Answer:
The height of the cylinder is 4 x units.
The area of the cylinder’s base is One-fourthπx2 square units
Step-by-step explanation:
Formula for volume of the cylinder:
V = r² π h
Volume of the cylinder=
πx^3
Diameter=x
Radius (r)=diameter/2
=x/2
V = r² π h
πx^3=(x/2)^2πh
πx^3=(x^2/4)πh
Divide both sides by π
x^3=(x^2/4)h
Make h the subject of the formula
h=x^3÷x^2/4
=x^3×4 / x^2
=4x^3 / x^2
=4*x*x*x / x*x
h=4x
Area of the base:
B = r² π
Recall, r=x/2
B=(x/2)^2 * π
=(x^2/4)π
=πx^2/4
=1/4(πx^2)
The area of the cylinder’s base is One-fourthπx2 square units.
Answer:
B & E
Step-by-step explanation:
Edge 2020
Graph this compound inequality: 2.5 < x < 4.5
-5 4
-3
-2
-1 0
+ ++ +
1 2 3 4 5
o
Drag a point to the number line.
Answer:
Please find the attached the required inequality graph
Step-by-step explanation:
Given that inequality is 2.5 ≤ x ≤ 4.5, we have;
The region in the given inequality is the region between 2.5 and 4.5 inclusive
Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;
A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.
Which equation represents a line that is perpendicular to line FG? A. y=-1/2x+5 B. y=1/2x+2 C. y=-2x-3 D. y=2x-6
The equation of line which is perpendicular to the line FG is
y = -2x -3.
What is equation of line?
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
Formula for finding the equation of line from two points [tex](x_{1} ,y_{1} ) and (x_{2}, y_{2} )[/tex][tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]
What is the slope of two perpendicular lines?If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].
What is the slope intercept form of a line ?The slope intercept form of the line is given by y = mx + b
Where, m is the slope of a line.
According to the given question
We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.
Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]
⇒ The slope of the line which is parallel to line FG is -2
Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .
Hence, the equation of line which is perpendicular to the line FG is
y = -2x -3.
Learn more about the equation of a perpendicular line here:
https://brainly.com/question/20712656
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Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true? This triangle exists because the sum of any two side lengths is greater than the length of the third side. This triangle exists because the sum of 4 and 12 is less than 17. This triangle does not exist because the sum of any two side lengths is greater than the length of the third side. This triangle does not exist because the sum of 4 and 12 is less than 17.
Answer:
The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."
Answer:
This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17
Step-by-step explanation:
The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.
Triangle
Sides - 3, 4, 5
3+4=7
Meaning the two smaller sides add up to because greater than 5.
Non-Triangle
Sides - 5, 6, 13
5+6=11
This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.
Gemma’s Triangle
Sides - 4, 12, 17
4+12=16
Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.
I believe this is pretty easy but it's: solve for x using common denominators 3/4(x+2)=x/(x+3) Answer choices below:
Answer:
x = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{x}{x+2}[/tex]
multiply numerator/ denominator of [tex]\frac{x}{x+2}[/tex] by 4, thus
[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{4x}{4(x+2)}[/tex]
Since the denominators are common , equate the numerators, that is
4x = 3 ( divide both sides by 4 )
x = [tex]\frac{3}{4}[/tex]
If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
Answer:
Step-by-step explanation:
REcall that f(x) is a polynomial whose one of its roots is -3+i. The fundamental algebra theorem states that any polynomial of degree n has n complex roots. In the real case, it can be also interpreted as any polynomial can be factored in factors of degree at most 2.
Consider that given a polynomial of degree 2 of the form [tex]ax^2+bx+c[/tex] the solutions are given by
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In this case, the fact that x is real or complex depends on the number [tex]b^2-4ac[/tex] which is called the discriminant. When this number is negative, we have that x is a complex root. Let say that [tex]b^4-4ac<0[/tex] and that [tex]\sqrt[]{b^4-4ac}=di[/tex], so the roots are given by
[tex] x_1 = \frac{-b + di}{2a}, x_2 = x_1 = \frac{-b - di}{2a}[/tex]
this means that, whenever we have a complex root, the other root is the complex conjugate. Recall that the complex conjugate of a complex number of the form a+bi is obtained by changing the sign of the imaginary part, that is a-bi.
So, in our case since -3+i is a root, then -3-i necessarily is another root.
