Answers
The length of line segment AB by observation if the diagram in the task content is; 14.
What is the length of line segment AB?It follows from the task content that the line segment MN can be considered as parallel to line segment AB. This follows from the fact that the vertices of triangle MNO are midpoints of the line segments of triangle ABC.
Consequently, it can be concluded that line segment AB is twice the length of line segment MN and hence, BC = 2 × 7 = 14.
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Related Questions
pls help with Trigonometric
Answers
The value of the given trigonometry function is 2√15/15
Half anglesHalf angles are trigonometric identities used to express sine, cosine and tangent of half angles.
For instance the value of cos theta is expressed as shown below;
cosФ = cos(Ф/2+Ф/2)
cosФ = cos²Ф/2-sin²Ф/2
cosФ = cos²Ф/2-(1-cos²Ф/2)
cosФ = 1 - 2cos²Ф/2
Given the following parameters
cosФ = -7/15
Substitute
cosФ = 1 - 2cos²Ф/2
-7/15 = 1 - 2cos²Ф/2
-2cos²Ф/2 = -7/15 - 1
-2cos²Ф/2 = -8/15
cos²Ф/2 = 4/15
cosФ/2 = 2/√15
Rationalize
2/√15 * √15/√15
2√15/15
Hence the value of the given trigonometry function is 2√15/15
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What is the slope of the line represented by the equation y- 6 = 2(x+3)?
Answers
And m is slope and b is the y-intercept -
In this equation y-6=2(x+3)
m is 2 because if u multiply 2 to (x+3) it will become 2x+6
since m is 2 and b is 6
The slope is 2
And the y-int. is 6
So the slope is 2.
Answer: 2
Step-by-step explanation:
remember y=mx^2+c
where m = gradient = slope
∴ expand and simplify y-5=2(x+3)
y-5=2x+6
y=2x+11
m=2 ∴ slope: 2
find the zeros of the following
please solve step by step
1. x³+x²-4x-4=0
2. 2x³-11x²+17x-6=0
Answers
Question 1
[tex]x^3 + x^2 - 4x-4=0\\\\x^2 (x+1)-4(x+1)=0\\\\(x^2 -4)(x+1)=0\\\\(x-2)(x+2)(x+1)=0\\\\x=-2, -1, 2[/tex]
Question 2
By inspection, we know that [tex]x=2[/tex] is a root.
[tex]\frac{2x^3 - 11x^2 + 17x-6}{x-2}=2x^2 - 7x+3[/tex].
So, we can factor the equation as
[tex](x-2)(2x^2 - 7x+3)=0\\\\(x-2)(x-3)(2x-1)=0\\\\x=\frac{1}{2}, 2, 3[/tex]
The cost to produce a product is modeled by the function f(x) = 5x2 − 70x 258, where x is the number of products produced. complete the square to determine the minimum cost of producing this product. 5(x − 7)2 13; the minimum cost to produce the product is $13. 5(x − 7)2 13; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $258.
Answers
The minimum cost to produce the product is $7.
What are functions?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.To determine the minimum cost:
We have to determine the minimum cost of producing this product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].
Dividing the above equation by 5, we get
[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]
Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.
Since the coefficient of 'x' is 14, and half of 14 is '7'.
So, adding and subtracting from the above equation.
[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]
Now, we have to determine the minimum cost to produce the product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
[tex]f'(x) = 10x-70[/tex]
Now, let f'(x)=0
[tex]10x-70=0\\10x=70[/tex]
Therefore, x=7
Now, consider which is greater than 0.
Therefore, x= 7 is the minimum cost.
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Answer: The minimum cost to produce the product is $13.
I apologize for the late answer, hope this helps in the future!
Step-by-step explanation:
To complete the square, we need to rewrite the given function in the form:
f(x) = a(x - h)^2 + k
where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.
We start by factoring out the coefficient of x^2:
f(x) = 5(x^2 - 14x + 51.6)
To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:
f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)
= 5((x - 7)^2 + 13)
Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:
5(x − 7)2 + 13
On a number line, the directed line segment from q to s has endpoints q at –14 and s at 2. point r partitions the directed line segment from q to s in a 3:5 ratio. which expression correctly uses the formula (startfraction m over m n endfraction) (x 2 minus x 1) x 1 to find the location of point r?
