Answer:
The answer is "[tex]7.21 \times 10^{37}[/tex]".
Step-by-step explanation:
[tex]\to ^{n}_{C_r}=\frac{n!}{r!(n-r)!}[/tex]
[tex]=^{66}_{C_{33}} \times ^{66}_{C_{22}} \times ^{55}_{C_{1}} \\\\=\frac{66!}{33! (66-33)!} \times \frac{66!}{22! (66-22)!} \times \frac{55!}{1! (55-1)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times \frac{55\times 54!}{1! (54)!}\\\\=\frac{66!}{33! (33)!} \times \frac{66!}{22! (44)!} \times 55\\\\= 7219428434016265740 \times 182183167981760400\times 55\\\\[/tex]
[tex]= 7.21 \times 10^{18} \times 1.82\times10^{17}\times 55\\\\= 7.21 \times 10^{35} \times 1.82\times 55\\\\=721.721 \times 10^{35}\\\\=7.21\times 10^{37}[/tex]
ACTIVITY 1. Evaluate the following (a) sin60° (b) tan 34° (c)cos 124°
Answer:
(a) sin 60° = √ 3/ 2 OR 0.8660
(b) tan 34° = 0.6745
(c) cos 124° = − 0.5591
Shaun is planting trees along his driveway, and he has 66 redwoods and 66 pine trees to plant in one row. What is the probability that he randomly plants the trees so that all 66 redwoods are next to each other and all 66 pine trees are next to each other
Answer:
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
Step-by-step explanation:
The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
Desired outcomes:
Two cases:
6 redwoods(6! ways) then the 6 pine trees(6! ways)
6 pine trees(6! ways) then the 6 redwoods(6! ways)
So
[tex]D = 2*6!*6![/tex]
Total outcomes:
12 trees, so:
[tex]D = 12![/tex]
What is the probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other?
[tex]p = \frac{D}{T} = \frac{2*6!*6!}{12!} = 0.0022[/tex]
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
A television and DVD player cost a total of $1230. The cost of the television is two times the cost of the DVD player. Find the cost of each item
Answer:
Television = 820
DVD Player = 410
Step-by-step explanation: Imagine the television as 2, and the DVD player as 1. If you’re were to draw it out with boxes, you’d see that the tv has two boxes and the DVD player has 1 box. All are exactly the same amount, and there are a total of three boxes. So divided 1230 by 3 and you get 410. Using the idea of the boxes, the DVD player get’s one 410, and the tv gets two 410s, or 820.
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an
approximation for
90 m
40
2,794 square meters
1,256 square meters
974 square meters
O 6,844 square meters
The approximate area of the shaded region is 2794 m². The correct option is the first option 2794 square meters
From the question, we are to determine the approximate area of the shaded region
The area of the shaded region = Area of the triangle - Area of the circle
Area of triangle = 1/2 × base × height
Area of the triangle = 1/2 × 90 × 90
Area of the triangle = 4050 m²
Area of a circle = πr²
Where r is the radius
In the diagram,
Diameter = 40 m
∴ Radius = 40/2 = 20 m
Thus,
Area of the circle = π × 20²
Area of the circle = 3.14 × 400
Area of the circle = 1256 m²
Therefore,
The area of the shaded region = 4050 m² - 1256 m²
The area of the shaded region = 2794 m²
Hence,
The darkened area covers about 2794 m²
Learn more on Calculating area here: https://brainly.com/question/14989383
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HELP! NO SCAMS PLZ, i need to know how to write the proportion.
Answer:
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
4+z/y = 36/18
Step-by-step explanation:
a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:
16/4 = 18/y
Note that the arrangement depends on which of the triangles sides cones first.
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
b) Same rule in (a) applies to the sum as well. Hence;
4+z/y = 16+20/18
4+z/y = 36/18
Which congruency statement would not result in triangle BCD cong triangle QRS ?
Option C
Because in Side Angle Side there should be 2 sides and a angle stuffed between them.
In this If CD ≅ RS then √QRS is not ≅ and We cannot use SAS
Therefore the wrong statement is Option c
Answered by Gauthmath must click thanks and mark brainliest
Because in Side Angle Side there should be 2 sides and a angle stuffed between them.
In this If CD ≅ RS then √QRS is not ≅ . Option C is correct
To determine a congruency statement that would not result in Triangle BCD being congruent to Triangle QRS, we need to find a condition that does not satisfy the congruence criteria. The congruence of two triangles can be determined by considering their corresponding angles and sides.
