A company received 15 funding applications and want to select 8 of them to be funded. The number of different lists of successful applications is 6,435
Suppose we have n objects in total and we want to select r objects among total objects, the number of ways they can be selected is given by the combination formula:
ⁿCr = n! / [r! (n-r)!]
Data from the problem:
n = total applications = 15
r = number of selected applications = 8
Hence, the number of different lists of successful applications is:
¹⁵C₈ = 15! / [8! (15-8)!]
= 15! / [8! 7!]
= 6,435
Thus, the number of different lists can be selected is 6,435
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how large a sample is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05?
The required sample size for the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.
Given that the number of hours spent studying by students on large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours.
we want to find the size of the sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05.
Here, the margin of error is E=2 and the level of significance is α=0.05
The critical value is Zα/2=Z₀.₀₂₅
or the critical value is 1.96
Now, we will find the sample size
n=((Zα/2)×σ/E)²
n=(1.96×8.4/2)²
n=67.76
n≈68
Hence, the size of sample which is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05 is 68.
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Which points are on the graph of k(x)=(1/4)^x ?
Select each correct answer.
Responses
(−1, 4)
begin ordered pair negative 1 comma 4 end ordered pair
(0, 14)
begin ordered pair 0 comma 1 fourth end ordered pair
(3, 164)
begin ordered pair 3 comma 1 over 64 end ordered pair
(1, 4)
Answer:
(3, 1/64)
(−1, 4)
Step-by-step explanation:
took the test
Answer:
(3, 1/64)
(−1, 4)
Step-by-step explanation: toom the test :)
if roy is 4 years older than his brother and the product of their ages is 165, how old is roys younger brother
Roy's younger brother's age is 11 years.
According to the question,
We have the following information:
If Roy is 4 years older than his brother and the product of their ages is 165.
Now, let's take the age of Roy's younger brother to be x years.
Age of Roy = 4+x
So, we have the following expression:
x(4+x) = 165
[tex]x^{2} +4x-165=0[/tex]
Now, we will factorize this equation by splitting the middle term:
[tex]x^{2}[/tex]+15x-11x-165 = 0
Now, taking x as a common factor from the first two terms and -11 as a common factor from the last two terms:
x(x+15)-11(x+15) = 0
Taking (x+15) as a common factor:
(x+15) (x-11) = 0
x+15 = 0 and x-11 = 0
x = -15 and x = 11
Now, we know that age can not be negative.
Hence, Roy's younger brother is 11 years old.
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helium is pumped into a spherical balloon at a rate of 5 cubic feet per second. how fast is the radius increasing after 2 minutes?
The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³
Given,
The constant rate at which helium is pumped into the spherical balloon, r = 5 ft.³/s
We have to find the rate at which the radius of the balloon is increasing after 2 minutes.
Here,
dV/dt = (dV/dr) × (dr/dt)
Then,
dr/dt = (dV/dt) / (dV/dr)
The volume of balloon after 2 minutes (120 seconds) V₁₂₀ ;
V₁₂₀ = 120 s × 5 ft.³/s = 600 ft.³
The radius of balloon after 2 minutes ;
V = 4/3 π r³
dV/dr = 4 π r²
r = [tex]\sqrt[2]{\frac{2}{4.\pi } V}[/tex]
Then,
r₁₂₀ = [tex]\sqrt[2]{\frac{2}{4.\pi } 600}[/tex] ≈ 9.77
dr/dt = (dV/dt) / (dV/dr) = 5 / 4π r²
At t = 2 minutes (120 seconds), r ≈ 9.77 feet
dr/dt ≈ 5 / 4π 9.77² ≈ 4.16 × 10⁻³
That is,
The rate at which the radius of the balloon is increasing after 2 minutes is 4.16 × 10⁻³
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Sierra Left a 4.50$ tip for a waiter what was 18% of the bill before the tip
Answer:
$25.00
Step-by-step explanation:
Total amount of bill is $25.
