The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.
How to estimate population mean?Let X the random variable that represent the diameters of interest for this case, and for this case we know the following info
Where [tex]$\mu=205$[/tex] and [tex]$\sigma=1.5$[/tex]
Let the probability be
[tex]$P(205-0.3=204.7 < \bar{X} < 205+0.3=205.3)$$[/tex]
For this case they select a sample of n = 79 > 30, so then we have enough evidence to utilize the central limit theorem and the distribution for the sample mean can be approximated with:
[tex]$\bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$[/tex]
To simplify this problem is utilizing the normal standard distribution and the z score given by:
[tex]$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]
To find the z scores for each limit and we got:
[tex]$z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778$$[/tex]
[tex]$z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778$$[/tex]
To find this probability:
P(-1.778 < Z < 1.778) = P(Z < 1.778) - P(Z < -1.778)
simplifying the above equation, we get
= 0.962 - 0.0377
= 0.9243
The interest exists the probability that the mean diameter of the sample shafts would vary from the population mean by more than 0.3 inches utilizing the complement rule we got:
P = 1 - 0.9243 = 0.0757
The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.
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On average, people breath 10,000 times per night with a standard deviation of 1400. You study 50 people and record how many breaths they take per night. What is the probability that the average of all participants in the study was fewer than 10,200 breaths each night?I want answer with step by step.
ANSWER
[tex]\begin{equation*} 0.84375 \end{equation*}[/tex]EXPLANATION
We want to find the probability that the average of all participants in the study was fewer than 10,200 breaths each night.
To do this, first, we have to find the z-score corresponding to the sample mean:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]where x = sample mean
μ = population mean
σ = standard deviation
n = sample size
Therefore, the z-score is:
[tex]\begin{gathered} z=\frac{10200-10000}{\frac{1400}{\sqrt{50}}}=\frac{10200-10000}{\frac{1400}{7.0711}} \\ z=\frac{200}{197.99} \\ z=1.01 \end{gathered}[/tex]Now, using the standard normal table, we can find P(z < 1.01).
Therefore, the probabilityis:
[tex]P(z<1.01)=0.84375[/tex]That is the answer.
Which of the following is the correct expansion of the binomial (x + y)6?
A.
x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6
B. x6 + 155y + 6x4y2 + 20x³y3 + 6x²y + 15xy5+y6
C. x6 + 6x55+ 15x4y4 + 20x³y3 + 15x²y² + 6xy¹+y6
D. x6 + 6x5y + 20x4y² + 15x³y3 + 20x²y4 + 6xy5+y6
Option a is correct using algebric formulas.
What is (x + y)³ and (x + y + z)² formula?(x + y)³ = x³ + y³ +3xy( x + y )
(x + y + z)² = x² + y² + z² + 2( xy + yz + zx )
So breaking it into
(( x + y )³)² = (x³ + y³ +3xy( x + y ))²
(x³ + y³ +3xy( x + y ))² = x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )
x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )
So after rearranging the terms
we get (x + y)^6 as
x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6
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Use statement and reason.
Answer:
Step-by-step explanation:
A rectangular gardan is surrounded by a walk of uniform width. The area of the garden is 200 square yards. If the dimensions of the garden plus the walkway are 18 yards by 26 yards, find the dimensions of the garden.
***NOTE*** This is a Quadratic Word Problem, so please use the Quadratic Method when solving and show all steps!!
Answer: [tex]6\sqrt{6}+4 \times 6\sqrt{6}-4[/tex] yards
Step-by-step explanation:
Let the length of the walkway be x yards. Then,
[tex](18-2x)(26-2x)=200\\\\4x^2 -88x+468=200\\\\4x^2-88x+268=0\\\\x^2 -22x+77=0\\\\x=\frac{22 \pm \sqrt{22^2 -4(77)}}{2}\\\\=11 \pm 3\sqrt{6}[/tex]
However, [tex]x=11+3\sqrt{6} > 18[/tex], which is illogical, so we take [tex]x=11-3\sqrt{6}[/tex].