Here are the possible congruency statements:
Angle-Angle-Side (AAS): If we have two angles of one triangle congruent to two angles of the other triangle, and the included side between these angles congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.
Angle-Side-Angle (ASA): If we have two angles of one triangle congruent to two angles of the other triangle, and a side adjacent to one of these angles congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.
Side-Angle-Side (SAS): If we have two sides of one triangle congruent to two sides of the other triangle, and the included angle between these sides congruent, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.
Side-Side-Side (SSS): If we have all three sides of one triangle congruent to the corresponding sides of the other triangle, we can establish congruence. This statement could result in Triangle BCD being congruent to Triangle QRS.
Based on these congruency statements, there is no option that would not result in Triangle BCD being congruent to Triangle QRS. All four statements have the potential to establish congruence between the two triangles.
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a) Express the prime number 31 as the difference of two squares? 31 =
Answer:
31 = 16²-15²
Step-by-step explanation:
16² = 256
15² = 225
256 - 225 = 31
In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 2000. In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.
Required:
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared with the proportion in 1999
Answer:
The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
1999:
20 out of 100 in the bottom third, so:
[tex]p_1 = \frac{20}{100} = 0.2[/tex]
[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
10 out of 100 in the bottom third, so:
[tex]p_2 = \frac{10}{100} = 0.1[/tex]
[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternative hypothesis, we test if the proportion has been reduced, that is, the subtraction of the proportion in 1999 by the proportion in 2001 is positive. So:
[tex]H_1: p_1 - p_2 > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of at least 0.1, which is the p-value of z = 2.
Looking at the z-table, the p-value of z = 2 is 0.9772.
1 - 0.9772 = 0.0228.
The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Find the length of BC, last one
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.
tan(54) = 16/BC
BC = 16/tan(54)
BC = 11.62 units
Hope this helps!
Find the transpose of AB
Answer:
see above is the answer handwriting is bad sorry for that
. Two mutually exclusive projects have projected cash flows as follows:
YEAR PROJECT A PROJECT B
0 Ksh. -2m Ksh. -2m
1 1m 0
2 1m 0
3 1m 0
4 1m 6m
Required:
a) Determine the internal rate of return for each project. [2 Marks]
b) Determine the net present value for each project at discount rates of 0, 5,10,20,30, and 35 percent. [2 Marks]
c) Plot a graph of the net present value of each project at the different discount rates. [2 Marks]
d) Which project would you choose? Why? [ 2 Marks]
e) What is each project’s MIRR if the cost of capital is 12 percent?
Answer:
yes
Step-by-step explanation:
Solve.
69) One number is 2 less than a second number.
Twice the second number is 16 more than 4 times
the first. Find the two numbers.
Answer:
-4,-6
Step-by-step explanation:
x = y-2
2y = 4x+16
2y = 4(y-2) + 16
2y = 4y -8 + 16
-2y = 8
y = -4
x = -6
What is the key difference between simple interest and compound interest, and how does this difference affect the effectiveness of each? PLSSS HELP I HAVE ONE DAY LEFT
Answer:
The key difference between simple interest and compound interest is that in simple interest, the interest is calculated based on the principal amount of the loan.
The formula is principal multiplied by time by rate divided by 100.
Compound interest on the other hand, has to do with the principal amount and accumulated interest on previous periods.
The difference affects the effectiveness of each because in SI, interest is calculated once, while in CI, there's accumulated interest.
Which of the following shows the extraneous solution to the logarithmic equation below?
2 log Subscript 5 Baseline (x + 1) = 2
Answer:
x=4
Step-by-step explanation:
log5(x+1)=1, (x+1)=5, x=4
Answer:
x= -6
Step-by-step explanation:
i got it wrong and the answer is -6
The manager at a smoothie stand keeps track of the number of protein smoothies and berry smoothies sold each day and the total money received. On Saturday, a total of 43 smoothies were sold, and the money collected was $314. If protein smoothies are sold for $10 and berry smoothies are sold for $6, how many protein smoothies and berry smoothies were sold?
Answer:
Protein smoothie =14
Berry Smoothie= 29
Step-by-step explanation:
Let number of protein smoothie be X
Let number of berry smoothie be Y
1. X+Y=43
Y=43-X
2. 10X+6Y=314
5X+3Y= 157
5x+3(43-x)=157 (substitute)
5x+129-3x=157
2x=157-129
x=14
X+Y=43
Y=43-14
Y=29
Brainliest please~
What is the period of the graph of y = 5 sin (pi x) + 3?