Answers
The coordinates of point r(-8,0).
What is midpoint formula in coordinate geometry?The coordinates of the point r(x,y) which divides the line segment joining the points p([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and q([tex]x_{2}[/tex],[tex]y_{2}[/tex]) internally in the ratio :[tex]m_{1}[/tex][tex]m_{2}[/tex] are
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
Given that,
Two end points on the line q(-14,0) and s(2,0). point r(x,y) is the partition of the line segment from q to s in a ratio 3:5
[tex]m_{1}[/tex] = 3 and [tex]m_{2}[/tex] = 5
By using the midpoint formula
[tex]\left(\frac{m_{1}x_{2}+ m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1}+m_{2} }\Rifgt)[/tex]
[tex]\left(\frac{3(2)+ 5(-14) }{3+5 } ,\frac{3(0)+ 5(0) }{3+5 }\Rifgt)[/tex]
[tex]\left(\frac{-64}{8 } ,\frac{0 }{8 }\Rifgt)[/tex]
[tex]\left(-8 ,0\Rifgt)[/tex]
Hence, The coordinates of point r(-8,0).
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what is the digit of 7 in 906point7
Answers
• 9 has a value of 900 and is in the hundreds place
• 0, despite being in the tens place, has a value of 0
• 6 has a value of 6 and is in the ones place
• 7 has a value of 0.7, 70%, or 7/10 because it is one place to the right of the decimal point and is therefore not a full number
The digit of 7 in 906.7 is 7/10. If you need additional help, let me know and I will gladly assist you.
The slope of the line shown in the graph is __ and the y-intercept of the line __
Answers
Answer:
slope
(0, 6) and (-9, 0)
0 - 6 / -9 - 0 = -6/-9 = 2/3
y intercept is when the line intercepts the y axis and x = 0
The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6
Answer:
slope is 2/3
y intercept is 6
Step-by-step explanation:
We can find the slope of the line by using two point
(-9,0) and (0,6)
The slope formula is
m = ( y2-y1)/(x2-x1)
= ( 6 - 0) /( 0 - -9)
= (6-0)/(0+9)
= 6/9
= 2/3
The y intercept is where it crosses the y axis ( the value where x is 0)
The y intercept is 6
The line y= mx + c is parrallel to the line y=2x + 8
The distance AB is 9 units
Find the value of m and the value of c.
Answers
Answer: 2 and -10 respectively
Step-by-step explanation:
m in the equation is 2 as it is parallel to a line with a slope of 2
Both point A and B are on the x-axis so both of them have a y value of 0
To find the x value of A, we have to substitute y = 0 into the equation
2x + 8 = 0
x = -4, so the coordinate for A is A(-4,0)
As AB is 9 units, we can figure out that B(5,0)
Substitute x = 5 and y = 0 into the equation y = 2x + c to find c
0 = 2(5) + c
c = -10
So m = 2 and c = -10
The black graph is the graph of y =f(x). Choose the equation for the red graph. A. y - 1 = f() B. y + 1 = f() C. = f(x - 1) D. f(x)
Answers
Answer: C
Step-by-step explanation:
The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.
The smallest bone on the body, the stirrup-shaped stapes found in the middle ear, has a typical length of less than 0.33 cm. how long in inches is the typical maximum length of the stapes?
Answers
Answer:
0.13 inches.
Step-by-step explanation:
1 inch = 2.54 cm
So 1 cm = 1/ 2.54 in
0.33 cm = 0.33/2.54 in
= 0.13 inches.
A girl get n cedis pocket money money each week. she saves her money for five weeks and buys a present for her mother which cost gh 7900 i. write an expression for the amount of the money left ii.what is the minimum amount she needs to save each week to be able to afford the gift
Answers
An expression for the amount of the money left = (5n-7900) cedis
The minimum amount she needs to save each week to be able to afford the gift: n = 7900/5.
What is a word problem?The term "word problem" refers to a type of math question where the answer is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real world."