So,
[tex]18-2x=18-2(11-3\sqrt{6})=6\sqrt{6}-4\\\\26-2x=26-2(11-3\sqrt{6})=4+6\sqrt{6}[/tex]
In ▲ABC, side AC is extended through C to D. If m<dcb=50 which is the longest side of triangle abc?
Answer:
AB
Step-by-step explanation:
the angles DCB and ACB are supplementary angles (together 180°).
simply because the sum of all angles around a single point on one side of a line is suggests 180° (it represents a half-circle).
so, the inner angle ACB is
ACB = 180 - 50 = 130°
because the sum of all angles in a triangle is also always 180°, there are only 50° left for the other 2 angles.
so, the inner angle at C is clearly the largest angle in the triangle ABC.
the larger an angle, the longer the opposing side.
the largest angle has the longest opposing side in the triangle.
the opposing side of the inner angle C is AB. and that is therefore the longest side in the triangle ABC.
Rule for Input/output table Input values: 1, 2, 3, 4, n Output values: -4,-2,0,2
Answer:
[tex]a_{n}[/tex] = 2n - 6
Step-by-step explanation:
there is a common difference between consecutive terms , that is
- 2 - (- 4) = 0 - (- 2) = 2 - 0 = 2
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 4 and d = 2 , then
[tex]a_{n}[/tex] = - 4 + 2(n - 1) = - 4 + 2n - 2 = 2n - 6
the rule is then 2n - 6
3. Use your answer from #2 for x, and find the measure of both angles. Select 2 answers.
A
B
116
61°
64°
119⁰
2x-15
3x + 5
None of the available possibilities is an equivalent expression.
Supplemental methods add up to 180 degrees, just like all other options.
An equivalent expression is what?If two expressions function the same way while having different looks, they are said to be comparable. Two identical algebraic expressions have the same value when the same value(s) for the variable are entered (s).
No one in the available possibilities satisfies the requirement of a comparable expression.
2x - 15 + 3x + 15 = 180
2x - 10 + 3x = 180
5x - 10 = 180
5x - 10 + 10 = 180 +10
add the numbers
5x = 190
5x /5 = 190 5
x = 38
As a result, none of the possibilities shown are identical expressions.
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28-6x=2x-84
Prove: x = 14
28-6x = 2x -84
Add 6x to both sides:
28 = 8x -84
Add 84 to both sides
112 = 8x
Divide both sides by 8
X = 112/8
X = 14
Hari's weekly allowance varies depending on the number of chores he does. He received $18 in allowance the week he did 20 chores, and $12 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.
The equation of his allowance in slope-intercept form is y = 0.5x + 8
He received $18 in allowance the week he did 20 chores.
He received $12 in allowance the week he did 8 chores.
The ordered pairs will be (8,12) and (20,18)
The slope intercept form is
y = mx + b
Where m is the slope
b is the y intercept
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
m = (18-12)/(20-8)
m = 6/12
= $0.5 per chores
Now we have to find b,
Substitute the value of any ordered pair in the slope intercept form
12 = 0.5×8+b
12 = 4+b
b = 12-4
b = 8
Hence, the equation of his allowance in slope-intercept form is y = 0.5x + 8
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Given the points:
(5,2) and (3,-4)
Select the THREE equations that represent the line that passes
through them.
The equations of the line according to the given points will be:
3x - y - 13 = 06x - 2y - 26 = 012x - 4y - 52 = 0We know that,
The equation of a line passing through two points is:
( y -y 1) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 )
(y - 2) / (x - 5) = (-4 - 2) / (3 - 5)
=> (y - 2) / (x - 5) = -6 / -2
=> y - 2 = 3 (x - 5)
=> 3x - 15 - y + 2 = 0
=> 3x - y - 13 = 0
Some more equations of the same line can be calculated just by multiplying the coefficients of x and y so that they remain proportional to the previous equation.
For Example,
6x - 2y - 26 = 012x - 4y - 52 = 0Here we can see that the coefficients of x and y and also the constant term are proportional to every equation compared with each other.
These lines are also called coincident lines.
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Part AType an equation to represent the cost of the topsoil.Part BHow does the cost of the topsoil compare to the cost of the mulch?
