Using the permutation formula, it is found that the number of different orders of top-three finishers that are possible is given as follows:
[tex]nPr = \frac{14!}{11!} = 2184[/tex].
The order in which the cars finish is important, hence the permutation formula is used instead of the combination formula.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]nPr = \frac{n!}{(n-r)!}[/tex]
In this problem, 3 cars are taken from a set of 14, hence the number of different orders is given as follows:
[tex]nPr = \frac{14!}{11!} = 2184[/tex].
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Find the value of x. The figure shows complementary angles. The label for the first angle is x plus 9 degrees. The label for the second angle is 44 degrees.
The value of x, when two angles are complementary with one angle value is x plus 9 degrees and the second angle value is 44 degrees, is 37 degrees.
What is complementary angles?The two angles are called complementary angles, when the sum of these two angle is equal to the 90 degrees.
Suppose there are two angle, angle A and angle B. These two angles will be complementary if,
[tex]m\angle A+m\angle B=90^o[/tex]
The figure shows complementary angles.
The label for the first angle is x plus 9 degrees (x+9). The label for the second angle is 44 degrees 44.As, both the angles are complementary. Thus,
[tex](x+9)+44=90\\x+9+44=90\\x+53=90\\x=90-53\\x=37^o[/tex]
Thus, the value of x, when two angles are complementary with one angle value is x plus 9 degrees and the second angle value is 44 degrees, is 37 degrees.
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Find the sum. Express your answer in simplest form.
Answer:
[tex]\frac{10x^2+3}{y^2+4}[/tex]
Step-by-step explanation:
When adding rational numbers, if the denominator is the same you simply keep the denominator (bottom of fraction) as it is and apply the operation given to the numerator ( top of fraction )
So we have [tex]\frac{6x^2+5}{y^2+4} +\frac{4x^2-2}{y^2+4} =\frac{(6x^2+5)+(4x^2-2)}{y^2+4}[/tex]
==> remove parenthesis and apply signs
[tex]\frac{x^2+5+4x^2-2}{y^2+4}[/tex]
==> simplify numerator by combining like terms
[tex]\frac{10x^2+3}{y^2+4}[/tex]
and we are done!
Note:
like terms are terms with the same variable and exponent
An example of like terms are 6x^7 and 3x^7 as they have x as a variable and a power of 7
The like terms being combined here were (6x² and 4x²) and (5 and -2)
Answer:
[tex]\frac{10x^{2} +3}{y^{2}+4 }[/tex]
Step-by-step explanation:
[tex]\frac{6x^{2} +5}{y^{2}+4 } +\frac{4x^{2} -2}{y^{2}+4 }[/tex]
make the common denominator
[tex]\frac{6x^{2} +5+4x-2}{y^{2}+4 }[/tex]
combone the like terms
[tex]\frac{10x^{2} +5-2}{y^{2}+4 }[/tex]
subtract numbers
[tex]\frac{10x^{2} +3}{y^{2}+4 }[/tex]
PLSSS HELP PLSSSSSSSSSS
A line intersects the points
(-2, 3) and (-5, 6).
m = -1
Write an equation in point-slope form
using the point (-2, 3).
y- [?] =
(x- .
..)
Help please can someone solve this
a = 165/360 × pi10^2
Answer:
Use a TI84 calculator.
Step-by-step explanation:
There is no way to solve this by hand on paper as the answer is an indefinite number.
Joseph notebook cover is 12 inches by 8 inches.he put a wildlife sticker on the notebook.if the sticker is 3 inches by 2 inches.how much of the notebook cover is still showing?
What is the value of y? A. 30° B. 60° C. 120° D. 40°
Answer:
Its B
Step-by-step explanation:
60+60+60=180
Triangle=180
Evaluate 1/4r+7/24 when r=1/6
Step-by-step explanation:
If r is 1/6 then we'll have 1/4*1/6+7/24.
Firstly we will multiply 1/4 and 1/6 which will give us 1/24.