What is the first step in solving word problem?Read the problem in its full to get a clear understanding of what you need to do in order to solve it before you start. Following reading it, you may choose which components of the issue need to be resolved the most and which ones are not.
According to the given data:She gets n cedis a week.
she will get n x 5 cedis for 5 wks =5n cedis.
She buys a present worth 7900.
An expression for the amount of the money left = (5n-7900) cedis.
The minimum amount she needs to save each week to be able to afford the gift.
5n-7900 = 0
n = 7900/5.
7900/5 = ____ per week
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Hazel is measuring two prisms whose bases are squares.
Given the volume V and the base's side length a of the first prism, Hazel uses the formula
h=V/a^2
to compute its height h to be 10 centimeters.
The base of the second prism has the same side length, but has 5 times the volume. What is its height?
Answers
The height of the second square base prism is 50 cm.
How to find volume of a square base prism?The volume of the first square base prism is represented as follows:
v = ha²
where
h = heighta = side length of the baseTherefore, the height of the prism is 10 cm.
v = 10a²
Hence, the volume of the initial prism is 5 times the volume. Therefore,
v = 5(10a²)
v = 50a²
Therefore,
50a² = ha²
divide both sides by a²
50a² / a² = ha² / a²
50 = h
h = 50 cm
Therefore, the height of the second square base prism is 50 cm.
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Robert bought a combination of 15 colored and normal pencils. Each pencil wad $0.60 and each colored pencil was $0.45. In total he paid $8.70. How many colored pencil and pencil did he buy?
Show equation
Answers
Answer:
Robert bought 13 colored pencils and 2 pencils
Step-by-step explanation:
13 x 0.60 = 7.8
2 x 0.45 = 0.9
7.8 + 0.9 = 8.70
13 colored pencils are $7.80
2 pencils are $0.9
15 total is $8.70
Five hats and three shirts cost $176. Three hats and five shirts cost $208. What is the cost of one hat?
The cost of one hat is __ dollars.
Answers
Let hats be x
Let shirts be y
We can set up a system of equations to figure out the cost of one hat.
5x+3y = 176 and 3x+5y = 208
Since we are finding the cost of the hats, we will need to isolate x from the equation. We can first get rid of y. One way we can do that is by multiplying the first equation with 5 and the second one with -3, effectively making y add up to 0 when we solve for x.
5(5x+3y = 176) --> 25x+15y = 880
-3(3x+5y = 208) --> -9x-15y = -624
We can now add the 2 equations together and solve for x.
25x+15y = 880
-9x-15y = -624
+>>>>>>>>>>>>>>>
16x = 256
x = 16
So the the cost of one hat is 16 dollars.
Answer:
$16
Step-by-step explanation:
Define the variables:
Let x = cost of one hatLet y = cost of one shirtCreate two equations using the defined variables and the given information.
Equation 1
Five hats and three shirts cost $176.
⇒ 5x + 3y = 176
Equation 2
Three hats and five shirts cost $208.
⇒ 3x + 5y = 208
Rewrite Equation 2 to make y the subject:
[tex]\implies \sf 3x+5y-3x=208-3x[/tex]
[tex]\implies \sf 5y=208-3x[/tex]
[tex]\implies \sf \dfrac{5y}{5}=\dfrac{208-3x}{5}[/tex]
[tex]\implies \sf y=\dfrac{208-3x}{5}[/tex]
Substitute the found expression for y into Equation 1 and solve for x:
[tex]\implies \sf 5x+3\left(\dfrac{208-3x}{5} \right)=176[/tex]
[tex]\implies \sf 5x+\dfrac{624-9x}{5}=176[/tex]
[tex]\implies \sf 5x+124.8-1.8x=176[/tex]
[tex]\implies \sf 3.2x+124.8=176[/tex]
[tex]\implies \sf 3.2x+124.8-124.8=176-124.8[/tex]
[tex]\implies \sf 3.2x=51.2[/tex]
[tex]\implies \sf \dfrac{3.2x}{3.2}=\dfrac{51.2}{3.2}[/tex]
[tex]\implies \sf x=16[/tex]
Therefore, the cost of one hat is 16 dollars.