Step 1
Write the equation of a line in slope point form
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Where;
[tex]\begin{gathered} y_2=\text{ 60} \\ x_2=2 \\ y_1=\text{ 30} \\ x_1=\text{ 1} \end{gathered}[/tex]Step 2
Find the equation to represent the cost of the topsoil.
[tex]y-30=\frac{60-30}{2-1}(x-1)[/tex][tex]\begin{gathered} y-30\text{ = }\frac{30}{1}(x-1) \\ y-30=30x-30 \\ y=30x-30+30 \\ y=30x \end{gathered}[/tex]The equation that represents the cost of the topsoil is
y=30x
Step 3
Find how the cost of the topsoil compares to the cost of the mulch.
[tex]\begin{gathered} \text{The equation for the cost of the mulch y, in dollars is} \\ y=25x \\ \text{for x cubic yards of mulch} \\ \text{The equation for the cost of topsoil, y in dollars is} \\ y=30x \\ for\text{ x cubic yards of topsoil} \end{gathered}[/tex][tex]undefined[/tex]
You pick a card at random without putting the 1st card back you pick a second card at random what is the probability of picking an even number and then picking an even number
We will have the following:
First, we can see that the probability of picking an even number at first is:
[tex]P_1=\frac{3}{6}\Rightarrow P_1=\frac{1}{2}[/tex]And then, the probability of picking another even card without replacing the previous one will be:
[tex]P_2=\frac{2}{5}[/tex]Now, the probability of this happening one after the other will be:
[tex]\begin{gathered} P_3=P_1P_2\Rightarrow P_3=\frac{1}{2}\ast\frac{2}{5} \\ \\ \Rightarrow P_3=0.2 \end{gathered}[/tex]So, the probability will be of 20%.
How do I solve y-1=3(x-4)
Step-by-step explanation:
open the bracket
y - 1 = 3x - 12
add 1 to both sides
y = 3x - 11
I think that should be it
What is the polar form of -9-91√3 ?
09 (cos()+ i sin())
O 9 (cos (4T) + i sin (4))
O 18 (cos ()+sin())
O 18 (cos (4) + i sin (4T))
3
The polar form of the rectangular form - 9 - i 9√3 is 18 · [cos (4π / 3) + i sin (4π / 3)]. (Correct choice: A)
What is the polar form of a complex number in rectangular number?
Herein we find a complex number in rectangular form, that is, a complex number of the form a + i b, whose polar form has to be found. Complex numbers in polar form are defined by the following expression:
z = r · (cos θ + i sin θ)
r = √(a² + b²)
θ = tan⁻¹ (b / a)
Where:
r - Norm of the complex number.θ - Direction of the complex number, in radians.a, b - Components of the complex number in rectangular form.If we know that a = - 9 and b = - 9√3, then the complex number in polar form is:
r = √[(- 9)² + (- 9√3)²]
r = 18
θ = tan⁻¹ √3
θ = 4π / 3
The polar form is 18 · [cos (4π / 3) + i sin (4π / 3)].
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Triangle ABC is translated T(x,y) --> (x + 2, y - 3). What are the coordinates of the image of triangle ABC after this translation?
The coordinates of the image of triangle ABC would be A (-1, -1), B (3, 2), and C (4, -6) after translation, and if the original coordinates are A(-3,2) B(1,5) C(2,-3).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Let assume A(-3,2) B(1,5) and C (2,-3) are original coordinates
The following translation is being used: (x, y) ⇒ (x + 2, y - 3)
First, take your x-coordinates and add them by two because it is the translation utilized to solve for your x-coordinate.
You would receive the following for yours x's: A (-1, y ) B (3, y) C (4, y)
Next, remove three from each of your y-coordinates because it is the translation being utilized to solve for your y-coordinate.
You would receive the following for your y's: A (x, -1) B (x, 2) C (x, -6)
Finally, you would take each one and put it together, or piece it together.
Hence, the coordinates of the image of triangle ABC after translation would be A (-1, -1), B (3, 2), and C (4, -6).
