A number is chosen at random from the first 100 positive integers. Find the probability that the number is a multiple of 7.
[tex] |\Omega|=100\\
|A|=14\\\\
P(A)=\dfrac{14}{100}=\dfrac{7}{50}=14\% [/tex]
Divide 420 in the ratio of 2:1
What is the first step to solve the following equation? x^2-2x=0
Write the partial fraction decomposition of the given rational expression. startfraction 5 x plus 2 over x superscript 4 baseline minus 4 x squared endfraction
Answer:
Step-by-step explanation:
Given is a rational algebraic expression in x as
[tex]\frac{5x+2}{x^4-4x^2}[/tex]
First let us factorize the denominator.
[tex]x^2(x^2-4)\\=x^2(x+2)(x-2)[/tex]
Let the given term be
[tex]\frac{A}{x} +\frac{B}{x^2} +\frac{C}{x-2} +\frac{c}{x+2} \\\\=\frac{Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)}{x^4-4x^2}[/tex]
Equate the numerator to get
[tex]Ax(x^2-4)+B(x^2-4)+cx^2(x+2)+Dx^2(x-2)[/tex]=[tex]5x+2[/tex]
Substitute x =-2
[tex]4D (-4) = -8\\D=\frac{1}{2}[/tex]
Now substitute x =2
We get
[tex]16C=12\\C=\frac{3}{4}[/tex]
Put x=0
[tex]-4B=2\\B=\frac{-1}{2}[/tex]
Next equate X cube terms to 0 on right side
[tex]A+C+D=0\\A=\frac{-5}{4}[/tex]
Hence partial fraction is
[tex]\frac{-1}{2x^2} -\frac{5}{4x} +\frac{1}{2(x+2)} +\frac{3}{4(x-2)}[/tex]
To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
Explanation:To decompose the rational expression startfraction 5x + 2 over x4 - 4x2 endfraction into partial fractions, we need to factor the denominator. The denominator can be factored as x2(x2 - 4) which gives us two distinct linear factors x and x + 2, and a repeated linear factor x - 2. Therefore, we can express the rational expression as follows: startfraction A over x + B over x2 + C over (x - 2)2.
To find the values of A, B, and C, we can use the method of equating coefficients. By multiplying both sides of the equation by the common denominator, we can eliminate the fractions and solve for the unknowns. Finally, we substitute the values of A, B, and C back into the partial fraction decomposition expression.
Therefore, the partial fraction decomposition of the given rational expression is startfraction A over x + B over x2 + C over (x - 2)2, where A, B, and C are the determined coefficients.
The diagonal of the floor of a square room is 6 meters.what is the length of a side of the room? round to the nearest tenth.
The equation sin(40o) =b/20 can be used to determine the length of line segment AC. What is the length of AC? Round to the nearest tenth.
Convert \dfrac{23}{50} 50 23 start fraction, 23, divided by, 50, end fraction to a percent.
let f(x)=1-x*2 and g(x)=1-x find (fg)(x)
Manuel bought a balloon (that is a perfect sphere) with a radius of 2 \text{ cm}2 cm2, space, c, m. He wanted his balloon to be bigger, so he blew 222 big breaths of air into the balloon. Each big breath increased the balloon's radius by 1 \text{ cm}1 cm1, space, c, m. What is the ratio of the current volume of the balloon to the original volume of the balloon?
Answer:
8 times
Step-by-step explanation:
I found the volume of the sphere. Then increased it how many times he blew. That was the ratio.
Also, Khan :)
The ratio of the current volume of the balloon to the original volume of the balloon is 8.
What is the volume of a sphere?The volume of a sphere is given by (4\3)πr³ where r is the radius of the sphere.
The initial volume of the balloon = [tex]\frac{4}{3} \pi 2^{3}[/tex]
The initial volume of the balloon =[tex]\frac{32}{3} \pi[/tex]
Radius of the balloon after first breath = 2+1 =3cm
The Radius of the balloon after the second breath = 2+2=4cm
So, the new volume of the balloon = [tex]\frac{4}{3} \pi 4^{3}[/tex]
The new volume of the balloon = [tex]\frac{256}{3} \pi[/tex]
The ratio of new volume to the initial volume = [tex]\frac{\frac{256}{3 } \pi }{\frac{32}{3}\pi }[/tex]
The ratio of new volume to the initial volume =8
Hence, the ratio of the current volume of the balloon to the original volume of the balloon is 8.
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BRAINLIEST!!PLEASE HELP MEE
The Nichols family consists of 8 children and 2 adults. The family minivan can safely transport a total of 7 family members, including an adult driver.
Which number line illustrates the capacity of the Nichols minivan as an inequality?
Area of figure? Geometry help???
Rafael has ridden 14 miles of a bike course. The course is 40 miles long. What percentage of the course has Rafael ridden so far
Which transformation will be equivalent to rotating a figure 270° counterclockwise? A) reflecting over the x-axis and the y-axis
B) translating left 3 units and down 5 units
C) Reflecting over the y-axis and then reflecting over the line y = x
D) Reflecting over the y-axis and then reflecting over the line y = -x
Answer:
D) Reflecting over the y-axis and then reflecting over the line y = -x
Step-by-step explanation:
When the figure is rotate clock-wise or anti clock-wise then the coordinate of figure is get changed and this new coordinate can be find on the basis of degree of rotation.
