Answer:
[tex]p = 2[/tex] if given vectors must be linearly independent.
Step-by-step explanation:
A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:
[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]
In other words, the following system of equations must be satisfied:
[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)
[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)
[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)
By Eq. 1:
[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]
Eq. 1 in Eqs. 2-3:
[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]
[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]
[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)
[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)
By Eq. 3b:
[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]
Eq. 3b in Eq. 2b:
[tex](p-2)\cdot \alpha_{2} = 0[/tex]
If [tex]p = 2[/tex] if given vectors must be linearly independent.
The sum of two numbers is 15. One number is 101 less than the other. Find the numbers.
Answer:
The numbers:
-43 and 58
Step-by-step explanation:
a + b = 15
a = b - 101
then:
(b-101) + b = 15
2b = 15+101
2b = 116
b = 116/2
b = 58
a = b - 101
a = 58 - 101
a = -43
Check:
a + b = 15
-43 + 58 = 15
PLS HELP :Find all the missing elements:
Answer:
[tex]\large \boxed{\mathrm{34.2}}[/tex]
Step-by-step explanation:
[tex]\sf B= arcsin (\frac{b \times sin(A)}{a} )[/tex]
[tex]\sf B= arcsin (\frac{7 \times sin(40\°)}{8} )[/tex]
[tex]\sf B = 0.59733 \ rad = 34.225\°[/tex]
What value of x makes this equation true?
17 5 - 7 = -4
x=
y Su
What value of x makes this equation true? X/6-7=-4
Answer:
x=18
Step-by-step explanation:
x/6 - 7 = -4
x/6 = 3
(x/ 6) * 6 = 3*6
x = 18
what number must be added to the sequence of 7,13 and 10 to get an average of 13
Answer:
22
Step-by-step explanation:
We can write an equation:
(7+13+10+x)/4=13
x represents the number that needs to be added to get an average of
(7+13+10+x)/4=13
(30+x)/4=13
30+x=52
x=22
The number is 22
Hope this helps! Have a wonderful day :)
v divided by 5 is equal to 60.
Answer:
[tex]\boxed{v=300}[/tex]
Step-by-step explanation:
Hey there!
To find v we’ll set up the following,
v ÷ 5 = 60
To get v by itself we’ll do
5*60 = 300
v = 300
Hope this helps :)
A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?
Answer:
Total expected amount = $0.04375
Step-by-step explanation:
We need to calculate probability of getting heads on every combination of coin tosses
HHH = 1/8 = 3 heads
HHT = 1/8 = 2 heads
HTH = 1/8 = 2 heads
HTT = 1/8 = 1 head
THH = 1/8 = 2 heads
THT = 1/8 = 1 head
TTH = 1/8 = 1 head
TTT = 1/8 = 0 head
So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175
Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225
Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375
Total expected amount = 0.00375 + 0.0225 + 0.0175
Total expected amount = $0.04375
In which set(s) of numbers would you find the number -832 a. whole number b. irrational number c. integer d. rational number e. real number f. natural number
Answer:
integer of course
Step-by-step explanation:
an integer can either be negative or positive.
i need help really bad
Answer:
see explanation
Step-by-step explanation:
If f(x) and [tex]f^{-1}[/tex] are inverse functions, then
f([tex]f^{-1}[/tex])(x) = x
Thus substitute x = [tex]f^{-1}[/tex] (x) into f(x)
f([tex]\frac{x+6}{5}[/tex] )
= 5 ([tex]\frac{x+6}{5}[/tex] ) - 6
= x + 6 - 6
= x
Thus f(x) and [tex]f^{-1}[/tex] (x) are inverse functions
In a frequency distribution of 290 scores, the mean is 99 and the median is 86. One would expect this distribution to be:
Answer:
positively skewed to the right
Step-by-step explanation:
The measure of the central tendency is a profound way to describe the mean, median and mode. The measure of central tendency indicates where the center of distribution tends to be. The measure of central tendency provide a validity and answers whether the scores are high or generally low.
In this measure,The mean is usually pulled to the tail. The skewed is determined by where the tail goes, to the right side , it is positively skewed and to the left side , it is known as negatively skewed distribution.
Given that:
In a frequency of distribution of 290 scores,
the mean = 99
the median = 86
One would expect this distribution to be; positively skewed to the right since the mean value is greater than the median value.
