If the order of choice is relevant, use permutation. We have to choose 5 objects in a total of 9:
[tex]9\times8\times7\times6\times5=15120\text{ ways}[/tex]Obs: Initially we have 9 objects, you choose one, then we have 8, you choose another, then you have 7..... (this is the reasoning)
If the order of choice is not relevant, use a combination. This can be done by the equation above:
[tex]C_{9,5}=\frac{9!}{(9-5)!\times5!}[/tex][tex]C_{9,5}=\frac{9!}{4!\times5!}[/tex][tex]C_{9,5}=\frac{9\times8\times7\times6\times5!}{4!\times5!}[/tex][tex]C_{9,5}=\frac{9\times8\times7\times6}{4\times3\times2\times1}[/tex][tex]C_{9,5}=126\text{ ways}[/tex]Obs: It is a combination of 9 elements chosen 5 by 5.
About how many 6 foot boards can be cut from a 32 3/4foot board?
a. 5 boards
b. 10 boards
c. 4 boards
d. 8 boards
Please help!!! Will give brainlest
A hemisphere has a radius of 8 cm. Find the volume of the hemisphere
Given:
A hemisphere has a radius of 8 cm.
Required:
To find the volume of the hemisphere.
Explanation:
The formula for volume of the hemisphere is,
[tex]V=\frac{2}{3}\pi r^3[/tex][tex]\begin{gathered} V=\frac{2}{3}\times3.14\times8^3 \\ \\ =\frac{2}{3}\times3.14\times512 \\ \\ =1071.786cm^3 \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} V=1071.86cm^3 \\ \approx1071.9cm^3 \end{gathered}[/tex]Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the value of x?
____________________________________________________________________________________________________________
The value of x is 71 degree .
What is isosceles triangle ?Triangles that have two sides at least equally spaced apart are said to be isosceles. As three-sided enclosed polygons with three sides, triangles are known to exist. Depending on the length of their sides, triangles can be categorized as equilateral, isosceles, or scalene.
The three interior angles of a triangle will always have a sum of 180°. A triangle cannot have an individual angle measure of 180°, because then the other two angles would not exist (180°+0°+0°).
So ,
x +x+38 = 180
2x = 180 -38
2x = 142
x = 71
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Construct two different trinomials that have a greatest common factor of 5x²y³ ?
The two different trinomials that have a greatest common factor of [tex]5x^{2} y^{3}[/tex] are:
a) [tex]35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}[/tex]
b) [tex]25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\[/tex]
Let us verify,
a) Consider the trinomial [tex]35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}[/tex],
The Greatest Common Factor of 35, 5, 15 is 5
The Greatest Common Factor of [tex]x^{2} ,x^{4} ,x^{3} =x^{2}[/tex]
The Greatest Common Factor of [tex]y^{5} ,y^{9} ,y^{3} = y^{3}[/tex]
There is no G.C.F for z because it is missing in the 3rd term.
So, the G.C.F of the trinomial [tex]35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}[/tex] = [tex]5x^{2} y^{3}[/tex]
b) Consider the trinomial [tex]25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\[/tex],
The Greatest Common Factor of 25, 5, 10 is 5
The Greatest Common Factor of [tex]x^{4} ,x^{7} ,x^{2} =x^{2}[/tex]
The Greatest Common Factor of [tex]y^{3} ,y^{8} ,y^{4} = y^{3}[/tex]
There is no G.C.F for z because it is missing in the 2nd term.
So, the G.C.F of the trinomial [tex]25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z = 5x^{2} y^{3}[/tex]
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5 5/6 or 5.6 which is greater
The mixed fraction form
[tex]5\frac{5}{6}[/tex]is equivalent to
[tex]5+\frac{5}{6}[/tex]since 5/6 is equal to 0.8333, then
[tex]5\frac{5}{6}=5.83333[/tex]Therefore, since 5.83333 is greater than 5.6, then 5 5/6 is greater than 5.6
A group of hikers tracked how long it took to hike a 20-mile trail. They hiked 3.75 miles in 3 hours, 7.5 miles in 6 hours, and 12 miles in 8 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.8 miles per hour.