Given information:
The amount of tip = $4.50
The percentage given = 18%
4.50 of 18% is $25
drew thinks the answer to the question 3/7 ÷ -2/3 is -6/21. Is drew correct.
No drew is incorrect and the right answer to this question is - 9/14 which can be calculated by using BODMAS rule.
What is BODMAS rule?
It stands for Bracket Of Division Multiplication Addition Subtraction which is a simple rule for solving calculation. It means first we solve brackets of a statement and so on.
Main Body:
Given :
⇒3/7÷ 2/3
This can be solved by changing the division to multiplication and taking reciprocal of the term behind it.
⇒3/7×-3/2
⇒-9/14
Hence the correct answer to the statement is -9/14.
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Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below: A. The thickness of the slices will be dx for both methods. B. When using the shell method, we cut the region into small slices perpendicular to the x-axis. C. When using the disk method, we cut the region into small slices perpendicular to the x-axis. D. The volume of the solid of revolution can be interpreted as the limit of Riemann sums. E. When using the shell method, we cut the region into small slices parallel to the x-axis. F. The shell method will always result in a less complicated integral. G. When using the disk method, we cut the region into small slices parallel to the z-axis.
The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.
(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using shell method, we cut region into small slices parallel to x-axis.
In the question ,
seven statements are given about a solid of revolution obtained by rotating a region R around the x-axis.
we have to find statement which are true .
Option (a)
Thickness of the slide is dx for disk method and
dy for the shell method while rotating about x - axis ,
So , statement of option(a) is false .
Option(b)
In shell method , elementary cylinders are drawn with axis of symmetry same as axis of rotation ,
thus the cylinder elements will be parallel to x axis rather than being perpendicular to the x axis ,
So , statement of option (b) is false .
Option(c)
In disk method , the slices are cut perpendicular to the axis of rotation , since we are rotating the region about x axis ,
Thus , slices are cut perpendicular to the x axis .
statement of option (c) is True .
Option (d)
As in 2D , the bounded area can be interpreted as a limit of Riemann sums , Similarly in 3D , the volume formed by rotating the bounded region about the x axis can be interpreted as a limit of Riemann sums .
So , statement of option(d) is True .
Option(e)
When using shell method, we cut region into small slices perpendicular to the x-axis .
So , statement of option(e) is False .
Option(f)
There can be both the kinds of cases , like in some cases disk method is easier than shell method and
in other cases shell method can be easier than disk method .
So , statement of option(f) is False .
Option(g)
When using disk method, we cut region into small slices perpendicular to x-axis .
So , statement of option (g) is False .
Therefore , The true statements are (c) When using disk method, we cut region into small slices perpendicular to x-axis.
(d) Volume of solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using shell method, we cut region into small slices parallel to x-axis.
The given question is incomplete , the complete question is
Consider a solid of revolution obtained by rotating a region R around the x-axis. Select all the True statements below:
(a) The thickness of the slices will be dx for both methods.
(b) When using the shell method, we cut the region into small slices perpendicular to the x-axis.
(c) When using the disk method, we cut the region into small slices perpendicular to the x-axis.
(d) The volume of the solid of revolution can be interpreted as the limit of Riemann sums.
(e) When using the shell method, we cut the region into small slices parallel to the x-axis.
(f) The shell method will always result in a less complicated integral.
(g) When using the disk method, we cut the region into small slices parallel to the z-axis.
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The figure shows three quadrilaterals on a coordinate grid:
A coordinate plane is shown. Quadrilateral D has sides measuring 3 units and 1 unit. Quadrilateral F has sides measuring 3 units and 1 unit. Quadrilateral E has sides measuring 2 units and 6 units.
Which of the following statements is true about the three quadrilaterals? (4 points)
Group of answer choices
D and E are similar but not congruent.
F and D are similar but not congruent.
E and F are similar and congruent.
D and E are similar and congruent.