Fiona wrote the linear equation y = y equals StartFraction 2 over 5 EndFraction x minus 5.x – 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s? x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 2 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 2 EndFraction.y =
Answer:
D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{2}{5}x - 5[/tex]
Required
Determine its equivalent
From the list of given options, the correct answer is
[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]
This is shown as follows;
[tex]y = \frac{2}{5}x - 5[/tex]
Multiply both sides by [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]
Open Bracket
[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]
[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]
Subtract x from both sides
[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]
[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]
Multiply both sides by -1
[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]
[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]
Reorder
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Hence, the correct option is D
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Answer:
The 4th option
Step-by-step explanation:
Use a definition, postulate, or theorem to find the value of x in the figure described. Point E is between points D and F. If DE = x − 3, EF = 6x + 5, and DF = 8x − 3, find x. Select each definition, postulate, or theorem you will use. A)definition of segment bisector B)definition of midpoint C)Linear Pair Theorem D)Segment Addition Postulate The solution is x =?
Answer:
Option (D)
x = 5
Step-by-step explanation:
Since point E is in the mid of the segment DF,
Therefore, by the Segment addition postulate,
DF = DE + EF
Since DF = (8x - 3), DE = (x - 3) and EF = (6x + 5)
By substituting these values in the given postulate,
(8x - 3) = (x - 3) + (6x + 5)
8x - 3 = (x + 6x) + (5 - 3)
8x - 3 = 7x + 2
8x - 7x = 3 + 2
x = 5
Therefore, x = 5 will be the answer.
Answer:
x=6 and D
Step-by-step explanation:
Given below are descriptions of two lines. Line 1: Goes through (-2,10) and (1,1) Line 2: Goes through (-2,8) and (2,-4)
Answer:
Option (2)
Step-by-step explanation:
1). If two lines have the same slope, lines are defined as parallel.
m₁ = m₂
2). If the multiplication of the slopes of two lines is (-1), lines will be perpendicular.
m₁ × m₂ = (-1)
Line 1 : It passes through two points (-2, 10) and (1, 1).
Slope of the line 1 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{1+2}{10-1}[/tex]
= [tex]\frac{3}{9}[/tex]
m₁ = [tex]\frac{1}{3}[/tex]
Line 2 : It passes through two points (-2, 8) and (2, -4).
Slope of the line 2 = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{8+4}{-2-2}[/tex]
= [tex]-\frac{12}{4}[/tex]
m₂ = -3
Since, m₁ × m₂ = [tex]\frac{1}{3}\times (-3)[/tex]
= (-1)
Therefore, given lines are perpendicular to each other.
Option (2) is the correct option.
Find the missing side or angle.
Round to the nearest tenth.
Answer:
b=2.7
Step-by-step explanation:
using sine rule,,,
Step-by-step explanation:
So for this problem, we need the missing angle A. From there, we can use the law of sines to compute length of b.
So the sum of the interior angles of a triangle is 180. With that in mind, we can make an equation to fine the measure of angle A.
53 + 80 + A = 180
133 + A = 180
A = 47
Now that we have the angle of A, we can use the law of sines to fine the length of b.
b / sin(B) = a / sin(A)
b = sin(B) * a / sin(A)
b = sin(80) * 2 / sin(47)
b = 2.693
Now round that to the nearest tenth to get
b = 2.7
Cheers.
A box is filled with 8 blue cards, 6 red cards, and 6 yellow cards. A card is chosen at a random from the box. What is the probability that the card is not red ? Write your answer as a fraction.
Answer:
14/20 or .7 or 70%
Step-by-step explanation:
Total Number of cards: 20
Number of Red cards: 6
The leftover cards: 20 -6 = 14
The probability of not getting a red = 14/20
14/20 as a decimal = 14/20 = 70/100 = .7
14/20 as a percent = 14/20 = 70/100 = 70%
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.
Answer:
[tex]V_2=305.14\ \text{inch}^3[/tex]
Step-by-step explanation:
The volume of a gas in a container varies inversely as the pressure on the gas.
[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]
If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?
So, using the above relation.
So,
[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]
So, the new volume is [tex]305.14\ \text{inch}^3[/tex].
4 Which object has the shape of a
rectangular prism?
O pencil
O book
O scissors
Solve 5(2x + 4) = 15. Round to the nearest thousandth.
