Answers
The height of the cone is (c) 5 cm.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.So, the volume of a cone is: V = 1/3πr²h
V is 83.73 and r is 4.Now, calculate the height of the cone as follows:
V = 1/3πr²h83.73 = 1/3π4²h83.73 = 1/3π16h3(83.73) = 3.14(16)h251.19 = 50.24hh = 251.19/50.24h = 4.9999Rounding off: 5 cm
Therefore, the height of the cone is (c) 5 cm.
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Related Questions
write an equation and solvefour times the complement of an angle is 40° lessthan twice the angles supplement. Find the angle,its complement, and its supplement
Answers
Let the angle be 'x' degrees.
The complement (C) of the corresponding angle will be,
[tex]C=90-x[/tex]And the supplement (S) of the corresponding angle will be,
[tex]S=180-x[/tex]According to the condition given in the problem,
[tex]4C=2S-40^{}[/tex]Substitute the values,
[tex]\begin{gathered} 4(90-x)=2(180-x)-40 \\ 360-4x=360-2x-40 \\ -4x=-2x-40 \\ 4x-2x=40 \end{gathered}[/tex]Simplify the expression further,
[tex]\begin{gathered} 2x=40 \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]Substitute this value of 'x' to obtain the complement and supplement angles as follows,
[tex]\begin{gathered} C=90-20=70 \\ S=180-20=160 \end{gathered}[/tex]Thus, the angle measures 20 degrees, its complement measures 70 degrees, while its supplement measures 160 degrees.
XYZ is a right-angled triangle. A is a point on line XZ and B is a point on line XY. XA = XB What is the size of angle XAB? xzy= 34 degrees
Answers
A. Monkey man
Step-by-step explanation:
M+o+n+k+e
Ashley pounds 98 pounds one year ago .If she weight 112 pounds what is the percent increase in her weight ?
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Answer:
The increase to the nearest percent is 14%
Step-by-step explanation:
[tex]\frac{112 - 98}{98}[/tex] The percent of increase is the weight change over the original amount
.14285714285 To change a decimal to a percent, move the decimal two places to the right.
Rounded to the nearest percent is
14%
I need to double check 15 I got answer B
Answers
We will have that the area of one sector of the circle will be:
[tex]A=(\frac{45}{360})\pi(20in)^2\Rightarrow A=\frac{25\pi}{2}in^2[/tex]So, the solution is option B.
(Combining Equations)What is the result of subtracting the second equation from the first ? -4x - 2y = -2x - 2y = 9
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Subtract the second equation from the first,
[tex]\begin{gathered} -4x-2y=-2 \\ - \\ x-2y=9 \\ (-4x-x)-(2y-\lbrack-2y\rbrack)=-2-9 \\ -5x-2y+2y=-11 \\ -5x+0=-11 \\ -5x=-11 \\ \text{Divide both sides by -5} \\ \frac{-5x}{-5}=\frac{-11}{-5} \\ x=\frac{11}{5} \end{gathered}[/tex]select the reason that best supports statement 6 in the given proof please help me image attached
Answers
Answer:
B. Distributive Property
Step-by-step explanation:
You want to know the reason in the proof that best supports the transition from 5. 99-3x = 12(x+2) to 6. 99-3x = 12x+24.
TransformationYou will notice that in the transition from
5. 99-3x = 12(x+2)
to
6. 99-3x = 12x+24
the expression 12(x+2) has been replaced by the expression 12x+24.
Distributive propertyThe property of addition and multiplication that makes it true that ...
12(x +2) = 12x +24
is the distributive property of multiplication over addition. That property tells you that parentheses can be eliminated by multiplying each of the terms inside by the factor outside.
can some one clarify this question, i think ik the answer but i need some elses opinion Find m
Answers
hello
to solve this question, we simply need to add two quadrants that make up mto get m[tex]\begin{gathered} m<\text{WYV}=60^0 \\ m<\text{VYU}=85^0 \end{gathered}[/tex][tex]\begin{gathered} m<\text{WYU}=<\text{WYV}+m<\text{VYU} \\ m<\text{WYU}=60^0+85^0 \\ m<\text{WYU}=145^0 \end{gathered}[/tex]from the calculations above, the value of m
A psychology test has personality questions numbered 1, 2, 3, intelligence questions numbered 1, 2, 3, 4, and attitudequestions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?