The rules of rotation is:
When rotation = 90° clock-wise, the vertices is get changed to (-y, x) from (x, y).When rotation = 180° clock-wise, the vertices is get changed to (-x, -y) from (x, y).When rotation = 270° clock-wise, the vertices is get changed to (y, -x) from (x, y).Thus, Option (D) is correct option.
The velocity of sound in air is given by the equation
please only answer if you're gonna show work
There are five apples and you take three away. how many apples do you have?
Answer: 2 apples
Step-by-step explanation:
Logic
What is the volume of the coffee in a can if the can has a radius of 4 inches and a height of 9 inches? (use 3.14 for π.) 113.04 in.3 226.08 in.3 339.12 in.3 452.16 in.3?
The volume of the coffee in the can if the can has a radius of 4 inches and height of 9 inches is 452.16 inches³.
The can must be in the shape of a cylinder.
The formula to find the volume of the cylinder is,
Volume of cylinder = π r² h
Here r is the radius of the base of the cylinder and h is the height of the cylinder.
Given, Radius, r = 4 inches and Height, h = 9 inches
Volume of the coffee = π (4)² (9)
= 144 π
= 144 × 3.14
= 452.16 inches³
Thus, the volume of the coffee in the can is 452.16 inches³.
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The three undefined terms in geometry are point , line, and plane. True or false
A sphere has a radius of 12 meters. What is the approximate volume of the sphere? Use 3.14 for π . Round your answer to the nearest whole number.
Jack has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have?
A plane intersects a double-napped cone only at the cone's vertex.
Which terms describe the degenerate conic section that is formed?
Select each correct answer.
degenerate parabola
degenerate ellipse
line
degenerate hyperbola
point
pair of intersecting lines
In addition to ...
degenerate ellipse
point
it is also a degenerate circle (special case of ellipse).
___
The vertex of a double-napped cone is a point. So, the intersection of only the vertex with a plane is a point, not a degenerate parabola (a line) or degenerate hyperbola (pair of crossing lines).
Essentially, the plane must intersect at an angle greater than the angle of the edge of the cone with the axis of the cone. If the plane is not at the vertex, such an intersection angle will result in a circle or ellipse. As the plane gets closer to the vertex, the ellipse gets smaller, degenerating to a single point.
Answer:
The answer is:
Degenerate ellipse.
Point.
Step-by-step explanation:
We know that when a plane intersects a double-napped cone only at the cone's vertex then the cross-section that is obtained is the point.
Also we know that a point is also considered as a circle with radius 0.
and a circle is also a kind of a ellipse when the length of both the transverse and conjugate axis are equal.
Hence, the term that best describe the degenerate conic section that is formed is:
degenerate ellipse
point
which function is a quadratic function?
Answer:
y = -2x² - x is quadratic function.
Step-by-step explanation:
Given : Function .
To find : Which function is a quadratic function.
Solution : We have given that functions .
Quadratic function: A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers.
We can see from given options
y = -2x² - x in form of f(x) = ax² + bx + c,
Where, a = -2 , b = -1 c = 0
Therefore, y = -2x² - x is quadratic function.
A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours.
Answer:
At 10 PM both candles will be same height.
Step-by-step explanation:
Let h represent the number of hours.
We have twelve inch candle and an 18 inch candle are lit at 6pm and the 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns 2 inch every hour.
Height 18 inch candle after h hours, = 18 - 2h
Height 12 inch candle after h hours, = 12 - 0.5h
At same height we have
18 - 2h = 12 - 0.5h
1.5 h = 18 - 12
h = 4 hours.
Time = 6 PM + 4 hours = 10 PM
At 10 PM both candles will be same height.
Answer:
At 10 PM, both the candles will be of same height.
Step-by-step explanation:
Two candles are lit at 6 PM.
The length of candles is 12 inch and 18 inch.
The rate of burning of 12 inch candle is 0.5 inch per hour.
The rate of burning of 18 inch candle is 2 inch per hour.
Let [tex]h[/tex] represents the number of hours of burning.
In [tex]h[/tex] hours, the remaining length of the 12 inch candle will be,
[tex]l_1=12-0.5\times h[/tex]
In [tex]h[/tex] hours, the remaining length of the 18 inch candle will be,
[tex]l_2=18-2\times h[/tex]
Now, it is required to find the time at which the length of both the candles will be same.
So, the time [tex]h[/tex] in hours will be,
[tex]l_1=l_2\\12-0.5h=18-2h\\1.5h=6\\h=4\rm hour[/tex]
So, after 4 hours, both the candles will be of same length.
Therefore, the time will be [tex]6+4=10[/tex] PM. At 10 PM, both the candles will be of same height.
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If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square
Answer: Yes, the 3 foot 3 foot square opening in your ceiling is big enough to insert a 4x8 piece of plywood.
In a 3x3 foot square, we can form two right triangles with same diagonal side or hypotenuse. .