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A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 3y 4z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ 4 (3y 4z = 1) ⋅ 4 (y z = 6) ⋅ −3 (3y 4z = 1) ⋅ 3
Answers
Option C is correct (y + z = 6) ⋅ −3
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.As per the statement -
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6 ....[1]
Equation Q: 3y + 4z = 1 ....[2]
Multiply the equation [1] by -3 to both sides we have;
-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)
Add equation [2] and [3] to eliminate the y-term;
z = -17
Therefore, the possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3
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The complete question is -
A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ 4
(3y + 4z = 1) ⋅ 4
(y + z = 6) ⋅ −3
(3y + 4z = 1) ⋅ 3
The Williard family was saving up for their summer vacation. Mrs. Williard had $475.88 in their savings account for the trip. Mr. Williard received a bonus at work for $609.00 that he is saving for the trip. If the trip will cost the Warren's a total of $1675.98, how much more money do they need for their vacation
Answers
Answer:
$591.10
Step-by-step explanation:
First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.
Solve the system of equations.
y equals x plus 8
y equals 3 x plus 2
Answers
The solution to the system of equations is x = 3 and y = 11
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y equals x plus 8
y equals 3 x plus 2
Rewrite properly as
y = x + 8
y = 3x + 2
Substitute y = x + 8 in y = 3x + 2
x + 8 = 3x + 2
Evaluate the like terms
2x = 6
Divide by 2
x = 3
Substitute x = 3 in y = x + 8
y = 3 + 8
Evaluate
y = 11
Hence, the solution to the system of equations is x = 3 and y = 11
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The solution to the system of equation is as follows:
x = 3
y = 11
How to solve the system of equation?y = x + 8
y = 3x + 2
Using substitution method,
3x + 2 = x + 8
subtract x from both sides
3x - x + 2 = x - x + 8
2x + 2 = 8
subtract 2 from both sides
2x + 2 - 2 = 8 - 2
2x = 6
divide both sides by 2
2x / 2 = 6 / 2
x = 3
y = 3 + 8 = 11
y = 11
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Find the least positive integer N so that the value of 2020 + N
is both
• a perfect cube, and
• a multiple of 56.
Answers
Answer:724
Step-by-step explanation: Let us go through trail and error method.
Question: Need to find N, so that 2020+ N should be a perfect cube, as well as a multiple of 56.
2744 is the first number we get after 2020 and it is a cube of 14. ___ equation -01
Let us divide, 2744 with 56.
i.e., 2744/56= 49. ___ equation -02
As per 1st and 2nd equation 2744 meets with the condition. And we can consider it as 2020+ N.
i.e., 2020+N= 2744
N= 2744-2020
Therefore; N= 724.
Answer:
724,
Step-by-step explanation:
14^3 = 2744 is the next perfect cube > 2020.
2744 / 56 = 49.
So that fits the requirements in the question.
So N = 2744 - 2020
= 724,
Create an equivalent system of equations using the sum of the system and the first equation. x 4y = 8 4x y = 2 x 4y = 8 5x y = 2 x 4y = 8 5x 5y = 2 x 4y = 8 4x 5y = 10 x 4y = 8 5x 5y = 10
Answers
An equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
What are equations?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal.[tex]3x+5=14[/tex], for example, is an equation in which [tex]3x+5[/tex] and [tex]14[/tex] are two expressions separated by a '=' sign.Given:
[tex]x+4y=8\\4x+y=2[/tex]
Add the above equations to get:
[tex]x+4y+4x+y=8+2\\x+4y+4x+y=10\\5x+5y=10[/tex]
Therefore, an equivalent system of equations using the sum of the system and the first equation is:
[tex]x+4y=8\\5x+5y=10[/tex]
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The correct question is given below:
Create an equivalent system of equations using the sum of the system and the first equation.
x + 4y = 8
4x + y = 2
x + 4y = 8
5x + y = 2
x + 4y = 8
5x + 5y = 2
x + 4y = 8
4x + 5y = 10
x + 4y = 8
5x + 5y = 10
Solve for n
-19=-8+n
Answers
Answer:
8-18=n
-10=n
therefore
n=-10
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{n = -11}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{-19 = -8 + n}[/tex]
Find: [tex]\textsf{Solve for n}[/tex]
Solution: In order to solve for n we need to add 8 to both sides which would cancel -8 on the right side and isolate n giving us the value of n.