Equate whats inside (arguments) [tex]\sin[/tex] with base period of sine function [tex]2\pi[/tex] and solve for x to get period,
[tex]\pi x=2\pi\implies x=2[/tex]
So the period of the graph of the given function is precisely 2.
Hope this helps :)
Answer:
Step-by-step explanation:
bvjvhvghj
What is 3.24 ( 4 repeating) as a fraction?
Answer:
81/25
Step-by-step explanation:
change 3.24 into faction
324 over 100 because there are two decimal points .
simplfy into the smallest fraction
the answer is 81 over 25
Can you please help me
Answer:
Step-by-step explanation:
⅝ - 5/9 = 5/72
Express the prime number 19 as the difference of two squares? 19 =
Answer:
The two squares are 81 and 100, and their difference is 19
Step-by-step explanation:
Hey there!
Let's take out the square of 1st ten natural numbers to find out the exact answer.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
Now; You can take any of these numbers and subtract from their squares.
So, let's check 6² and 5²
36-25 = 11 which is not equal to 19
Again check for 10²-9²
100 - 81 = 19 (True value)
Therefore, 19 can be expressed as the difference of square of 10 and 9.
Hope it helps!
If one ruler and three pencils cost N120 and two
rulers and one pencil cost N140. Find the cost of
one ruler and one pencil
Answer:
N80
Step-by-step explanation:
One ruler is N60 and one pencil is N20.
write your answer in simplest radical form
Answer:
please tell me the complete question
Determine if the statement is always, sometimes, or never true:
An equilateral triangle is an acute triangle.
never
always
sometimes
The answer is always your welcome
Answer:
always
Step-by-step explanatia;won:
Walnut High Schools Enrollment is exactly five times as large as the enrollment at walmut junior high the total enrollment for the two schools is 852 what is the enrollment at each school
Answer:
Enrollment at walnut junior = 142
Enrollment at walnut high = 710
Step-by-step explanation:
Let :
Enrollment at walnut junior = x
Enrollment at walnut high = 5x
Total enrollment in both schools = 852
Mathematically ;
x + 5x = 852
6x = 852
x = 142
5x = 142 * 5 = 710
Hence,
Enrollment at walnut junior = 142
Enrollment at walnut high = 710
Alex purchased
1/2
of a gallon of milk. He put
2/11
of the milk in a smoothie. How much of a gallon of milk did Alex put in his smoothie?
Answer:
1/11 of a gallon
Step-by-step explanation:
He used 2/11 of 1/2 gallon
2/11 * 1/2 = 1/11 of a gallon
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
Step 1: Find how much of a gallon he used
[tex]\frac{2}{11} * \frac{1}{2} =\frac{2}{22}[/tex]
[tex]\frac{2}{22}=\frac{1}{11}[/tex]
Answer: [tex]\frac{1}{11}[/tex]
A spectator can hear the sound of football after 3 seconds of it's bouncing. What is the distance of the ball from the spectator?
I will give BRAINLIEST to the answer
Answer:
1020m = 1.02km
Step-by-step explanation:
Speed of sound is about 340m/s.
it takes 3s for the sound to reach the ear of the spectator, thus the sound-source is 340 * 3m ( 1020m ) away.
Question
If a triangle has sides of length x x + 2, and x - 4, what is the perimeter of the triangle in terms of x?
О 3х - 6
03x - 2
3x + 2
O 3x + 6
9514 1404 393
Answer:
(b) 3x -2
Step-by-step explanation:
The perimeter is the sum of the side lengths:
P = (x) +(x +2) +(x -4)
P = (x +x +x) +(+2 -4)
P = 3x -2
What is the value of the expression below? (27^2/3)^1/2
A. 9
B. 81
C. 27
D. 3
Answer:it’s 3
Step-by-step explanation:
Source trust me bro
need confirmation on this....
Answer:
X + 2y = 1
3x + y = 13
Step-by-step explanation:
A and b are the coefficients of X and y
I wasn't sure about my answer so used Gauthmath
Order the expressions from least to greatest.
Anwser
4 then 5 then 6
Answer:
This the right order:
4^2+2^2 = 20
5^2= 25
6^2-6 = 30
Which table represents a proportional relationship?
9514 1404 393
Answer:
C)
Step-by-step explanation:
The table that has a constant ratio between y and x values is the one that represents a proportional relationship.
A) 2/4 ≠ 4/16
B) 1/1 ≠ 4/16
C) 6/8 = 12/16 = 18/24 = 30/40, a proportional relationship
