[tex]\\ \rm\Rrightarrow {}^{35}C_{12}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{35!}{12!(35-12)!}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{35!}{12!23!}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1.0333148e+40}{12383157381152686026522624000000}[/tex]
[tex]\\ \rm\Rrightarrow 834451800[/tex]
Answer:
834,451,800
Step-by-step explanation:
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
Binomial Coefficient
[tex]\large \text{$ \rm ^{n}C_r=\dfrac{n!}{(n-r)!r!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35!}{(35-12)!12!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35!}23!12!} $}[/tex][tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35!}{23!12!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=\dfrac{35 \times 34 \times 33 \times ... \times 25 \times 24}{12!} $}[/tex]
[tex]\large \text{$ \rm \implies ^{35}C_{12}=834451800 $}[/tex]
Find p write your answer in simplest radical form
Answer:
[tex]p =[/tex] [tex]7\sqrt{2}[/tex]
Step-by-step explanation:
The side length ratio for a 45-45-90 angle triangle is [tex]1:1:\sqrt{2}[/tex]
The length of the bottom adjacent side of the 90-degree angle is 7, so p would be [tex]7\sqrt{2}[/tex]
.. Discuss the nature of the root of equation x2 + 2x + 3 = 0
Answer:
No real rootsStep-by-step explanation:
Given equation:
x² + 2x + 3 = 0On comparing the equation by ax² + bx + x = 0, We get: a = 1, b = 2 and c = 3
To Find the nature of the roots of the equation firstly we need to find the discriminant of the equation. The expression b²- 4ac is called the discriminant.
[tex]~[/tex]
Two Distinct real roots, if b² - 4ac > 0Two equal real roots, if b² - 4ac = 0No real roots, if b² - 4ac < 0[tex] \\ \: \: \dashrightarrow \: \: \: \sf {b}^{2} - 4ac = 0 \\ \\ \\\: \: \dashrightarrow \: \: \: \sf (2)² - 4 \times 1 \times 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 4 \times 1 \times 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 12 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf {\underline{\boxed{\sf{\purple{ -8 > 0}}}}} \\ \\ [/tex]
The discriminant is smaller than 0.
Hence, Equation has no real roots (no solution)The length and width of a rectangle are consecutive even integers. The perimeter is 92 meters. Find the length and width!
Answer:
w represents the width
w + 2 represents the length
2(w + w +2) = 76 formula for perimeter
w + w + 2 = 38 divide both sides by 2
2w + 2 = 38 combine like terms
2w = 36 subtract 2 from both sides
w = 18 divide both sides by 2
✓ Be sure your photo is not blurry
7x-3(5x+2)-6(7+2x)
Answer:
-20x-48
Step-by-step explanation:
7x-(15x +6)-6(7+2x)
7x-(15x+6)-(42+12x)
7x-15x-6-42-12x
(7x -15x-12x)+(-6-42)
=-20x-48
Answer:
-20x - 48
Step-by-step explanation:
7x - 3(5x +2) - 6*(7 + 2x) = 7x + (-3)*5x + (-3)*2 + (-6)*7 + (-6)*2x
= 7x - 15x - 6 - 42 - 12x
= 7x - 15x - 12x - 6 -42 {Combine like terms}
= -20x - 48
On a number line 1.77 would be located where?
Step-by-step explanation:
1.77 would be closer to 2
how do I solve this?
Which conditional probabilities are correct? check all that apply. p(d | f) = startfraction 6 over 34 endfraction p(e | d) = startfraction 7 over 25 endfraction p(d | e) = startfraction 7 over 25 endfraction p(f | e) = startfraction 8 over 18 endfraction p(e | f) = startfraction 13 over 21 endfraction
The conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
How to determine the true conditional probabilities ?The conditional probability P(A|B) is calculated using:
P(A | B) = P(A and B)/P(B)
Using the above formula and the data in the complete question (see attachment), we have the following computations:
P(D | F) = 6/34
P(E | D) = 7/25
P(D | E) = 7/18
P(F | E) = 8/18
P(E | F) = 8/34
By comparing the above computations with the options, the conditional probabilities that are correct are P(D | F) = 6/34, P(E | D) = 7/25 and P(F | E) = 8/18
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Answer:
A, B, D
Step-by-step explanation:
yw :)
30 POINTS. HELP!
Which of the three types of discontinuities (removable, jump, and infinite), would be represented by a limit that can only be found by simplifying a rational expression or multiplying by a conjugate? Why?
Answer:
jump equation
bu multiplying by a conjugate
Suppose your friend's parents invest $ 10,000 in an account paying 5% compounded annually. What will the balance be after 8 years?
Answer:
A = $14,745.544
Step-by-step explanation:
The equation for compound interest is
A = P (1+i)t
A = final value
P = amount invested (principal) (10000)
i = interest rate, expressed as a decimal (.05)
t = number of years invested (8)
This formula assumes annual compounding.
Plugging in what we know.