Answers
Answer:
7/9.
Step-by-step explanation?
Total number of questions: 3 + 4 + 2 = 9.
Number of Intelligence questions: 4
Number of questions that have an odd number: 5
The probability of a question is Intelligence questions = 4/9
The probability a question has an odd number = 5/9
The probability a question is Intelligence questions and has an odd number = 2/9
The probability a question is Intelligence question OR has an odd number is:
4/9 + 5/9 - 2/9 = 7/9.
Find a standard form of the equation for the circle with the following property
Answers
Solution:
Given:
[tex]Endpoints\text{ }(-7,5)\text{ and }(-5,-1)[/tex]To get the equation of the circle, the center of the circle and the radius are needed.
The center of the circle is the midpoint of the endpoints.
Using the midpoint formula;
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} M=(\frac{-7+(-5)}{2},\frac{5+(-1)}{2}) \\ M=(\frac{-12}{2},\frac{4}{2}) \\ M=(-6,2) \end{gathered}[/tex]Hence, the coordinates of the center of the circle is (-6,2)
The length of the diameter can be gotten using the distance between two points formula;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \\ Hence, \\ d=\sqrt{(-5-(-7))^2+(-1-5)^2} \\ d=\sqrt{2^2+(-6)^2} \\ d=\sqrt{4+36} \\ d=\sqrt{40} \end{gathered}[/tex]The diameter is twice the radius. Hence, the radius is;
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{\sqrt{40}}{2}=\frac{2\sqrt{10}}{2} \\ r=\sqrt{10} \end{gathered}[/tex]Hence, the equation of the circle with center (-6,2)
[tex]with\text{ radius }\sqrt{10}[/tex]Using the standard form of the equation of a circle;
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where: \\ (h,k)\text{ }is\text{ }the\text{ center} \\ r\text{ is the radius} \\ h=-6 \\ k=2 \\ r=\sqrt{10} \end{gathered}[/tex]Hence, the equation is;
[tex]\begin{gathered} (x-(-6))^2+(y-2)^2=(\sqrt{10})^2 \\ (x+6)^2+(y-2)^2=10 \end{gathered}[/tex]Therefore, the equation of the circle is;
[tex](x+6)^{2}+(y-2)^{2}=10[/tex]
Nathan and some friends are going to the movies. At the theater, they sell a bag of popcorn for $6 and a drink for $4. How much would it cost if they bought 5 bags of popcorn and 7 drinks? How much would it cost if they bought pp bags of popcorn and dd drinks?Total cost, 5 bags of popcorn, and 7 drinks: Total cost, p bags of popcorn and d drinks:
Answers
a) Since the cost of a bag of popcorn is $6 and the cost of a drink is $4,
[tex]\begin{gathered} T=6\cdot5+7\cdot4 \\ \Rightarrow T=30+28=58 \\ \Rightarrow T=58 \end{gathered}[/tex]Therefore, the answer to the first question is $58.
b) Substitute 5 for p and 7 for d in the expression above; therefore,
[tex]T=6p+4d[/tex]The total cost is given by the equation T=6p+4d, where T is in dollars, p is the number of bags of popcorn and d is the number of drinks.
3. Identify the solution to the system of equations by graphing:(2x+3y=12y=1/3 x+1)
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Given equations are
[tex]2x+3y=12[/tex][tex]y=\frac{1}{3}x+1[/tex]The graph of the equations is
Red line represents the equation 2x=3y=12 and the blue line represents the equation y=1/3 x=1.
Una clase tiene 42 alumnos. Se puede determinar que 3/9 son niños y 4 6 son niñas, ¿Cuántos niños y cuantas niñas hay en la clase?
Answers
The number of boys and girls that are in this class is equal to 28 students and 14 students respectively.
How to determine the number of boys?In order to determine the number of boys that are in this class with a total population of 42 students, we would have to multiply the total number of students by the fraction representing only the number of boys as follows:
Number of boys, B = 4/6 × Total number of students
Substituting the given parameters into the formula, we have;
Number of boys, B = 4/6 × 42
Number of boys, B = 4 × 7
Number of boys, B = 28 students.
