Calculating the volume of a cylinder the radius is squared,
If the radius was 8 when 8 is squared you get 64
If the radius is multiplied by 1/2 the radius would become 4, 4 squared is 16
16 / 64 = 1/4
The volume would be 1/4 the original volume, so it would be 4 times smaller.
Final answer:
Halving the diameter of a cylinder makes its volume four times smaller, because the volume depends on the square of the radius, and reducing the diameter by half means the radius is also halved.
Explanation:
When the diameter of a cylinder is multiplied by 1/2, the radius of the cylinder is also reduced to half its original size. To understand the impact on the volume, we examine the volume formula for a cylinder: V = (pi = 3.1416) times r^2 times h, where V is the volume, r is the radius, and h is the height. If both the diameter and radius are reduced by half, the volume of the cylinder will be reduced by a factor of 1/2^2 for the radius squared part of the formula.
Volume is directly proportional to the square of the radius, so taking the original volume formula V =
times (original radius)^2 times h and then applying the radius reduction, we get the new volume V' =
times (1/2 times original radius)^2 times h = 1/4 times original volume. Therefore, the volume of the cylinder becomes four times smaller when the diameter (and thus radius) is halved.
In the figure below, ∠APE and ∠EPD are congruent.
What is the arc measure of AC on circle P in degrees?
Answer:
P = 54 so
arc AC = 150
Step-by-step explanation:
The measure of AC on circle P in degrees is 118degrees
To get the measure of the arc AC on the circle, we will use the formula for calculating the angle at a point.
The sum of the angle at a point is 360 degrees, hence:
arc AB + arcBC + arcCD + arc DE + arcEA = 360
If ∠APE and ∠EPD are congruent, this means that arc DE = arcEA. The equation becomes:
arc AB + arcBC + arcCD + arc DE + arcDE = 360
Substitute the given angles into the expression:
arc AB + arcBC + arcCD +2arcDE = 360
126 + 74 + 42 + 2arcDE = 360
242 + 2arcDE = 360
2arcDE = 360 - 242
2arcDE = 118
arcDE = 118/2
arcDE = 59
arcAC = 2(arcDE)
arcAC = 2(59)
arcAC = 118 degrees
Hence the measure of AC on circle P in degrees is 118degrees
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What is the volume of a cube with a side length that measures 112 ft?
Answer:
1,404,928 is the volume of a cube with a side length that measures 112 ft
Answer:
1,404,928 is the volume
Rebeckah answered 42 of the 60 questions correctly on a test. Which method should she use to find the percent of questions she answered correctly? First, subtract 42 from 60 to find the ratio of questions answered correctly to total questions, which is . Then, add 40 to the numerator and denominator to find the percent: . First, find the ratio of questions answered correctly to total questions, which is . Then, add 40 to the numerator and denominator to find the percent: . First, subtract 42 from 60 to find the ratio of questions answered correctly to total questions, which is . Then, simplify the ratio to . Finally, multiply the numerator and denominator by 10 to find the percent: . First, find the ratio of questions answered correctly to total questions, which is . Then, simplify the ratio to . Finally, multiply the numerator and denominator by 10 to get
Answer:
The last option
Step-by-step explanation:
To find a percentage of something you need
[tex]\frac{expected}{total}*100[/tex]
The expected is correct marks, the total is the total amount - then you multiply by 100 to turn the decimal into a percentage.
Answer:
the answer is D
Step-by-step explanation:
nelson scores 27 out of 40 in a history test. workout his score as a percentage.
Answer:
Step-by-step explanation:
25
Answer:
27 X
__ = __
40 100
cross multiply divide. meaning 27*100 = 40*X. -> 2700 = 40*X. also meaning the answer is 2700 divided by 40 = X.
plug 2700/40 into a calculator. answer 67.5%
Step-by-step explanation:
Please help, geometry
Step-by-step explanation:
As it is a quadrilateral so sum of all angles of quadrilateral is equal to 360°
14x - 11° + 8x + 7° + 5x + 18° + 10x + 13° = 360°
37x+ 27° = 360°
37x = 360° - 27°
37x = 333°
x = 333° / 37
Therefore x = 9°
Now
<B = 8 * 9° + 7° = 79°
Hope it will help you.
Answer: The answer is 79.0°
Step-by-step explanation:
A quadrilateral will always have 360° and four sides. Keep that in mind, that's a universal rule of geometry.