Add 8 to both sides
[tex]\textsf{-19 + 8 = -8 + 8 + n}[/tex][tex]\textsf{-19 + 8 = n}[/tex][tex]\textsf{-11 = n}[/tex]Therefore, the final answer would be that n is equal to -11.
Part B The mass of an average grain of rock salt is about 40 times the mass of an average grain of table salt. If you multiply the mass of table salt in standard notation by 40, what value do you get?
Answers
Answer:
0.012
Step-by-step explanation:
We know the standard notation of table salt is 0.003, so we simply multiply 40 by this.
answer - 0.0003 X 40 = 0.012
What is the equation of this graph?
Answers
The equation of the parabola given in the graph is:
(x - 5)² = -8(y + 4).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
a(y - k) = (x - h)²
In which a = 4p is the leading coefficient.
In this problem, the vertex is at point (5,-4), hence h = 5, k = -4, and the equation is:
a(y + 4) = (x - 5)²
The focus is at y = -6, which means that p = -6 - (-4) = -2, hence the leading coefficient is:
a = 4p = 4(-2) = -8
Hence the equation is:
(x - 5)² = -8(y + 4).
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Membership to two different clubs are represented by the equations below. The x-value represents the number of months dues are paid. The y-value represents the total cost of dues over time. How many months will it take for the membership of both clubs to be the same?
y = 3x − 5
4x − 3y = 5
2 months
5 months
3 months
4 months
Answers
It would take 2 months for the membership of both clubs to be the same
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the total cost of dues over x months, hence given that:
y = 3x - 5 (1)
Also:
4x - 3y = 5
y = (4x - 5)/3 (2)
For the membership of both clubs to be the same:
3x - 5 = (4x - 5)/3
9x - 15 = 4x - 5
x = 2
It would take 2 months for the membership of both clubs to be the same
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[tex]4 {}^{x } + 6 {}^{x} = 9 {}^{x} [/tex]
please find x. and with explanation thanks
Answers
So, the value of x is 1.19
The question is an exponential equation
What is an exponential equation?An exponential equation is a mathematical expression between two quantities in which one variable is raised to a power of the other variable.
How to find x?
Since [tex]4^{x} + 6^{x} = 9^{x}[/tex],
Dividing through by 4ˣ, we have
[tex]\frac{4^{x} }{4^{x} } + \frac{6^{x} }{4^{x} } = \frac{9^{x} }{4^{x} } \\1 + (\frac{6}{4})^{x} } = (\frac{9}{4})^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3^{2} }{2^{2} })^{x} } \\1 + (\frac{3}{2})^{x} } = (\frac{3}{2})^{2x} }[/tex]
Let y = (3/2)ˣ
So,
1 + y = y²
y² - y - 1 = 0
Using the quadratic formula to find y,
[tex]y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
where a = 1 b = -1 and c = -1
Substituting the values of the variables into the equation, we have
[tex]y = \frac{-(-1) +/- \sqrt{(-1)^{2} - 4\times 1 \times (-1)} }{2\times 1}\\= \frac{1 +/- \sqrt{1 + 4} }{2}\\= \frac{1 +/- \sqrt{5} }{2}\\= \frac{1 - \sqrt{5} }{2} or \frac{1 + \sqrt{5} }{2}\\= \frac{1 - 2.236}{2} or \frac{1 + 2.236}{2}\\= \frac{- 1.236}{2} or \frac{3.236}{2}\\= -0.618 or 1.618[/tex]
Since y = (3/2)ˣ
Takung logarithm of both sides, we have
㏒y = ㏒(3/2)ˣ
㏒y = x㏒(3/2)
x = ㏒y/㏒(3/2)
x = ㏒y/㏒1.5
Since we do not have logarithm of a negative number, we use y = 1.618.
