9514 1404 393
Answer:
the end of the whole number and the beginning of the fraction
Step-by-step explanation:
The word "and" means the whole part and the fractional part should be considered together as having a value equal to their sum. It signifies the separation between the whole-number part and the fractional part.
__
It has the same meaning as when used in a decimal mixed number:
1.2 = "one and two tenths"
Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation of 0.2 feet. A sample of 41 men's step
lengths is taken
Step 2 of 2: Find the probability that the mean of the sample taken is less than 2.2 feet. Round your answer to 4 decimal places, if necessary,
Answer:
0% probability that the mean of the sample taken is less than 2.2 feet.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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.
Mean of 2.5 feet and a standard deviation of 0.2 feet.
This means that [tex]\mu = 2.5, \sigma = 0.2[/tex]
Sample of 41
This means that [tex]n = 41, s = \frac{0.2}{\sqrt{41}}[/tex]
Find the probability that the mean of the sample taken is less than 2.2 feet.
This is the p-value of Z when X = 2.2 So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}[/tex]
[tex]Z = -9.6[/tex]
[tex]Z = -9.6[/tex] has a p-value of 0.
0% probability that the mean of the sample taken is less than 2.2 feet.
A college admissions officer takes a simple random sample of 90 entering freshman and computes their mean mathematics sat score to be 436. assume the population standard deviation is σ = 101. Based on a 99% confidence interval for the mean mathematics SAT score, is it likely that the mean mathematics SAT score for entering freshmen class is greater than 460?
Answer:
460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.
The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.
460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460
Name two characteristics of the Fibonacci Series that you observed.
Answer:
See the answers below
Step-by-step explanation:
Name two characteristics of the Fibonacci Series that you observed.
If we take a closer look at the Fibonacci series, we will notice the following characteristics
1.The next number is the sum of the two preceding numbers
2. Another interesting characteristic is evidenced in the convergence of the sequence
The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 9 vans and 14 buses with 710 students. High School B rented and filled 13 vans and 5 buses with 371 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Answer:
Buses - 43 people
Vans - 12 people
Show that the set of nonsingluar 2 by 2 matrices is not a vector space. Show also that the set of singular 2 by 2 matrices is not a vector space.
Answer:
a) 2 nonsingular 2 by 2 matrices are not closed when added together hence it is not a vector space( i.e. their sum = singular and not nonsingular )
b) 2 singular 2 by 2 matrices is not closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )
Step-by-step explanation:
a) Prove that nonsingular 2 by 2 matrices is not a vector space
2 nonsingular matrices are not closed when added together hence it is not a vector space ( i.e. their sum = singular and not nonsingular )
vector A = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] + vector B = [tex]\left[\begin{array}{ccc}0&1\\1&0\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&1\\1&1\\\end{array}\right][/tex] ( singular vector )
b) Prove that singular 2 by 2 matrices is not a vector space
2 singular 2 by 2 matrices is not closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )
Vector C = [tex]\left[\begin{array}{ccc}1&0\\0&0\\\end{array}\right][/tex] + vector D = [tex]\left[\begin{array}{ccc}0&0\\0&1\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( nonsingular vector )
(a+b)²=hihihihihihihihiihihihi
Answer:
(a+b)²=a²+b²+2ab
Step-by-step explanation:
The square of sum of two terms is equal to the squared plus squared plus times product of and . In mathematics, the plus whole squared algebraic identity is called in three ways. The square of sum of two terms identity.
Find the area for me pls
this figure can be divided into three parts one is rectangle other one is semicircle and the third one is one fourth of the circle .so let's find the area of each figure one by one. For the rectangle 12×8 =96
for semicircle that is on the top it has the radius 6 which is a half of 12
so area of the semicircle is
[tex] \frac{1}{2} \pi \: r {}^{2} \\ \frac{1}{2} \times 3.14 \times 6 {}^{2} \\ 3.14 \times 18 \\ 56.52[/tex]
no that's fine. 80 of the 1/4 of the other Circle
[tex] \frac{1}{4} \pi {}^{2} \\ \frac{1}{4} 3.14 \times 8 {}^{2} \\ 3.14 \times 16 \\ 50.24[/tex]
add all these areas
96+56.52+50.24 =202.76
An expression is shown below:
3(m + 5 + 9m)
Part A: Write two expressions that are equivalent to the given expression. (3 points)
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)
The answers are as follows part A = 30m+15 part B =3m+15+27m
and partC = 30m+15
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.