Here, the sum of all sides is equal to 360°. Therefore, we make an equation:
[tex](14x-11) + (8x+7) + (5x+18) + (10x + 13) = 360[/tex]
Simplify by adding and subtracting like terms.
[tex]37x +27=360[/tex]
Isolate x by first passing the 27 to the other side.
[tex]37x = 333[/tex]
Divide by 37 to isolate x.
[tex]x = 9[/tex]
To find m∠B, we plug in x to [tex](8x+7)[/tex]
which gives you: [tex](8*9+7) = 79[/tex]
The answer is 79.0°
Curious if it is correct? Let's double check.
Plug in the x=9 to all the x values and add them up. You should get 360, which makes the answer correct.
I need to buy some cardboard to build a box 12 inches long, 8 inches wide and 10 inches high. How much cardboard is needed to build the box
You will need 592 square inches of cardboard to build the box.
To determine how much cardboard is needed to build the box, we calculate the surface area of the box.
The box has six faces: two of each dimension.
Calculating the area of each pair of faces:
Two faces of (12 in x 8 in):
2 x (12 x 8) = 2 x 96 = 192 square inches
Two faces of (12 in x 10 in):
2 x (12 x 10) = 2 x 120 = 240 square inches
Two faces of (8 in x 10 in):
2 x (8 x 10) = 2 x 80 = 160 square inches
Sum the areas of all faces:
192 + 240 + 160 = 592 square inches
What is the vertex form of the equation
y= -x^2+10x-30
Answer:
The answer to your question is Vertex = (5 , -5)
Step-by-step explanation:
Data
Equation y = - x² + 10x - 30
Process
1.- Add 30 units in both sides
y + 30 = -x² + 10x - 30 + 30
2.- Simplify
y + 30 = -x² + 10x
3.- Factor -1 in the right side
y + 30 = -(x² - 10x )
4.- Complete the perfect square trinomial
y + 30 - 5²= -(x² - 10x + 5²)
5.- Simplify
y + 30 - 25 = -(x² - 10x + 25)
y + 5 = -(x - 5)²
6.- Find the vertex
Vertex = (5 , -5)
Mr.Hawkins gets two bonus payments every year this year his bonus payment was 1/4of his salary his second payment was 1/8 of his salary what is the fraction for his combined bonus payments?
Answer:
3/8
Step-by-step explanation:
1/4 + 1/8 = 2/8 + 1/8 = 3/8
After you give the fractions a common denominator, you can add their numerators to find the numerator of the result.
Mr. Hawkins's combined bonus payments are 3/8 of his salary.
Esther needs a bin for her hair bows. A yellow bin has a length of 11.4 inches, a width of 4.2 inches, and a height of LaTeX: \frac{8}{3}8 3 inches. A red bin has a length of 9 inches, a width of 5.45 inches and a height of LaTeX: \frac{11}{5}11 5 inches. What is the volume of the bin with the greatest volume? Explain your answer.
Answer:
Yellow Bin
Step-by-step explanation:
Yellow Bin
Length = 11.4 inches,
Width = 4.2 inches,
Height = [tex]\frac{8}{3}[/tex]
Volume of the yellow bin=LWH[tex]=11.4 X 4.2 X \frac{8}{3}=127.68 \:cubic \:inches[/tex]
Red Bin
Length = 9 inches,
Width = 5.45 inches,
Height = [tex]\frac{11}{5}[/tex]
Volume of the red bin=LWH[tex]=9X 5.45 X \frac{11}{5}=107.91 \:cubic \:inches[/tex]
The yellow bin has a greater volume since 127.68 is greater than 107.91.
What is the difference of the rational expressions below?
Answer: A
Step-by-step explanation:
We need to get the denominators to be same first before we can do anything to the numerator.
The LCD (lowest common denominator) is [tex]3x^{3}[/tex]. To find the LCD, multiply the denominators together: [tex]x^{3}[/tex] · [tex]3x[/tex] = [tex]3x^{3[/tex].
Below, we are trying to get the denominators to equal the same or to [tex]3x^{3}[/tex].
[tex]\frac{3}{3} (\frac{4}{x^{3} } ) - \frac{x^{2} }{x^{2} } (\frac{2x-1}{3x} )[/tex]
[tex]\frac{12}{3x^{3} } - \frac{2x^{3}-x^{2} }{3x^{3} }[/tex]
Now that the denominators are the same, we can subtract the numerators from each other.