If -3 + i is a root then -3 - i is too.
Therefore, the answer is -3 - i
Quadrilateral ABCD is a kite. A kite. Angle A is 90 degrees, angle B is unknown, angle C is 130 degrees, angle D is unknown. What is the measure of angle B? degrees
Answer:
70 degrees
Step-by-step explanation:
(360 - 90 - 130)/2=70
evaluate 1/2^-2x^-3y^5 for x=2 and y=-4
Answer:
[tex] - \frac{1}{32} [/tex]Step-by-step explanation:
Given,
x = 2
y = - 4
Now, let's solve:
[tex] \frac{1}{ {2}^{ - 2} \: {x}^{ - 3} \: {y}^{5} } [/tex]
plug the values
[tex] \frac{1}{ {2}^{ - 2} \: {(2)}^{ - 3} \: {( - 4)}^{5} } [/tex]
A negative base raised to an odd power equals a negative
[tex] \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {( - 4}^{5}) } [/tex]
Determine the sign of the fraction
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {4}^{5} } [/tex]
Write the expression in exponential form with a base of 2
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {2}^{10} } [/tex]
Calculate the product
[tex] - \frac{1}{ {2}^{5} } [/tex]
Evaluate the power
[tex] - \frac{1}{32} [/tex]
Hope this helps...
Best regards!!
3. In the diagram, PRST and PQWV are rectangles. Q, V
and U are midpoints of PR, PU and PT respectively.
Find the area of the shaded region.
======================================================
Work Shown:
A = area of trapezoid RSTU
A = height*(base1+base2)/2
A = ST*(UT+RS)/2
A = 14*(5+10)/2
A = 105 square cm
-----------------------
B = area of rectangle PQWV
B = length*width
B = WV*PV
B = 7*2.5
B = 17.5 square cm
If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.
-----------------------
C = total shaded area
C = A + B
C = 105 + 17.5
C = 122.5
You have a standard number cube. What is the probability of rolling a number less than 3, and then rolling a prime number? A. 1/3 B. 1/2 C. 1/36 D. 1/6
Hey Mate !
Your Answer is given in the snip below !!
Please do mark me as brainliest !!!
(ANSWER= (D) [tex]\frac{1}{6}[/tex] )
Explanation
Answer:
You have a standard number cube.
What is the probability of rolling a number less than 3, and then rolling a prime number?
D. 1/6
What is the difference? StartFraction 2 x + 5 Over x squared minus 3 x EndFraction minus StartFraction 3 x + 5 Over x cubed minus 9 x EndFraction minus StartFraction x + 1 Over x squared minus 9 EndFraction StartFraction (x + 5) (x + 2) Over x cubed minus 9 x EndFraction StartFraction (x + 5) (x + 4) Over x cubed minus 9 x EndFraction StartFraction negative 2 x + 11 Over x cubed minus 12 x minus 9 EndFraction StartFraction 3 (x + 2) Over x squared minus 3 x EndFraction
Answer:
[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]First option is the correct option.
Step-by-step explanation:
[tex] \frac{2x + 5}{ {x}^{2} - 3x } - \frac{3x + 5}{ {x}^{3} - 9x } - \frac{x + 1}{ {x}^{2} - 9 } [/tex]
Factor out X from the expression
[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x( {x}^{2} - 9)} - \frac{x + 1}{ {x}^{2} - 9} [/tex]
Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression
[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x(x - 3)(x + 3) } - \frac{x + 1}{(x - 3)(x + 3)} [/tex]
Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )
[tex] \frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]
Multiply the parentheses
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)} [/tex]
When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]
Distribute -x through the parentheses
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x }{x(x - 3)(x + 3)} [/tex]
Using [tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex] , simplify the product
[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x}{x( {x}^{2} - 9)} [/tex]
Collect like terms
[tex] \frac{ {x}^{2} + 7x + 15 - 5}{x( {x}^{2} - 9)} [/tex]
Subtract the numbers
[tex] \frac{ {x}^{2} + 7x + 10}{ x({x}^{2} - 9)} [/tex]
Distribute x through the parentheses
[tex] \frac{ {x}^{2} + 7x + 10}{ {x}^{3} - 9x} [/tex]
Write 7x as a sum
[tex] \frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x } [/tex]
Factor out X from the expression
[tex] \frac{x(x + 5) + 2x + 10}{ {x}^{3} - 9x} [/tex]
Factor out 2 from the expression
[tex] \frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x } [/tex]
Factor out x + 5 from the expression
[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]
Hope this helps...