Then we will add 1/24 and 7/24 which will give us 8/24.
Then we reduce it to it's lowest term that is 1/3.TRY THIS.
How many times greater is 9x10^100 than 3x10^40
Answer:
9x10^100= 9e+100 3x10^40= 3e+40
Step-by-step explanation:
100-40 = 60
Lucy used 1 1/8 yards of cloth to make a dress. How many dresses can she make in 10 yards of cloth? How many yards of cloth will remain unused?
What is the surface area?
5 m
7 m
4 m
140 m squared
16 m squared
166 m squared
156 m squared
Answer:
166 m²
Step-by-step explanation:
Surface Area
2(length x breadth) + 2(length x height) + 2(breadth x height)2(7 x 4) + 2(7 x 5) + 2(4 x 5)2(28) + 2(35) + 2(20)56 + 70 + 40110 + 56166 m²Write the following number in standard decimal form.
nine thousand two hundred nineteen ten-thousandths
Answer:
0.9219
Step-by-step explanation:
Starting at the deccimal point and going right, the places are: tenths (one decimal place), hundredths, thousandths, ten-thousandths. So that the number is ten-thousandths means it has four decimal places. Those digits are given in the problem "nine thousand two hundred nineteen"
PLS HELPPPP!!! I WILL GIVE BRAINLIEST IF CORRECT
The answer would be C
Hope this helps
Answer:
SW
Step-by-step explanation:
Work out the surface area of this solid prism.
HELP QUICK PLEASE!! Which equation models the data in the table?
y=x−3
y = x + 3
y = 4x
y = x + 2
x y
4 1
6 3
8 5
10 7
The answer is option B
Answer:
A. y = x - 3
Step-by-step explanation:
By examining the table, we can see that all y-values have a constant correlation to each x-value by -3. Therefore, the best answer is y = x - 3.
x + 3 would change to y-values to 7, 9, 11, 13.
4x would change the y-values to 16, 24, 32, 40.
x + 2 would change the y-values to 6, 8, 10, 12.
hope this helps!
If a scale dilates a two-dimensional object by a factor of 2/3 it means that …
a.
the image is one-and-a-half times smaller than the object
b.
the image is two units big, while the object is three units big
c.
the object is half the size of the image
d.
the object is two-thirds the size of the image
Hello Please Find The Answer To This Question (easy) part 4
Answer:
y=[tex]\frac{7}{4}[/tex]x-5
Step-by-step explanation:
by using this website
its a graphing calculator
desmos. com/calculator
Over the past week, 40% of the phone calls to Alicia's cell phone were from her son. Let's say you know that her son called her 12 times. Find out how many total calls she received.
She received 12 calls from her son and 30 calls in total.
40% of 30 is 12.
What is the reference angle for 192º?
Answer:
78º
Step-by-step explanation:
Note : -
In mathematics, the reference angle is defined as the acute angle and it is measuring less than 90 degrees. It is always the smallest angle, and it makes the terminal side of an angle with the
x - axis.
Step 1 : -
Find where 192º lies in which quadrant.
192º lies in 3rd quadrant ( between
180º and 270º )
Step 2 : -
Subtract : 270 - 192
270 - 192 = 78º
( Since, 192º is greater than 180º, is subtracted from 270º )
Answer : -
78º is the reference angle for 192º.
help please please please
Step-by-step explanation:
Correct option is A)
Let Q(h,k) be the image of P(3,3) w.r.t the line mirror x+y=0
a
h−p
=
b
k−q
=
a
2
+b
2
−2×(ap+bq+c)
1
h−3
=
1
k−3
=
2
−2(6)
⇒h−3=k−3=−6
⇒h=−3,k=−3
So, the image is Q(−3,−3).
In the second transformation, point Q is translated horizontally 3 units to the left and vertically 3 units up.
So, the coordinates of new image is (−3−3,−3+3) i.e. (−6,0)
In the third transformation, point (−6,0) is reflected w.r.t the line y=x
So, the final image is (0,−6).