[tex]\frac{ 12 - (2x^{3} -x^{2})\\}{3x^{3} } \\[/tex]
[tex]\frac{12-2x^{3} +x^{2} }{3x^{3} }[/tex]
Now, we can just reorganize the variables.
Answer: A or [tex]\frac{-2x^{3} + x^{2}+12 }{3x^{3} }[/tex]
What does vertex in graphs mean?
If tan B = 1.6732, what is the measure of B to the nearest tenth of a degree
Answer:
59.1 °
Step-by-step explanation:
-Given that Tan B=1.6732
-Angle B is equivalent to the tan inverse of the tan B value:
[tex]\angle B=Tan^{-1}B\\\\\angle B=Tan^{-1}(1.6732)\\\\=59.1350\approx59.1\textdegree[/tex]
Hence, angle B is 59.1 °
To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732.
The measure of angle B is approximately 59.7 degrees.
Explanation:To find the measure of angle B, you can use the inverse tangent function (arctan) to find the angle whose tangent is 1.6732. First, convert the tangent value to radians by using the formula tan(B) = opposite/adjacent. Then, take the arctan of B to find the measure in radians. Finally, convert the radians to degrees by multiplying by 180/pi.
Step-by-step:
Convert the tangent value to radians: tan(B) = opposite/adjacent => B = arctan(1.6732)Convert radians to degrees: B (in degrees) = B (in radians) * 180/piPlugging in the given value, B ≈ 59.7 degrees to the nearest tenth of a degree.
Learn more about measure of angle B here:https://brainly.com/question/2046046
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At Central High School, 85% of all senior girls attended and 65% of all senior boys attended the Spring Dance. Of all attendees, 20% won a prize. A. Assuming that the number of senior girls at Central High School is about equal to the number of senior boys, estimate the probability that a randomly selected senior won a prize at the dance. Explain. Enter your answer. B. Construct Arguments If you knew whether the selected student was a boy or a girl, would your estimate change
Answer:
a) 0.30 (30%)
b) Boy: 0.13 (13%) , Girl : 0.17 (17%)
Step-by-step explanation:
Given:-
- The probability of senior girls attend spring dance, P(GA) = 0.85
- The probability of senior boys attend spring dance, P(BA) = 0.65
- The probability that an attendee wins a prize, P(W) = 0.20
Find:-
Estimate the probability that a randomly selected senior won a prize at the dance.
Construct Arguments If you knew whether the selected student was a boy or a girl, would your estimate change
Solution:-
- First realize that the probability for any senior student to attends the spring dance and winning a prize are independent events.
- So for independent events, the probability that a "girl or a boy" attends the spring dance and wins a prize can be determined:
P ( GA & W ) = P(GA)*P(W) = 0.85*0.20 = 0.17 (17%)
P ( BA & W ) = P(BA)*P(W) = 0.65*0.20 = 0.13 (13%)
P ( (BA & W) U (GA & W) ) = P ( BA & W ) + P ( GA & W )
= 0.17 + 0.13
Answer = 0.3 (30%)
- So the estimate probability that a randomly selected senior won a prize at the dance is 0.3 or 30% of all attendee.
- If the randomly selected senior was a girl would be the proportion of people who won the prize.
P ( GA & W ) = 0.17 (17%)
- Similarly, If the randomly selected senior was a boy would be the proportion of people who won the prize.
P ( BA & W ) = 0.13 (13%)
Answer:
a) 30%
b) the estimate wouldnt change as far as the probabilities is been maintained. thre can only be a shift in the gender probability depending on whether there are more number of boys or girls.
Step-by-step explanation:
a) Prob( all senior girl attended) = 85%
Prob ( all senior boy attended) = 65%
Prob( won a price) = 20%
Prob( a senior girl attends and win a price) = 85% x 20%
= 17%
Prob ( a senior boy attends and win a price) = 65% x 20%
= 13%
Prob( a senior won a price) = 17% + 13%
= 30%
b) The estimate wouldnt change as far as the probabilities is been maintained. thre can only be a shift in the gender probability depending on whether there are more number of boys or girls.
c^2=4? Anyone want to help?
Answer: c=2
Step-by-step explanation: the square root of c^2 equals the squae root of 4 which is 2 so your left with c=2
Which ordered pair is a solution of the equation?
y - 4= 7(x – 6)
Choose 1 answer:
A. Only 5,4
B. Only 6,5
C both 5,4 and 6,5
D. Neither
if angle 5 is 120 degrees, what is the measure of angle 6?
