is equal to 0.2083, the closest answer choice to this value is 19/24.
To learn more about probability here:
https://brainly.com/question/30034780
#SPJ4
