Answer:
The committee of 8 members can be selected in 990,675 different ways.
Step-by-step explanation:
The order in which the teachers and the students 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]
In this question:
4 teachers from a set of 6.
4 students from a set of 37.
Then
[tex]T = C_{6,4}C_{37,4} = \frac{6!}{4!2!} \times \frac{37!}{4!33!} = 990675[/tex]
The committee of 8 members can be selected in 990,675 different ways.
Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309.Select the 98% confidence interval for Adam’s set of data.a. 46.94 to 71.33b. 46.94 to 79.46c. 55.45 to 79.46d. 55.45 to 70.95
Answer:
Option D, 55.45 to 70.95
Step-by-step explanation:
Alpha = 1 – confidence interval
Alpha = 1 – 0.98 = 0.02
Sample size = n = 8
t (alpha/2) ; (n-1) = t (0.02/2) ; (8-1) = t 0.01, 7 = 2.998
Mean = sum of all frequencies /total number of frequency = 505.6/8 = 63.2
s = 7.309
E = t (0.01;7) * s/sqrt n
Substituting the given values, we get –
E = 2.998 * 7.309 /sqrt (8)
E = 7.75
98% confidence interval
Mean – E and Mean + E
63.2 – 7.75 and 63.2 + 7.75
(55.45, 70.95)
Answer: 55.45 to 70.95
Step-by-step explanation:
What is it quadratic, radical, rational?
Answer:
quadratic formula is ur answer for letter B
A health clinic dietician is planning a meal consisting of three foods whose ingredients are summarized as follows: One Unit ofFood I Food II Food IIIUnits of Protein 10 15 20Units of Carbohydrates 1 2 1Units of Iron 4 8 11Calories 80 120 100The dietician wishes to determine the number of units of each food to use to create a balanced meal containing at least 40 units of protein, 6 units of carbohydrates, and 12 units of iron, and with as few calories as possible. Use solver to find how many units of each food should be used in order to minimize calories.
Answer:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Step-by-step explanation:
Protein Carbohydrates Iron calories
Food 1 (x₁) 10 1 4 80
Food 2 (x₂) 15 2 8 120
Food 3 (x₃) 20 1 11 100
Requirements 40 6 12
From the table we get
Objective Function z :
z = 80*x₁ + 120*x₂ + 100*x₃ to minimize
Subjet to:
Constraint 1. at least 40 U of protein
10*x₁ + 15*x₂ + 20*x₃ ≥ 40
Constraint 2. at least 6 U of carbohydrates
1*x₁ + 2*x₂ + 1*x₃ ≥ 6
Constraint 3. at least 12 U of Iron
4*x₁ + 8*x₂ + 11*x₃ ≥ 12
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
With the help of an on-line solver after 6 iterations the optimal solution is:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
A cone has a height of 3 feet. The diameter of the base is 8 feet. What is the approximate volume of the cone in feet to the nearest hundreth?
Answer:
12.56 feet cubed
Step-by-step explanation:
Diameter of 8= radius of 4
4 x 3.14=12.56
12.56x3=37.68
37.68/3=12.56
The square below represents one whole.
What percent is represented by the shaded area?
%
The anwser is 6%
Answer:
the answer is 6%
hdhxbxcbxbxszznzj
Data with 950 observations are drawn from a bell-shaped distribution with a mean of 78 and a standard deviation of 19. Approximately how many observations are more than 116
Answer: there are 22 observations that are more than 116.
Step-by-step explanation:
Let x be the random variable.
Given: Sample size = 950
Mean = 78
Standard deviation = 19
The probability that the observations are more than 116 is given by :-
[tex]P(X>116)=P(\dfrac{X-mean}{standard \ deviation}>\dfrac{116-78}{19})\\\\=P(Z>2)\\\\=1-P(Z<2)\\\\=1-0.9772\ \ \ [\text{Using p-value calculator}]\\\\=0.0228[/tex]
Number of observations are more than 116 = [tex]0.0228\times950[/tex]
[tex]=21.66\approx22[/tex]
Hence, there are 22 observations that are more than 116.
An angle measures. What is the measure of its complement? (b) An angle measures 48 . What is measure 26 of its supplement?