No, it is not proportional because 3.75 miles in 3 hours is not equivalent to 7.5 miles in 6 hours.
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
Answer:
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
Step-by-step explanation:
first lets find out how far they hiked per hour3.75 mi in 3 hourswe need to do 3.75÷3= and we get 1.25 mi an hour now we need to do the next oneit is 7.5 mi in 6 hoursso we are gonna do 7.5÷6=and we get 1.25 mi an hournow lets do the last one12 mi in 8 hourswe are gonna do 12÷9=and we get 1.5 mi in an hourso the 3 hours and 6 hour are proportional so it would be: No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.The correct relationship between the hikers distance and time is;
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
A group of hikers tracked how long it took to hike a 20-mile trail.
And, They hiked 3.75 miles in 3 hours, 7.5 miles in 6 hours, and 12 miles in 8 hours.
Now,
Find the proportional as;
For hiked 3.75 miles in 3 hours,
Proportional = 3.75 / 3
= 1.25
For hiked 7.5 miles in 6 hours,
Proportional = 7.5 / 6
= 1.25
For hiked 12 miles in 8 hours,
Proportional = 12 / 8
= 1.5
Thus, The correct relationship between the hikers distance and time is;
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
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I will show you a pic
first we can separate the values with exponents that having the same base can be reduced
so
[tex]\begin{gathered} \frac{4.8\times2.2}{1.2}\times\frac{10^8\times10^{-6}}{10^4} \\ \\ \frac{4.8\times2.2}{1.2}\times10^{8-6-4} \\ \\ \frac{4.8\times2.2}{1.2}\times10^{-2} \end{gathered}[/tex]now do the multiplication between 4.8 and 2.2 and reduce the fraction
[tex]\begin{gathered} \frac{10.56}{1.2}\times10^{-2} \\ \\ 8.8\times10^{-2} \\ =0.088 \end{gathered}[/tex]so, the right option is B
Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4
sodas for $8.50. How much would an order of slice of cheese pizza and 3 sodas cost? 3
O $3.25
• $5.25
• $7.75
• $17.25
Cost of 1 slice of pizza and 3 sodas = $5.25
What is Linear Programming?When the requirements of a mathematical model are represented by linear relationships, the best result can be obtained using a technique known as linear programming (LP), also known as linear optimization. A particular type of mathematical programming is linear programming. Formally speaking, linear programming is a method for optimising a linear objective function under the constraints of linear equality as well as linear inequality. Convex polytopes, a set defined as that of the intersection of a finite number of half spaces, which are defined by a linear inequality, make up its feasible region. A real-valued affine (linear) function defined on the this polyhedron serves as its objective function. If there is a point in the polytope in which this function does have the smallest (or largest) value, a linear programming algorithm locates it.
Let the cost of 1 slice of pizza be x and cost of 1 soda be y.
Now,
Richard bought 3 slices of pizza and 2 sodas for $8.75
Therefore, [tex]3x+2y=8.75[/tex]
Jordan bought 2 slices of pizza and 4 sodas for $8.50
Therefore, [tex]2x+4y=8.50[/tex]
Solving above equations, we get [tex]x=2.25[/tex] and [tex]y= 1[/tex].
Cost of 1 slice of pizza and 3 sodas = 2.25 + 3*1
= 2.25 + 3
= 5.25
Hence, Cost of 1 slice of pizza and 3 sodas = $5.25
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Write the quadratic function in standard form.G(x) = x2 - 8x
Okay, here we have this:
Considering the provided quadratic function, we are going to rewrite in standard form, so we obtain the following:
So to rewrite the function in standard form we will complete the square:
[tex]\begin{gathered} x^2-8x \\ =x^2-8x+(-4)^2-(-4)^2 \\ =(x-4)^2-(-4)^2 \\ g(x)=(x-4)^2-16 \end{gathered}[/tex]And from this equation we get that the vertex is (4, -16)
Therefore the correct graph is the one in the upper right corner.
35. The school is planning to build a new stadium over the summer.The cost to rent a construction crane for a dayl is $750 plus $250per hour to use. What is the rate of change of cost with respectto hours rented?