Similarly, we we would have to multiply the total number of students by the fraction representing only the number of girls as follows:
Number of girls, G = 3/9 × Total number of students
Number of girls, G = 3/9 × 42
Number of girls, G = 1/3 × 42
Number of girls, G = 42/3
Number of girls, G = 14 students.
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Complete Question:
A class has 42 students. It can be determined that 3/9 are boys and 4/6 are girls, how many boys and girls are there in the class?
You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 4 minutes and you record the data point of (12,y), what is the value of y? Use slope to justify your answer
Answers
Answer:
51
Step-by-step explanation:
so we can use the variable x for minutes & y for water level. (4,17) is what we start with. its asking after 12 minutes what is the water level, 4 x 3 is 12 so we would multiply 17 x 3 as well which is 51.
A helicopter pilot sights a landmark an an angle of depression of 34°. The altitudeof the helicopter is 1,748 feet. To the nearest foot, what is the horizontal distancefrom the helicopter to the landmark?
Answers
For the question, we will be making a sketch showing the features in the question.
From the sketch and the question, the angle of depression = 34 degrees
The helicopter height above the ground (altitude) = 1,748 ft
L represents the landmark
x = horizontal distance from the helicopter to the landmark
To solve the question, we need to bring out the right triangle from the sketch
Angle e = 34 degrees (alternate to the angle of depression given)
To get x, we make use of the trigonometrical ratio of tan
[tex]\begin{gathered} \tan \text{ }\theta=\frac{opposite}{adjacent} \\ \text{From the right triangle, the opposite = 1748} \\ \text{The adjacent = x} \\ \theta=34^0 \\ \tan \text{ 34 =}\frac{\text{1748}}{x} \\ \text{Making x the subject of the formula, we have} \\ x=\frac{1748}{\tan 34} \\ x=\frac{1748}{0.6745} \\ x=2591.55 \end{gathered}[/tex]Therefore, the horizontal distance from the helicopter to the landmark to the nearest foot is 2592 feet.
solve the following system of equations-5x-3y=-16-3x+2y=-21x=y=
Answers
-5x - 3y = -16
-3x + 2y = -21
Solving for y the first equation:
-5x + 16 = 3y
y = (-5/3)x + (16/3)
Using this value of y into the second equation:
-3x + 2(-5/3)x + 2(16/3) = -21
-3x - (10/3)x + 32/3 = -21
Multiplying all by 3:
-9x - 10x + 32 = -63
-19x = -63 - 32 = -95
x = 95/19
Using this value of x into the y we found with the first equation:
y = (-5/3)x + 16/3
y = (-5/3)(95/19) + 16/3 = -475/57+ 304/57 = -171/57
y = -171/57
x = -31/19 = -1.6315
y = -171/57 = -3
Answer:
x = -1.6315
y = -3
the circumference of a circle is 18pi ft. what is the area in square feet.
Answers
We have first the formula of the circumference of a circle
[tex]C=2\pi r[/tex]In order to know the area we need to know the radius of the circle, it can be obtained using the formula above and the next information.
C=18pi
r is the radius
[tex]18\pi=2\pi r[/tex]then we isolate the r
[tex]\begin{gathered} r=\frac{18\pi}{2\pi} \\ r=9 \end{gathered}[/tex]the radius is 9 ft
then we can calculate the area using the next formula
[tex]A=\pi r^2[/tex]we substitute the value of the radius
[tex]\begin{gathered} A=\pi(9)^2 \\ A=81\pi ft^2 \\ A=254.47ft^2 \end{gathered}[/tex]Make a table for the graph labeled hours studies average grade
Answers
We can easily create a table with the first column labeled "hours studied" and second column labeled "average grade".
The hours studied are:
0, 1, 2, 3, and 4
The respective average grades are:
56, 75, 85, 90, 100
The table can look like this:
Answer:
To make the table, you must correlate the average test grade with the hours spent studying.
The graph shows the idea that the more we learn, the higher will be our test grades.
The table is attached.
find the zeros algebraically: f(x)=x^4-8x^3+5x^2+14x
Answers
The given equation is:
x^4-8x^3+5x^2+14x
In this question, we have to find the zeros algebraically. Hence, we need to find the values of x that satisfy the equation.