Was this answer helpful?
Alicia walked down a hill, stopping for a break when she was halfway down the hill. Her change in elevation from the top of the hill to the
bottom of the hill was - 376 feet.
Which expressions represent half the change in elevation on Alicia's walk?
Select the two correct expressions.
(-376)
2
(-376)
(-2)
-1978)
376
2
-(1976)
Answer:
we can not help you sorry its a really inportant test
Step-by-step explanation:
How much interest will Hannah
earn in 6 months if
she deposits
$630 in a savings account at a
6.5% interest rate?
keeping in mind that a year has 12 months, thus 6 months is really 6/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$630\\ r=rate\to 6.5\%\to \frac{6.5}{100}\dotfill &0.065\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases} \\\\\\ I = (630)(0.065)(\frac{1}{2}) \implies I\approx 20.48[/tex]
The figure shows a line graph and two shaded triangles that are similar
Answer:
we know that
the equation for calculating the slope of a line is
m=(y2-y1)/(x2-x1)
look for any two points on the graph
let
A(0,0)
B(3,1)
m=(1-0)/(3-0)------> m=1/3
the slope is 1/3 throughout the line
therefore
the answer is the option
B-It is 1/3 throughout the lineStep-by-step explanation:
Question 9 of 10
Which of the following is a polynomial?
what is 2 x 2,000,000
Answer: 4,000,000
Please, please give me brainliest! I'm trying to become the next rank :) Thanks!
Answer: Heyaa!
The Answer Is... 4000000
Step-by-step explanation:
Multiple them together :
Hopefully this helps you !
- Matthew ~
can anyone help me find the area ty
How would I organize the calculation
Answer:
52 should be the answer
Step-by-step explanation:
first, love the parathesis. subtract 7-2
second 3 raised to the second power
third times 3 raised to the third power by 5 the answer a few u substrates 7-2
fourth 14 divide 2
finally I would add (14/2) 7 + 45 (which is 9 times 5)
read through it carefully by the end if the problem, you should have 52 as the ans
In how many ways can 3 students from a class of 17 be chosen for a field trip?
Answer:
1360
Step-by-step explanation:
5. Find h(j+1) if h(x)=4x² + 3x - 2
In h(x) = 4x^2 + 3x - 2, there is an x contained with h as well as an x in the expression. To find h(j + 1), we'll need to plug in (j + 1) everywhere that there is an x.
h(j + 1) = 4(j + 1)^2 + 3(j + 1) - 2
h(j + 1) = 4(j^2 + 2j + 1) + 3j + 3 - 2
h(j + 1) = 4j^2 + 8j + 4 + 3j + 3 - 2
h(j + 1) = 4j^2 + 11j + 5
Hope this helps!
Write the equation of each line in slope‐intercept form.
Answer:
y = -x +4
Step-by-step explanation:
Hi there!
We are given the equation of a line, and we want to write the equation of this line in slope-intercept form
Slope-intercept form is written as y=mx+b, where m is the slope and b is the value of y at the y-intercept
First, we need to find the slope of the line
The slope (m) can be calculated from 2 points, using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
First, let's find 2 points on the line:
The intercepts - the points where the line hits the x and y axis are a good place to start; the intercepts of this line are (4,0) and (0, 4), which will also work for calculating the slope
Let's label the values of these 2 points to avoid any confusion and mistakes when calculating.
[tex]x_1=4\\y_1=0\\x_2=0\\y_2=4[/tex]
Substitute into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{4-0}{0-4}[/tex]
Subtract
m=[tex]\frac{4}{-4}[/tex]
Divide
m = -1
The slope of the line is -1
We can substitute that into our equation:
y = -x + b (when -1 is the leading coefficient, only adding a minus sign in front of the variable will suffice)
Now we need to find b
As said earlier, b is the value of y at the y intercept
The point of the y intercept is (0, 4), and the value of y at this point is 4
So substitute 4 as b into the equation
y = -x + 4
Hope this helps!