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Listen to this on the day she was born, a baby leopard had 9 spots. Each day 4 more spots appeared. After 5 days, how many spots did the baby have?
Answer:29
Step-by-step explanation:
9+4 spots times five days
Evaluate each expression using the values given in the table.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the question,
We have that:
[tex]\begin{gathered} a)\text{ f (1) =2 and g(1) =0} \\ We\text{ n}eed\text{ evaluate :} \\ (fog\text{ ) (1) = f(g(1)) = f (0) =-1} \\ \text{Then, (fog)(1) = - 1} \end{gathered}[/tex][tex]undefined[/tex]The values of each composite function are:
a) -1
b) -1
c) 2
d) 0
e) 2
f) -4
We have,
These are composite functions.
It is written as:
(f o g) (x) = f (g(x))
Now,
From the table, the values for each function f and g at specific values x are taken.
a.
(f o g)(1)
f(g(1)) = f(0) = -1
b.
(f o g) (-1)
f(g(-1)) = f(0) = -1
c.
(g o f) (-1)
g(f(-1)) = g(-2) = 2
d.
(g o f) (0)
g(f(0)) = g(-1) = 0
e.
(g o g) (-2)
g(g(-2)) = g(2) = 2
f.
(f o f) (-1)
f(f(-1)) = f(-2) = -4
Thus,
The values of each composite function are:
-1, -1, 2, 0, 2, and -4.
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Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
Drag each description to explain each part of both expressions.
Both Adam and Rena re both correct regarding the expression.
What is an expression?An expression simply means an illustration that can be used to represent a scenario or situation.
From the information, Adam writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
In this case, they are both correct. This can be illustrated as:
= 1 - 0.75d
= 0.25d
Note that the information was answered based on the information given.
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Plot the ordered pair and state which quadrant or on which axis the point lies
Answer:
Explanation:
Given the ordered pair (-2, 4 1/2), where x = -2 and y = 4 1/2 = 9/2 = 4.5. Plotting this point, we'll have;
Note that quadrants are numbered in an anti-clockwise manner with the top right portion of the graph as Quadrant I. Looking at the plotted point, we can see that it lies in Quadrant II.
Using Cramer's Rule, the solution to the system of equations
6x - 5y = -4
-7x + 3y = -1
can be written in the form
( Dx , Dy )
( D D )
What is the value of D?
Answer's
Step-by-step explant
100 brainly!!! Which of the following functions is graphed below?
Answer: the answer is B
pls help due nowwwwwwwwwwwwwww
Answer:
A
Step-by-step explanation:
once tearra started buying games her money decreased by $35.50
You are planning to place a bet on your local sports team, the red sparrows. the sparrow's have a past record of 4-5 (4 wins, 5 losses) at this venue. however you also know that their record is 2-7 in games where it rains and it has rained at 60% of their games this season. 4 if the red sparrows win their game what is the probability that it rained at that game?
The probability that it rained at that game is 0.49.
Probability is the the ratio of a particular event with total number of event. It tells the possibility that an event can occur.
Probability that it rains P(R) = 0.60
probability that it won't rain P(R') = 1-0.60
= 0.4
Red sparrows have a past record of 4 wins and 5 loses when it does not rain, that is
P( winning/R') = 4/9 (win% = 4/total that is 5+4 which is 9)
P( lose/R') = 5/9 (lose % = 5/total)
When it rain the past record is 2 wins and 7 loses
P( win/R ) = 2/9
P( lose/R ) = 7/9
P (win) = P(R)*P(win/R) + P(R')*P(win/R')
= 4/9*0.4 + 2/9*0.6
If red sparrows win, then the probability that it rained at game
P (R/win) = P ( R η win) / P (win)
= 0.49
Therefore, we can conclude that the the probability that it rained at that game is 0.49.
