Answer:
45 ways
Step-by-step explanation:
Combination method is appropriate for this question since it deals with arrangement.
i.e [tex]^{n}C_{r}[/tex] = [tex]\frac{n!}{(n - r)!r!}[/tex]
Since 8 records are to be selected from 10 available records. Then, the number of ways for the arrangement of the records can be determined as;
Let n = 10 and r = 8
[tex]^{10}C_{8} }[/tex] = [tex]\frac{10!}{(10 - 8)!8!}[/tex]
= [tex]\frac{10!}{2!8!}[/tex]
= [tex]\frac{10*9*8*7*6*5*4*3*2!}{2!8*7*6*5*4*3*2!}[/tex]
= [tex]\frac{10*9}{2}[/tex]
= 45
Therefore, the number of ways by which the records can be arranged is 45.
Write a function rule for the area of a rectangle whose length is 5in. more than its width. what is the area of the rectangle when its width is 8in.?
Answer:
40in^2
Step-by-step explanation:
How to find vertex form with vertex: (3,6) and y intercept: 2
Answer:
f(x) = - ⁴/₉(x - 3)² + 6Step-by-step explanation:
The vertex form of the equation of the parabola with vertex (h, k) is:
f(x) = a(x - h)² + k
So for vertex (3, 6) it will be:
f(x) = a(x - 3)² + 6
y intercept: 2 means f(0) = 2
f(0) = a(0 - 3)² + 6
2 = a(-3)² + 6
2 -6 = 9a + 6 -6
-4 = 9a
a = ⁻⁴/₉
Therefore:
The vertex form of quardatic function with vertex: (3,6) and y intercept: 2 is
f(x) = - ⁴/₉(x - 3)² + 6
The vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
The vertex: (3,6) and y-intercept: 2
As we know,
The parabola equation:
f(x) = a(x - h)² + k
Here (h, k) is the vertex of the parabola and a is the leading coefficient.
f(x) = a(x - 3)² + 6
f(x) = 2 at x = 0
2 = a(0 - 3)² + 6
a = -4/9
f(x) = -4/9(x - 3)² + 6
Thus, the vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2
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Help I mark brainliest
Answer:
-r ^3
Step-by-step explanation:
What is the y-intercept of the function y = 3x + 33 ?
Answer:
33
Step-by-step explanation:
Answer:
it is 33 because you start off at 0 with 33
Step-by-step explanation:
geometry work find the value of b
Answer:
63
Step-by-step explanation:
I know I did it
(20 POINTS PLEASE HELP)
Find the reciprocal of the expression.
10b/2b+8
See image attatched below for the options given
Answer:
it the first one cause you adding so it 8b plus 2
Step by step please
9x^2 -3х + 16 = 6
Answer:
Step-by-step explanation:
Rewrite
9
x
2
as
(
3
x
)
2
.
(
3
x
)
2
−
16
Rewrite
16
as
4
2
.
(
3
x
)
2
−
4
2
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
where
a
=
3
x
and
b
=
4
.
(
3
x
+
4
)
(
3
x
−
4
)
Write an equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6.
Answer:
y = -5/3 * x - 40/3
Step-by-step explanation:
A perpendicular line has an opposite and a reciprocal of the slope.
Your equation should be:
-5y = -3x +6
Divide all parts by -5.
y = 3/5x - 6/5
Since the perpendicular line has an opposite and a reciprocal of the slope, the slope will be -5/3.
Now you must make an equation in point-slope form. This is an example of that form. You will need at least one point to make this equation work. In this case we have (-8,0).
In put the y and x coordinates like this:
y - 0 = -5/3(x - (-8)
Start solving the equation.
y - 0 = -5/3(x + 8)
y - 0 = -5/3 * x - 40/3
y = -5/3 * x - 40/3
This is your equation.
y = -5/3 * x - 40/3
(You can make it -5/3x in your answer but it looks weird online. You may think that it is -5 divided by 3 times x, but it actually is 5/3 times x. That's why I wrote it as y = -5/3 * x - 40/3)
9514 1404 393
Answer:
5x +3y = -40
Step-by-step explanation:
When the equation of a line is given in standard form, the equation of the perpendicular line can be found by swapping the coefficients of x and y, and negating one of them.
Here, that means the equation ...
3x -5y = constant
becomes
5x +3y = new constant
The value of the new constant is found by putting the given point coordinates in the expression on the left:
5x +3y = 5(-8) +3(0) = -40
The equation of the perpendicular line is ...
5x +3y = -40
Which graph represents a function?
Answer:
1
Step-by-step explanation:
it is right ok stop now
PLS
SOLVE !!!!