Best regards!!
The difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]
The expression is given as:
[tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex]
Factorize the denominators
[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x^2 - 9)} - \frac{x + 1}{x^2 - 9}[/tex]
Apply the difference of two squares to the denominators
[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x - 3)(x + 3)} - \frac{x + 1}{(x - 3)(x + 3)}[/tex]
Take LCM
[tex]\frac{(2x + 5)(x + 3) - 3x - 5 -x(x + 1) }{x(x - 3)(x + 3)}[/tex]
Expand the numerator
[tex]\frac{2x^2 +6x + 5x + 15 - 3x - 5 -x^2 - x }{x(x - 3)(x + 3)}[/tex]
Collect like terms
[tex]\frac{2x^2 -x^2 - x +6x + 5x - 3x+ 15 - 5 }{x(x - 3)(x + 3)}[/tex]
Simplify
[tex]\frac{x^2+7x+ 10 }{x(x - 3)(x + 3)}[/tex]
Factorize the numerator
[tex]\frac{(x+5)(x+ 2) }{x(x - 3)(x + 3)}[/tex]
Expand the denominator
[tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]
Hence, the difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
Which of the following options could represent a possible set of interior angles of a triangle? 100°, 130°, and 130° 30°, 70°, and 80° 25°, 3°, and 35° 45°, 105°, and 120°
Answer:
2) 30, 70, 80
Step-by-step explanation:
Well there has to be 3 angles that all add up to 180°.
1)
100+130+130
=360
2)
30+70+80
= 180
3)
25+3+35
=63
4)
45 + 105 + 120
=150
150+120
270
HELP PLEASEEEEEEEEEEEEE! Soup can be packaged in two different containers: a box and a cylinder. The dimensions of the box are 7.5 cm by 4.7 cm by 14.5 cm. The cylinder has a radius of 3.3 cm and a height of 10 cm. Determine which container uses less material to make and find out which container holds more soup. Create a design for each container shape. Be sure to name your soup!
Answer:
Step-by-step explanation:
Use the following formulas:
surface area of rectangular prism: A = 2wl + 2lh + 2hw
volume of rectangular prism: lwh
surface area of cylinder: A=2πrh+2πr^2
volume of cylinder: V=πr^2h
using these formulas, the surface area of the box is 424.3
the volume of the box is about 511.3
the surface area of the cylinder is about 275.77
the volume is 342.12
knowing this, the cylinder uses less material but the box holds more soup.
Can someone help me ASAP???!!
Answer:
25x ²−49y ²
Step-by-step explanation:
We need to find product of (5x+7)(5x−7y)
By using identity (a+b)(a−b)=a −b ²
We have a=5x,b=7y
Thus (5x+7y)(5x−7y)=(5x) ²−(7y)
let me know if it was helpful
25x² - 49y²
Step-by-step explanation:
To Find:
The product of (5x - 7y)(5 x + 7)
How to solve:
Just need to use the formula of a² - b² = (a+b)(a-b)
let's assume a = 5x and b = 7x
Solution:
(5x - 7y)(5 x + 7) = (5x)² - (7y)²
= 25x² - 49y²
Hence required answer is 25x² - 49y².
heLp would be appreciated for the image below :))
Answer:
A
Step-by-step explanation:
The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles.
Using Pythagoras' identity in either of the 2 right triangles, then
([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²
[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides )
[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )
x² = 144 ( take the square root of both sides )
x = [tex]\sqrt{144}[/tex] = 12 → A
4. A number m is such that when it is divided by 30, 36, and 45 the remainder is always 7,
find the smallest possible value of m
Answer:
187
Step-by-step explanation:
A number m is such that when it is divided by 30, 36 and 45 the remainder is always 7.
We should first find the LCM of 30, 36 and 45
We get that the LCM of the three numbers is 280 (working attached).
So now;
[tex]\frac{180}{30}[/tex] = 6
[tex]\frac{180}{36}[/tex] = 5
[tex]\frac{180}{45}[/tex] = 4
But we need a number that leaves a remainder of 7 so we add 7 to 180 to get; 180 + 7 = 187.