A = 10000(1.05)^8
A = 10000 (1.47745544)
A = $14,745.544
Please help me on this question I’m very confused I will give you brainless??
To solve this problem, we need to use the theorem which states that the sum of angles in a triangle is equal to 180 degrees. The value of m<FED is equal to 120 degrees. From the diagram given, m<CBD is complimentary with m<BED
Sum of Angles in a TriangleThe value of m<FED can be calculated by summing the entire entity and equating to 180 degrees.
Data;
m<FED = (16x - 8)m<EFD = 35m<EDF = 2x + 9[tex]35+(16x-8)+(2x+9) = 180[/tex]
Reason: The sum of angles in a triangle is equal to 180 degrees.
But we would need to solve for the value of x.
[tex]35+(16x-8)+(2x+9) = 180\\35 + 16x - 8 + 2x + 9 = 180\\36+ 18x = 180\\180 - 36 = 18x\\18x = 144\\x = \frac{144}{18} \\x = 8[/tex]
Let's substitute the value of x into m<FED
[tex]m < FED = 16x - 8\\x = 8\\m < FED = 16(8) - 8 \\m < FED = 128 - 8\\m < FED = 120^0[/tex]
The value of m<FED is equal to 120 degrees.
From the diagram given, m<CBD is complimentary with m<BED
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The Ferris wheel at the museum park has a height requirement of 48 inches your little sister is 45 inches tall how much taller does she need to go before she can ride the Ferris wheel
Answer:
3 inches
Step-by-step explanation:
48 - 45 = 3
Help. Please and thanks
Step-by-step explanation:
24.
AC = 12 = cos(angle) × AB = cos(angle) × 13
imagine a circle with center in A and radius 13.
that is why we can say AC = cos(angle) × radius, and BC = sin(angle) × radius.
cos(angle) = 12/13 = 0.923076923...
angle = 22.61986495...°
so, B is the right answer.
25.
we have a right-angled triangle.
from the point in the ground, where the ladder starts, to the point on the wall, where the ladder ends, and the point on the ground right under the wall point.
at this ground point there is the right angle.
at the ladder ground point we have 70°.
so, the angle at ladder/wall point is
180 - 90 - 70 = 20°.
remember, the sum of all angles in a triangle is always 180°.
the ladder itself (20 ft) is the Hypotenuse (the baseline opposite of the 90° angle).
the height of the ladder/wall point is one leg (and what we need to calculate), and the ground distance from the ladder/ground point to the point right under the ladder/wall point is the second leg.
we can use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being always opposite of the associated angles.
so, we have
20/sin(90) = 20/1 = 20 = height/sin(70)
height = 20×sin(70) = 18.79385242... ft
so, D is the right answer.
Find any 2 irrational no. Between 0.1 and 0.12
0.10100100010000 and 0.110100100010000 are two irrational numbers between 0.1 and 0.12.
Step-by-step explanation:
Any two irrational Numbers between 0.1 and 0.12 will be those numbers which will be=> greater than 0.1 and smaller than 0.12
And those numbers are = 0.10100100010000 and 0.110100100010000.You can also choose any other numbers too.
___________________Irrational Number :
Irrational numbers are non terminatingNon recurring / repeatingYou wish to test the following claim (
H
a
) at a significance level of
α
=
0.002
.
H
o
:
μ
=
63.5
H
a
:
μ
<
63.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size
n
=
62
with mean
M
=
56.3
and a standard deviation of
S
D
=
13.2
.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Using the t-distribution, it is found that the desired measures are given as follows:
The test statistic is t = -4.29.The p-value is of 0.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 63.5, that is:
[tex]H_0: \mu = 63.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:
[tex]H_1: \mu < 63.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]
t = -4.29.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.
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3.2 × 10^7
write in expanded form
Answer:
32000000
Step-by-step explanation:
3.2 x 10 = 32
you will have 10^6 left
32 x 10^6 = 32000000
just add 6 zeroes
Answer:
32, 000, 000.
Step-by-step explanation:
3.2 x 10^7 <======= move the decimal 7 places to the right
32,000,000.
You accidentally dropped a coin from the top of 12 stairs. What is the probability that it will land on the fifth step heads up?
This is a probability question! I need help ASAP
Answer:
The answer is 1/24
Step-by-step explanation:
1stepout of the 12 is the 5th so 1/12 and divid by 2 because you want it to land on heads.
Maya has savings of $40,000. She invests in a bond mutual fund that pays 5% interest each year. Ignoring compounding, what are Maya's total savings after 20 years?
Answer:50,000 x 0.04 x 20=40,000
The total saving after 20 years 50,000+40,000=90,000$
given that (3x+2) is a factor of 3x^3+bx^2-3x-2. find the value of b?
Answer:
[tex]b = 2[/tex].
Step-by-step explanation:
By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].
Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:
[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].
Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:
[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].
Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:
[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].
[tex]b = 2[/tex].
look at the attachment and solve
The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.