So, x = ㏒y/㏒1.5
x = ㏒1.618/㏒1.5
x = 0.2090/0.1761
x = 1.19
So, the value of x is 1.19
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help help help help help help pleaseeeeee
Answers
The maximum height is; 180 ft and the Total time in the air is 12 seconds
How to solve projectiles?We are given the equation that represents the height of the rocket as;
d = 60t - 5t²
Taking the derivative of the formula gives us;
d' = 60 - 10t.
-10t represents the acceleration. The 60 represents the initial velocity.
Set 60 - 10t = 0 and solve for t to get;
t = 60/10 = 6seconds.
That's when the maximum height occurs. Plug that value of t into the original quadratic equation to get the maximum height.
d(6) = 60t - 5t²
d(6) = 60(6) - 5(6²)
d(6) = 180
So, maximum height is about 180 ft.
Thus, total time in air = 2 * 6 = 12 seconds
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For a fundraiser, 1000 raffle tickets are sold, and the winner is chosen at random. There is only one prize, $500 in cash. You buy one ticket. What is the probability you will win the prize of $500
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Answer:
1/1000 = 0.001
Step-by-step explanation:
Out of the 1000 tickets only one will be chosen. And since you only bought one ticket you would get a 1/1000 chance to get chosen. If you turn 1/1000 into a decimal you get 0.001 or 0.1%. Say if you bought 2 tickets you would get a 2/1000 chance which would be a 0.2% chance and so on.
If f(x + 1) = x + 2 then f(x - 1) is
Answers
Answer: [tex]\Large\boxed{f(x-1)=x}[/tex]
Step-by-step explanation:
Given function
f(x + 1) = x + 2
Isolate [ x + 1 ] on the right-hand side
f(x + 1) = x + 1 + 1
f(x + 1) = (x + 1) + 1
Substitute [ x + 1 ] with x
f(x) = x + 1
Substitute [ x ] with [ x - 1 ]
f(x - 1) = (x - 1) + 1
[tex]\Large\boxed{f(x-1)=x}[/tex]
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Find the probability of rolling a sum less than 5 or a sum greater than 7 when a pair of dice is rolled.
Answers
Answer:
Step-by-step explanation:
Solution
There are 36 possible ways to combine two dice. The ones you are interested in, are in the table below
Numbers less that 5 are with their probabilities
Number Probability How done.
2 1/36 1 + 1
3 2/36 2 + 1 1 + 2
4 3/36 2 + 2 1 +3 3 + 1
Total 6/36 1/6
Greater than 7
Number Probability How done
8 5/36 6+2 2+6 5 +3 3+5 4 + 4
9 4/36 6+3 3 + 6 5+4 4+ 5
10 3/36 6+4 4 +6 5 + 5
11 2/36 5+6 6 + 5
12 1 /36 6 + 6
Total 15/36
Answer
15/36 + 1/6 = 15/36 + 6/36 = 21/36
Final Answer: 7/12
Create the smallest cone possible with the tool, and record the values of the radius, height, and volume in terms of . Then scale the original CONE
by the given scale factors, and record the resulting volumes (in terms of 7), to verify that the formula V=V xk³ holds true for a cone.
Answers
The Created cone with the possible record of the the values of the radius, and height is given in the image attached.
How do yo create the volume of the smallest cone?A scale factor is known to be a number that is known to often multiplies (doubles or triples, etc.,“scales”) a given quantity.
Since the volume is not attached, it will be manually created here.
Note that the resulting volumes must be in terms of 7.
Hence:
Volume Formula: V=V x k³
When scale factor is 2, radius = 4, height = 8, then volume will be:
7π x 2³
= 56π
When scale factor is 3, radius = 6, height = 18, then volume will be:
7π x 3³
= 189π
When scale factor is 4, radius = 8, height = 24, then volume will be:
7π x 4³
= 448π
Hence the volume that will be fixed into the scale factor diagram will be:
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Powers of 10 and Exponents (number 4 is a 10 incase u can’t see of the ripped page.)
Answers
Answer:
below
Step-by-step explanation:
2) 10², the second power of ten
3) 10⁴, the fourth power of ten
4) 1000
5) 400
6) 90,000
7) 10
8) 100,000
9) 50
10) 7000
11) 8
12) 24 x 10⁴
13) 93,000,000
Answer + Step-by-step explanation: