Answer:
[tex]\frac{1}{4845}[/tex] probability that you and your 3 friends will be selected.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the volunteers are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
You and the 3 friends(4 people), from a set of 4. So
[tex]D = C_{4,4} = \frac{4!}{4!0!} = 1[/tex]
Total outcomes:
20 people from a set of 20. So
[tex]T = C_{20,4} = \frac{20!}{4!16!} = 4845[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1}{4845}[/tex]
[tex]\frac{1}{4845}[/tex] probability that you and your 3 friends will be selected.
Which of the following parabolas is 2 units higher than y=2x2−4x−1, but has the same shape and opens in the same direction?
Answer:
y=2x^2-4x+1
Step-by-step explanation:
i hope that’s right :)
I need this please help me
Solve for x when sin(4x)=1/2
the most simple answere please
Answer:
x=7.5
Step-by-step explanation:
To cancel out the sin function we need to mulitplly it by sin⁻¹ (you can usually access this button if you press 2nd-->sin)
so sin⁻¹(.5)=30
30=4x
x=7.5
Solve for X (round to the nearest hundred)
Step-by-step explanation:
We use tangent because it uses opposite over adjacent.
So,
tan 33 = x/46
or
46 * tan 33 = x
Type this into the calculator and you get around 29.87
Solve for 44.
51°
64 = [?]
44 42=72°
57°
I
Answer:
look at the picture i have sent
Answer:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
Step-by-step explanation:
we are given a triangle
and we want to figure out the missing exterior angle of the triangle
in order to so
remember
the straight line theorem
therefore we get:
[tex] \displaystyle {72}^{ \circ} + \angle4 = {180}^{ \circ} [/tex]
cancel 72° from both sides:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
Alternate way:recall that,
if a side of a triangle is extended then exterior angle so formed equal to the sum of the two opposite interior angles
so we acquire:
[tex] \displaystyle {51}^{ \circ} + {57}^{ \circ} = \angle4 [/tex]
simplify addition:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
Express tan(-310°) as a function of a positive acute angle in
terms of tan x
guessing
360 - 310 = 50
-tan(50)
aylor and Natsumi are making block towers out of large and small blocks. They are stacking the blocks on top of each other in a single column. Taylor uses 4 large blocks and 2 small blocks to make a tower 63.8 inches tall. Natsumi uses 9 large blocks and 4 small blocks to make a tower 139.8 inches tall. How tall is each large block and each small block
Answer:
The height of a large block is of 12.1 inches and of a small block is of 7.7 inches.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x i the height of a large block.
y is the height of a small block.
Taylor uses 4 large blocks and 2 small blocks to make a tower 63.8 inches tall.
This means that:
[tex]4x + 2y = 63.8[/tex]
Simplifying by 2:
[tex]2x + y = 31.9[/tex]
So
[tex]y = 31.9 - 2x[/tex]
Natsumi uses 9 large blocks and 4 small blocks to make a tower 139.8 inches tall.
This means that:
[tex]9x + 4y = 139.8[/tex]
Since [tex]y = 31.9 - 2x[/tex]
[tex]9x + 4(31.9 - 2x) = 139.8[/tex]
[tex]9x + 127.6 - 8x = 139.8[/tex]
[tex]x = 12.1[/tex]
[tex]y = 31.9 - 2x = 31.9 - 2(12.1) = 7.7[/tex]
The height of a large block is of 12.1 inches and of a small block is of 7.7 inches.
Can you pls find the surface area AND volume? ITS WORTH 50 points
Answer:
64
Step-by-step explanation:
Answer:
Solution given:
r=4in
h=4in
surface area=2πr(r+h)=2π*4(4+4)=64π or201.06ft²
Volume=πr²h=π*4²*4=64π or 201.06ft³
True or False:
In the diagram, ∠1 and ∠2 are adjacent angles.
Explain your thinking.
Answer:
false
Step-by-step explanation:
adjacent angles should share a common arm and a common vertex. no arms are common and vertex of first angle is CAB whereas the vertex of second angle is DAE
Answer: false
Step-by-step explanation:
Adjacent angles are angles share the same vertex and the same common side. They are two angles that are right next to each other.
What is the greatest common factor of 12 and 20?
OA) 2
O B) 3
4
D) 6
Answer:
4
Step-by-step explanation:
You can divide both numbers by four and get an even answer
Answer:
4
Step-by-step explanation:
Find the length of the third side. If necessary, write in simplest radical form. 9 5
Step-by-step explanation:
[tex](9) {}^{2} = (5) {}^{2} + (x) {}^{2} \\ 81 = 25 + {x}^{2} \\ {x}^{2} = 56 \\ x = 2 \sqrt{14} = 7.4[/tex]
Find the domain of the rational function.
C(x) = x+9/X^2 -16
Answer:
Domain = {x : x ≠ 4 , -4} or (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)
Step-by-step explanation:
TO FIND :-
Domain of [tex]C(x) = \frac{x + 9}{x^2 - 16}[/tex]SOLUTION :-
Domain of a function is a value for which the function is valid.