Phân biệt giá cấp 2 được áp dụng đối với
Second-degree price discrimination occurs when a company charges a different price for different quantities consumed, such as quantity discounts on bulk purchases.
mark me brainliestt :))
Doris has a fish pond 15 by 18 ft. She wants to put grass in a strip of uniform with around the pond. She has enough grass seed for 234 ft squared. How wide will the strip be? Round your answer to the nearest tenth, when appropriate
Check the picture below.
so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so
[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]
now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena
[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]
Answer:
3 feet
Step-by-step explanation:
Let x be the width of the grass strip.
So the length of the grass strip=18+2x
Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2
But the available grass seed is enough for 234 ft squared
4x^2+66x=234
4x^2+66x-234=0
x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)
x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8
x={-66+-(90)}/8
Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)
So the width of the strip is 3 feet.
Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet
Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet
Therefore the strip is 3 feet wide
3x + 1 over 4y2
What is the value of the expression above when x = 3 and y = 4? You must show all work and calculations to receive full credit.
Answer: Pretty sure its the value of the expression is 11
Step-by-step explanation:
Step 1. Add and evaluate 4x and 1/3y^2
Step 2. After evaluating, add 4(2) and 1/3 (3)^2
Step 3. 8 + 1/3(9)
Step 4. 8 + 3 = 11
Step 5. Value of Expression = 11
Answer:
13
Step-by-step explanation:
There is a study on exercise and health: a group of women who have been exercising regularly for 5 years are grouped and given a wellness exam and compared to a group of women who have not exercised in the past five years. What kind of data collection is this?
Experiment
Survey
Simulation
Observational Study
Answer:
Survey Data Collection.
Step-by-step explanation:
This is a survey because there are survey questionnaires (wellness exam).
Answer:
Observational Study Is the Answer
A school principal wants to know more about the number of students absent each day. He counts the number of students absent each day for one week: {24, 18, 31,
Answer:
6.27
Step-by-step explanation:
We are to obtain the standard deviation of the given values :
{24, 18, 31,25, 34}
The standard deviation = √(Σ(x - mean)²/ n)
The mean = (ΣX) /n
Using calculator to save computation time :
The standard deviation, s = 6.27 (2 decimal places)
find the equation of the line perpendicular to the given line, through the given point x=-3; (1,8)
Answer:
y = 8
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify
[Line] x = -3
Point (1, 8)
Step 2: Find Perpendicular Line
A vertical line's slope is undefined.
The negative reciprocal of an undefined slope is 0.
Define perpendicular slope: m = 0Substitute in m [Slope-Intercept Form]: y = 0x + bSimplify: y = bGiven point (1, 8), our y-value is equal to 8.
∴ the perpendicular line is y = 8.
Given that a*b = 2ab - 3b. Determine 2*(3*5)
Answer:
15
Problem:
Given that a*b = 2ab - 3b. Determine 2*(3*5)
Step-by-step explanation:
First we find 3*5 using rule a*b = 2ab - 3b.
3*5=2(3)(5)-3(5)
3*5=30-15
3*5=15
Now we are left with 2*15 in which we will still use the rule a*b=2ab-3b.
2*15=2(2)(15)-3(15)
2*15=60-45
2*15=15
Therefore, 2*(3*5)=15.
What is the difference of the polynomials?
(5x^3 + 4x^2) - (6x^2 - 2x - 9)
Answers:
A.) -x^3 + 6x^2 + 9
B.) -x^3 + 2x^2 - 9
C.) 5x^3 - 2x^2 - 2x - 9
D.) 5x^3 - 2x^2 + 2x + 9
Answer:
D
Step-by-step explanation:
We want to find the difference between the two polynomials:
[tex](5x^3+4x^2)-(6x^2-2x-9)[/tex]
Distribute the negative:
[tex]=(5x^3+4x^2)+(-6x^2+2x+9)[/tex]
Rearrange the terms:
[tex]=(5x^3)+(4x^2-6x^2)+(2x)+(9)[/tex]
Combine like terms. Hence:
[tex]=5x^3-2x^2+2x+9[/tex]
Our answer is D.
if y equal to-1 calculate the value of the expression
Answer:
thiếu giữ liệu không thể trả lời được
Step-by-step explanation:
. Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y.
1) Viết các phán đoán sau đây dưới dạng công thức:
a) Nhiều người yêu thương A. (Thay A bằng chính tên của em).
b) A yêu thương nhiều người. (Thay A bằng chính tên của em).
B làm k cho mình KQ với
Here are the first three terms of a different sequence.
1
3
9
Write down two numbers that could be the 4th term and the 5th term of this sequence.
Give the rule you have used to get your numbers.
please helpp
Step-by-step explanation:
everything can be found in the picture
How many ways can a person toss a coin 16 times so that the number of heads is between 7 and 14 inclusive
50626 ways with a probability of 0.77
Step-by-step explanation:If a coin is tossed once, there are two possible results - a head or a tail. i.e 2¹ = 2
If the coin is tossed twice, there are four possible results - 4 heads no tail, 4 tails no head, 1 head 3tails or 2 heads 2 tails. That is 2² = 4
If the coin is tossed thrice, there are eight possible results. That is 2³ = 8.
Now, if the coin is tossed 16 times, there are 2¹⁶ = 65536 likely results.
From these 16 tosses, let's calculate the number of ways of achieving or selecting 7, 8, 9, 10, 11, 12, 13 or 14 heads. We use the combination formula given as follows;
Cₙ, ₓ = n! ÷ [ (n-x)! (x)! ]
Where;
n = number of tosses
x = number of selection
number of ways of getting 7 heads;
n = 16
x = 7
=> C₁₆, ₇ = 16! ÷ [ (16-7)! (7)! ]
=> C₁₆, ₇ = 16! ÷ [ (9)! (7)! ]
=> C₁₆, ₇ = 11440
number of ways of getting 8 heads;
n = 16
x = 8
=> C₁₆, ₈ = 16! ÷ [ (16-8)! (8)! ]
=> C₁₆, ₈ = 16! ÷ [ (8)! (8)! ]
=> C₁₆, ₈ = 12870
number of ways of getting 9 heads;
n = 16
x = 9
=> C₁₆, ₉ = 16! ÷ [ (16-9)! (9)! ]
=> C₁₆, ₉ = 16! ÷ [ (7)! (9)! ]
=> C₁₆, ₉ = 11440
number of ways of getting 10 heads;
n = 16
x = 10
=> C₁₆, ₁₀ = 16! ÷ [ (16-10)! (10)! ]
=> C₁₆, ₁₀ = 16! ÷ [ (6)! (10)! ]
=> C₁₆, ₁₀ = 8008
number of ways of getting 11 heads;
n = 16
x = 11
=> C₁₆, ₁₁ = 16! ÷ [ (16-11)! (11)! ]
=> C₁₆, ₁₁ = 16! ÷ [ (5)! (11)! ]
=> C₁₆, ₁₁ = 4368
number of ways of getting 12 heads;
n = 16
x = 12
=> C₁₆, ₁₂ = 16! ÷ [ (16-12)! (12)! ]
=> C₁₆, ₁₂ = 16! ÷ [ (4)! (12)! ]
=> C₁₆, ₁₂ = 1820
number of ways of getting 13 heads;
n = 16
x = 13
=> C₁₆, ₁₃ = 16! ÷ [ (16-13)! (13)! ]
=> C₁₆, ₁₃ = 16! ÷ [ (3)! (13)! ]
=> C₁₆, ₁₃ = 560
number of ways of getting 14 heads;
n = 16
x = 14
=> C₁₆, ₁₄ = 16! ÷ [ (16-14)! (14)! ]
=> C₁₆, ₁₄ = 16! ÷ [ (2)! (14)! ]
=> C₁₆, ₁₄ = 120
Therefore, the total number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 heads is the sum of the results above. i.e
11440 + 12870 + 11440 + 8008 + 4368 + 1820 + 560 + 120 = 50626 ways
P(getting number of heads between 7 and 14 inclusive) = [number of ways of achieving 7, 8, 9, 10, 11, 12, 13 or 14 ] ÷ [total number of possible outcomes]
= [tex]\frac{50626}{65536}[/tex]
= 0.77
27. Find the length of the segment LK. (G.CO.C.10)
Show your work! (2pts)
J
1
3x
L
K
X + 6
Click to add speaker notes
Answer:
9
Step-by-step explanation:
the only thing we can say for sure is that JL is splitting the triangle and also its baseline IK in half.
so, both sides of the baseline must be equal :
3x = x + 6
2x = 6
x = 3
=> LK = x + 6 = 3 + 6 = 9
Write the expression. Then, complete the statements.
twice the difference of a number and seven
The word "twice" means multiplication by 2 v
The words "the difference of indicate
Perimeter of a 14cm,10cm,6cm and 20cm shape?