Using the Pythagorean theorem/formula, we can find the length of the hypotenuse or the longest side of the triangle ( c) given the two sides a and b
Substitute values a=3 and b=3 to formula
a^2^+b^2^=C^2^=
3^2^+3^2^=C^2^=
9+9= C^2^
C= square root of 18
C=4.24
A 4x8 piece of plywood can be inserted in a 4.24 opening diagonally.
If BC is tangent to circle O and OB is a radius, what kind of triangle is OBC?
C) the function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit. part
a.determine the vertex. what does this calculation mean in the context of the problem? part
b.determine the x-intercepts. what do these values mean in the context of the problem?
Danielle built a ramp with a stopping block at the bottom for her scout troop’s pinewood derby. She wants to paint the top and sides of the ramp. Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Did Danielle calculate the area correctly? If not, what was her mistake?
A. Yes, Danielle calculated the area correctly.
B. No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
C. No, Danielle needs to add 1 triangle to the ramp and remove 1 rectangle from the block.
D. No, Danielle needs to remove 1 triangle from the ramp and add 1 rectangle to the block.
Answer:
Actually its b).
Step-by-step explanation:
She only wants to paint the top and sides of the ramp therefore you will have to take off the bottom parts of the ramps aka b).
No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. The space inside the perimeter or limit of a closed shape is referred to as the "area".
Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Danielle calculated some extra Areas.
As, per the discussion Danielle do not need to calculate the part ramp and block that coincides.
Thus, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
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ANY HELP WOULD BE REALLY APPRECIATED
Suppose Brett and Andre each throw a baseball into the air. The height of Brett's baseball is given by h(t) = −16t^2 + 79t + 6, where h is in feet and t is in seconds. The height of Andre's baseball is given by the graph below (it's the attached image). Brett claims that his baseball went higher than Andre's, and Andre says that his baseball went higher.
1. Who is right? Fill out the table below to justify your answer. Approximate
when necessary (table is second attached image).
1. Brett was right because her baseball reached a maximum height of 103.52 feet.
2. A table that justifies Brett's claim is shown below.
In Mathematics and Geometry, the maximum value of any function is a point on the graph where the function reaches its highest point. Additionally, the maximum value of Brett's quadratic function can be determined by finding the axis of symmetry;
Axis of symmetry, x = -b/2a
[tex]h(t) = -16t^2 + 79t + 6[/tex]
where:
a = -16, b = 79, and c = 6.
By substituting the values of a and b into the formula, we have;
Axis of symmetry, x = -79/2(-16)
Axis of symmetry, x = 79/32 = 2.46875.
Now, we can determine the maximum value (vertex) as follows;
[tex]h(t) = -16t^2 + 79t + 6\\\\h(2.46875) = -16(2.46875)^2 + 79(2.46875) + 6[/tex]
h(2.46875) = 103.52 feet.
Based on the graph, we can logically deduce that the maximum height attained by Andre's baseball was below 80 feet. Hence, Brett was right.
Lastly, we would complete the table as follows;
t Brett Andre
0 6 6
1 69 58
2 100 78
3 99 67
4 66 6
5 0
In conlusion, we can logically deduce that Brett was right because her baseball reach a maximum height of 103.52 feet, which was greater than Andre's.
NEED HELPPPPPPP!!!!!!! PLEASE!!!!!!!!
Which statement best describes the graph of -x3 - x2 + 4x + 4?
A. It starts down on the left and goes up on the right and intersects the axis at x = -2, 2, and 4.
B.It starts down on the left and goes up on the right and intersects the axis at x = -2, -1, and 2.
C.It starts up on the left and goes down on the right and intersects the x-axis at x = -2, -1, and 2.
D.It starts up on the left and goes down on the right and intersects the axis at x = -2, 2, and 4.
Firstly, simplife the function [tex] -x^3-x^2+4x+4 [/tex] in the following way:
[tex] -x^3-x^2+4x+4=-(x^3+x^2)+4(x+1)=-x^2(x+1)+4(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=-(x+2)(x+1)(x-2) [/tex].
There are three x-intercepts: x=-1; x=2 and x=-2 (therefore, options A and D are incorrect).
Since before brackets is sign "-", you should state that graph starts down on the left (you can check this substituting smaller negative number than -2 into function expression. For example, if x=-10, then f(-10)=-(-10+2)(-10+1)(-10-2)=-(-8)(-9)(-12)>0) and goes up on the right (you can check this substituting greater positive number than 2 into function expression. For example, if x=10, then f(-10)=-(10+2)(10+1)(10-2)=-(12)(11)(8)<0).
Answer: correct choice is B.
Pleaseee helpppp!!!!!!!!!!!!!!!!
A biology class of 24 students decides to measure the height of each student and then calculate the average height for the class. which of these is a possible source of error in this activity?
Answer: The possible source of error in this activity is " the accuracy of making and recording measurements"
The height of each and every student in the class has to be taken very accurately. Even if there was a single error in either making the calculation or even recording it, the average height will take a hit and will result in the entire exercise being a failure.
Hence, it’s very important to accurately measure the height and record and even have a second person do the same activity so that the numbers recorded are accurate.