The cost function is given by
C(t)=250t+750
Where
C(t) is the cost to rent a crane in t hours of use in a day.
t is the number of hours of use
And the derivatitve of the cost function with respect to t is given by
dC/dt=250
Hence, the rate of change of cost with respect to hours rented 250 dollars per hour
Please help
20 POINTS!
What function translates the function f(x)= |x| to the right 2 units and up 10 units?
Answer:
f(x) = |x-2| + 10
Step-by-step explanation:
Evaluate the indefinite integral. ft-53 at 1250 + c 5 - + 2 - 125t + c 312 - 30t + 75 + 6 O r4 - 15+ 7512 - 125t + c
Given:
[tex]∫(t-5)^3\text{ dt}[/tex]Let's evaluate the integral:
[tex]\begin{gathered} ∫(t-5)^3\text{ dt} \\ \\ =\frac{1}{4}(t-5)^4+c \\ \\ ^{} \end{gathered}[/tex]Thus, we have:
[tex]\frac{1}{4}(t^4-20t^3+150t^2-500t+625)+C[/tex]Expand using distributive property:
[tex]\begin{gathered} (\frac{t^4}{4}-\frac{20t^3}{4}+\frac{150t^2}{4}-\frac{500t}{4}+\frac{625}{4})+C \\ \\ \\ =\frac{t^4}{4}-5t^3+\frac{75t^2}{2}-125t+C \end{gathered}[/tex]ANSWER:
[tex]=\frac{t^4}{4}-5t^3+\frac{75}{2}t^2-125t+C[/tex]What is the solution for x in the given equation?
Answer:
42/11 or 4.454545..
Step-by-step explanation:
square both sides
(SQRT(9x+7) + SQRT(2x))^2 = 7^2
9x+7 + 2x = 49
11x = 42
x = 42/11 or 4.4545...
Gabriel has a coin jar full of nickles and pennies. There are tweleve more pennies than nickles. He has a total of $6.06. Are these statements true or false.
n = number of nickles
p = number of pennies
Therefore,
p = 12 + n
1 nickel = 0.05 dollars
1 penny = 0.01 dollars
Therefore,
[tex]\begin{gathered} n(0.05)+(12+n)0.01=\text{6}.06 \\ 0.05n+0.12+0.01n=6.06 \\ 0.06n+0.12=6.06 \\ \text{0}.06n=6.06-0.12 \\ 0.06n=5.94 \\ n=\frac{5.94}{0.06} \\ n=99 \end{gathered}[/tex]Therefore,
p = 12 + 99 = 111
n = 99
One linear equation for the sytem is p + 5n = 606 is true
The system has one solution is true.
....................................................//////.
Answer:
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Answer:
yES uwuuuuuuuuu
Step-by-step explanation:
which of the following are the solution to -8×2-8=-32?
f(x) = -3x²
Find f(10)
Answer:
f(10) = -300
Step-by-step explanation:
f(x) = -3x^2
f(10) = -3(10)^2
f(10) = -3(100)
f(10) = -300
(Please help, will be marked brainliest) What is the evaluated version of x^2-xy-5x-4?
The evaluated version of ((x²-xy)-5x)-(4(2xy+2x²) is:
-x • (7x + 9y + 5)
Given, the expression is ((x²-xy)-5x)-(4(2xy+2x²)
open the brackets.
x²-xy-5x-8xy-8x²
pull out the like terms.