Final answer:
Without more context, the measure of angle 6 cannot be determined from the given information that angle 5 is 120 degrees.
Explanation:
To determine the measure of angle 6, we need additional information about the context in which angle 5 and angle 6 are related. Since the question does not provide sufficient details, such as whether the angles are supplementary, complementary, or part of a geometric figure like a triangle or polygon, it's not possible to provide the measure of angle 6 based solely on the given information that angle 5 is 120 degrees. In geometry, the relationships between angles often depend on the shapes they are part of or the lines intersecting with them. If angle 5 and angle 6 are supplementary angles (angles that add up to 180 degrees), for instance, we could subtract the measure of angle 5 from 180 degrees to get angle 6. However, without more details, we cannot accurately provide the measure of angle 6.
Plz helppppppppppp me with these
Answer:
help with what tho
Step-by-step explanation:
Answer:
with what I can't see it
Step-by-step explanation:
Evaluate 5 + (-4) +(-7) + 2.
Answer:
-4
Step-by-step explanation:
Evaluate the expression (2a)3
Final answer:
To evaluate the expression (2a)³, we cube the numeric term, resulting in 8, and multiply the exponent of the variable 'a' by 3, which gives us the final result of 8a³.
Explanation:
The expression given, (2a)³, requires us to cubing of exponentials. Cubing in mathematics involves raising a number or expression to the third power. In this case, the number 2 and the variable a are multiplied together first, and then that result is raised to the power of three. To evaluate this expression, you would do the following steps:
Cube the digit term in the usual way, which is 2 cubed or 23, which equals 8.Multiply the exponent of the exponential term by 3. Since the original expression has the variable 'a' to the first power, multiplying the exponent by 3 means 'a' will now have an exponent of 3.Combining these results, the expression (2a)³ becomes 8a³.
A group of finance managers at a car dealership estimates thatt 23% of all cars purchased last year were leases.If a sample of 800 cars sold last year obtained, what is the that more than 208 cars are going to be leased? Draw and label the appropriate curve. Your work must include caculator commands
Answer:
p = 0.52392
Step-by-step explanation:
Here we have
p = 23% = 0.23
[tex]\hat p[/tex] = 208/800 = 0.26
n = 800
q = 1-p = 0.77
α = 5% = 0.05
Here we have
Z test given by
[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{pq}{n}}}[/tex]
From which we have
From the Cpdf we have Probability = 0.0219, z = 2.016
Therefore from the z score = 0.0683, p = 0.52392 from z table.
um i need help with this.
Answer:
none
Step-by-step explanation:
Aiden put two-fifths of his Money into his piggy bank. He had $15 left in his pocket to buy a toy. How much money did aiden have before he put some into his bank?
Answer:25
Step-by-step explanation:
15x 2/5=25
Answer:
$37.50
Step-by-step explanation:
[tex]\frac{2}{5}[/tex] of Aiden's money is $15. Half of [tex]\frac{2}{5}[/tex] is [tex]\frac{1}{5}[/tex], so you have to find half of $15 to find out what [tex]\frac{1}{5}[/tex] of Aiden's money is.
15/2 = 7.5. [tex]\frac{1}{5}[/tex] of Aiden's money is $7.50.
7.5 × 5 = 37.5, so Aiden had $37.50 before he put some into his piggy bank.
Yasmin arrived home from play practice at 4:25 pm. The walk took 15 minutes. Practice began 20 minutes after the final bell and lasted for a half hour. When did school end
Answer:
Step-by-step explanation3:45
Answer:
3:20 p.m
Step-by-step explanation:
A radio antenna is kept perpendicular to the ground by three wires of equal length. The wires touch the ground at three points on a circle whose center is at the base of the antenna. If the wires touch the ground at (9,-19),(-21,-19), and(14,16), what are the coordinates of the base of the antenna?