I WILL MARK THE BRAINLIEST
Answer:
A is two; B is nine; C is one
Good Luck!
a) C has to be either one or zero (but I'm assuming the solution you're wanting is when C=1). This is because A+B + Whatever is carried can only be a number 0-19, meaning only a 1 can be carried to the third column.
b) if C is 1, then in the ones place, B+A must = 11
c) if the carried 1 + a + b = 10 + a, then a can be substituted and we find that b = 9; and a =2
find the slope
help with this please it’s due soon :)
Determine whether each triangle with sides of 28 yd, 195 yd, and 197 yd is a right triangle
Answer:
yes it is
Step-by-step explanation:
to have a right traingle two sides cannot be equal and the first added and squared cannot be more than the last side squared
If f(x) = 3x - 1 and 2f(b) = 28, what is the value of f(2b)?
Answer:
=29
Step-by-step explanation:
2f(b)=28
divide by 2
f(b)=14
f(b)=3b-1
3b-1=14
add 1 on both sides
3b=15
divide by 3
b=5
f(5)=14
let's plug that in
f(2×5)=3(2×5)-1
f(10)=30-1
f(10)=29
The value of f(2b) is 29 if f(x) = 3x - 1 and 2f(b) = 28 the answer is 29.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 3x - 1 and 2f(b) = 28
Plug x = b
f(b) = 3b - 1
2f(b) =2(3b - 1)
2f(b) = 28
28 = 2(3b - 1)
b = 5
f(2b) = f(2(5)) = f(10)
f(10) = 3(10) - 1
f(10) = 30 - 1 = 29
Thus, the value of f(2b) is 29 if f(x) = 3x - 1 and 2f(b) = 28 the answer is 29.
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so far, Jim has burned 5.22 calories. He wants to burn a total of 600 calories. how many more calories must jim burn?
Answer:
594.78
Step-by-step explanation:
600-5.22 = 594.78
Answer:The answer should be 626.4
Step-by-step explanation:
Find the total interest:
$520 at 2%
for 6 years
The interest is %2 of 520 which, if you do the math, is 10.4 cents. You want to find out how much interest it is for 6 years so you have to multiply them.
10.4 x 6 = 62.4
The total interest for 6 years is $62.4
your welcome
26=6k+8-6+2k
Need ASAP
Answer: k = 3
Step-by-step explanation:
Answer:
k=3
Step-by-step explanation:
26=6k+8-6+2k
combine all common integers from the same side, (8-6) and (6k+2k).
8-6=2
6k+2k=8
Which now translates the equation to 26=8k+2.
26=8k+2
continue by moving the (2) to the other side, do so by subtracting 26-2.
26-2=24
24=8k
Lastly, move the 8 to the other side of the equation by dividing 24/8.
24/8=3
Therefore, k=3
Can someone explain this to me if you can.
Answer: I wish I can help, but I don't know how to explain it
Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold.
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept.
Answer:
Part A: The higher the temp the more ice cream sold.
Part B
Step-by-step explanation:
The admission fee at an amusement park is $1.50 for children and $6.40 for adults. On a certain day, 286 people entered the park, and the admission fees collected totaled $1164. How many children and how many adults were admitted?
Answer:
Adult= 150 and Children=136
Step-by-step explanation:
I'm confused on how to do that?
Answer:
(8, 0), (12, 4), (16, 8)
Step-by-step explanation:
m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
(20, 12)
(4, - 4)
m = [tex]\frac{-4-12}{4-20}[/tex] = 1
y - 12 = (1)(x - 20)
y = x - 8
y = 8 - 8 = 0
y = 12 - 8 = 4
y = 16 - 8 = 8
SHOW YOUR WORK
43.01-2.75
Answer:
the answer is 40.26, you first subtract 2 to get 41.01 then subtract .75 to get 40.26, not exactly sure what work you want to be shown
Step-by-step explanation:
A license plate is made of three letters and three numbers. How many different license plates are possible? (Recall there are 26 letters in the alphabet and 10 single digit numbers 0-9).
Using the permutations formula, it is found that: 11,232,000 different license plates are possible
----------------------------------------------------
The order in which the letters and the numbers appear is important(123ABC is a different plate than A123BC), which means that the permutations formula is used to solve this question.
----------------------------------------------------
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
----------------------------------------------------
In this question:
3 letters from a set of 26.3 digits from a set of 10.Thus:
[tex]T = P_{26,3}P_{10,3} = \frac{26!}{23!}\times\frac{10!}{7!} = 11,232,000[/tex]
11,232,000 different license plates are possible
A similar problem is given at https://brainly.com/question/16812463
Company A charges $3.25 per spirit banner. The equation C=2.45x represents the cost in dollars, C, for x spirit banners at Company B. How much more would it cost to purchase 80 spirit banners from the more expensive company?