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Make r the subject of m=√6a+r/5r
Answer:
r=√6a/5m-1
Step-by-step explanation:
m=√6a+r/5r
cross multiply
5mr=√6a+r
5mr-r=√6a
factorise
r(5m-1)=√6a
divide both sides by the coefficient of r
r=√6a/5m-1
hope it helps
please mark brainliest
Answer:
hope it helps u
MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER
For which equations is 8 a solution? Select the four correct answers. x + 6 = 2 x + 2 = 10 x minus 4 = 4 x minus 2 = 10 2 x = 4 3 x = 24 StartFraction x Over 2 EndFraction = 16 StartFraction x Over 8 EndFraction = 1
The equations with a solution of 8 are:
x+2=10, x -4 = 4, 3x = 24, and x/8 =1
This is further explained below.
What are equations?An equation is a formula that, in mathematics, expresses the equivalence of two expressions by linking them with the equals symbol =. In other words, an equation is a mathematical expression.
An equation is a mathematical statement that demonstrates that two mathematical expressions have the same value. This is the most basic version of the definition of an equation in algebra.
For example, the phrase "3x + 5" = 14 is an equation, in which the two expressions "3x + 5" and "14" are separated by the symbol for "equal."
Now we consider all equations given
1)
x+6 = 2
x = 2-6
x = -4
2)
Considering question 2 equation to see if it equals 8
x+2=10
x = 10-2
x = 8
3)
Considering question 3 equation to see if it equals 8
x -4 = 4
x = 4+4
x = 8
4)
Considering question 4 equation to see if it equals 8
x-2=10
x = 10+2
x = 12
5)
Considering question 5 equation to see if it equals 8
2x = 4
x = 2
6)
Considering question 6 equation to see if it equals 8
3x = 24
x = 8
7)
Considering question 7 equation to see if it equals 8
x/2 = 16
x = 32
8)
Considering question 8 equation to see if it equals 8
x/8 =1
x = 8
In conclusion, only equations:
x+2=10, x -4 = 4, 3x = 24, and x/8 =1 have the solution of 8
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The solution set of which of the following equations is the set of real numbers that are 3 units from -2?
A |x+2|=3
B|x-2|=3
C |x+3|=-2
D |x-3|=2
E |x+3|=2
The solution set of real numbers that are 3 units from -2 is :
|x +2| = 3
What is a solution set?Any value of a variable that makes the specified equation true is referred to as a solution. A solution set is the collection of all variables that satisfy the equation. To find the solution set of an equation with a given domain, first plug each domain value into the equation to obtain the respective range values. Make ordered pairs out of these values and write them down as a set. That set is our solution.Here
Function : |x +2| = 3
since ,
|x +2| = 3 => x + 2 = 3 ∨ x + 2 = -3
x = 3 - 2 ∨ x = -3 - 2
x = 1 ∨ x = -5
| - 2 - 1 | = | -3| = 3
| -2 -(-5) | = | -2 + 5 | = 3.
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Dylan enjoys ramen noodles and music downloads. His monthly budget for these two items is 15 dollars. If the price of a package of ramen noodles is $1.48 and the price of a music download is $1.15, what is Dylan's opportunity cost of a music download? (Round your answer to the nearest tenth. For example: 1.4).
Data:
• Monthly budget: $15
,• Price of a package of ramen: $1.48
,• Price of a music download: $1.15
Procedure:
[tex]\frac{15}{1.48}\approx10.1[/tex]Answer: 10.1
-0.01a^4*(-10a^5)^3[tex]-0.01a^4*(-10a^5)^3[/tex]
It seems there is some missing info on this question. However, if you are simplifying, then the simplified version of the given expression would be...
[tex]10a^1^9[/tex]
Hope this helps!
Write 100 minutes in hours and minutes.
Answer:
1 hour and 40 minutes
Step-by-step explanation:
60 minutes in an hour
we have 100 minutes
100 - 60 = 40
in 100 minutes we already have 1 hour
now we have 40 minutes left
can 40 minutes make another 60?
No.
so 100 minutes make
1 hour and 40 minutesIf you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved. What am I?
Answer: The moon
Step-by-step explanation:
The cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
∵ The volume of the cone (V )= 1/3πhr²
The number of faces of a regular cone is one, which we may partition vertically into two halves.
This means one base face and lateral face
Now, the number of faces in one half equals the number of faces in the original form.
This meets the conditions outlined in the question.
So, the cone is a solid form.
Thus, the cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."
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