Answer:
The coordinates of the base of the antenna is (-6. 1)
Step-by-step explanation:
Here we are required to find the center of a circle given points on the circumference
The equation of a circle is
(x - h)² + (y - k)² = r²
Where:
x and y are points on the circumference
h and k are coordinates of the center of the circle and
r = The radius of the circle
Since we have the values for the points on the circumference, we are left with three unknowns, which we can find with three equations as follows;
By plugging in the values for x and y at the respective points we get,
At (9, -19) → (9 - h)² + (-19 - k)² = r²...............(1)
At (-21, -19) → (-21 - h)² + (-19 - k)² = r².....,...(2)
At (14, 16 ) → (14 - h)² + (16 - k)² = r² ............(3)
Solving, we get from (1) (-19 - k)² = r² - (9 - h)²
Plugging in the value of (-19 - k)² in equation (2) we get
(-21 - h)² + r² - (9 - h)² = r²
So that (-21 - h)² - (9 - h)² = r² - r² = 0
and (-21 - h)² - (9 - h)² = 0 gives
60·h +360 = 0 or h = -6
Plugging in the value of h = -6 in equation (3) we get
(14 - (-6))² + (16 - k)² = r²
20² + (16 - k)² = r² .................(4)
similarly from equation (1) we get
(9 - (-6))² + (-19 - k)² = r²
15² + (-19 - k)² = r² ................(5)
Subtracting equation (5) from (4) gives
20² - 15² + (16 - k)² - (-19 - k)² = 0
Which gives
-70·k + 70 = 0
or k = 1
Therefore the coordinates of the base of the antenna = (-6. 1).
find the zero of the polynomial
2x²+9x+4
Answer:
x=-4 or x=-1/2=-0.500
Step-by-step explanation:
Answer:
x= -4 or x= -0.5
Step-by-step explanation:
use a quadratic formula calculator or graph it on desmos
is 29 a monomial please help
Answer:
it is
Step-by-step explanation:
Any number, all by itself, is a monomial, like 5 or 2700.
Answer:
Yes it is a monomial
Step-by-step explanation:
There's only one number, there's no operations to do so its a monomial :)
Solve for x
-18x+21>-15 or 20x-13>27
Answer:
all value of x are equal
Step-by-step explanation:
A student solved 3/x-4 =x/7 in six steps as shown.Which statement is an accurate interpretation of the students work
Answer:
A student solved 3/x−4=x/7 in six steps, as shown:
Step 1: 3=x(x−4)/7
Step 2: 21=x(x−4)
Step 3: 21=x^2−4(x)
Step 4: 0=x^2−4(x)−21
Step 5: 0=(x−7)(x+3)
Step 6: x=−3, x=7
Which statement is an accurate interpretation of the student's work?
A.The student solved the equation correctly.
B.The student made an error in step 2.
C.The student made an error in step 5.
D.Only x=7 is a solution to the original equation.
Option A is the right choice.
Step-by-step explanation:
Given:
An equation and its step-wise work.
We have to check whether the steps are correct or not.
The equation is:
⇒ [tex]\frac{3}{x-4} = \frac{x}{7}[/tex]
Solution:
⇒ [tex]21=x(x-4)[/tex] ...cross multiplying terms.
⇒ [tex]21=x^2-4x[/tex]
⇒ [tex]x^2-4x-21=0[/tex]
⇒ [tex]x^2-7x+3x-21=0[/tex] ...using middle term splitting
⇒ [tex]x(x-7)+3(x-7)=0[/tex]
⇒ [tex](x+3)(x-7)[/tex]
⇒ [tex]x=-3\ and\ x=7[/tex]
The student have solved the question correctly.
40 - 5n = -2 need explanation as well
Answer: n = 8.4
Step-by-step explanation:
40 - 5n = -2
First, subtract 40 from each side of the equation
-5n = -42
Then, divide each side by -5
n = 8.4
The -5 and -42 cancel each other out when dividing, so n = 8.4 is positive.
Answer:
n=8.4
Step-by-step explanation:
To solve, we need to isolate the variable, n
40 -5n =-2
Subtract 40 from both sides
40-40-5n= -2 -40
-5n= -42
Divide both sides by -5
-5n/-5=-42/-5
n=42/5
n=8.4
Radiationâ machines, used to treatâ tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3â meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.82.8 âmeters?
Answer:
71.75 milliroentgens per hour
Step-by-step explanation:
The intensity(I) of Radiation varies inversely as the square of the distance (D) from the machine.
This is written as:
[tex]I \propto \frac{1}{D^2} \\$Introducing the constant of Variation k$\\I = \frac{k}{D^2} \\$When D=3 meters, I=62.5 milliroentgens per hour$\\62.5= \frac{k}{3^2}\\k=62.5 X 9 =562.5\\$Substituting K=562.5 into the variation equation$\\I = \dfrac{562.5}{D^2} \\$Therefore, When D=2.8 meters$\\Intensity,I = \dfrac{562.5}{2.8^2}=$71.75 milliroentgens per hour$[/tex]