Answer:
$64.00
Step-by-step explanation:
Company A:
C = 3.25x
3.25 x 80 = 260
Company B:
C = 2.45x
2.45 x 80 = 196
How much more?
260 - 196 = 64
Difference in Total price for 80 unit is $84
Given that;Per spirit cost in company A = 3.5 per spirit
Cost equation for company B = C = 2.45x
Find:Difference in Total price for 80 unit
Computation:Difference in Total price for 80 unit = 80[3.5 - 2.45]
Difference in Total price for 80 unit = 80[1.05]
Difference in Total price for 80 unit = $84
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A bag contains 36 calculators. This number is 75% of the number of calculators that can fit in the bag. How many calculators can the bag hold when filled?
Find the value of X and Y in this triangle.
Step-by-step explanation:
if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)
if leg b is unknown, then. b = √(c² - a²)
for hypotenuse c missing, the formula is. c = √(a² + b²)
Answer:
[tex] \sin(60) = \frac{45}{x} \\ [/tex]
[tex] x = \frac{45}{ \sin(60) } [/tex]
x=5 1.96
Step-by-step explanation:
[tex] \tan(30) = \frac{y}{45} [/tex]
[tex]y = 45 \tan(30) [/tex]
y=25.98
Elena and Jada are 24.5 miles apart on a path when they start moving toward each other. Elena bikes at a constant speed of 8 miles per hour, and Jada runs at a constant speed of 6 miles per hour. How long does it take until Elena and Jada meet? Explain your reasoning.
Answer:
when they reach each other Elana would have gone 16 miles for 2 minutes And jada would for a minite to reach elana
Step-by-step explanation:
What is the opposite of each number?
Drag the answer into the box to match each number.
Answer: If it has a negative sign then drag it to one that doesn't have one and vice-versa
Step-by-step explanation:
so 0.005 would be -0.005
Answer:
the opposite of 0.005 is -0.005
the opposite of 1/2 is -1/2
the opposite of 0 is 0
the opposite of -2 is 2
Step-by-step explanation:
it's asking me to order them from least to greatest how do I do that with tables
Hi there! Hope this helps.
Answer:
Look below.
Step-by-step explanation:
I didn't know if you wanted the answer or just an explanation, so I'll give you an explanation for now.
Look at all of the tables and find the one with the smallest, 2nd smallest, and 3rd smallest numbers and keep going up until you get to the biggest number.
PLEEEEAASEEE HEEELPPP MEEE
Answer:
The measure of the vertex angle is 100°
Step-by-step explanation:
In Δ MNO
∵ Δ MNO is an isosceles triangle with base MO
∴ NM = NO
→ In an isosceles triangle, the base angles are equal in measures
∵ ∠M and ∠O are the base angles isosceles ΔMNO
∴ m∠M = m∠O
∵ m∠M = (3x + 10)°
∵ m∠O = (5x - 10)°
→ Equate their measures
∴ 5x - 10 = 3x + 10
→ Add 10 to both sides
∵ 5x - 10 + 10 = 3x + 10 + 10
∴ 5x = 3x + 20
→ Subtract 3x from both sides
∴ 5x - 3x = 3x - 3x + 20
∴ 2x = 20
→ Divide both sides by 2 to find x
∵ [tex]\frac{2x}{2}[/tex] = [tex]\frac{20}{2}[/tex]
∴ x = 10
→ Substitute the value of x in the measures of ∠M and ∠O to find them
∵ m∠M = 3(10) + 10 = 30 + 10
∴ m∠M = 40°
∵ m∠O = 5(10) - 10 = 50 - 10
∴ m∠O = 40°
→ The sum of the measures of the interior angles of a Δ is 180°
∵ m∠M + m∠O + m∠N = 180°
∵ 40 + 40 + m∠N = 180
→ Add the like terms
∴ 80 + m∠N = 180
→ Subtract 80 from both sides
∴ 80 - 80 + m∠N = 180 - 80
∴ m∠N = 100°
∵ ∠N is the vertex angle of Δ MNO
∴ The measure of the vertex angle is 100°
A small kite starts 3.7meters off the ground and rises at 6.2 meters per second. A large kite starts at 20.65 meters off the ground and drops at a rate of 5.1 meters per second. After how many seconds are the kites at the same height? Write and solve an equation.
Answer: The kites are at the same height at 15.41s
Step-by-step explanation:
Step 1
Let t represent the time in seconds.
The equation that represents when both small and large kite are at the same height is given as
3.7 + 6.2t =20.65 +5.1t
Step 2----- Solving
3.7 + 6.2t =20.65 +5.1t
Taking like terms and subtracting
6.2t-5.1t = 20.65- 3.7
1.1t =16.95
t = 16.95/1.1
t=15.41s
The kites are at the same height at 15.41s