Part A:- Two expressions that are equivalent to the given expressions are:-
3m + 15 + 27m
30m + 15
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties.
3 ( m + 5 + 9m )
Open the bracket by multiplying 3 by what is in the bracket
3m + 15 + 27m
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m.
3 ( m + 5 + 9m )
Open the bracket by multiplying 3 by what is in the bracket
3m + 15 + 27m
Collect like terms together
3m + 27m + 15
= 30m + 15
To know more about Expression follow
https://brainly.com/question/723406
#SPJ2
For the data set 4, 5, 10, 11, 15, the mean, x, is 9. What is the standard
deviation?
The formula for the sample standard deviation is a -
Jo-;2(x-
z(x -- Hoje
Use the table to help you.
4.
5
10
11
15
X-8
(x - x?
-5
25
-4
16
1
1
2
4.
6
36
Sum= 82
Round your answer to the nearest tenth.
Answer:
4.53
Step-by-step explanation:
Given the data :
4, 5, 10, 11, 15
The mean = 9
The standard deviation of a sample :
s = √[Σ(x - mean)²/(n-1)]
s = √[((4-9)² + (5-9)²+(10-9)² + (11-9)² + (15-9)²) / (5-1)]
s = √(25+16+1+4+36)/4
s = √20.5
s = 4.527
s = 4.53
Answer:
4.5
Step-by-step explanation:
5.1.3
help me find the perimeter of this square. if you can do it step by step please!
Answer:
396
Step-by-step explanation:
It's a square.
That means that all four sides are equal.
So the two expressions you have been given are equal.
2.5x + 76.5 = 12x - 9 Subtract 2.5x from both sides.
-2.5x -2.5x
76.5 = 9.5x - 9 Add 9 to both sides
9 9
85.5 = 9.5x Divide by 9.5
85.5/9.5 = x
x = 9
That is just the value for x. It is not the answer
Side = 12x - 9
Side = 12*9 - 9
Side = 108 - 9
Side = 99
The perimeter = 4 * Side
The perimeter = 4 * 99
Perimeter = 396
(x-2)(-5x^2+x)=(x)(-5x^2)+(x)(x)+(-2)(-5x^2)+(-2)(x) is an exsample of
this is an example of linear equations is one variable
Hellllllllllp! Someone help
Answer:
4. (2, 3)
5. (0, 1)
7. (-1, 2)
Step-by-step explanation:
I hope this helps! Have a nice dayy! :)
You're very close. Choices D and E are two of the three answers. The third answer is choice G (-1,2)
In short, the 3 answers are Choices D, E and GIf you plug the coordinates of the points into the inequality, you should get a true statement.
For instance, let's try the coordinates of choice G
[tex]-2x + 3y\ge 3\\\\-2(-1) + 3(2)\ge 3\\\\2 + 6\ge 3\\\\8\ge 3\\\\[/tex]
Which is true since 8 is indeed greater than 3. That verifies point G is a solution point. A similar story happens with points D and E as well.
----------
If you tried something like choice A, then,
[tex]-2x + 3y\ge 3\\\\-2*(2) + 3(-3)\ge 3\\\\-4 - 9\ge 3\\\\-13\ge 3\\\\[/tex]
Which is false because -13 is not greater than 3, and -13 is not equal to 3 either. So choice A is a non-answer. You should find that choices B, C, and F are also non-answers.
----------
The graph is below. Notice how points D, E and G are either in the blue shaded region or on the boundary. The boundary line is solid (due to the "or equal to" as part of the inequality sign), so points on the solid boundary line are part of the solution set. The graph is a quick way to visually confirm the answers. I used GeoGebra to make the graph.
So that's why the 3 answers are D, E and G.
characteristics of the median
Answer:
Median: The median is the middle value of the data set when the data is arranged in ranking order. It always lies at the center of the data set and not affected by the extreme values or outliers. For the calculation of median, the variable should be measured at least at the ordinal level.
For this question I am sure the answer is 81% as you divide 45 and 55. However, it is stating my answer is incorrect even though I put 0.81% as well. Did I round wrong or is the answer wrong completely?
Answer:
it says round to the nearest 10th so it wouldn't be 81, it would be 81.8%
work out 8^2/3
^2/3 means to the power of 2/3
Hi there!