Note: The roots (values of x) are equal to the power of the equation. Therefore, the given equation will have 4 roots
Therefore,
x^4-8x^3+5x^2+14x = 0
or
x(x^3-8x^2+5x+14) = 0
=> x = 0 and x^3-8x^2+5x+14 = 0
Therefore, the first root is x = 0.
Now,
x^3-8x^2+5x+14 = 0
To simplify that, try putting different values of x (starting from 1 and -1). The value that makes both sides equal to zero would be the solution.
Let's start with (1):
For x = 1
(1)^3 - 8(1)^2 + 5(1) + 14 = 0
1 -8(1) + 5 + 14 = 0
-1 -8 +5 + 14 = 0
- 9 + 19 = 0
10 = 0
It is false, therefore, x = 1 is not the solution.
For x = -1
(-1)^3 - 8(-1)^2 + 5(-1) + 14 = 0
-1 -8(1) - 5 + 14 = 0
-1 -8 -5 + 14 = 0
- 14 + 14 = 0
0 = 0
hence, x = -1 is the second solution.
If x = -1 is the solution, (x + 1) should be the factor of x^3-8x^2+5x+14. Therefore, the whole equation can be divided by factor
x^3-8x^2+5x+14 / (x+1). = x^2 - 9x + 14. (using division)
Now, let's find the roots of x^2 - 9x + 14
x^2 - 9x + 14 = 0
x^2 - 7x - 2x + 14 = 0
x(x - 7) - 2 (x - 7) = 0
(x - 7) (x - 2) = 0
or
x - 7 = 0. and x - 2 = 0
x = 7 and x = 2
Therefore, the zeros of the given equation are, 0, -1, 2 and 7.
15. I need help on this question. How do you do it?
Answers
Solution:
Given the expression:
[tex]-5^2[/tex]This expression is evaluated as
[tex]\begin{gathered} -5\text{ multiplied in 2 places} \\ \Rightarrow-5\times-5 \\ =25 \end{gathered}[/tex]Hence,
[tex]-5^2[/tex]is evaluated to be 25
A normal distribution has a mean of 101 and a standard Deviation of 12. find the probability that a value selected at random is in the following interval.at most 13
Answers
Answer:
84.134%
Explanation:
First, determine the value of the z-score.
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ =\frac{113-101}{12} \\ =\frac{12}{12} \\ z-score=1 \end{gathered}[/tex]Next, we determine the probability that a value selected at random is at most 113:
[tex]\begin{gathered} P(X\le113)=P(x\le1)_{} \\ =0.84134 \\ =84.134\% \end{gathered}[/tex]Thus, the probability that a value selected at random is in the given interval is 84.134%.
Find y if the line through (5, 1) and (6, y) has a slope of 3.
Answers
Answer:
Y = 32
Step-by-step explanation:
Y = mx + c, with a slope of 3
Y = 3x + c
Substitute values:
1 = 3 (5) + c
1 = 15 + c
c = -14
Rewrite formula:
Y = 3x - 14
Y = 3 (6) + 14
Y = 18 + 14
Y = 32
Hope this helps :)
Answer:
y = 4
Step-by-step explanation:
y = mx + b is the slope intercept form of a line.
We need an m (slope and a b(y-intercept)
They give us the slope, so we have to find the b
slope = 3
y = 1
x = 5
We need and x and y on the line and the point (5,1) gives us that.
y = mx + b
1 = 3(5) + b
1 = 15 + b Subtract 15 from both sides of the equation
-14 = b
Now we have the m (slope of 3) and the b (the y-intercept of -14)
y = mx + b
y = 3x -14 Now plug is the x (6) from the point given and solve for its y
y = 3(6) -14
y = 18 - 14
y = 4
Evaluate when n=5 4n
Answers
We are given an expression "4n"
The question says to evaluate this expression when n = 5
Here, evaluation simply means, finding the value of "4n" when n = 5. This is a simple problem of substitution. By substitution I mean replacing every occurence of n in the given expression by 5. This would be done as follows:
Given expression = 4n
Note that here 4 is being multiplied to n.
Replacing n by 5, we get the result as:
[tex]4\text{ }\times\text{ 5 = 20 }[/tex]From here, we can conclude that the value of expression "4n" for n = 5 will be 20.
