The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.
How to illustrate the volume?Let's assume that the height and radius are 14cm and 7cm. The volume will be:
= πr²h
= 3.14 × 7² × 14
= 2154.04cm³
When the radius and height are reduced to 5cm and 9cm, the volume will be:
= πr²h
= 3.14 × 5² × 9
= 706.5cm³
This illustrates that the volume reduces when the height and radius reduces.
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Which value is included in the solution set for the inequality graphed on the number line? A number line going from negative 4 to positive 4. An open circle is at negative 2. Everything to the left of the circle is shaded.
The value included in the solution to the given inequality is:
x = -5.
What is the inequality that models this situation?Everything to the left of the circle at x = -2 is shaded, that is, all values less than x = -2, hence the inequality is:
x < -2.
Researching the problem on the internet, the options for the values that belong to the solution are:
-5, -2, 0, 3.
Due to the open circle, -2 is not in the inequality, 0 and 3 are greater than -2, hence they are not in the inequality, then the value included in the solution to the given inequality is:
x = -5.
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What is the equation of the line that passes through the point (3, -1) and is perpendicular to the equation y = -3x + 2? A. y=-3x+8
B. y = -3x
C. y=(1/3)x
D. Y =(1/3)x-2
Answer:
A) y = –3x+8
Step-by-step explanation:
first off, a negative equation means the graph is downward sloping from left to right –> \. So with this in mind you can immediately eliminate C and D because they are upward sloping graphs. B also doesn't work because it doesn't go through (3,–1). This leaves A as the right answer
the constant number is the number on the y-axis. So, for –3x+2, +2 is the y-coordinate on the y-axis. the slope is -3x meaning down 3, right 1. –3x+8 is the only answer that is perpendicular.
Two poles have a height of 9 m and 2 m, respectively. A
string is used to connect the poles. If the poles are 24 m
apart, what is the minimum length of the string?
Answer:
25
Step-by-step explanation:
please answer with everything needed i appreciate everyones help
Step-by-step explanation:
d = price of 1 drink
s = price of 1 sandwich
3d + 5s = 25.05
4d + 2s = 13.8
we can do this by combining both equations so that they is only one variable left.
e.g. multiply equation 1 by 4 and equation 2 by 3, and then subtract equation 2 from equation 1 :
12d + 20s = 100.2
- 12d + 6s = 41.4
------------------------------
0 14s = 58.8
s = 58.8/14 = $4.20
3d + 5s = 25.05
3d + 5×4.2 = 25.05
3d + 21 = 25.05
3d = 4.05
d = 4.05/3 = $1.35
so, each drink costs $1.35.
On a statistic exam, a class of 25 students had a mean score 75.2 and a standard deviation of 5.7. using the empirical rule, what would be the range of scores for 95% of the class?
The range of scores for 95% of the class is 63.8 to 86.6 using the empirical rule.
What is the empirical rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations.
The empirical rule specifically states that 68 percent of data will fall inside the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.
According to the question,
μ=75.2 and σ=5.7
So, according to the empirical rule, the range of scores for 95% of the class:
μ – 2σ =75.2-2*5.7=63.8
and μ + 2σ=75.2+2*5.7=86.6
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The table represents an exponential function
X123
1648366
4
y
9
What is the multiplicative rate of change of the
function?
of
0 0 00
ON W/NW/
02
The multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
We have a table that shows an exponential function.
As we know the exponential function:
y = a(b)ˣ
Plug x = 1, y = 6
6 = ab ...1
Plug x = 2, y = 4
4 = ab² ...2
Divide equations 1 and 2
ab²/ab = 4/6
b = 2/3
Plug the value of b in the 1 equation.
a(2/3) = 6
a = 9
y = 9(2/3)×
The multiplicative rate = 9
Thus, the multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.
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In the air, it had an average speed of 16 \text{m/s}m/start text, m, slash, s, end text. In the water, it had an average speed of 33 \text{m/s}m/start text, m, slash, s, end text before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.
How long did the stone fall in the air and how long did it fall in the water?
The time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.
What is Speed?Speed is the distance covered by an object in a fixed period of time. It is measured in m/sec.
The average speed in air is 16m/sec.
The average speed in water is 33m/sec.
The total time taken is 12 seconds.
Total distance covered = Total time taken * speed at which it covered the distance
Let the time taken to fall in air is t
So, the time taken in water will be 12-t
The total distance is equal to
127 = 16*t + 3(12-t)
127 = 16t + 36 - 3t
127 - 36 = 16t - 3t
91 = 13t
t = 91/13 = 7 seconds
12-t = 12-7 =5 seconds
Therefore, the time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.