-7x²-9xy-5x
= -x • (7x + 9y + 5)
Hence after evaluating ((x²-xy)-5x)-(4(2xy+2x²), we get -x • (7x + 9y + 5)
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8) Evaluate the algebraic expression for the value given: 4 - 2x;when x=6 2pointsO 12O 16-8This is a required question
We are given the following expression:
[tex]4-2x[/tex]We are asked to find the value of the expression when x = 6. To do that, we replace the value of "x" in the expression:
[tex]4-2(6)[/tex]Solving the operations we get:
[tex]4-12=-8[/tex]please help for 50 points (geometry)
Answer:
A
Step-by-step explanation:
Answer:
h = 2
k = 5
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Given:
B = Midpoint = (6, 0)A = (x₁, y₁) = (3h+4, 1-2h)C = (x₂, y₂) = (k-3, k-2)Substitute the given values into the formula:
[tex]\implies (6, 0)=\left(\dfrac{k-3+3h+4}{2},\dfrac{k-2+1-2h}{2}\right)[/tex]
[tex]\implies (6, 0)=\left(\dfrac{k+3h+1}{2},\dfrac{k-2h-1}{2}\right)[/tex]
Equating the x-values to create an expression for k:
[tex]\implies \dfrac{k+3h+1}{2}=6[/tex]
[tex]\implies k+3h+1=12[/tex]
[tex]\implies k+3h=11[/tex]
[tex]\implies k=11-3h[/tex]
Equating the y-values to create an expression for k:
[tex]\implies \dfrac{k-2h-1}{2}=0[/tex]
[tex]\implies k-2h-1=0[/tex]
[tex]\implies k-2h=1[/tex]
[tex]\implies k=2h+1[/tex]
Equate the expressions for k and solve for h:
[tex]\implies 2h+1=11-3h[/tex]
[tex]\implies 5h=10[/tex]
[tex]\implies h=2[/tex]
Substitute the found value of h into one of the equations for k and solve for k:
[tex]\implies k=2(2)+1[/tex]
[tex]\implies k=4+1[/tex]
[tex]\implies k=5[/tex]
to get the paint color moss green, 2 parts violet paint mixed with 3 parts yellow paint. how many parts yellow paint should be mixed with 5 parts violet paint and **EXPLAIN THE ANSWER STEP BY STEP!**
Answer:
7.5 parts yellow
Step-by-step explanation:
The color moss green has violet and yellow paint mixed in the proportion 2 to 3. You want to know the number of parts of yellow paint that should be mixed with 5 parts of violet paint.
ProportionThe proportion can be written different ways. We like to put the unknown value in the numerator. (x is the number of parts of yellow paint)
yellow : violet = 3 : 2 = x : 5
Expressed as fractions, the proportion is ...
[tex]\dfrac{3}{2}=\dfrac{x}{5}\\\\5\times\dfrac{3}{2}=x\qquad\text{multiply by 5}\\\\\dfrac{15}{2}=x=7.5\qquad\text{simplify}[/tex]
7.5 parts yellow paint should be mixed with 5 parts violet paint.
__
Additional comment
If you kept the proportion as violet : yellow, then the unknown value would be in the denominator. The solution to that proportion requires another step. Here, we just needed to multiply by the denominator value to find the unknown.
In an investigation, Detective Cortez discovered a photograph that showed his number one suspect at the scene of the crime. To get a better look, he enlarged the picture by a scale factor of 8/1. If the original photo measured 4 inches by 3.6 inches, what were the dimensions of the enlargement?
The dimensions of the enlargement will be: 32 inches by 28.8 inches.
How do we get the new dimensions?The new dimensions can be gotten with the formula below:
Scale factor = Dimensions of new image / Dimensions of the original image.
Dimensions of new image = Scale factor × Dimensions of the original image
8 × 4 = 32 inches
8 × 3.6 = 28.8 inches.
Therefore, the new dimensions of the enlargement will be:
3 inches by 28.3 inches.
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May I please get help with this. For I have tried many times but still could not get the correct answer or how to recreate the dilation
a) From the graph,
shortest side length of original figure = 1/2 units
By dilating the original figure by 4, we would multiply each length by 4
Thus,
shortest side length of final figure = 1/2 x 4 = 2 units
b) shortest side length of the final figure = 4 x shortest side length of the original figure
c) A dilation with a positive scale factor greater than 1 gives an enlarged figure.Thus, the answer is False
d) After dilation, the original and final figures are similar. Thus, the answer is False
9. The population of a small city that is 320 square miles is 2.8 million. What is the population density per square miles of the city? A. 8750 people per square mile B. 87500 people per square mile C. 1,250 people per square mile D. 12,500 people per square mile
We are given the population and the area of the city and asked to calculate the population density.