»»————- ★ ————-««
I believe your answer is:
4
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\8^{\frac{2}{3}}\\-----------\\\text{Recall the Exponent Rule: }} a^{\frac{b}{c}} = \sqrt[c]{a^b}\\\\\rightarrow {\frac{\text{Power}}{\text{Root Index}}\\\\[/tex]
[tex]-----------[/tex]
[tex]\rightarrow 8^{\frac{2}{3}}\\\\\rightarrow \sqrt[3]{(8^2)}\\\\\rightarrow\sqrt[3]{64}\\\\\rightarrow \boxed{4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
4
Step-by-step explanation:
[tex]8^{\frac{2}{3} }[/tex]
=[tex](2)^3*\frac{2}{3}[/tex]
=[tex](2)^\frac{3*2}{2}[/tex]
=[tex](2)^\frac{6}{3}[/tex]
=[tex]2^2[/tex]
=4
A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 150 pound requires 144 milligrams of medicine. what is the weight of a patient who requires 174.72 milligrams of medicine
9514 1404 393
Answer:
182 lbs
Step-by-step explanation:
You can write the proportion for the required patient weight (w) as ...
weight/medicine = w/(174.72 mg) = (150 lb)/(144 mg)
w = (150 lb)(174.72/144) . . . . . multiply by 174.72 mg
w ≈ 182 lb
The patient's weight is 182 pounds.
if a labour earns Rs 6360 in a year find his earning in one month
There are 12 month in a year :
6360 ÷ 12 = 530
Thus the labour earns Rs 530 in a month .
To find this out we will divide 6360 by 12 (as there are 12 months in an year) 6360/12 = 530 . Therefore answer = rs 530
Pls follow and mark brainliest.
Find the 23rd term of the arithmetic sequence with the terms a1 27 and d = 16.
Answer:
379
Step-by-step explanation:
a23 = 27 + (23-1)(16)
= 27 + (22)(16)
= 27 + 352
= 379
I need help on this too please it’s hard
Answer:
Y=x
Step-by-step explanation:
The y and x values are the same
Answer:
y = x
Step-by-step explanation:
a 45° line with the origin passing through the origin has the equation y=x.
Have a nice day.
PLZ I NEED HELPPPPPPPP
The harmonic mean of two real numbers x and y equals 2xy/(x + y). By computing the harmonic and geometric means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.
Answer:
Conjecture : 2xy / ( x + y ) ≤ √xy
Step-by-step explanation:
Harmonic mean of x and y = 2xy/( x + y )
Formulate a conjecture about their relative sizes
we will achieve this by computing harmonic and geometric means
Geometric mean = √xy
harmonic mean = 2xy/( x + y )
Conjecture : 2xy / ( x + y ) ≤ √xy
attached below is the proof
A tank contains 1000L of pure water. Brine that contains 0.04kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.06kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions. 1. How much salt is in the tank after t minutes
Answer:
s(t) = 160/3 ( 1 - e^(-3t / 200) )
Step-by-step explanation:
volume of pure water in tank = 1000 L
Brine contains 0.04kg of salt/L
Inflow rate of Brine containing 0.04kg of salt/L = 5L/min
Brine containing 0.06 kg of salt/L
Inflow rate of Brine containing 0.06 kg of salt/L = 10L/min
Solution is thoroughly mixed and drains from tank at 15L/min
a) Determine the amount of salt is in the tank after t minutes
rate of salt entering = 0.2 + 0.6 = 0.8 kg/min
rate of salt leaving = s/1000 * 15
amount of salt at time (t) = s(t)
initial condition s( 0 ) = 0
ds/dt = 0.8 - 15s/1000 = 0.8 - 3s/200
200 ds/dt = ( 160 - 3s )
-200/3 In ( 160 - 3s ) = t + c
Given that ; t = 0 , s = 0
c = - 200/3 In ( 160 )
∴ -200/3 In ( 160 - 3s ) = t - 200/3 In ( 160 )
- 200/3 [ In ( 60 - 3s ) - In ( 160 ) ] = t
therefore:
In ( 160 - 3s / 160 ) = -3t/200
= ( 160 - 3s / 160 ) = e ^ (-3t/200 )
Hence amount of salt in tank after t minutes
s(t) = 160/3 ( 1 - e^(-3t / 200) )