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of 5
→
Krutika can type 6000 words in 80 minutes.
Mark can type 4200 in 60 minutes.
David can type 5850 words in 90 minutes.
Who types at the fastest rate of words per minute
Answer:
Krutika
Step-by-step explanation:
Lets convert each person's typing rate to words/min.
Krutika:
80 minutes = 6000 words
1 minute = (6000/80) words
= 75 words
Typing Rate: 75 words / min
Mark:
60 minutes = 4200 words
1 minute = (4200/60) words
= 70 words
Typing Rate: 70 words / min
David:
90 minutes = 5850 words
1 minute = (5850/90) words
= 65 words
Typing Rate: 65 words / min
From the above, we can see Krutika has the fastest rate of words per minute.
una fracción de reducción a su mínima expresión en igual a 1/8. si la suma de sus terminos es 72. hallar la diferencia entre ellos
Por lo tanto el número es p/q = 8/64.
¿Qué es una fracción?Fracción es un número que se puede representar en forma de p/q, donde q no es igual a cero.
It is given that
En su forma más simple, el número es 1/8
Sea el número p/q
p + q = 72 (dado)
p/q = 1/8
q = 8p
p+8p = 72
9p = 72
p = 8
q = 8p
q = 8 * 8 = 64
Por lo tanto el número es p/q = 8/64.
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Urgent! I really need help
Answer:
58.0°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides of a right triangle and trig functions of the acute angles.
ApplicationHere, the hypotenuse of the triangle is given (17 cm), as is the side adjacent to angle x (9 cm). This suggests using the relation ...
Cos = Adjacent/Hypotenuse
cos(x) = (9 cm)/(17 cm) = 9/17
The angle for this cosine value is found using the inverse trig function.
x = arccos(9/17)
x ≈ 58.034°
Rounded to the nearest tenth, the angle is ...
x = 58.0°
__
Additional comment
Of course, the angle y is the complement of this:
y = 32.0°
URGENT: Mr. Donaldson drove from his house to Bigfoot, Texas at 70 mph. On his return trip he followed the same route, but since his car wasn't running well, he only averaged 50 mph. If the total round trip took 6 hours, how many hours did it take Mr. Donaldson to drive from his house to Bigfoot?
Answer:
2 hours
Step-by-step explanation:
Because if the total round trip took 6 hours then it mustve taken him 2 hours to drive there at 70mph and 4 hours to drive back at 50mph.
The table shows ordered pairs of the function y = 16 + 0.5x .
A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 2, 0
The missing values represented by x and y are 8 and 20, that is
(x, y) = (8, 20)
The function y = 16 + 0.5x is a linear equation that can be solved graphically. This means the values of both variables x and y can be found on different points along the straight-line graph.
The ordered pairs simply mean for every value of x, there is a corresponding value of y.
The 2-column table has values for x and y which all satisfy the equation y = 16 + 0.5x. Taking the first row, for example, the pair is given as (-4, 14).
This means when x equals negative 4, y equals 14.
Where y = 16 + 0.5x
y = 16 + 0.5(-4)
y = 16 + (-2)
y = 16 - 2
y = 14
Therefore the first pair, just like the other four pairs all satisfy the equation.
Hence, looking at the options given, we can determine which satisfies the equation
(option 1) When x = 0
y = 16 + 0.5(0)
y = 16 + 0
y = 16
(0, 16)
(option 2) When x = 5
y = 16 + 0.5(5)
y = 16 + 2.5
y = 18.5
(5, 18.5)
(option 3) When x = 8
y = 16 + 0.5(8)
y = 16 + 4
y = 20
(8, 20)
From our calculations, the third option (8, 20) is the correct ordered pair that would fill in the missing values x and y.
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In 1996, the price of a rare stamp inclusive of 3% GST was $3500. In 2010, the price of the same stamp
inclusive of 7% GST was 225% higher than that in 1996. Find
(a) the price of the stamp inclusive of GST in 2010,
(b) the amount of GST on the stamp in 2010,
(c) the percentage increase in amount of GST on the stamp from 1996 to 2010.