The function [tex]C(x) = \frac{x + 9}{x^2 - 16}[/tex] is valid until the denominator is 0.
So make sure that the denominator must not be 0.
[tex]=> x^2 - 16 > 0[/tex]
Find the values of x for which the denominator becomes 0. To find it , you'll have to solve the above inequality.
Add 16 to both the sides[tex]=>x^2 - 16 + 16 > 0 + 16[/tex]
[tex]=> x^2 > 16[/tex]
[tex]=> x > \sqrt{16}[/tex]
[tex]=> \boxed{x > 4} \: or \:\boxed{x > -4}[/tex]
We can say that 4 & -4 can't be domains because these values will make the function undefined.
Now try putting values of x such that -4 < x < 4. You'll observe that the function will be valid for all those values of x between -4 & 4.
CONCLUSION :-
The function will be valid for any value of 'x' except 4 & -4. So in :-
Interval notation , it can be written as → (-∞ , -4) ∪ (-4 , 4) ∪ (4 , ∞)
Set builder notation , it can be written as → {x : x ≠ 4 , -4}
some please help asap !!
Answer:
The answer should be 0.66
The sum of two integers is 2. Their difference is 10.
What are the two integers?
-14 and -4
B
4 and 14
-2 and 4
D
-4 and 6
What is the length of the third side?
Answer:
√115
Step-by-step explanation:
14²= 9² + x²
x= √14²-9² = √115
Step-by-step explanation:
using Pythagores theorem
h²=p²+b²
14²=p²+9²
p²=196-81
p=√115
p=10.72
stay safe healthy and happy...ordered pairs does not represent a function?
{(5,−2),(−6,−4),(−2,3),(−1,−4)}
\{(-3, 4), (-8, 0), (3, -8), (-3, -4)\}{(−3,4),(−8,0),(3,−8),(−3,−4)}
\{(6, 3), (-1, 5), (-7, 3), (3, 0)\}{(6,3),(−1,5),(−7,3),(3,0)}
\{(3, 9), (2, 7), (9, 9), (4, -3)\}{(3,9),(2,7),(9,9),(4,−3)}
Answer:
1. \{(-3, 4), (-8, 0), (3, -8), (-3, -4)\}{(−3,4),(−8,0),(3,−8),(−3,−4)}
Step-by-step explanation:
The x values are repeating
Question Hannah wanted to investigate whether there was a difference in the time spent in the checkout line between two grocery stores in a large city. She went to Grocery Store J on a Monday morning and recorded the time, in minutes, it took 30 customers to go through a checkout line. Then she went to Grocery Store K on Monday afternoon and recorded the time it took 30 customers to go through a checkout line. Hannah calculated the mean number of minutes for the customers in each line. She intends to conduct a two-sample t-test for a difference in means between the two stores. Have all conditions for inference been met?
Answer:
Yes. All the conditions for inference have been met.
Step-by-step explanation:
The conditions for inference are:
a) The sample must be random. The selections of the 30 customers in each Grocery Store were not biased in any way.
b) The sampling distribution must be approximately normal.
c) The observations of the samples were independent.
d) Adequate of sample size. 30 customers represent an adequate sample
e) The variances are not known as they were disclosed in this case.
Which expression means the same as "the quotient of 8 less than x and 4"?
Answer:
(x - 8) -4
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!
Answer:
I think it's 18
Step-by-step explanation:
because I'm looking at 12/8 to be a ratio, that means that the size of the bigger figure had decreased by 12/8 or 1.5
then I divided the 27 by 1.5 to get the area of the small one which was 18.
Three times the square of a number is greater than a second number. The square of the second number increased by
6 is greater than the first number. Which system of inequalities represents these criteria?
0 xz>y and y2 + 6
o *x2>y and y2 +6>x
• 3x2 > y and y2 + 6>x
O 3x2 > y and y2 +6
(i don’t know the answer i just clicked on one)
The correct set of inequalities are - [tex]3x^{2} > y[/tex] and [tex]y^{2}+6 > x[/tex].
We have three times the square of a number is greater than a second number and the square of the second number increased by 6 is greater than the first number.
We have to find which system of inequalities mentioned represents this situation.
What is an inequality?An inequality is mathematical relation which compares two or more mathematical expressions.
In the question, it is given that -
Three times the square of a number is greater than a second number. Let the first number be [tex]x[/tex] and the second number be [tex]y[/tex].
According to question -
[tex]3x^{2} > y[/tex]
and - the square of the second number increased by 6 is greater than the first number. We can write this statement mathematically as -
[tex]y^{2}+6 > x[/tex]
Hence, the correct set of inequalities are - [tex]3x^{2} > y[/tex] and [tex]y^{2}+6 > x[/tex]
To solve more questions on inequalities, visit the link below -
https://brainly.com/question/20383699
#SPJ2
What is the volume of this solid figure made with cubes?