Answer:
The perimeter is 50 cm.
Step-by-step explanation:
P= 14 + 10 + 6 + 20= 50 cm
Given g(x) -x + 4, solve for a when g(x) = 8.
Answer:
x = 12
Step-by-step explanation:
g(x) - × + 4 =0
put g(x) = 8
so, 8 - x + 4 = 0
x = 12
Answer:
x = - 4
Step-by-step explanation:
Given g(x) = - x + 4 and g(x) = 8 , the equate the right sides, that is
- x + 4 = 8 ( subtract 4 from both sides )
- x = 4 ( multiply both sides by - 1 )
x = - 4
Triangle LMN is reflected on y = x and then translates to the left one unit. Which of the following graphs represents the sequence of transformations that maps triangle LMN onto its image?
The attached graph represents the sequence of transformations
How to determine the sequence?The coordinates of the triangle LMN are
L = (-6, 1)
M = (-4, 3)
N = (-1, 1)
When reflected on y = x, we have:
L' = (1, -6)
M' = (3, -4)
N' = (1, -1)
When translated 1 unit left, we have:
L'' = (0, -6)
M' = (2, -4)
N' = (0, -1)
See attachment for the sequence of transformations
Read more about transformation at:
https://brainly.com/question/11709244
#SPJ1
Please I really need help
=======================================================
Explanation:
The triangular face has area of base*height/2 = 8*2/2 = 16/2 = 8 square feet.
Multiply this with the depth of the prism to get 8*12 = 96 cubic feet
----------
For any prism, the volume formula is
V = (area of base)*(depth of prism)
The term "depth" can be replaced with "height" and it's the same idea.
In this problem, we have a triangular prism because the parallel sides are triangles.
A positive real number is 4 less than another. if the sum of the squares of the two numbers is 72, then find the numbers
Answer:
x+4=72
x=72-4
x=68
Step-by-step explanation:
let x be one number and 4 be anothe number then sum of the two number be x and 4
Distribution of Sample Proportions
Susan really loves the lemon-flavored Fruity Tooty candies, but there always seems to be a lot of grape-flavored candies in each bag. To determine whether this is because grape candies are so popular or because each bag contains fewer lemon candies, Susan randomly picks a Fruity Tooty candy from her bag, records its flavor, and places it back in the bag. Each bag contains a mixture of cherry, grape, apple, lemon, and orange flavors. Which statement about Susan's distribution of sample proportions is true?
a) The distribution of the count of picking a cherry candy cannot be modeled as approximately normal if Susan picks candies over 200 times.
b) The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times.
c) The sample proportion of drawing an orange candy is not a binomial distribution.
d) The distribution of lemon candy can be modeled as normal if Susan picks candies 10 times.
Answer:
Option B, The distribution of apple candy can be modeled as normal if Susan picks candies over 75 times
Step-by-step explanation:
The distribution of apple candies can be represented as normal curve and hence the sample proportion for this is true and can be drawn.
The rest other cases do not represent a normal distribution and hence it will not be easy to plot curve for these samples.
hence, option B is correct
Find the quotient of 4x^3-12x² + 8x/ - 4x
O x2 + 3x - 2
O x²-12x + 4
O -x2 – 3x + 2
O x² + 12x - 4
Answer:
-x^2+3x-2
Step-by-step explanation:
I think one of the signs are wrong in the equation.
Time (hours) 3.2, 4.8, 7.2, t, 12.4
Distance (miles) 80, 120, 180, 245, t
Answer:
t=2 plz mark me as brainliest
Step-by-step explanation:
m26 is (2x - 5) and m_8 is (x + 5)º
What is m 3?
12
9
3 4
56
78
Answer:
12
Step-by-step explanation:
12 is the coefficient