Based on the price of the stamp in 1996, and the increase in 2010, the following are true:
a. price in 2010 = $7,875.b. amount of GST on the stamp in 2010 = $515.19c. percentage increase in GST from 1996 to 2010 = 405%.How much has the price of the stamp changed in 2010?The price in 2010 was:
= 3,500 x 225/100
= $7,875
The GST in 2010 is:
= (7,875 / 1.07) x 7%
= $515.19
The GST in 1996 is:
= (3,500 / 1.03) x 3%
= $101.94
The increase in the GMT is:
= (515.19 - 101.94) / 101.94
= 405%
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Please help sorry for the bad picture
Answer:
70°
Step-by-step explanation:
Due to the fact that the angle is on a straight line, therefore the angle(110°) is equal the inside/opposite to the angle(q°):
q°=180°(since it's on a straight line) -110°
q°= 70°
Please assist me on this question please
Answer:
12 units
Step-by-step explanation:
x is to 16 as 9 is to x
x/16 = 9/x cross multiply
x^2 = 144
x =12
Helen got a 7% reduction in the price of a pair jeans that are normally $32. What is the approximate percent in the price?
A percentage is a way to describe a part of a whole. The approximate percent decrease in the price is 21.87%, thus, the correct option is B.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the reduction in the price is $7, while the original cost is $32. Therefore, the approximate percent decrease in the price is,
Percentage decrease = 7/32 × 100%
= 21.87%
Hence, the approximate percent decrease in the price is 21.87%, thus, the correct option is B.
The correct question is:
Helen got a $7 reduction in the price of a pair of jeans that are normally $32. What is the approximate percent decrease in the price?
The percent decrease is approximately 15%.
The percent decrease is approximately 21%.
The percent decrease is approximately 43%.
The percent decrease is approximately 78%
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factorizacion de x^4+12x^3-64x^2=0
Hello,
x⁴ + 12x³ - 64x² = 0
x²(x² + 12x - 64) = 0
x² = 0 or x² + 12x - 64 = 0
x = 0
∆ = b² - 4ac = 12² - 4 × 1 × (-64) = 400
x1 = (-b -√∆)/2a = (-12 - 20)/2 = -32/2 = -16
x2 = (-b + √∆)/2a = (-12 + 20)/2 = 8/2 = 4
S = {-16 ; 0 ; 4 }
→ factorizacion de x⁴ + 12x³ - 64x² : x(x - 4)(x + 16)
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequality:
–3(2x – 5) < 5(2 – x)
= -6x + 15 < 10 - 5x
= -x < -5
= x > 5
The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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Answer: The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right. What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.Given the inequality:–3(2x – 5) < 5(2 – x)= -6x + 15 < 10 - 5x= -x < -5= x > 5The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Step-by-step explanation:
A cupcake recipe calls for 1/6 cups of milk, and you have
7/8 cups of milk in the
refrigerator. How many cups of milk will you have remaining after baking the
cupcakes?
The circumference of a circle is ________
A.The distance around the circle
B.The length of the radius
C.The length of the diameter
D.2 pi
Answer:
2 22/7 ×r
..
...
...
...
...
...
look at image...........
Answer:
Step-by-step explanation:
2x + 3y = 6
y = x/3 - 3
Since the second equation is already solved for y, we can easily use the substitution method.
Substitute y in the first equation with x/3 - 3
2x + 3(x/3 - 3) = 6
2x + x - 9 = 6
3x = 15
x = 5
Now use the second equation, and x = 5, to solve for y.
y = x/3 - 3
y = 5/3 - 3 = 5/3 - 9/3
y = -4/3
Answer: (5, -4/3)
Answer:
your answer would be B
Step-by-step explanation:
Triangle Z W X is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W X is b, the length of X Y is a, the length of Y Z is 5, and the length of W Y is 6.
What is the approximate value of b, rounded to the nearest tenth?
7.2 units
7.8 units
8.6 units
9.4 units
The approximate value of b in the triangle is D. 9.4 units.
How to calculate the value?From the information, it should be noted that WZY and XWY are similar triangle.
The corresponding ratio will be:
XW/WZ = XY/WY = WY/ZY
The calculation of WZ using Pythagoras will be 7.81.
This will be substituted into the ratio.
b/7.81 = 6/5
5b = 46.86
b = 9.4 units.
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2. State the domain and range of the relation shown. Is the relation a function?
Y=3x+1
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](-\infty, \infty)[/tex]The relation is a function.Step-by-step explanation:
The domain and range of all linear functions is the set of real numbers.
Please answer with everything needed i appreciate everyones help:)
Answer:
Hey there....
Step-by-step explanation:5
This is ur answer....
Expression : -x + 5Working :-
x = Unknown number
x + 5 = Sum of the number and Five
x + 5 - 2x = Previous sum decreased by the the twice of the unknown number.