A survey asks "would you like to see more or less government spending on natural disasters?" Of the 1496 respondents, 723 responded "more" or "much more". The population of interest consists of
A) the proportion of American adults who would respond "more" or "much more"
B) the 723 respondents who responded "more" or "much more"
C) the 1496 respondents
D) all American adults
E) the proportion of respondents who responded "more" or "much more"
Answer:
D) all American adults
Step-by-step explanation:
The 1496 respondents are the sample of the survey that was used to represent the population of interest, which is the total population from which the sample was drawn and the population from which the researchers want to find conclusions.
Looking at the alternatives, the only one that fits the description is alternative D) all American adults .
A television set costs $350 cash. When bought on hire purchse, a deposit of $35 is required, followed by 12 monthly payments of $30. How much is saved by paying cash?
Answer:
$45
Step-by-step explanation:
find the hire purchase price: 12 months x $30 = $360 + $35 deposit = $395
difference: 395 - 350 = $45
In a school, half of the 300 students saw Zootopia, 180 students saw Finding Dory, and 45 students did not see either movie. How many students saw both movies?
Answer:
150
Step-by-step explanation:
Answer:
150 = half of 300
± 180
230
soooo 230 students
Step-by-step explanation:
Audrey charges a flat fee of $4 for each delivery plus a certain amount,in dollars per mile, for each mile she drives. For a distance of 30 miles, Curtis and Audrey charge the same amount
Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y minutes, what portion of the leaves do they rake in one minute if they work together?
Answer:
in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves working together.
Step-by-step explanation:
If Maya rakes the leaves in x minutes, then, in one minute she rakes [tex]\frac{1}{x}[/tex] leaves.
In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes [tex]\frac{1}{y}[/tex] leaves.
Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: [tex]\frac{1}{x}+ \frac{1}{y}[/tex]
Now, to simplify this expression:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}[/tex]
Thus, in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves.
The text classifies information systems as either operations or management support information systems. Which one of the following would not be classified as an operations support system?
A. Transaction processing systems
B. Process control systems
C. Enterprise collaboration systems
D. Decision support systems
Answer:
D. Decision support systems
Step-by-step explanation:
Operation Support System, sometimes referred to a group of computer programs that is used by the communications service provider for carrying out various operations or functions, such as monitoring, controlling, analyzing and managing a telephone or computer network.
It is often used by professionals such as Network planners, service designers, operations, architects and engineering teams in the service provider.
There are however, types of Operation Support System which are being used for different and specific purpose. They are classified into the following categories:
1. Transaction Processing Systems
2. Process control system
3. Enterprise collaboration system
4. Enterprise Resource
Hence, from the question above, the DECISION SUPPORT SYSTEM is not classified as Operation Support System.
how many digits are in the decimal expansion of 2^34
Answer:
2^34 = 17179869184
I hope this helps :)
Solve for x. 3 1 2 140
Answer:
Hey there!
Angle QRS is 70, and since it is located on the circle, we have a useful formula. If 141x-1 is called y, then 70 is half of that.
Thus, we have 141x-1=140
141x=141
x=1
Hope this helps :)
verify the trigonometric identity: tan(2π - x) = tan(-x)
Answer:
See Below
Step-by-step explanation:
Taking Right Hand Side to verify the identity:
tan ( 2π - x)
Resolving Parenthesis
tan 2π + tan (-x)
We know that tan 2π = 0
0 + tan (-x)
=> tan(-x) = Left Hand Side
Hence Proved
Answer:
[tex]\boxed{ \sf {view \: explanation}}[/tex]
Step-by-step explanation:
[tex]\Rightarrow \sf tan ( 2\pi - x)=tan(-x)[/tex]
[tex]\sf Apply \ distributive \ law.[/tex]
[tex]\Rightarrow \sf tan (2\pi) + tan (-x) =tan(-x)[/tex]
[tex]\sf Apply : tan(2\pi) =0[/tex]
[tex]\Rightarrow \sf 0 + tan (-x) =tan(-x)[/tex]
[tex]\Rightarrow \sf tan (-x) =tan(-x)[/tex]
[tex]\sf Hence \ verified.[/tex]
please Evaluate 27 times ( 1/3) to the 3 power. A). 1 B). 3 C). 9 D). 27
Answer:
you want to follow PEMDAS so you would multiply 27 by 1/3 to get 81.003, which you would round to 81, then you would multiply 8 to the third power and you would get 512.