Last question! Please show work. Really need to get this done in 1 hour
Answer:
x = 1, y = 2 , z = 3
Step-by-step explanation:
[tex]6x\:+\:2y\:-4z\:=\:-2 \ \ \ \ \ \ \ \ \ -----( 1 ) \:\\\\-3x-4y\:+2z\:=\:-5 \ \ \ \ \ \ ------( 2 ) \:\\\\4x-\:6y\:+3z\:=\:1 \ \ \ \ \ \ \ \ \ \ \ \ ------- ( 3 ) \\\\( 2 ) \times 2=> -6x -8y + 4z = -10 \ \ \ \ \ \ \ -----( 4)[/tex]
Now add ( 1 ) and (4)
[tex]6x +2y -4z = - 2\\\\-6x-8y - 4z = -10\\\\=>0x -6y + 0 = - 12\\\\-6y = -12[/tex]
y = 2
Now multiply ( 1 ) by 2 and (3) by 3
[tex](1) \times 2 => 12x + 4y -8z = -4\\\\(3) \times 3 => 12x -18y +9z = 3\\\\Subtract \ the \ equation : ( 1) - ( 3) => 0x +22y -17z = -7[/tex] ------ ( 5 )
Substitute y = 2 in ( 5 ) :
[tex]22(2) - 17z = - 7\\\\ 44 - 17z = - 7\\\\ -17z = - 7 - 44\\\\ -17z = -51\\\\[/tex]
z = 3
Substitute z = 3 and y = 2 in ( 1 ) :
[tex]6x + 2y - 4z = - 2\\\\6x + 2( 2) -4( 3) = -2\\\\6x + 4 - 12 = -2\\\\6x - 8 = - 2\\\\6x = - 2 + 8 \\\\6x = 6\\[/tex]
x = 1
How tall is the table?
120cm
90cm
I
The values of variables, such as the height of the table can be found by writing equations of their relationships
The height of the table is 105 cm
The reason the above height value is correct is as follows;
Known parameters:
The diagram shows a table, a cat and a mice
Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice
From the given diagram, we have;
Height of the table + Height of the cat - Height of the mice = 120 cm
∴ x + y - z = 120...(1)
Height of the table + Height of the mice - Height of the cat = 90 cm
∴ x + z - y = 90...(2)
Adding equation (1) to equation (2) gives;
x + y - z + (x + z - y) = 120 + 90 = 210
x + y - z + (x + z - y) = 210
However;
x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x
∴ x + y - z + (x + z - y) = 2·x = 210
x = 210/2 = 105
Therefore;
The height of the table, x = 105 cm
Learn more about word problems leading on simultaneous equations here:
https://brainly.com/question/16513646
please helpppppppppppp
Answer:
3
Step-by-step explanation:
4.5x 2 = 9
[tex]\sqrt{9}[/tex]= 3
The half life of Co-60 is 5.20 years. How many milligrams of a 1.00mg sample remains after 6.55 years
Answer:
For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on.
Step-by-step explanation:
You can figue out the rest.
Find the greatest common factor of 8a and 6a?
Answer:
2a.
Step-by-step explanation:
6 = 2 * 3
8 = 2 * 2 * 2 - 2 is common to both sets of factors.
So the GCF of 6 and 8 is 2.
For the 2 a's it is a.
What’s an example for y=1/2x-6 real world problems
Max is participating at a school bake sale. Each cookie he sells costs 50 cents. Unfortunately, it took 6 dollars to buy the materials for the cookies. Find how much money would it take for Max to break even.
Answer:
Step-by-step explanation:
4 years ago when Mary was 6, she was one half the age of her brother.
How old is her brother now?
Solution :
Let brother's age be = x
Four years ago, brothers age was = (x - 4)
Four years ago Mary was = 6
She was half the age of her brother
[tex]6 = \frac{1}{2} (x - 4)[/tex]
How would I solve this?
Answer:
20°
Step-by-step explanation:
perpendicular from the center on a chord of a circle always bisects the chord.
AR=BR
∴m arcAC=m arc BC=20°
A cyclist travels at a rate of 12 kilometers per hour. What is the rate in kilometers per minute? How many kilometers will the cyclist travel in 20 minutes? Do not round your answer.
Answer:
0.2&4
Step-by-step explanation:
There are 60 minutes in one hour, so 12 divided by 60 is the answer.
0.2 kilometers * 20 = 4