The true statements about the three quadrilateral is
D and E are similar but not congruent.F and D are similar but not congruent.The measurements of quadrilateral D = 3 units and 1 units
The measurements of quadrilateral F = 3 units and 1 units
The measurements of quadrilateral E = 2 units and 6 units
The similar figure defined as the figures that have the same shape but not same size
The congruent is defined as the figures that have the same shape and size
Here D and F are congruent but they are not similar because they have same size
D and E are similar but not congruent because of same shape and different size.
Hence, true statements about the three quadrilateral is
D and E are similar but not congruent.F and D are similar but not congruent.Learn more about congruent here
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hi guys the question and numbers are in the image. could someone explain this in detail pls? I need to be able to do this by myself to.
Square root of 15.625
Square root of 15.625 is 3.906
What in mathematics is a square root?
A number can be generated by multiplying the square root of that number by itself. The word" square root" is represented by the symbol" sqrt" square root of, end square root. The reverse of squaring a number is chancing the square root.
How is the square root calculated?
The result of multiplying a number by itself yields its square value, while the square root of a number can be set up by looking for a number that, when squared, yields the original value. It follows that a a = b if" a" is the square root of"b."
Find the nearest perfect square, in this case 16 .
Subtract 4 from the number (15.625) (the square root of 16). The outcome is around 3.906
Calculate 3.953 by averaging 4 and 3.906. This approximate value represents the square root of 15.625.
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Write a linear function rule for the data in the table. x 0 1 2 3 4 y 3 1 –1 –3 –5 A. f(x) = 2x + 3 B. f(x) = –2x + 3 C. f(x) = 2x – 6 D. f(x) = –2x – 6
Answer:
f(x) = –2x + 3
Step-by-step explanation:
For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as.
For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic are as follows:
p-value = 0.09 is the probability of obtaining a value for the test statistic.
We are going step by step
Step 1) the p-value is the probability of obtaining a value for the test statistic at least as extreme as that provided by the sample
Step 2) Here the Confidence level is equal to 0.95
So the level of significance is equal to 0.05
p-value = 0.09
Since the p-value is higher than the level of significance that we do not reject the null hypothesis.
Hence the answer, the p-value = 0.09 is the probability of obtaining a value for the test statistic.
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If a triangle is equiangular, then the triangle is a(n) _ triangle
Equilateral
O Isosceles
Scalene
O Right
If the triangle is equiangular, then the triangle is an equilateral triangle.
What is equiangular triangle?
A triangle with three equal interior angles is called an equiangular triangle. In an equiangular triangle, the measure of each of its interior angles is 60
What is equilateral triangle?
an equilateral triangle is a triangle that has all its sides equal in length. Also, the three angles of the equilateral triangle are congruent and equal to 60 degrees. The sum of all three angles of an equilateral triangle is equal to 180 degrees. 60° + 60° + 60° = 180°.
As we can see, that in equilateral triangle, all the angles are of 60, as same as of equiangular triangle.
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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books. Determine the number of small boxes sent and the number of large boxes sent
The number of small boxes sent is 6 and the number of large boxes sent is 3.
Given:
Each small box can hold 20 books and each large box can hold 35 books. There were twice as many small boxes sent as large boxes, which altogether can hold 225 books.
Let x be the number of small boxes and y be the number of large boxes.
20x + 35y = 225
x = 2y
20(2y) + 35y = 225
40y + 35y = 225
75y = 225
divide by 75 on both sides
75y/75 = 225/75
y = 225/75
y = 3 large boxes.
x = 2y
= 2*3
x= 6 small boxes.
Therefore the number of small boxes sent is 6 and the number of large boxes sent is 3.
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What’s the answer for this equation: x<-x+7(x-2)
Answer:
x > 2.8
Step-by-step explanation:
x < -x + 7(x - 2)
Expand using the Distributive Property
x < -x + 7x - 14
x < 6x - 14
Subtract x from both sides
0 < 6x - 14 - x
0 < 5x - 14
Add 14 for both sides
5x > 14
x > 14/5
x > 2.8
From a balloon 849 feet high, the angle of depression to the ranger headquarters is 55°11'. How far is the
headquarters from a point on the ground directly below the balloon (to the nearest foot)?