Step-by-step explanation:
27(1/3)^3
81^3
512
A 10-sided die numbered 1 to 10 is rolled once. Find these probabilities.
A. Pr(8)
B. Pr(odd)
C. Pr(even)
D. Pr(less than 6)
E. Pr(prime) (remember that 1 is not prime)
F. Pr(3 or 8)
G. Pr(8, 9 or 10)
H. Pr(greater than 9)
^please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?
^and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you
Answer:
A. Pr(8) = 1/10
B. Pr(odd) = 1/2
C. Pr(even) = 1/2
D. Pr(less than 6) = 1/2
E. Pr(prime) = 2/5
F. Pr(3 or 8) = 1 / 5
G. Pr(8, 9 or 10) = 3/10
H. Pr(greater than 9) = P(10) = 1/10
Step-by-step explanation:
We assume a FAIR 10-faced die, meaning there is an equal probability of throwing any one of the ten numbers.
With 10 possible outcomes each with equal probability, the probability of throwing any number is 1/10.
(It is preferable to work with fractions in probability because fractions are exact numbers, while decimals can often be rounded, or truncated).
A. Pr(8) means probability of throwing an 8, therefore Pr(8) = 1/10
B. Pr(odd) there are 5 odd number from 1 to 10, so Pr(odd) = 5/10 = 1/2
C. Pr(even) there are 5 even number from 1 to 10, so Pr(even) = 5/10 = 1/2
D. Pr(less than 6) there are 5 numbers less than 6 (between1 to 10),
so Pr(less than 6) = 5/10 = 1/2
E. Pr(prime) (remember that 1 is not prime)
A prime number is an integer not divisible by any number except one and itself.
Between 1 to 10, the four prime numbers are 2,3,5,7
therefore Pr(prime) = 4/10 = 2/5
F. Pr(3 or 8)
(3 or 8) make 2 successful outcomes out of 10, so Pr(3 or 8) = 2/10 = 1 / 5
G. Pr(8, 9 or 10)
similarly, (8,9 or 10) make three successful possible outcomes out of 10, so
P(8,9 or 10) = 3/10
H. Pr(greater than 9)
there is only one successful outcome, namely "10" out of 10 possible outcomes. So
P(greater than 9) = P(10) = 1/10
1. please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?
A die is singular for dice, which can take up any number of faces. With a 10-faced solid, we can make a 10-faced die numbered 1 to 10.
2. and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you
See solutions above.
Answer:
Remember that standard probabilities are defined as the ratio between the number of favorable cases, and the total number of possible events.
In this case, we have a 10-sided die, which means its faces are numbered from 1 to 10, which gives us 10 total number of possible events. In other words, the denominator of the ratio is going to be 10.
Now we're able to find each probability.
(A) Probability of getting an 8:[tex]P_{8} =\frac{1}{10}=0.10[/tex]
The numerator is 1 because there's only one number 8 in the die, that means the number of favorable cases is 1, and, as we said before, the total number of possible events is 10.
(B) Probability of getting an odd number:[tex]P_{odd} =\frac{5}{10}=0.5[/tex]
The numerator is 5 because there are 5 odd numbers from 1 to 10. In other words, there are 5 favorable cases to this probability.
(C) Probability of getting an even number:[tex]P_{even}=\frac{5}{10}=0.5[/tex]
There are 5 even numbers from 1 to 10, that's why we had the same probability.
(D) Probability of getting a number less than 6:We know that there are only 5 numbers less than 6 for this die.
[tex]P_{<6}=\frac{5}{10}=0.5[/tex]
(E) Probability of getting a prime number:A prime number is such that it can be divided only by itself and the unit. So, there are four prime numbers from 1 to 10, which are 2, 3, 5, 7.
[tex]P_{prime}=\frac{4}{10}=0.4[/tex]
(F) Probability of getting 3 or 8:When we are going to find the probability of an event "or" another, we must sum those favorable cases.
[tex]P_{3 \ or \ 8} =\frac{1+1}{10}=\frac{2}{10}=0.2[/tex]
(G) Probability of getting 8, 9, or 10:In this case, we need to some all three favorable cases. The die has only one 8, one 9 and one 10. So, the probability is
[tex]P_{8,9,10}=\frac{1+1+1}{10}=\frac{3}{10} =0.3[/tex]
(H) Probability of getting a number greater than 9:We know that there's only one number greater than 10 on such die.