[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]
Answer:
[tex]\huge\boxed{x=-0.5}[/tex]
Step-by-step explanation:
[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]
X = y + 12
How to solve for variable
Answer:
x-y=12
Step-by-step explanation:
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
a) What is the cost of a chicken shawarma wrap?
$10.99
b) What is the cost of one order of spiced potatoes?
$4.99
c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
Step-by-step explanation:
Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,
Cost of a chicken sharwarma wrap = x
Cost of an order of spiced potatoes = y
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
Hence, the Equations needed to solve the question is:
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of x in Equation 2
Equation 2 by coefficient of x in Equation 1
3x + 2y = $42.95 .............Equation 1 × 5
5x + 4y = $74.91 ................Equation 2 × 3
15x + 10y = 214.75..............Equation 3
15x + 12y = 224.73..............Equation 4
Subtract Equation 3 from Equation 4
2y = 9.98
y = 9.98/2
y = 4.99
Therefore, y = Cost of an order of spiced potatoes = $4.99
Subtitute 4.99 for y in Equation 1
3x + 2y = $42.95 .............Equation 1
3x +2(4.99) = 42.95
3x + 9.98 = 42.95
3x = 42.95 - 9.98
3x = 32.97
x = 32.97/3
x = 10.99
x = Cost of a chicken sharwarma wrap = $10.99
Therefore,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
A segment with endpoints at $A(2, -2)$ and $B(14, 4)$ is extended through $B$ to point $C$. If $BC = \frac{1}{3} \cdot AB$, what are the coordinates for point $C$? Express your answer as an ordered pair.
Answer:
C = (18, 6)
Step-by-step explanation:
You have ...
AB : BC = 1 : 1/3 = 3 : 1
(B -A) / (C -B) = 3/1 . . . . . another way to write the distance relation
B -A = 3(C -B) . . . . . . . . . multiply by (C-B)
4B -A = 3C . . . . . . . . . . . add 3B
C = (4B -A)/3 . . . . . . . . . divide by 3 to get an expression for C
C = (4(14, 4) -(2, -2))/3 = (54, 18)/3
C = (18, 6)
I need help with this math problem please (3x+2)(5x-7)
Answer:
Hey there!
Using the foil method: (3x+2)(5x-7)
15x^2+10x-21x-14
15x^2-11x-14
Let me know if this helps :)
In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle. A straight line is shown and is marked with three angles. The first angle measures 50 degrees. The second angle measures 60 degrees. The third angle is labeled x. The line between the 40 degree angle and angle x extends below the straight line. The angle formed is labeled angle y. Write and solve an equation to determine the measure of angle y.
Step-by-step explanation:
sorry but u should provide with a diagram for better understanding of ur question
ASAP Which graph has a correlation coefficient, r, closest to 0.75?
Answer:
C. Graph C
Step-by-step explanation:
In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.
Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.
Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.
Graph C has a correlation coefficient, r, that is closer to 0.75.
Answer: graph A ‼️
Step-by-step explanation:
Five more than the square of a number Five more than twice a number Five less than the product of 3 and a number Five less the product of 3 and a number Twice the sum of a number and 5 The sum of twice a number and 5 The product of the cube of a number and 5 The cube of the product of 5 and a number. 5 + x2 5 + 2x 5 - 3x 3x - 5 2x + 5 2(x + 5) 5x3 (5x)3 WILL MARK BRAINLIEST AND DON'T PUT A FAKE ANSWER TO GET POINTS EITHER CUS I NEED HELP
Answer:
BelowStep-by-step explanation: Let all unknown no be x
Five more than the square of a number
= [tex]5 + x^2[/tex]
Five more than twice a number ;
[tex]5+2x\\= 2x+5[/tex]
Five less than the product of 3 and a number ;
[tex]5- 3x\\= 3x-5[/tex]
Twice the sum of a number and 5 ;
[tex]2(x+5)\\[/tex]
The sum of twice a number and 5 ;
[tex]2x+5[/tex]
The product of the cube of a number and 5;
[tex]x^3 \times 5\\=5x^3[/tex]
The cube of the product of 5 and a number ;
[tex](5\times x)^3\\(5x)^3[/tex]
Please answer this correctly without making mistakes
Answer:
Put 1/10 in the box.
Step-by-step explanation:
Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.
Best Regards!