The distance from the headquarters to a point on the ground directly below the balloon (to the nearest foot) is 1221 feet
How to find the distance requiredThe distance is calculated using tangent of the angle using the formula
tan x = opposite / adjacent
From the question it can be deduced that
x = 55°11'
opposite = the required distance
adjacent = 849 feet
solving for the opposite
tan x = opposite / adjacent
tan 55°11' = opposite / 849
opposite = 849 * tan 55°11'
opposite = 1220.793
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help I WILL GIVE BRAINLIEST
what is the answer for 63 divided by (5-48 equal
Answer:
-35.4
Step-by-step explanation:
Using PEMDAS divide 63 first by 5 and u will get:
63÷5=12.6Now we have 12.6-48. If we subtract them together we will get:
12.6-48= -35.4Hence, the answer is -35.4
Jace works as a salesperson at an electronics store and sells phones and phone accessories. Jace earns a $11 commission for every phone he sells and a $3 commission for every accessory he sells. On a given day, jace made a total of $102 in commission from all accessory and phone sales and he sold twice as many accessories as phones. Determine the number of phones sold and the number of accessories sold.
The sales of phones and accessories should be 6 and 12 each, correspondingly.
Explain the term commission?A simple definition of commission accounting is an income or expense incurred by the business throughout the course of a transaction. Usually, commission-based real estate companies or other sales organizations employ this style of bookkeeping.The data stated in question-
For each phone he sells, Jace receives a $11 commission, and for each accessory, he receives a $3 commission. Jace sold twice quite so many components as phones on any given day, generating a commission of $102 from both types of transactions.Let 'P' be the number of the phones sold.
Then, the accessory sold be '2P'.
The equation will form for the total cost will be;
11P + 3(2P) = 102
11P + 6P = 102
17P = 102
P = 102 / 17 =
P = 6 (number of sold phones)
Accessories sold = 2P = 2 x 6 = 12
Thus, the sales of phones and accessories should be 6 and 12 each, correspondingly.
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Last week, the price of apples at the grocery store was $1.75 per pound This week, the price has decreased by 20%. What are the prices of apples this week?
Answer:
The prices of apples this week is $1.40.
Step-by-step explanation:
First, convert the 20% into 0.20, then on a calculator, type this equation into it:
0.20 x 1.75 = 0.35
0.35 isn't the answer, but we use 0.35 to subtract it from 1.75:
1.75 - 0.35 = $1.40
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Heya hiya party people just need sum help!
If the equation for the this graph is f(x)= 2x - 3 and g(x) comes from translating f(x) down 2 units, what is the equation for g(x)?
g(x) = 2x - 3
g(x) = x + 1
g(x) = 2x - 5
g(x) = -x -5
Answer: a is the correct answer
Step-by-step explanation:
use the picture to determine x and y
The unknown value of x and y from the attached picture of a square is 8 and 11 respectively.
What is the variable in the square?A square is a four sided polygon with 4 equal angles and length.
The angle at each corner of a square = 90°The fourth corner = 90° - 36°
= 54°
Recall,
Alternate angles are equal
So,
(4x + 4)° = 36°
substract 4 from both sides
4x = 36 - 4
4x = 32
divide both sides by 4
x = 32/4
x = 8
(4y + 10)° = 54°
substract 10 from both sides
4y = 54 - 10
4y = 44
divide both sides by 4
y = 44/4
y = 11
In conclusion, the value of the following given equations are:
(4x + 4)° = 36°
4(8) + 4 = 36
32 + 4 = 36
36° = 36°
(4y + 10)° = 54°
4(11) + 10 = 54
44 + 10 = 54
54 ^= 54°
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Iterative formula please help me thank you!!