$3.44 at the Farmers market at a grocery store the same oranges cost $8.40 for a bag of 20 find the better deal by calculating the unit rate for both locations how much would be saved per orange by purchasing oranges at the locations with the better deal solve the word problemFarmers market unit rate --------------grocery store unit rate ------------------better deal -------------how much is saved ------------A $0.01/ orangeslB $0.41 / orangeC grocery storeD Farmers marketE $0.43 / orangeF $0.40 / OrangeG $0.10 / Orange
Answers
Given :
At the farmer market : a bag of 8 oranges cost $3.44
At the grocery store : a bag of 20 oranges cost $8.4
So, the unit rate at the farmer market = 3.44/8 = $0.43/ orange
And the unit rate at the grocery store = 8.4/20 = $0.42/ orange
So, the better deal is the grocery store
how much is saved ?
the saving = 0.43 - 0.42 = $0.01/ orange
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answers
Answer:
1/4
Step-by-step explanation:
you just look at rise over run from one point to another and simplify.
Geometry Problem - Given: segment AB is congruent to segment AD and segment FC is perpendicular to segment BD. Conclusion: Triangle AEG is isosceles. (Reference diagram in picture)
Answers
As the triangle AEF has 2 angles with the same measure, triangle AEF is isosceles.
Find the slope of the lines (-3,-1) and (-6,-10)
Answers
m = rise/run = (-10 - (-1))/(-6 - (-3)) = -9/-3 = 3
the slope of the line is equal to 3.
Kindly assist in answering these questions
Answers
The point of origin on the graph is (0,0) and the constant of proportionality is equal to 3.
Equation of LineThe equation of a straight line is y=mx + c. y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.
In the given question, we are asked to find several values relating to the graph attached.
5) The point of origin on the graph is at (0,0) because the graph passes through the center along the straight line.
6) The constant of proportionality (k) is the value before the variable x.
The equation of the line is y = 3x.
The constant of proportionality of the equation is equal to 3.
7) The value of the ratio k is given as y/x
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i need help please,solve and explain it's 4th grade math.. thank you.
Answers
What you can say about 12th, 18th and the 21st child, depends if these numbers are multiples of 4 (every 4th child is wearing spectacles), 3 (every 3rd child is a girl) and 2 (every 2nd child is wearing a white shirt).
If a numer is multiple of another one, then the quotient between them is an integer number.
for 12th:
12/4 = 3
12/3 = 4
12/2 = 6
12 is multiple of 3, 4 and 6.
Then, 12th child is wearing spectacles, a white shirt and is a girl.
for 18th:
18/4 = 4.5
18/3 = 6
18/2 = 9
18 is multiple of 3 and 2.
Then, 18th child is a girl and is weraing a white shirt
for 21th:
21/4 = 5.25
21/3 = 7
21/2 = 11.5
21 is multiple of 3.
THen, 21st child is a girl.
Write a proportional that relates the corresponding sides. You must use all of the sides for both triangles in your statement.
Answers
Given
Answer
[tex]\Delta HGF\approx\Delta HKL[/tex]GF is proportional to KL
HG is proportional to HK
HF is proportional to HL
A sample of 7 adult elephants had an average weight of 12,572 pounds. The standard deviation for the sample was 26 pounds. Find the 95% confidence interval of the population mean for the weights of adult elephants. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.
Answers
Answer
[tex]CI=(12553<\mu<12591)[/tex]Explanation
The confidence interval formula is given by
[tex]\begin{gathered} CI=\bar{x}\pm z\frac{s}{\sqrt[]{n}} \\ \text{Where;} \\ CI\text{ is the 95 percent confidence interval} \\ \bar{x}\text{ is the average weight }=12572 \\ z\text{ is the confidence value }=1.96 \\ s\text{ is the sample standard deviation }=26 \\ n\text{ is the sample size }=7 \end{gathered}[/tex]This implies that
[tex]\begin{gathered} CI=12572\pm1.96(\frac{26}{\sqrt[]{7}}) \\ CI=12572\pm\frac{50.960}{2.646} \\ CI=12572\pm19.259 \\ CI=(12552.741,12591.259) \\ CI=(12553<\mu<12591) \end{gathered}[/tex]The 95% confidence interval of the population mean for the weights of adult elephants is (12553 < μ < 12591)