Recall that the population density is the calculation that consists of dividing the population by the area. Then, in this case it would be
[tex]\frac{2.8\text{ million}}{320\text{ square miles}}=\frac{2800000}{320}=8750[/tex]Then, the population density is 8750 habitants per square mile
82, 964 to the neatest ten thousand
Answer:
im pretty sure its 90000
Step-by-step explanation:
Sarah draws figure EFGH in the coordinate plane. She rotates figure EFGH 90" clockwise around vertex E to form image EF'G'H.Draw the image EFG'Hon the coordinate plane.
To first start our problem, we will draw some coordinate axis at point E, since we are rotating the figure around this vertex. We get something like this
We are going to fix the point E. But we are going to rotate the figure in the direction in which the arrow shows. Since it is a 90° rotation, our goal is to align the blue vertical line, with the red horizontal line, following the direction of the black arrow. The picture would look like this
Note that the lengths of the new figure should remaing the same. That is, the side H' E should have a length of 3 squares and the length of H' G' should be 2 squares.
12.y- 7=4(x +4)15.y +5 =-5(x-3)18.y + 11=1/3(X+3)
the equation in the standard form is Ax + By = C
12.
[tex]\begin{gathered} y-7=4\mleft(x+4\mright) \\ y-7=4x+16 \\ y-7+7=4x+16+7 \\ y=4x+23 \\ y-4x=4x-4x+23 \\ -4x+y=23 \end{gathered}[/tex]15.
[tex]\begin{gathered} y+5=-5(x-3) \\ y+5=-5x+15 \\ y+5-5=-5x+15-5 \\ y=-5x+10 \\ 5x+y=10 \end{gathered}[/tex]18.
[tex]\begin{gathered} y+11=\frac{1}{3}(x+3) \\ y+11=\frac{1}{3}x+1 \\ y+11-11=\frac{1}{3}x+1-11 \\ y=\frac{1}{3}x-10 \\ -\frac{1}{3}x+y=-10 \end{gathered}[/tex]1 Find the length of the side CD in the pentagon ABCDE.
In order to find the length of the side CD in the pentagon ABCDE we would need to find the distance between the two points (4,-2) and (8, 2)
We would use the following formula:
[tex]d=\sqrt[]{(x1-x2)^2+(y1-y2)^2}[/tex]plug in x1= 4, x2= 8, y1=-2, y2=2
So,
[tex]d=\sqrt[]{(4-8)^2+(-2-2)^2}[/tex][tex]d=\sqrt[]{(-4)^2+(-4)^2}[/tex][tex]d=\sqrt[]{32}[/tex]d=5,65
The length of the side CD in the pentagon ABCDE would be 5,62
Choose the correct graph of the system of inequalities:y ≥ 5x - 4y < -2x + 3
Given:
The inequalities are,
[tex]\begin{gathered} y\ge5x-4 \\ y<-2x+3 \end{gathered}[/tex]To find:
The correct graphs.
Explanation:
Let us find the intercepts.
For the first inequality,
When x = 0, we get,
[tex]\begin{gathered} y=0-4 \\ y=-4 \end{gathered}[/tex]When y = 0, we get
[tex]\begin{gathered} 0=5x-4 \\ 5x=4 \\ x=0.8 \end{gathered}[/tex]So, the intercepts are
[tex](0.8,0),(0,-4)[/tex]For the second inequality,
When x = 0, we get,
[tex]\begin{gathered} y=0+3 \\ y=3 \end{gathered}[/tex]When y = 0, we get
[tex]\begin{gathered} 0=-2x+3 \\ -2x=-3 \\ x=1.5 \end{gathered}[/tex]So, the intercepts are
[tex](1.5,0),(0,3)[/tex]So, the graph becomes,
Anya says that with 24 counters she can make only 6 possible arrays. Todd says he can make 8 arrays. Who is correct? Explain.
Both Anya and Todd are correct that with 24 counters both 6 arrays and 8 arrays are possible.
Whats is an array?
An array is a set of items, images, or numbers arranged in rows and columns. Arrays are practical illustrations of multiplication theories (among other ideas in mathematics).
Here 24 can also be expressed as 6x4 and 8x3 therefore both ways are possible.
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