The value of x₃ , starting with x₁ = 8 is 4.578
Given in the question ,
The iterative formula for the sequence is
=> xₙ₊₁ = 5 - 2 / xₙ
Also , x₁ = 8
Putting n = 2 in iterative formula
x₂ = 5 - 2 / x₁
Substituting the value of x₁
=> x₂ = 5 - 2 / 8
=> x₂ = 5 - 1 / 4
=> x₂ = (20 - 1)/4
=> x₂ = 19/4
=> x₂ = 4.75
Now , putting n = 3
x₃ = 5 - 2 / x₂
Substituting the value of x₂
=> x₃ = 5 - 2 / x₂
=> x₃ = 5 - 2 / 4.75
=> x₃ = 5 - 0.421
=> x₃ = 4.578
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Jessica cuts a ribbon with a length of 12 inches into three pieces such that the length of one piece is 312 inches and the lengths of the other two are the same. What is the length of each of the other two pieces?.
The length of each of the other two pieces = 0.
Jessica cuts a ribbon with a length of 12 inches into three pieces.
The length of one piece is [tex]3\frac{1}{2}[/tex]
The lengths of the other two are the same
To find out the length of each of the other two pieces:
Based on the given conditions, we write formula as
(3-3)÷2
The sum of two opposites equals O: [tex]\frac{3-3}{2}[/tex]
Apply Zero property of Multiplication: 0
So we get the result = 0
Hence the answer if the length of each of the other two pieces = 0.
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Chris is decorating a bulletin board with boarders. She will put them along each side of the bulletin board (on the
Perimeter of rectangle) with Length 2.6 meters and width 1.2 meters. How much would she use?
Write numerical answer only (no sentences, no units)
Pls do it step by step on how to do it
Answer: 7.6 meters.
Step-by-step explanation:
1.2(2) + 2.6(2)
2.4 + 5.2
7.6
Remember, perimeter is L(2) + W(2).
The population of bacteria in an experiment
increases by 90% each day. If there were 100
bacteria at the beginning, how many would
there be after 5 days?
Hel
Skip
Answer:
450 bacteria
Step-by-step explanation:
90 percent of 100 is 90 90x5 is 450
last answer is 3 btw
Answer:
the rd one
Step-by-step explanation:
its the -21/2
if u need help tell me
4 in has a force of 50 applied. What is the pressure?
The pressure applied on a cubic object with side 4inches with 50N force is 50N/m
What is Pressure?Pressure is defined as the physical force exerted on an object. The force applied is perpendicular to the surface of objects per unit area. The basic formula for pressure is F/A (Force per unit area). Unit of pressure is Pascals (Pa).
1 inch= 0.025m
4inches= 0.025×4= 0.1m
Pressure = Force/area
area= 0.1×0.1= 0.01m^2
therefore Pressure= 50/0.01
= 5000N/m^2
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It’s due today! I need help asap!!
a) Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.
b) Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.
Define PEMDAS.According to the PEMDAS rule, the computation wrapped in brackets or the parenthesis comes first in the order of operation. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and finally addition and subtraction.
Given,
Expressions:
a) 5² - 9 ÷ 3
Using PEMDAS,
Squaring,
25 - 9 ÷ 3
Dividing,
25 - 3
Subtracting,
22
Using PEMDAS, the value of expression 5² - 9 ÷ 3 is 22.
b) 8 + 6 - 2× 2 -3²
Using PEMDAS,
Squaring,
8 + 6 - 2 × 2 - 9
Multiplying,
8 + 6 - 4 - 9
Adding,
14 - 4 -9
Subtracting,
1
Using PEMDAS, the value of expression 8 + 6 - 2× 2 -3² is 1.
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the time (in hours) required to repair a machine follows an exponential distribution, and the mean repair time is 2.5 hours. (a) what is the probability that a repair will take less than 2 hours?
0. 63212 is the probability that a repair will take less than 2 hours.
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.
P( X > 2 ) = 1 - P ( X/ leq2 )
= 1 - F( 2)
= 1 - [tex]e^{0.5 * 2}[/tex]
= 0. 63212.
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