-x + 5 = combine the terms
•••••••••••••••••••••••••••••••••••••••••••••••••••••••••
Hope it helps!
Brainliest pls!
Have a good day!^^
Step-by-step explanation:
x is the number.
(x + 5) - 2x : the sum of the number and 5 decreased by twice the number.
or simplified without the brackets
x + 5 - 2x = 5 - x
it is not clear if you need the general expression showing both conditions (the first up there), or the then simplified result
5 - x
Pleaseeeeeee helppppl asap
Answer:
37
Step-by-step explanation:
Let's use the rule GEMDAS (Grouping, Exponents, Multiply, Divide, Add, Subtract) from left to right. Therefore, we will simplify the equation in the parentheses. [tex]2^{3} = 8. (1-8= -7)[/tex]. -(-7) creates a double negative, deeming the 7 positive, because when there is two negatives the number will turn into a positive. [tex]7^{2}[/tex] = 49, -3 x 4= -12. Therefore the final form of the equation will be 49 - 12 = 37.
Let me know if there are mistakes.
On a coordinate plane, quadrilateral J K L M with diagonals is shown. Point J is at (4, 5), point K is at (5, 1), point L is at (1, 2), and point M is at (1, 5).
Which statement proves that quadrilateral JKLM is a kite?
∠M is a right angle and MK bisects ∠LMJ.
LM = JM = 3 and JK = LK = StartRoot 17 EndRoot.
MK intersects LJ at its midpoint.
The slope of MK is –1 and the slope of LJ is 1.
Answer:
MK intersect LJ at midpoint that's my opinion
Answer:
B. LM = JM = 3 and JK = LK = √17.
Step-by-step explanation:
∠M is a right angle and MK bisects ∠LMJ.
LM = JM = 3 and JK = LK = StartRoot 17 EndRoot.
MK intersects LJ at its midpoint.
The slope of MK is –1 and the slope of LJ is 1.
If the base area of the square pyramid below is 96 ft² and the height is 8 ft, what is the volume?
Answer:
256 ft^3
Step-by-step explanation:
Volume of pyramid = 1/3 base area * height
= 1/3 96 ft^2 * 8 ft = 256 ft^3
Calculate the perimeter of this shape.
Answer:
58cm
Step-by-step explanation:
in the simple way the shape is a rectangle so some of the sizes are equal will be added since the perimeter is the distance around it
simplify completely
[tex]\dfrac{x^2+12x+35}{3x+15}=\dfrac{x^2+12x+35}{3(x+5)}=\dfrac{x^2+5x+7x+35}{3(x+5)}=\dfrac{x(x+5)+7(x+5)}{3(x+5)}=\\=\dfrac{(x+5)(x+7)}{3(x+5)}=\dfrac{x+7}{3}[/tex]
Answer:
(x+7) / 3
Step-by-step explanation:
Factorise the Top half to give :
x² + 12x+ 35 = (x+5)(x+7)
Factorise the bottom half to give :
3(x+5)
Cancel (x+5) from top and bottom to give :
(x+7) / 3
So our final answer is Option 3
Hope this helped and have a good day
Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose 18 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.(a) No samples are mutated.(b) At most one sample is mutated.(c) More than half the samples are mutated.Round your answers to two decimal places (e.g. 98.76).
Probability that no samples are mutated is 0.83, probability that at most one sample is mutated is 0.9812 and probability that more than half the samples are mutated is 0.
Given percentage of rejuvenated mitochondria defective is 1%, and sample size is 18.
Binomial distribution is the probability of exactly x successes on n repeated trials and X can have two outcomes.
P(X=x)=[tex]C_{n,x} p^{x}(1-p)^{n-x}[/tex]
percentage of defective rejuvendated mitochondria=1%
p=0.01
Sample size=18
n=18
a) No samples are mutated
This means P(X=0)=[tex]C_{18,0}(0.01)^{0} (0.99)^{18}[/tex]
=0.83
b) At most one sample is mutated.
P(X<=1)=P(X=0)+P(X=1)
so,
P(X=0)=[tex]C_{18,0} (0.01)^{0} (0.99)^{18}[/tex]
=0.83
P(X=1)=[tex]C_{18,1}(0.01)^{1} (0.99)^{17}[/tex]=
=0.1512
P(X<=1)=0.83+0.1512
=0.9812
c) More than half the samples are mutated.
P(X>9)=P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)
Using two decimals digits precision all will be 0.
Hence Probability that no samples are mutated is 0.83, probability that at most one sample is mutated is 0.9812 and probability that more than half the samples are mutated is 0.
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