[tex]P_{>10}=\frac{1}{10}=0.1[/tex]
Lastly, "die" refers to this special 10-sided dice. In other problems, you can find "a die" with more faces even. But, in general, "die" refers to a dice.
A school has 6 3/4 kg of detergent in stock. During ' Use Your Hands ' campaign, each class will be given 3/8 kg of detergent. There are 28 classes in the school.
(a) What fraction of the school will be supplied with the detergent in stock?
(b) How much detergent will be required altogether for the whole school?
(c) How much more detergent does the school need to order?
(d) If the school gives out the detergent in stock to the 15 lower secondary classes first,
(i) how much detergent will be given out;
(ii) how much detergent in stock will be left?
Answer:
Step-by-step explanation:
Total stock available = 6 x 3/4 = 18/4
Detergent given to each class=3/8
Total number of classes in the school = 28
Total detergent required by the school=3/8*28
=42/4
a. Fraction if the school who will get the detergent=18/42
b. Total required detergent for the whole school= 42/4
c. School needs to order = 42/4 - 18/4
= 24/4
= 6
d. i. Detergent given out to 15 classes = 15 x 3/8
= 45/8
ii. There will be no detergent left in stock
Large samples of women and men are obtained, and the hemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2:
negative 1.76 g divided by dL less than mu 1 minus mu 2 less than minus 1.62 g divided by dL
−1.76 g/dL<μ1−μ2<−1.62 g/dL. Complete parts (a) through (c) below.
a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?
Answer:
a) Because the confidence interval does not include 0 it appears that there
is a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.
b)There is 95% confidence that the interval from −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2
c) 1.62 < μ1−μ2< 1.76
Step-by-step explanation:
a) What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?
Given:
95% confidence interval for the difference between the two population means:
−1.76g/dL< μ1−μ2 < −1.62g/dL
population 1 = measures from women
population 2 = measures from men
Solution:
a)
The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in men is not equal and that the women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in men.
b)
There is 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.
c)
If we interchange men and women then
confidence interval range sign will become positive.μ1 becomes the population mean of the hemoglobin level in menμ2 becomes the population mean of the hemoglobin level in women So confidence interval becomes:1.62 g/dL<μ1−μ2<1.76 g/dL.
There is a significant difference between the mean level of hemoglobin in women and in men.
How to interpret the confidence intervalThe confidence interval of the mean is given as:
[tex]-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL[/tex]
The above confidence interval shows that the confidence interval is exclusive of 0.
This means that 0 is not part of the confidence interval
Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.
Read more about confidence intervals at:
https://brainly.com/question/17097944
A shopkeeper sold an article at 20 % discount and made a loss of Rs 90. If he had
sold it at 5 % discount, he would have gained Rs 90. Find the cost price and the
marked price of the article.
Answer:
The cost price of the article is Rs 1050
The marked price of the article Rs 1200
Step-by-step explanation:
The given discount on the article = 20%
The amount loss = Rs 90
With a discount of 5% the amount gained = Rs 90
Let the cost price of the article = X
Let the marked price of the article = Y
Therefore, we have;
(1 - 0.2) × Y = X - Rs 90
(1 - 0.5) × Y = X + Rs 90
Which gives;
0.8·Y = X - Rs 90 .......................(1)
0.95·Y = X + Rs 90.....................(2)
Subtracting equation (1) from equation (2), we have;
0.95·Y-0.8·Y = X + Rs 90 - (X - Rs 90) = X - X + Rs 90 + Rs 90 = Rs 180
0.15·Y = Rs 180
Y = Rs 180/0.15 = Rs 1200
Therefor, the marked price of the article = Rs 1200
From;
0.8·Y = X - Rs 90, we have;
0.8×Rs 1200 = X - Rs 90
X = 0.8× 1200 + 90 = Rs 1050
Therefore, the cost price of the article = Rs 1050.
Solve this linear equation for x: 7 + 4 (5/4x - 1) = 18
Answer:
x=3
Step-by-step explanation:
7+4(5/4x-1)=18
7+5x-4=18
3+5x=18
5x=15
x=3
Answer:
x = 3
Step-by-step explanation:
18 = 7 + 4([tex]\frac{5}{4}[/tex]x - 1)
18 = 7 + 5x - 4
18 = 3 + 5x
15 = 5x
x = 3