5 cubic units
O
15 cubic units
0
20 cubic units
O 23 cubic units
Quick answerrrr
Answer: 5
Step-by-step explanation:
hope this help get a A
Which number line shows the solution of -3x + 6 > 12
Answer:
x < -2
Step-by-step explanation:
subtract 6 from each side
-3x > 6
divide both sides by -3
x < -2
(with inequalities you must flip the sign if you divide by a negative number)
1) Jim took out a loan for $500. The rate is 8%. How much does Jim owe in interest if he pays it back in 4 1/2 years?
2) What is the balance that Jim owes for his loan?
Answer:
ito yung link o /fhytuewfxnopjbfw/ yan na po
Find the length of the leg x. Enter the exact value, not a decimal approximation.
Grandma decides to pay for her new granddaughter's education. She gives
her one penny on her first birthday, and doubles the gift every year. Round
to the nearest hundredth. Do not use a dollar sign, numerical values only.
What will be the total of all the gifts on the girl's 18th birthday?
Answer:
Around 0.40
Step-by-step explanation
If she doubles the gift every year, do 18x2=36, 36 rounds to 40 or 0.40.
The total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is evaluated as 2621.43 dollars
What is the sum of the terms of a geometric series till nth term?Lets suppose the geometric sequence has its initial term is [tex]a[/tex], multiplication factor is r, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
The sequence would look like [tex]a, ar, \cdots, ar^{n-1},\cdots[/tex]
For this case, we are specified that:
Grandma gives 1 penny on first birthday of her granddaughterGrandma increases the gift by doubling the previous birthday gift.That shows that the gift amounts each year will form a geometric sequence where a = 1, and r = 2 (as amounts are doubled).
The gift amounts would look like:
[tex]\\1, 2, 4, \cdots\\or\\1, 2\times 1, 2^2 \times 1, \cdots[/tex]
We have to find these terms' sum till 18th term(18th term is the gift of her 18th birthday).
Thus, we have: n = 18, a = 1, and r = 2.
The sum will be:
[tex]S_n = \dfrac{a(r^n-1)}{r-1} = \dfrac{1(2^{18}-1)}{2-1} = 2^{18} - 1 = 262143 \: \rm cents[/tex]
There are 100 cents in 1 dollars,
Thus, 1 cent = 0.01 dollars,
and thus, 262143 cents form 2621.43 dollars.
Thus, the total of all the gifts on the girl's 18th birthday given from her grandma for this considered case is evaluated as 2621.43 dollars
Learn more about sum of terms of geometric sequence here:
https://brainly.com/question/1607203
f(n)=2n+1
g(n)=3n
Find f(n)+g(n)
Answer:
5n + 1
Step-by-step explanation:
f(n) + g(n) is just 2n + 1 + 3n , adding the two functions together!
Those expressions combine to 5n + 1 :)
Comprehension Question
Answer the question correctly for 30 dollars.
Read the sentence from paragraph 2.
If we continue throwing plastic bags in the garbage, our landfills will become towering mountains of trash.
What does this sentence show?
.A. the author’s use of humor to change the tone of the passage
B. the author’s use of exaggeration to make a point about landfills
C. the author’s use of details to support his argument for paper bags
D. the author’s use of description to provide personal experience on the topic
Answer:
B.
Step-by-step explanation:
Our landfills will not actually become towering mountains of trash, that's just a hyperbole used by the author to show the destructive impact that trash in large quantities can have.
What is the least common multiple of 3, 10, and 15?
Answer:
30
Step-by-step explanation:
30/3 = 10
30/10 = 3
30/15 = 2
Hope this helps!
A Survey of 85 company employees shows that the mean length of the Christmas vacation was 4.5 days, with a standard deviation of 1.2 days. Construct a 95% confidence interval for the population's mean length of vacation. ( , ) Round your answer to two decimal digits Construct a 92% confidence interval for the population's mean length of vacation. ( , ) Round your answer to two decimal digits
Answer:
The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).
The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).
Step-by-step explanation:
We have the standard deviations for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 85 - 1 = 84
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 84 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.989.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.989\frac{1.2}{\sqrt{85}} = 0.26[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.26 = 4.24 days
The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.26 = 4.76 days
The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).
92% confidence interval:
Following the sample logic, the critical value is 1.772. So
[tex]M = T\frac{s}{\sqrt{n}} = 1.772\frac{1.2}{\sqrt{85}} = 0.23[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.23 = 4.27 days
The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.23 = 4.73 days
The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).
what is the answer to 3(x-2)+15=-3(x-3)
i will give brainliest
Answer:
x = 0
Step-by-step explanation:
3(x - 2) + 15= -3(x - 3)
3x - 6 + 15 = -3x + 9
3x + 9 = -3x + 9
3x + 3x = 9 - 9
6x = 0
x = 0