What is a perpendicular bisector?A perpendicular bisector of a line segment is a line segment that is perpendicular to and passes through the middle of the line segment (left figure). A line segment's perpendicular bisector can be drawn using a compass by drawing circles centred at and with radius and connecting their two intersections.
The construction that is been demonstrated in the figure is The first mark for constructing a perpendicular bisector.
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3) A customer in a bookstore is interested in eleven books on sale.
How many ways can she select three books to buy?
What is the circumference of the circle? (use 3.14 for pi)
(WORTH 30 POINTS)
Answer:
119.32
Step-by-step explanation:
[tex]A = 2 * 3.14 * 19 = 119.32[/tex]
Determine whether the function x2 = –y – 2 is quadratic or not. Explain.
Answer:
Yes, it is.
Step-by-step explanation:
A quadratic function always has [tex]x^{2}[/tex] [tex]x[/tex]≠0The function x² = -y - 2 is a quadratic function.
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.
As per the given data:
The function is x² = -y - 2
Rearranging the function:
y = x² - 2
A quadratic function is always of the form:
y = ax² + bx + c, where a, b and c are real numbers with a not equal to 0.
We can write y = x² - 2 as:
y = x² + 0(x) - 2, here a = 1, b = 0, c = -2
Hence, the function x² = -y - 2 is a quadratic function.
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Given that A, O & B lie on a straight line segment, evaluate obtuse ∠AOC.
The diagram is not drawn to scale.
∠AOC=
Answer:
AOC = 124°
Step-by-step explanation:
Angle on a straight line is 180°, therefore, the sum of the three angles shown is 180;
This can be written like so:
(3x + 94) + (x + 30) + (2x - 4) = 180
This equation can be solved to find x:
6x + 120 = 180
6x = 180 - 120
6x = 60
x = 10
AOC = 3(10) + 94
= 30 + 94
= 124
Answer:
angle AOC = 124
Step-by-step explanation:
3x + 94 + x + 30 + 2x - 4 = 180 ( ^'s on a STR line)
6x = 180 - 120
6x = 60
x = 10
sub x into 3x + 94
3(10) + 94 = 124
i need help with this math
Answer:
(-0.6, 8.4)
Step-by-step explanation:
so first, we have to find out what x is. because y is equal to itself, we can substitute to get
[tex]x+9=-4x-6\\5x+9=6\\5x=-3\\x=-\frac{3}{5}[/tex]
now we can plug in the value of x to find y
[tex]y=-\frac{3}{5} +9\\y=8\frac{2}{5}=8.4[/tex]
your answer is written in the form (x,y) so the answer is (-0.6, 8.4)
Answer: Heyaa! ~
Your Answers are... (-0.6, 8.4)
Step-by-step explanation:
Hopefully this helps you!
~ Lets solve:
Use one equation to find an expression for one of the variables in terms of the other variable. Then substitute that expression in place of that variable in the second equation. You can then solve this equation as it will now have only one variable.
Is 2/3 < 3/4 , or is 3/4 < 2/3 ? Explain how you know.
Answer:2/3 < 3/4
Step-by-step explanation: 3/4 is greater than 2/3.
share the ration .....
Answer:
Tom: £166
Ben: £581
Step-by-step explanation:
In the ratio 2 : 7 there are 9 portions total (2 + 7 = 9).
£747 / 9 = £83
For Tom:
£83 * 2 = £166
For Ben:
£83 * 7 = £581
Checking our work:
Since the decimals are the same, this means the ratios are equal.
2/7 = 0.2857
166/581 = 0.2857
Write the equation of the line in fully simplified slope-intercept form.
Answer:
The answer to writing this graph in fully simplified slope-intercwpt form is y = 1/5x - 7.
Help me plsssssssssssss
Answer:
3/1/4
That's the expression represents Lena's speed in miles per hour
Question 5 of 25
Which graph shows a system with an infinite number of solutions?
A. Graph A
B. Graph C
C. Graph B
Answer:
The answer is Graph C.
Step-by-step explanation:
Both the equation of each other are the same in Graph C..
Answer:
B. Graph C
The lines are together, so every point they pass is a solution
The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows: Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245 Cleveland 126 Orlando 146 Dallas 123 Phoenix 139 Denver 120 Pittsburgh 134 Detroit 144 San Francisco 167 Houston 173 Seattle 162 Los Angeles 160 St. Louis 145 Miami 192 Washington, D.C. 207
The mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
What is the mean?The mean is the average of a set of data or numbers.
It is a typical value that averagely represents the dataset.
The mean can be computed by dividing the total by the number of data values.
Data and Calculations:Atlanta $163
Minneapolis $125
Boston 177
New Orleans 167
Chicago 166
New York 245
Cleveland 126
Orlando 146
Dallas 123
Phoenix 139
Denver 120
Pittsburgh 134
Detroit 144
San Francisco 167
Houston 173
Seattle 162
Los Angeles 160
St. Louis 145
Miami 192
Washington, D.C. 207
Total = $3,181
Mean = $159.05 ($3,181/20)
Question Completion:What is the mean hotel room rate?
Thus, the mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
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