Answer:
To Oakdale to Milford:
2/5 mi
Step-by-step explanation:
1/10 + 3/20 + 3/20
1/10 = 2/20
then;
2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20
8/20 = 2/5
Stephanie is twice as old as her sister Rosa. If Stephanie is 18 years old, how old is Rosa?
Answer:
rose. is. 18/2=9 years old
Answer:
Stephanie is 18years old and she is twice older than her sister
so rosa is 18÷2(since stephanie is twice older than rosa
so rosa is 9 years old
wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of
Answer:
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Step-by-step explanation:
A test for the difference between two population means is to be performed.
As the population variances are known, the z-test will be used.
The hypothesis can be defined as follows:
H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂
Assume that the significance level of the test is, α = 0.05.
The critical region can be defined as follows:
The critical value of z for α = 0.05 is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]
Use a z-table.
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Find the value of x. A: 15 B: 12 C: 10 D: 8
Answer:
[tex]\boxed{\sf C. \ 10}[/tex]
Step-by-step explanation:
[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]
[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]
[tex]NH \times HT = MH \times HY[/tex]
[tex](x+20) \times 8=12 \times 20[/tex]
[tex]\sf Expand \ brackets \ and \ multiply.[/tex]
[tex]8x+160=240[/tex]
[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]
[tex]8x+160-160=240-160[/tex]
[tex]8x=80[/tex]
[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]
[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]
[tex]x=10[/tex]
The value of x is 10.
We have a circle and inside it two chords MY and NT intersect at point H.
We have to find the value of x in the figure.
What is intersecting chord theorem?According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then
AO x OB = CO x OD
Applying the chord intersecting theorem to the figure in the question, we get -
MH x HY = NH x HT
12 x 20 = (x+20) x 8
240 = 8x + 160
8x = 80
x = 10
Hence the value of x is 10.
To solve more questions on Circles and chords, visit the link below -
https://brainly.com/question/15568573
#SPJ5
In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find m∠NMC.
Answer:
∠NMC = 50°
Step-by-step explanation:
The interpretation of the information given in the question can be seen in the attached images below.
In ΔABC;
∠ A + ∠ B + ∠ C = 180° (sum of angles in a triangle)
∠ A + 70° + 50° = 180°
∠ A = 180° - 70° - 50°
∠ A = 180° - 120°
∠ A = 60°
In ΔAMN ; the base angle are equal , let the base angles be x and y
So; x = y (base angle of an equilateral triangle)
Then;
x + x + 60° = 180°
2x + 60° = 180°
2x = 180° - 60°
2x = 120°
x = 120°/2
x = 60°
∴ x = 60° , y = 60°
In ΔBQC
∠a + ∠e + ∠b = 180°
50° + ∠e + 40° = 180°
∠e = 180° - 50° - 40°
∠e = 180° - 90°
∠e = 90°
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
∠i = 50° - 40° = 10°
In ΔNQC
∠f + ∠i + ∠j = 180°
90° + 10° + ∠j = 180°
∠j = 180° - 90°-10°
∠j = 180° - 100°
∠j = 80°
From line AC , at point N , ∠y + ∠c + ∠j = 180° (sum of angles on a straight line)
60° + ∠c + ∠80° = 180°
∠c = 180° - 60°-80°
∠c = 180° - 140°
∠c = 40°
Recall that :
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
Then In Δ NMC ;
∠d + ∠h + ∠c = 180° (sum of angles in a triangle)
∠d + 90° + 40° = 180°
∠d = 180° - 90° -40°
∠d = 180° - 130°
∠d = 50°
Therefore, ∠NMC = ∠d = 50°
Suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. If 83 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams?
Answer: 0.129
Step-by-step explanation:
Let [tex]\overline{X}[/tex] denotes a random variable that represents the mean weight of babies born.
Population mean : [tex]\mu= \text{3316 grams,}[/tex]
Standard deviation: [tex]\text{324 grams}[/tex]
Sample size = 83
Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :
[tex]P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}<\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{-54}{\dfrac{324}{\sqrt{83}}})\\\\=1-[P(-1.518<Z<1.518)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-[P(Z<1.518)-P(z<-1.518)]\\\\=1-[P(Z<1.518)-(1-P(z<1.518))]\\\\=1-[2P(Z<1.518)-1]=2-2P(Z<1.518)\\\\=2-2(0.9355)\ [\text{By z-table}]\\\\=0.129[/tex]
hence, the required probability = 0.129
